src/HOL/BNF/Tools/bnf_gfp.ML
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renamed LFP low-level rel property to have ctor not dtor in its name
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(*  Title:      HOL/BNF/Tools/bnf_gfp.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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    Author:     Andrei Popescu, TU Muenchen
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Codatatype construction.
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*)
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signature BNF_GFP =
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sig
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  val bnf_gfp: mixfix list -> (string * sort) list option -> binding list ->
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    typ list * typ list list -> BNF_Def.BNF list -> local_theory ->
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    (term list * term list * term list * term list * thm * thm list * thm list * thm list *
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      thm list * thm list) * local_theory
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end;
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structure BNF_GFP : BNF_GFP =
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struct
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open BNF_Def
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open BNF_Util
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open BNF_Tactics
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open BNF_FP
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open BNF_FP_Sugar
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open BNF_GFP_Util
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open BNF_GFP_Tactics
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datatype wit_tree = Wit_Leaf of int | Wit_Node of (int * int * int list) * wit_tree list;
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fun mk_tree_args (I, T) (I', Ts) = (sort_distinct int_ord (I @ I'), T :: Ts);
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fun finish Iss m seen i (nwit, I) =
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  let
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    val treess = map (fn j =>
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        if j < m orelse member (op =) seen j then [([j], Wit_Leaf j)]
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        else
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          map_index (finish Iss m (insert (op =) j seen) j) (nth Iss (j - m))
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          |> flat
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          |> minimize_wits)
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      I;
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  in
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    map (fn (I, t) => (I, Wit_Node ((i - m, nwit, filter (fn i => i < m) I), t)))
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      (fold_rev (map_product mk_tree_args) treess [([], [])])
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    |> minimize_wits
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  end;
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fun tree_to_ctor_wit vars _ _ (Wit_Leaf j) = ([j], nth vars j)
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  | tree_to_ctor_wit vars ctors witss (Wit_Node ((i, nwit, I), subtrees)) =
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     (I, nth ctors i $ (Term.list_comb (snd (nth (nth witss i) nwit),
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       map (snd o tree_to_ctor_wit vars ctors witss) subtrees)));
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fun tree_to_coind_wits _ (Wit_Leaf _) = []
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  | tree_to_coind_wits lwitss (Wit_Node ((i, nwit, I), subtrees)) =
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     ((i, I), nth (nth lwitss i) nwit) :: maps (tree_to_coind_wits lwitss) subtrees;
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(*all BNFs have the same lives*)
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fun bnf_gfp mixfixes resBs bs (resDs, Dss) bnfs lthy =
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  let
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    val timer = time (Timer.startRealTimer ());
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    val live = live_of_bnf (hd bnfs);
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    val n = length bnfs; (*active*)
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    val ks = 1 upto n;
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    val m = live - n (*passive, if 0 don't generate a new BNF*);
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    val ls = 1 upto m;
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    val b = Binding.name (mk_common_name (map Binding.name_of bs));
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    (* TODO: check if m, n, etc., are sane *)
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    val deads = fold (union (op =)) Dss resDs;
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    val names_lthy = fold Variable.declare_typ deads lthy;
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    (* tvars *)
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    val ((((((((passiveAs, activeAs), allAs)), (passiveBs, activeBs)),
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      (passiveCs, activeCs)), passiveXs), passiveYs), idxT) = names_lthy
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      |> mk_TFrees live
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      |> apfst (`(chop m))
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      ||> mk_TFrees live
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      ||>> apfst (chop m)
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      ||> mk_TFrees live
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      ||>> apfst (chop m)
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      ||>> mk_TFrees m
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      ||>> mk_TFrees m
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      ||> fst o mk_TFrees 1
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      ||> the_single;
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    val Ass = replicate n allAs;
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    val allBs = passiveAs @ activeBs;
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    val Bss = replicate n allBs;
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    val allCs = passiveAs @ activeCs;
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    val allCs' = passiveBs @ activeCs;
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    val Css' = replicate n allCs';
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    (* typs *)
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    val dead_poss =
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      (case resBs of
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        NONE => map SOME deads @ replicate m NONE
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      | SOME Ts => map (fn T => if member (op =) deads (TFree T) then SOME (TFree T) else NONE) Ts);
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    fun mk_param NONE passive = (hd passive, tl passive)
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      | mk_param (SOME a) passive = (a, passive);
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    val mk_params = fold_map mk_param dead_poss #> fst;
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    fun mk_FTs Ts = map2 (fn Ds => mk_T_of_bnf Ds Ts) Dss bnfs;
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    val (params, params') = `(map Term.dest_TFree) (mk_params passiveAs);
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    val FTsAs = mk_FTs allAs;
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    val FTsBs = mk_FTs allBs;
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    val FTsCs = mk_FTs allCs;
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    val ATs = map HOLogic.mk_setT passiveAs;
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    val BTs = map HOLogic.mk_setT activeAs;
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    val B'Ts = map HOLogic.mk_setT activeBs;
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    val B''Ts = map HOLogic.mk_setT activeCs;
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    val sTs = map2 (fn T => fn U => T --> U) activeAs FTsAs;
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    val s'Ts = map2 (fn T => fn U => T --> U) activeBs FTsBs;
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    val s''Ts = map2 (fn T => fn U => T --> U) activeCs FTsCs;
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    val fTs = map2 (fn T => fn U => T --> U) activeAs activeBs;
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    val all_fTs = map2 (fn T => fn U => T --> U) allAs allBs;
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    val self_fTs = map (fn T => T --> T) activeAs;
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    val gTs = map2 (fn T => fn U => T --> U) activeBs activeCs;
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    val all_gTs = map2 (fn T => fn U => T --> U) allBs allCs';
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    val RTs = map2 (fn T => fn U => HOLogic.mk_prodT (T, U)) activeAs activeBs;
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    val sRTs = map2 (fn T => fn U => HOLogic.mk_prodT (T, U)) activeAs activeAs;
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    val R'Ts = map2 (fn T => fn U => HOLogic.mk_prodT (T, U)) activeBs activeCs;
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    val setsRTs = map HOLogic.mk_setT sRTs;
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   125
    val setRTs = map HOLogic.mk_setT RTs;
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   126
    val all_sbisT = HOLogic.mk_tupleT setsRTs;
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   127
    val setR'Ts = map HOLogic.mk_setT R'Ts;
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   128
    val FRTs = mk_FTs (passiveAs @ RTs);
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   129
    val sumBsAs = map2 (curry mk_sumT) activeBs activeAs;
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   130
    val sumFTs = mk_FTs (passiveAs @ sumBsAs);
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   131
    val sum_sTs = map2 (fn T => fn U => T --> U) activeAs sumFTs;
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   132
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    (* terms *)
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   134
    val mapsAsAs = map4 mk_map_of_bnf Dss Ass Ass bnfs;
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   135
    val mapsAsBs = map4 mk_map_of_bnf Dss Ass Bss bnfs;
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   136
    val mapsBsCs' = map4 mk_map_of_bnf Dss Bss Css' bnfs;
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   137
    val mapsAsCs' = map4 mk_map_of_bnf Dss Ass Css' bnfs;
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   138
    val map_Inls = map4 mk_map_of_bnf Dss Bss (replicate n (passiveAs @ sumBsAs)) bnfs;
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   139
    val map_Inls_rev = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ sumBsAs)) Bss bnfs;
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   140
    val map_fsts = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ RTs)) Ass bnfs;
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   141
    val map_snds = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ RTs)) Bss bnfs;
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   142
    fun mk_setss Ts = map3 mk_sets_of_bnf (map (replicate live) Dss)
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      (map (replicate live) (replicate n Ts)) bnfs;
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   144
    val setssAs = mk_setss allAs;
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   145
    val setssAs' = transpose setssAs;
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   146
    val bis_setss = mk_setss (passiveAs @ RTs);
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   147
    val relsAsBs = map4 mk_srel_of_bnf Dss Ass Bss bnfs;
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   148
    val bds = map3 mk_bd_of_bnf Dss Ass bnfs;
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   149
    val sum_bd = Library.foldr1 (uncurry mk_csum) bds;
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   150
    val sum_bdT = fst (dest_relT (fastype_of sum_bd));
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   151
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    val emptys = map (fn T => HOLogic.mk_set T []) passiveAs;
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   153
    val Zeros = map (fn empty =>
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   154
     HOLogic.mk_tuple (map (fn U => absdummy U empty) activeAs)) emptys;
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   155
    val hrecTs = map fastype_of Zeros;
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   156
    val hsetTs = map (fn hrecT => Library.foldr (op -->) (sTs, HOLogic.natT --> hrecT)) hrecTs;
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   157
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   158
    val (((((((((((((((((((((((((((((((((((zs, zs'), zs_copy), zs_copy2),
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   159
      z's), As), As_copy), Bs), Bs_copy), B's), B''s), ss), sum_ss), s's), s''s), fs), fs_copy),
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   160
      self_fs), all_fs), gs), all_gs), xFs), xFs_copy), RFs), (Rtuple, Rtuple')), (hrecs, hrecs')),
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   161
      (nat, nat')), Rs), Rs_copy), R's), sRs), (idx, idx')), Idx), Ris), Kss),
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      names_lthy) = lthy
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      |> mk_Frees' "b" activeAs
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      ||>> mk_Frees "b" activeAs
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   165
      ||>> mk_Frees "b" activeAs
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      ||>> mk_Frees "b" activeBs
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   167
      ||>> mk_Frees "A" ATs
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      ||>> mk_Frees "A" ATs
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   169
      ||>> mk_Frees "B" BTs
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      ||>> mk_Frees "B" BTs
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   171
      ||>> mk_Frees "B'" B'Ts
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   172
      ||>> mk_Frees "B''" B''Ts
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      ||>> mk_Frees "s" sTs
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   174
      ||>> mk_Frees "sums" sum_sTs
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   175
      ||>> mk_Frees "s'" s'Ts
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   176
      ||>> mk_Frees "s''" s''Ts
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   177
      ||>> mk_Frees "f" fTs
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   178
      ||>> mk_Frees "f" fTs
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   179
      ||>> mk_Frees "f" self_fTs
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   180
      ||>> mk_Frees "f" all_fTs
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   181
      ||>> mk_Frees "g" gTs
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   182
      ||>> mk_Frees "g" all_gTs
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   183
      ||>> mk_Frees "x" FTsAs
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   184
      ||>> mk_Frees "x" FTsAs
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   185
      ||>> mk_Frees "x" FRTs
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   186
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "Rtuple") all_sbisT
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   187
      ||>> mk_Frees' "rec" hrecTs
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   188
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "n") HOLogic.natT
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   189
      ||>> mk_Frees "R" setRTs
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   190
      ||>> mk_Frees "R" setRTs
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   191
      ||>> mk_Frees "R'" setR'Ts
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   192
      ||>> mk_Frees "R" setsRTs
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   193
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") idxT
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   194
      ||>> yield_singleton (mk_Frees "I") (HOLogic.mk_setT idxT)
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   195
      ||>> mk_Frees "Ri" (map (fn T => idxT --> T) setRTs)
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   196
      ||>> mk_Freess "K" (map (fn AT => map (fn T => T --> AT) activeAs) ATs);
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   197
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   198
    val passive_UNIVs = map HOLogic.mk_UNIV passiveAs;
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   199
    val passive_diags = map mk_diag As;
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   200
    val active_UNIVs = map HOLogic.mk_UNIV activeAs;
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   201
    val sum_UNIVs = map HOLogic.mk_UNIV sumBsAs;
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   202
    val passive_ids = map HOLogic.id_const passiveAs;
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   203
    val active_ids = map HOLogic.id_const activeAs;
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   204
    val Inls = map2 Inl_const activeBs activeAs;
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   205
    val fsts = map fst_const RTs;
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   206
    val snds = map snd_const RTs;
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   207
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   208
    (* thms *)
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   209
    val bd_card_orders = map bd_card_order_of_bnf bnfs;
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   210
    val bd_card_order = hd bd_card_orders
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   211
    val bd_Card_orders = map bd_Card_order_of_bnf bnfs;
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   212
    val bd_Card_order = hd bd_Card_orders;
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   213
    val bd_Cinfinites = map bd_Cinfinite_of_bnf bnfs;
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   214
    val bd_Cinfinite = hd bd_Cinfinites;
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   215
    val bd_Cnotzeros = map bd_Cnotzero_of_bnf bnfs;
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   216
    val bd_Cnotzero = hd bd_Cnotzeros;
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   217
    val in_bds = map in_bd_of_bnf bnfs;
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   218
    val in_monos = map in_mono_of_bnf bnfs;
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   219
    val map_comps = map map_comp_of_bnf bnfs;
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   220
    val map_comp's = map map_comp'_of_bnf bnfs;
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   221
    val map_congs = map map_cong_of_bnf bnfs;
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   222
    val map_id's = map map_id'_of_bnf bnfs;
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   223
    val map_wpulls = map map_wpull_of_bnf bnfs;
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   224
    val set_bdss = map set_bd_of_bnf bnfs;
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   225
    val set_natural'ss = map set_natural'_of_bnf bnfs;
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   226
    val srel_congs = map srel_cong_of_bnf bnfs;
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   227
    val srel_converses = map srel_converse_of_bnf bnfs;
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   228
    val srel_defs = map srel_def_of_bnf bnfs;
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   229
    val srel_Grs = map srel_Gr_of_bnf bnfs;
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   230
    val srel_Ids = map srel_Id_of_bnf bnfs;
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   231
    val srel_monos = map srel_mono_of_bnf bnfs;
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   232
    val srel_Os = map srel_O_of_bnf bnfs;
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    val srel_O_Grs = map srel_O_Gr_of_bnf bnfs;
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    val timer = time (timer "Extracted terms & thms");
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    (* derived thms *)
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    (*map g1 ... gm g(m+1) ... g(m+n) (map id ... id f(m+1) ... f(m+n) x)=
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      map g1 ... gm (g(m+1) o f(m+1)) ... (g(m+n) o f(m+n)) x*)
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    fun mk_map_comp_id x mapAsBs mapBsCs mapAsCs map_comp =
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      let
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        val lhs = Term.list_comb (mapBsCs, all_gs) $
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          (Term.list_comb (mapAsBs, passive_ids @ fs) $ x);
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        val rhs =
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          Term.list_comb (mapAsCs, take m all_gs @ map HOLogic.mk_comp (drop m all_gs ~~ fs)) $ x;
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      in
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        Skip_Proof.prove lthy [] []
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          (fold_rev Logic.all (x :: fs @ all_gs) (mk_Trueprop_eq (lhs, rhs)))
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          (K (mk_map_comp_id_tac map_comp))
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        |> Thm.close_derivation
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      end;
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    val map_comp_id_thms = map5 mk_map_comp_id xFs mapsAsBs mapsBsCs' mapsAsCs' map_comp's;
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    (*forall a : set(m+1) x. f(m+1) a = a; ...; forall a : set(m+n) x. f(m+n) a = a ==>
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      map id ... id f(m+1) ... f(m+n) x = x*)
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    fun mk_map_congL x mapAsAs sets map_cong map_id' =
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      let
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        fun mk_prem set f z z' =
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          HOLogic.mk_Trueprop
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            (mk_Ball (set $ x) (Term.absfree z' (HOLogic.mk_eq (f $ z, z))));
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        val prems = map4 mk_prem (drop m sets) self_fs zs zs';
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        val goal = mk_Trueprop_eq (Term.list_comb (mapAsAs, passive_ids @ self_fs) $ x, x);
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      in
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        Skip_Proof.prove lthy [] []
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          (fold_rev Logic.all (x :: self_fs) (Logic.list_implies (prems, goal)))
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          (K (mk_map_congL_tac m map_cong map_id'))
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        |> Thm.close_derivation
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      end;
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    val map_congL_thms = map5 mk_map_congL xFs mapsAsAs setssAs map_congs map_id's;
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    val in_mono'_thms = map (fn thm =>
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      (thm OF (replicate m subset_refl)) RS @{thm set_mp}) in_monos;
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    val map_arg_cong_thms =
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      let
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        val prems = map2 (curry mk_Trueprop_eq) xFs xFs_copy;
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        val maps = map (fn mapx => Term.list_comb (mapx, all_fs)) mapsAsBs;
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        val concls =
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          map3 (fn x => fn y => fn mapx => mk_Trueprop_eq (mapx $ x, mapx $ y)) xFs xFs_copy maps;
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        val goals =
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          map4 (fn prem => fn concl => fn x => fn y =>
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            fold_rev Logic.all (x :: y :: all_fs) (Logic.mk_implies (prem, concl)))
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          prems concls xFs xFs_copy;
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      in
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        map (fn goal => Skip_Proof.prove lthy [] [] goal
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          (K ((hyp_subst_tac THEN' rtac refl) 1)) |> Thm.close_derivation) goals
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      end;
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    val timer = time (timer "Derived simple theorems");
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    (* coalgebra *)
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    val coalg_bind = Binding.suffix_name ("_" ^ coN ^ algN) b;
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    val coalg_name = Binding.name_of coalg_bind;
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    val coalg_def_bind = (Thm.def_binding coalg_bind, []);
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    (*forall i = 1 ... n: (\<forall>x \<in> Bi. si \<in> Fi_in A1 .. Am B1 ... Bn)*)
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    val coalg_spec =
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      let
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        val coalgT = Library.foldr (op -->) (ATs @ BTs @ sTs, HOLogic.boolT);
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        val ins = map3 mk_in (replicate n (As @ Bs)) setssAs FTsAs;
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        fun mk_coalg_conjunct B s X z z' =
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          mk_Ball B (Term.absfree z' (HOLogic.mk_mem (s $ z, X)));
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        val lhs = Term.list_comb (Free (coalg_name, coalgT), As @ Bs @ ss);
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        val rhs = Library.foldr1 HOLogic.mk_conj (map5 mk_coalg_conjunct Bs ss ins zs zs')
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      in
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        mk_Trueprop_eq (lhs, rhs)
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      end;
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    val ((coalg_free, (_, coalg_def_free)), (lthy, lthy_old)) =
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      lthy
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      |> Specification.definition (SOME (coalg_bind, NONE, NoSyn), (coalg_def_bind, coalg_spec))
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      ||> `Local_Theory.restore;
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    val phi = Proof_Context.export_morphism lthy_old lthy;
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    val coalg = fst (Term.dest_Const (Morphism.term phi coalg_free));
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    val coalg_def = Morphism.thm phi coalg_def_free;
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    fun mk_coalg As Bs ss =
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      let
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        val args = As @ Bs @ ss;
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        val Ts = map fastype_of args;
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        val coalgT = Library.foldr (op -->) (Ts, HOLogic.boolT);
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      in
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        Term.list_comb (Const (coalg, coalgT), args)
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      end;
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    val coalg_prem = HOLogic.mk_Trueprop (mk_coalg As Bs ss);
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    val coalg_in_thms = map (fn i =>
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      coalg_def RS @{thm subst[of _ _ "%x. x"]} RS mk_conjunctN n i RS bspec) ks
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    val coalg_set_thmss =
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      let
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        val coalg_prem = HOLogic.mk_Trueprop (mk_coalg As Bs ss);
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        fun mk_prem x B = HOLogic.mk_Trueprop (HOLogic.mk_mem (x, B));
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        fun mk_concl s x B set = HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) B);
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        val prems = map2 mk_prem zs Bs;
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        val conclss = map3 (fn s => fn x => fn sets => map2 (mk_concl s x) (As @ Bs) sets)
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          ss zs setssAs;
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        val goalss = map3 (fn x => fn prem => fn concls => map (fn concl =>
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          fold_rev Logic.all (x :: As @ Bs @ ss)
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            (Logic.list_implies (coalg_prem :: [prem], concl))) concls) zs prems conclss;
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      in
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        map (fn goals => map (fn goal => Skip_Proof.prove lthy [] [] goal
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          (K (mk_coalg_set_tac coalg_def)) |> Thm.close_derivation) goals) goalss
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   351
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   352
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   353
    val coalg_set_thmss' = transpose coalg_set_thmss;
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parents:
diff changeset
   354
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   355
    fun mk_tcoalg ATs BTs = mk_coalg (map HOLogic.mk_UNIV ATs) (map HOLogic.mk_UNIV BTs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   356
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   357
    val tcoalg_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   358
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   359
        val goal = fold_rev Logic.all ss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   360
          (HOLogic.mk_Trueprop (mk_tcoalg passiveAs activeAs ss))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   361
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   362
        Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   363
          (K (stac coalg_def 1 THEN CONJ_WRAP
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   364
            (K (EVERY' [rtac ballI, rtac CollectI,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   365
              CONJ_WRAP' (K (EVERY' [rtac @{thm subset_UNIV}])) allAs] 1)) ss))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
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   366
        |> Thm.close_derivation
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7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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diff changeset
   367
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   368
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   369
    val timer = time (timer "Coalgebra definition & thms");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   370
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   371
    (* morphism *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   372
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   373
    val mor_bind = Binding.suffix_name ("_" ^ morN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   374
    val mor_name = Binding.name_of mor_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   375
    val mor_def_bind = (Thm.def_binding mor_bind, []);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   376
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   377
    (*fbetw) forall i = 1 ... n: (\<forall>x \<in> Bi. fi x \<in> B'i)*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   378
    (*mor) forall i = 1 ... n: (\<forall>x \<in> Bi.
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   379
       Fi_map id ... id f1 ... fn (si x) = si' (fi x)*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   380
    val mor_spec =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   381
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   382
        val morT = Library.foldr (op -->) (BTs @ sTs @ B'Ts @ s'Ts @ fTs, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   383
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   384
        fun mk_fbetw f B1 B2 z z' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   385
          mk_Ball B1 (Term.absfree z' (HOLogic.mk_mem (f $ z, B2)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   386
        fun mk_mor B mapAsBs f s s' z z' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   387
          mk_Ball B (Term.absfree z' (HOLogic.mk_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   388
            (Term.list_comb (mapAsBs, passive_ids @ fs @ [s $ z]), s' $ (f $ z))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   389
        val lhs = Term.list_comb (Free (mor_name, morT), Bs @ ss @ B's @ s's @ fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   390
        val rhs = HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   391
          (Library.foldr1 HOLogic.mk_conj (map5 mk_fbetw fs Bs B's zs zs'),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   392
           Library.foldr1 HOLogic.mk_conj (map7 mk_mor Bs mapsAsBs fs ss s's zs zs'))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   393
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
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parents: 49121
diff changeset
   394
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
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parents:
diff changeset
   395
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   396
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   397
    val ((mor_free, (_, mor_def_free)), (lthy, lthy_old)) =
49311
blanchet
parents: 49308
diff changeset
   398
      lthy
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parents: 49308
diff changeset
   399
      |> Specification.definition (SOME (mor_bind, NONE, NoSyn), (mor_def_bind, mor_spec))
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parents: 49308
diff changeset
   400
      ||> `Local_Theory.restore;
blanchet
parents: 49308
diff changeset
   401
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   402
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   403
    val mor = fst (Term.dest_Const (Morphism.term phi mor_free));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   404
    val mor_def = Morphism.thm phi mor_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   405
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   406
    fun mk_mor Bs1 ss1 Bs2 ss2 fs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   407
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   408
        val args = Bs1 @ ss1 @ Bs2 @ ss2 @ fs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   409
        val Ts = map fastype_of (Bs1 @ ss1 @ Bs2 @ ss2 @ fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   410
        val morT = Library.foldr (op -->) (Ts, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   411
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   412
        Term.list_comb (Const (mor, morT), args)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   413
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   414
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   415
    val mor_prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   416
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   417
    val (mor_image_thms, morE_thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   418
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   419
        val prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   420
        fun mk_image_goal f B1 B2 = fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   421
          (Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_subset (mk_image f $ B1) B2)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   422
        val image_goals = map3 mk_image_goal fs Bs B's;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   423
        fun mk_elim_goal B mapAsBs f s s' x =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   424
          fold_rev Logic.all (x :: Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   425
            (Logic.list_implies ([prem, HOLogic.mk_Trueprop (HOLogic.mk_mem (x, B))],
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   426
              mk_Trueprop_eq (Term.list_comb (mapAsBs, passive_ids @ fs @ [s $ x]), s' $ (f $ x))));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   427
        val elim_goals = map6 mk_elim_goal Bs mapsAsBs fs ss s's zs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   428
        fun prove goal =
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   429
          Skip_Proof.prove lthy [] [] goal (K (mk_mor_elim_tac mor_def))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   430
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   431
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   432
        (map prove image_goals, map prove elim_goals)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   433
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   434
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   435
    val mor_image'_thms = map (fn thm => @{thm set_mp} OF [thm, imageI]) mor_image_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   436
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   437
    val mor_incl_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   438
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   439
        val prems = map2 (HOLogic.mk_Trueprop oo mk_subset) Bs Bs_copy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   440
        val concl = HOLogic.mk_Trueprop (mk_mor Bs ss Bs_copy ss active_ids);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   441
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   442
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   443
          (fold_rev Logic.all (Bs @ ss @ Bs_copy) (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   444
          (K (mk_mor_incl_tac mor_def map_id's))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   445
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   446
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   447
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   448
    val mor_id_thm = mor_incl_thm OF (replicate n subset_refl);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   449
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   450
    val mor_comp_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   451
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   452
        val prems =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   453
          [HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   454
           HOLogic.mk_Trueprop (mk_mor B's s's B''s s''s gs)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   455
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   456
          HOLogic.mk_Trueprop (mk_mor Bs ss B''s s''s (map2 (curry HOLogic.mk_comp) gs fs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   457
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   458
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   459
          (fold_rev Logic.all (Bs @ ss @ B's @ s's @ B''s @ s''s @ fs @ gs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   460
            (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   461
          (K (mk_mor_comp_tac mor_def mor_image'_thms morE_thms map_comp_id_thms))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   462
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   463
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   464
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   465
    val mor_cong_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   466
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   467
        val prems = map HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   468
         (map2 (curry HOLogic.mk_eq) fs_copy fs @ [mk_mor Bs ss B's s's fs])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   469
        val concl = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs_copy);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   470
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   471
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   472
          (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs @ fs_copy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   473
            (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   474
          (K ((hyp_subst_tac THEN' atac) 1))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   475
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   476
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   477
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   478
    val mor_UNIV_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   479
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   480
        fun mk_conjunct mapAsBs f s s' = HOLogic.mk_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   481
            (HOLogic.mk_comp (Term.list_comb (mapAsBs, passive_ids @ fs), s),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   482
            HOLogic.mk_comp (s', f));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   483
        val lhs = mk_mor active_UNIVs ss (map HOLogic.mk_UNIV activeBs) s's fs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   484
        val rhs = Library.foldr1 HOLogic.mk_conj (map4 mk_conjunct mapsAsBs fs ss s's);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   485
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   486
        Skip_Proof.prove lthy [] [] (fold_rev Logic.all (ss @ s's @ fs) (mk_Trueprop_eq (lhs, rhs)))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   487
          (K (mk_mor_UNIV_tac morE_thms mor_def))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   488
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   489
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   490
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   491
    val mor_str_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   492
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   493
        val maps = map2 (fn Ds => fn bnf => Term.list_comb
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   494
          (mk_map_of_bnf Ds allAs (passiveAs @ FTsAs) bnf, passive_ids @ ss)) Dss bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   495
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   496
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   497
          (fold_rev Logic.all ss (HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   498
            (mk_mor active_UNIVs ss (map HOLogic.mk_UNIV FTsAs) maps ss)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   499
          (K (mk_mor_str_tac ks mor_UNIV_thm))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   500
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   501
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   502
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   503
    val mor_sum_case_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   504
      let
49458
blanchet
parents: 49457
diff changeset
   505
        val maps = map3 (fn s => fn sum_s => fn mapx =>
blanchet
parents: 49457
diff changeset
   506
          mk_sum_case (HOLogic.mk_comp (Term.list_comb (mapx, passive_ids @ Inls), s), sum_s))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   507
          s's sum_ss map_Inls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   508
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   509
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   510
          (fold_rev Logic.all (s's @ sum_ss) (HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   511
            (mk_mor (map HOLogic.mk_UNIV activeBs) s's sum_UNIVs maps Inls)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   512
          (K (mk_mor_sum_case_tac ks mor_UNIV_thm))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   513
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   514
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   515
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   516
    val timer = time (timer "Morphism definition & thms");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   517
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   518
    fun hset_rec_bind j = Binding.suffix_name ("_" ^ hset_recN ^ (if m = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   519
      string_of_int j)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   520
    val hset_rec_name = Binding.name_of o hset_rec_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   521
    val hset_rec_def_bind = rpair [] o Thm.def_binding o hset_rec_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   522
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   523
    fun hset_rec_spec j Zero hsetT hrec hrec' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   524
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   525
        fun mk_Suc s setsAs z z' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   526
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   527
            val (set, sets) = apfst (fn xs => nth xs (j - 1)) (chop m setsAs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   528
            fun mk_UN set k = mk_UNION (set $ (s $ z)) (mk_nthN n hrec k);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   529
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   530
            Term.absfree z'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   531
              (mk_union (set $ (s $ z), Library.foldl1 mk_union (map2 mk_UN sets ks)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   532
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   533
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   534
        val Suc = Term.absdummy HOLogic.natT (Term.absfree hrec'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   535
          (HOLogic.mk_tuple (map4 mk_Suc ss setssAs zs zs')));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   536
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   537
        val lhs = Term.list_comb (Free (hset_rec_name j, hsetT), ss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   538
        val rhs = mk_nat_rec Zero Suc;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   539
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   540
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   541
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   542
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   543
    val ((hset_rec_frees, (_, hset_rec_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   544
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   545
      |> fold_map5 (fn j => fn Zero => fn hsetT => fn hrec => fn hrec' => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   546
        (SOME (hset_rec_bind j, NONE, NoSyn),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   547
          (hset_rec_def_bind j, hset_rec_spec j Zero hsetT hrec hrec')))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   548
        ls Zeros hsetTs hrecs hrecs'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   549
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   550
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   551
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   552
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   553
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   554
    val hset_rec_defs = map (Morphism.thm phi) hset_rec_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   555
    val hset_recs = map (fst o Term.dest_Const o Morphism.term phi) hset_rec_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   556
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   557
    fun mk_hset_rec ss nat i j T =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   558
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   559
        val args = ss @ [nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   560
        val Ts = map fastype_of ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   561
        val bTs = map domain_type Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   562
        val hrecT = HOLogic.mk_tupleT (map (fn U => U --> HOLogic.mk_setT T) bTs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   563
        val hset_recT = Library.foldr (op -->) (Ts, HOLogic.natT --> hrecT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   564
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   565
        mk_nthN n (Term.list_comb (Const (nth hset_recs (j - 1), hset_recT), args)) i
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   566
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   567
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   568
    val hset_rec_0ss = mk_rec_simps n @{thm nat_rec_0} hset_rec_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   569
    val hset_rec_Sucss = mk_rec_simps n @{thm nat_rec_Suc} hset_rec_defs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   570
    val hset_rec_0ss' = transpose hset_rec_0ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   571
    val hset_rec_Sucss' = transpose hset_rec_Sucss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   572
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   573
    fun hset_bind i j = Binding.suffix_name ("_" ^ hsetN ^
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   574
      (if m = 1 then "" else string_of_int j)) (nth bs (i - 1));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   575
    val hset_name = Binding.name_of oo hset_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   576
    val hset_def_bind = rpair [] o Thm.def_binding oo hset_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   577
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   578
    fun hset_spec i j =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   579
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   580
        val U = nth activeAs (i - 1);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   581
        val z = nth zs (i - 1);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   582
        val T = nth passiveAs (j - 1);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   583
        val setT = HOLogic.mk_setT T;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   584
        val hsetT = Library.foldr (op -->) (sTs, U --> setT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   585
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   586
        val lhs = Term.list_comb (Free (hset_name i j, hsetT), ss @ [z]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   587
        val rhs = mk_UNION (HOLogic.mk_UNIV HOLogic.natT)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   588
          (Term.absfree nat' (mk_hset_rec ss nat i j T $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   589
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   590
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   591
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   592
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   593
    val ((hset_frees, (_, hset_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   594
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   595
      |> fold_map (fn i => fold_map (fn j => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   596
        (SOME (hset_bind i j, NONE, NoSyn), (hset_def_bind i j, hset_spec i j))) ls) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   597
      |>> map (apsnd split_list o split_list)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   598
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   599
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   600
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   601
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   602
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   603
    val hset_defss = map (map (Morphism.thm phi)) hset_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   604
    val hset_defss' = transpose hset_defss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   605
    val hset_namess = map (map (fst o Term.dest_Const o Morphism.term phi)) hset_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   606
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   607
    fun mk_hset ss i j T =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   608
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   609
        val Ts = map fastype_of ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   610
        val bTs = map domain_type Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   611
        val hsetT = Library.foldr (op -->) (Ts, nth bTs (i - 1) --> HOLogic.mk_setT T);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   612
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   613
        Term.list_comb (Const (nth (nth hset_namess (i - 1)) (j - 1), hsetT), ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   614
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   615
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   616
    val hsetssAs = map (fn i => map2 (mk_hset ss i) ls passiveAs) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   617
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   618
    val (set_incl_hset_thmss, set_hset_incl_hset_thmsss) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   619
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   620
        fun mk_set_incl_hset s x set hset = fold_rev Logic.all (x :: ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   621
          (HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) (hset $ x)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   622
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   623
        fun mk_set_hset_incl_hset s x y set hset1 hset2 =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   624
          fold_rev Logic.all (x :: y :: ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   625
            (Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (x, set $ (s $ y))),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   626
            HOLogic.mk_Trueprop (mk_subset (hset1 $ x) (hset2 $ y))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   627
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   628
        val set_incl_hset_goalss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   629
          map4 (fn s => fn x => fn sets => fn hsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   630
            map2 (mk_set_incl_hset s x) (take m sets) hsets)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   631
          ss zs setssAs hsetssAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   632
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   633
        (*xk : F(i)set(m+k) (si yi) ==> F(k)_hset(j) s1 ... sn xk <= F(i)_hset(j) s1 ... sn yi*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   634
        val set_hset_incl_hset_goalsss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   635
          map4 (fn si => fn yi => fn sets => fn hsetsi =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   636
            map3 (fn xk => fn set => fn hsetsk =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   637
              map2 (mk_set_hset_incl_hset si xk yi set) hsetsk hsetsi)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   638
            zs_copy (drop m sets) hsetssAs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   639
          ss zs setssAs hsetssAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   640
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   641
        (map3 (fn goals => fn defs => fn rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   642
          map3 (fn goal => fn def => fn rec_Suc =>
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   643
            Skip_Proof.prove lthy [] [] goal (K (mk_set_incl_hset_tac def rec_Suc))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   644
            |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   645
          goals defs rec_Sucs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   646
        set_incl_hset_goalss hset_defss hset_rec_Sucss,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   647
        map3 (fn goalss => fn defsi => fn rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   648
          map3 (fn k => fn goals => fn defsk =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   649
            map4 (fn goal => fn defk => fn defi => fn rec_Suc =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   650
              Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   651
                (K (mk_set_hset_incl_hset_tac n [defk, defi] rec_Suc k))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   652
              |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   653
            goals defsk defsi rec_Sucs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   654
          ks goalss hset_defss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   655
        set_hset_incl_hset_goalsss hset_defss hset_rec_Sucss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   656
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   657
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   658
    val set_incl_hset_thmss' = transpose set_incl_hset_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   659
    val set_hset_incl_hset_thmsss' = transpose (map transpose set_hset_incl_hset_thmsss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   660
    val set_hset_incl_hset_thmsss'' = map transpose set_hset_incl_hset_thmsss';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   661
    val set_hset_thmss = map (map (fn thm => thm RS @{thm set_mp})) set_incl_hset_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   662
    val set_hset_hset_thmsss = map (map (map (fn thm => thm RS @{thm set_mp})))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   663
      set_hset_incl_hset_thmsss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   664
    val set_hset_thmss' = transpose set_hset_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   665
    val set_hset_hset_thmsss' = transpose (map transpose set_hset_hset_thmsss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   666
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   667
    val set_incl_hin_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   668
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   669
        fun mk_set_incl_hin s x hsets1 set hsets2 T =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   670
          fold_rev Logic.all (x :: ss @ As)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   671
            (Logic.list_implies
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   672
              (map2 (fn hset => fn A => HOLogic.mk_Trueprop (mk_subset (hset $ x) A)) hsets1 As,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   673
              HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) (mk_in As hsets2 T))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   674
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   675
        val set_incl_hin_goalss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   676
          map4 (fn s => fn x => fn sets => fn hsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   677
            map3 (mk_set_incl_hin s x hsets) (drop m sets) hsetssAs activeAs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   678
          ss zs setssAs hsetssAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   679
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   680
        map2 (map2 (fn goal => fn thms =>
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   681
          Skip_Proof.prove lthy [] [] goal (K (mk_set_incl_hin_tac thms))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   682
          |> Thm.close_derivation))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   683
        set_incl_hin_goalss set_hset_incl_hset_thmsss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   684
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   685
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   686
    val hset_minimal_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   687
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   688
        fun mk_passive_prem set s x K =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   689
          Logic.all x (HOLogic.mk_Trueprop (mk_subset (set $ (s $ x)) (K $ x)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   690
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   691
        fun mk_active_prem s x1 K1 set x2 K2 =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   692
          fold_rev Logic.all [x1, x2]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   693
            (Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (x2, set $ (s $ x1))),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   694
              HOLogic.mk_Trueprop (mk_subset (K2 $ x2) (K1 $ x1))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   695
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   696
        val premss = map2 (fn j => fn Ks =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   697
          map4 mk_passive_prem (map (fn xs => nth xs (j - 1)) setssAs) ss zs Ks @
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   698
            flat (map4 (fn sets => fn s => fn x1 => fn K1 =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   699
              map3 (mk_active_prem s x1 K1) (drop m sets) zs_copy Ks) setssAs ss zs Ks))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   700
          ls Kss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   701
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   702
        val hset_rec_minimal_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   703
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   704
            fun mk_conjunct j T i K x = mk_subset (mk_hset_rec ss nat i j T $ x) (K $ x);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   705
            fun mk_concl j T Ks = list_all_free zs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   706
              (Library.foldr1 HOLogic.mk_conj (map3 (mk_conjunct j T) ks Ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   707
            val concls = map3 mk_concl ls passiveAs Kss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   708
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   709
            val goals = map2 (fn prems => fn concl =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   710
              Logic.list_implies (prems, HOLogic.mk_Trueprop concl)) premss concls
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   711
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   712
            val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   713
              map (fn phi => map (SOME o certify lthy) [Term.absfree nat' phi, nat]) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   714
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   715
            map4 (fn goal => fn cts => fn hset_rec_0s => fn hset_rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   716
              singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   717
                (Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   718
                  (mk_hset_rec_minimal_tac m cts hset_rec_0s hset_rec_Sucs))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   719
              |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   720
            goals ctss hset_rec_0ss' hset_rec_Sucss'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   721
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   722
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   723
        fun mk_conjunct j T i K x = mk_subset (mk_hset ss i j T $ x) (K $ x);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   724
        fun mk_concl j T Ks = Library.foldr1 HOLogic.mk_conj (map3 (mk_conjunct j T) ks Ks zs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   725
        val concls = map3 mk_concl ls passiveAs Kss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   726
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   727
        val goals = map3 (fn Ks => fn prems => fn concl =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   728
          fold_rev Logic.all (Ks @ ss @ zs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   729
            (Logic.list_implies (prems, HOLogic.mk_Trueprop concl))) Kss premss concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   730
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   731
        map3 (fn goal => fn hset_defs => fn hset_rec_minimal =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   732
          Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   733
            (mk_hset_minimal_tac n hset_defs hset_rec_minimal)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   734
          |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   735
        goals hset_defss' hset_rec_minimal_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   736
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   737
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   738
    val mor_hset_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   739
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   740
        val mor_hset_rec_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   741
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   742
            fun mk_conjunct j T i f x B =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   743
              HOLogic.mk_imp (HOLogic.mk_mem (x, B), HOLogic.mk_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   744
               (mk_hset_rec s's nat i j T $ (f $ x), mk_hset_rec ss nat i j T $ x));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   745
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   746
            fun mk_concl j T = list_all_free zs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   747
              (Library.foldr1 HOLogic.mk_conj (map4 (mk_conjunct j T) ks fs zs Bs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   748
            val concls = map2 mk_concl ls passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   749
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   750
            val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   751
              map (fn phi => map (SOME o certify lthy) [Term.absfree nat' phi, nat]) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   752
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   753
            val goals = map (fn concl =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   754
              Logic.list_implies ([coalg_prem, mor_prem], HOLogic.mk_Trueprop concl)) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   755
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   756
            map5 (fn j => fn goal => fn cts => fn hset_rec_0s => fn hset_rec_Sucs =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   757
              singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   758
                (Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   759
                  (K (mk_mor_hset_rec_tac m n cts j hset_rec_0s hset_rec_Sucs
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   760
                    morE_thms set_natural'ss coalg_set_thmss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   761
              |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   762
            ls goals ctss hset_rec_0ss' hset_rec_Sucss'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   763
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   764
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   765
        val mor_hset_rec_thmss = map (fn thm => map (fn i =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   766
          mk_specN n thm RS mk_conjunctN n i RS mp) ks) mor_hset_rec_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   767
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   768
        fun mk_prem x B = HOLogic.mk_Trueprop (HOLogic.mk_mem (x, B));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   769
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   770
        fun mk_concl j T i f x =
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   771
          mk_Trueprop_eq (mk_hset s's i j T $ (f $ x), mk_hset ss i j T $ x);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   772
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   773
        val goalss = map2 (fn j => fn T => map4 (fn i => fn f => fn x => fn B =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   774
          fold_rev Logic.all (x :: As @ Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   775
            (Logic.list_implies ([coalg_prem, mor_prem,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   776
              mk_prem x B], mk_concl j T i f x))) ks fs zs Bs) ls passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   777
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   778
        map3 (map3 (fn goal => fn hset_def => fn mor_hset_rec =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   779
          Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   780
            (K (mk_mor_hset_tac hset_def mor_hset_rec))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   781
          |> Thm.close_derivation))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   782
        goalss hset_defss' mor_hset_rec_thmss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   783
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   784
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   785
    val timer = time (timer "Hereditary sets");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   786
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   787
    (* bisimulation *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   788
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   789
    val bis_bind = Binding.suffix_name ("_" ^ bisN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   790
    val bis_name = Binding.name_of bis_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   791
    val bis_def_bind = (Thm.def_binding bis_bind, []);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   792
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   793
    fun mk_bis_le_conjunct R B1 B2 = mk_subset R (mk_Times (B1, B2));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   794
    val bis_le = Library.foldr1 HOLogic.mk_conj (map3 mk_bis_le_conjunct Rs Bs B's)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   795
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   796
    val bis_spec =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   797
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   798
        val bisT = Library.foldr (op -->) (ATs @ BTs @ sTs @ B'Ts @ s'Ts @ setRTs, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   799
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   800
        val fst_args = passive_ids @ fsts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   801
        val snd_args = passive_ids @ snds;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   802
        fun mk_bis R s s' b1 b2 RF map1 map2 sets =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   803
          list_all_free [b1, b2] (HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   804
            (HOLogic.mk_mem (HOLogic.mk_prod (b1, b2), R),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   805
            mk_Bex (mk_in (As @ Rs) sets (snd (dest_Free RF))) (Term.absfree (dest_Free RF)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   806
              (HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   807
                (HOLogic.mk_eq (Term.list_comb (map1, fst_args) $ RF, s $ b1),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   808
                HOLogic.mk_eq (Term.list_comb (map2, snd_args) $ RF, s' $ b2))))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   809
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   810
        val lhs = Term.list_comb (Free (bis_name, bisT), As @ Bs @ ss @ B's @ s's @ Rs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   811
        val rhs = HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   812
          (bis_le, Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   813
            (map9 mk_bis Rs ss s's zs z's RFs map_fsts map_snds bis_setss))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   814
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   815
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   816
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   817
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   818
    val ((bis_free, (_, bis_def_free)), (lthy, lthy_old)) =
49311
blanchet
parents: 49308
diff changeset
   819
      lthy
blanchet
parents: 49308
diff changeset
   820
      |> Specification.definition (SOME (bis_bind, NONE, NoSyn), (bis_def_bind, bis_spec))
blanchet
parents: 49308
diff changeset
   821
      ||> `Local_Theory.restore;
blanchet
parents: 49308
diff changeset
   822
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   823
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   824
    val bis = fst (Term.dest_Const (Morphism.term phi bis_free));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   825
    val bis_def = Morphism.thm phi bis_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   826
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   827
    fun mk_bis As Bs1 ss1 Bs2 ss2 Rs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   828
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   829
        val args = As @ Bs1 @ ss1 @ Bs2 @ ss2 @ Rs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   830
        val Ts = map fastype_of args;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   831
        val bisT = Library.foldr (op -->) (Ts, HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   832
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   833
        Term.list_comb (Const (bis, bisT), args)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   834
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   835
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   836
    val bis_cong_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   837
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   838
        val prems = map HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   839
         (mk_bis As Bs ss B's s's Rs :: map2 (curry HOLogic.mk_eq) Rs_copy Rs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   840
        val concl = HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's Rs_copy);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   841
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   842
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   843
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ Rs @ Rs_copy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   844
            (Logic.list_implies (prems, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   845
          (K ((hyp_subst_tac THEN' atac) 1))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   846
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   847
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   848
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   849
    val bis_srel_thm =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   850
      let
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   851
        fun mk_conjunct R s s' b1 b2 srel =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   852
          list_all_free [b1, b2] (HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   853
            (HOLogic.mk_mem (HOLogic.mk_prod (b1, b2), R),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   854
            HOLogic.mk_mem (HOLogic.mk_prod (s $ b1, s' $ b2),
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   855
              Term.list_comb (srel, passive_diags @ Rs))));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   856
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   857
        val rhs = HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   858
          (bis_le, Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   859
            (map6 mk_conjunct Rs ss s's zs z's relsAsBs))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   860
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   861
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   862
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ Rs)
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   863
            (mk_Trueprop_eq (mk_bis As Bs ss B's s's Rs, rhs)))
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   864
          (K (mk_bis_srel_tac m bis_def srel_O_Grs map_comp's map_congs set_natural'ss))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   865
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   866
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   867
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   868
    val bis_converse_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   869
      Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   870
        (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ Rs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   871
          (Logic.mk_implies
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   872
            (HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's Rs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   873
            HOLogic.mk_Trueprop (mk_bis As B's s's Bs ss (map mk_converse Rs)))))
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   874
        (K (mk_bis_converse_tac m bis_srel_thm srel_congs srel_converses))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   875
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   876
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   877
    val bis_O_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   878
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   879
        val prems =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   880
          [HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's Rs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   881
           HOLogic.mk_Trueprop (mk_bis As B's s's B''s s''s R's)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   882
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   883
          HOLogic.mk_Trueprop (mk_bis As Bs ss B''s s''s (map2 (curry mk_rel_comp) Rs R's));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   884
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   885
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   886
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ B''s @ s''s @ Rs @ R's)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   887
            (Logic.list_implies (prems, concl)))
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   888
          (K (mk_bis_O_tac m bis_srel_thm srel_congs srel_Os))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   889
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   890
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   891
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   892
    val bis_Gr_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   893
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   894
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   895
          HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's (map2 mk_Gr Bs fs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   896
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   897
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   898
          (fold_rev Logic.all (As @ Bs @ ss @ B's @ s's @ fs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   899
            (Logic.list_implies ([coalg_prem, mor_prem], concl)))
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
   900
          (mk_bis_Gr_tac bis_srel_thm srel_Grs mor_image_thms morE_thms coalg_in_thms)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   901
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   902
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   903
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   904
    val bis_image2_thm = bis_cong_thm OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   905
      ((bis_O_thm OF [bis_Gr_thm RS bis_converse_thm, bis_Gr_thm]) ::
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   906
      replicate n @{thm image2_Gr});
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   907
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   908
    val bis_diag_thm = bis_cong_thm OF ((mor_id_thm RSN (2, bis_Gr_thm)) ::
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   909
      replicate n @{thm diag_Gr});
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   910
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   911
    val bis_Union_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   912
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   913
        val prem =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   914
          HOLogic.mk_Trueprop (mk_Ball Idx
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   915
            (Term.absfree idx' (mk_bis As Bs ss B's s's (map (fn R => R $ idx) Ris))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   916
        val concl =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   917
          HOLogic.mk_Trueprop (mk_bis As Bs ss B's s's (map (mk_UNION Idx) Ris));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   918
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   919
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   920
          (fold_rev Logic.all (Idx :: As @ Bs @ ss @ B's @ s's @ Ris)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   921
            (Logic.mk_implies (prem, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   922
          (mk_bis_Union_tac bis_def in_mono'_thms)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   923
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   924
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   925
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   926
    (* self-bisimulation *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   927
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   928
    fun mk_sbis As Bs ss Rs = mk_bis As Bs ss Bs ss Rs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   929
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   930
    val sbis_prem = HOLogic.mk_Trueprop (mk_sbis As Bs ss sRs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   931
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   932
    (* largest self-bisimulation *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   933
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   934
    fun lsbis_bind i = Binding.suffix_name ("_" ^ lsbisN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   935
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   936
    val lsbis_name = Binding.name_of o lsbis_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   937
    val lsbis_def_bind = rpair [] o Thm.def_binding o lsbis_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   938
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   939
    val all_sbis = HOLogic.mk_Collect (fst Rtuple', snd Rtuple', list_exists_free sRs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   940
      (HOLogic.mk_conj (HOLogic.mk_eq (Rtuple, HOLogic.mk_tuple sRs), mk_sbis As Bs ss sRs)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   941
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   942
    fun lsbis_spec i RT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   943
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   944
        fun mk_lsbisT RT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   945
          Library.foldr (op -->) (map fastype_of (As @ Bs @ ss), RT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   946
        val lhs = Term.list_comb (Free (lsbis_name i, mk_lsbisT RT), As @ Bs @ ss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   947
        val rhs = mk_UNION all_sbis (Term.absfree Rtuple' (mk_nthN n Rtuple i));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   948
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
   949
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   950
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   951
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   952
    val ((lsbis_frees, (_, lsbis_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   953
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   954
      |> fold_map2 (fn i => fn RT => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   955
        (SOME (lsbis_bind i, NONE, NoSyn), (lsbis_def_bind i, lsbis_spec i RT))) ks setsRTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   956
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   957
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   958
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   959
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   960
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   961
    val lsbis_defs = map (Morphism.thm phi) lsbis_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   962
    val lsbiss = map (fst o Term.dest_Const o Morphism.term phi) lsbis_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   963
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   964
    fun mk_lsbis As Bs ss i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   965
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   966
        val args = As @ Bs @ ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   967
        val Ts = map fastype_of args;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   968
        val RT = mk_relT (`I (HOLogic.dest_setT (fastype_of (nth Bs (i - 1)))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   969
        val lsbisT = Library.foldr (op -->) (Ts, RT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   970
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   971
        Term.list_comb (Const (nth lsbiss (i - 1), lsbisT), args)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   972
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   973
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   974
    val sbis_lsbis_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   975
      Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   976
        (fold_rev Logic.all (As @ Bs @ ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   977
          (HOLogic.mk_Trueprop (mk_sbis As Bs ss (map (mk_lsbis As Bs ss) ks))))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   978
        (K (mk_sbis_lsbis_tac lsbis_defs bis_Union_thm bis_cong_thm))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   979
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   980
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   981
    val lsbis_incl_thms = map (fn i => sbis_lsbis_thm RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   982
      (bis_def RS @{thm subst[of _ _ "%x. x"]} RS conjunct1 RS mk_conjunctN n i)) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   983
    val lsbisE_thms = map (fn i => (mk_specN 2 (sbis_lsbis_thm RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   984
      (bis_def RS @{thm subst[of _ _ "%x. x"]} RS conjunct2 RS mk_conjunctN n i))) RS mp) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   985
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   986
    val incl_lsbis_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   987
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   988
        fun mk_concl i R = HOLogic.mk_Trueprop (mk_subset R (mk_lsbis As Bs ss i));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   989
        val goals = map2 (fn i => fn R => fold_rev Logic.all (As @ Bs @ ss @ sRs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   990
          (Logic.mk_implies (sbis_prem, mk_concl i R))) ks sRs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   991
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   992
        map3 (fn goal => fn i => fn def => Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
   993
          (K (mk_incl_lsbis_tac n i def)) |> Thm.close_derivation) goals ks lsbis_defs
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   994
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   995
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   996
    val equiv_lsbis_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   997
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   998
        fun mk_concl i B = HOLogic.mk_Trueprop (mk_equiv B (mk_lsbis As Bs ss i));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
   999
        val goals = map2 (fn i => fn B => fold_rev Logic.all (As @ Bs @ ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1000
          (Logic.mk_implies (coalg_prem, mk_concl i B))) ks Bs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1001
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1002
        map3 (fn goal => fn l_incl => fn incl_l =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1003
          Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1004
            (K (mk_equiv_lsbis_tac sbis_lsbis_thm l_incl incl_l
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1005
              bis_diag_thm bis_converse_thm bis_O_thm))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1006
          |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1007
        goals lsbis_incl_thms incl_lsbis_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1008
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1009
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1010
    val timer = time (timer "Bisimulations");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1011
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1012
    (* bounds *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1013
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1014
    val (lthy, sbd, sbdT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1015
      sbd_card_order, sbd_Cinfinite, sbd_Cnotzero, sbd_Card_order, set_sbdss, in_sbds) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1016
      if n = 1
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1017
      then (lthy, sum_bd, sum_bdT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1018
        bd_card_order, bd_Cinfinite, bd_Cnotzero, bd_Card_order, set_bdss, in_bds)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1019
      else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1020
        let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1021
          val sbdT_bind = Binding.suffix_name ("_" ^ sum_bdTN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1022
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1023
          val ((sbdT_name, (sbdT_glob_info, sbdT_loc_info)), lthy) =
49228
e43910ccee74 open typedefs everywhere in the package
traytel
parents: 49225
diff changeset
  1024
            typedef false NONE (sbdT_bind, params, NoSyn)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1025
              (HOLogic.mk_UNIV sum_bdT) NONE (EVERY' [rtac exI, rtac UNIV_I] 1) lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1026
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1027
          val sbdT = Type (sbdT_name, params');
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1028
          val Abs_sbdT = Const (#Abs_name sbdT_glob_info, sum_bdT --> sbdT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1029
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1030
          val sbd_bind = Binding.suffix_name ("_" ^ sum_bdN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1031
          val sbd_name = Binding.name_of sbd_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1032
          val sbd_def_bind = (Thm.def_binding sbd_bind, []);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1033
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1034
          val sbd_spec = HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1035
            (HOLogic.mk_eq (Free (sbd_name, mk_relT (`I sbdT)), mk_dir_image sum_bd Abs_sbdT));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1036
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1037
          val ((sbd_free, (_, sbd_def_free)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1038
            lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1039
            |> Specification.definition (SOME (sbd_bind, NONE, NoSyn), (sbd_def_bind, sbd_spec))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1040
            ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1041
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1042
          val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1043
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1044
          val sbd_def = Morphism.thm phi sbd_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1045
          val sbd = Const (fst (Term.dest_Const (Morphism.term phi sbd_free)), mk_relT (`I sbdT));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1046
49228
e43910ccee74 open typedefs everywhere in the package
traytel
parents: 49225
diff changeset
  1047
          val Abs_sbdT_inj = mk_Abs_inj_thm (#Abs_inject sbdT_loc_info);
e43910ccee74 open typedefs everywhere in the package
traytel
parents: 49225
diff changeset
  1048
          val Abs_sbdT_bij = mk_Abs_bij_thm lthy Abs_sbdT_inj (#Abs_cases sbdT_loc_info);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1049
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1050
          fun mk_sum_Cinfinite [thm] = thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1051
            | mk_sum_Cinfinite (thm :: thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1052
              @{thm Cinfinite_csum_strong} OF [thm, mk_sum_Cinfinite thms];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1053
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1054
          val sum_Cinfinite = mk_sum_Cinfinite bd_Cinfinites;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1055
          val sum_Card_order = sum_Cinfinite RS conjunct2;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1056
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1057
          fun mk_sum_card_order [thm] = thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1058
            | mk_sum_card_order (thm :: thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1059
              @{thm card_order_csum} OF [thm, mk_sum_card_order thms];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1060
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1061
          val sum_card_order = mk_sum_card_order bd_card_orders;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1062
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1063
          val sbd_ordIso = fold_thms lthy [sbd_def]
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1064
            (@{thm dir_image} OF [Abs_sbdT_inj, sum_Card_order]);
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1065
          val sbd_card_order =  fold_thms lthy [sbd_def]
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1066
            (@{thm card_order_dir_image} OF [Abs_sbdT_bij, sum_card_order]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1067
          val sbd_Cinfinite = @{thm Cinfinite_cong} OF [sbd_ordIso, sum_Cinfinite];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1068
          val sbd_Cnotzero = sbd_Cinfinite RS @{thm Cinfinite_Cnotzero};
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1069
          val sbd_Card_order = sbd_Cinfinite RS conjunct2;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1070
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1071
          fun mk_set_sbd i bd_Card_order bds =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1072
            map (fn thm => @{thm ordLeq_ordIso_trans} OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1073
              [bd_Card_order RS mk_ordLeq_csum n i thm, sbd_ordIso]) bds;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1074
          val set_sbdss = map3 mk_set_sbd ks bd_Card_orders set_bdss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1075
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1076
          fun mk_in_sbd i Co Cnz bd =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1077
            Cnz RS ((@{thm ordLeq_ordIso_trans} OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1078
              [(Co RS mk_ordLeq_csum n i (Co RS @{thm ordLeq_refl})), sbd_ordIso]) RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1079
              (bd RS @{thm ordLeq_transitive[OF _
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1080
                cexp_mono2_Cnotzero[OF _ csum_Cnotzero2[OF ctwo_Cnotzero]]]}));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1081
          val in_sbds = map4 mk_in_sbd ks bd_Card_orders bd_Cnotzeros in_bds;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1082
       in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1083
         (lthy, sbd, sbdT,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1084
           sbd_card_order, sbd_Cinfinite, sbd_Cnotzero, sbd_Card_order, set_sbdss, in_sbds)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1085
       end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1086
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1087
    fun mk_sbd_sbd 1 = sbd_Card_order RS @{thm ordIso_refl}
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1088
      | mk_sbd_sbd n = @{thm csum_absorb1} OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1089
          [sbd_Cinfinite, mk_sbd_sbd (n - 1) RS @{thm ordIso_imp_ordLeq}];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1090
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1091
    val sbd_sbd_thm = mk_sbd_sbd n;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1092
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1093
    val sbdTs = replicate n sbdT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1094
    val sum_sbd = Library.foldr1 (uncurry mk_csum) (replicate n sbd);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1095
    val sum_sbdT = mk_sumTN sbdTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1096
    val sum_sbd_listT = HOLogic.listT sum_sbdT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1097
    val sum_sbd_list_setT = HOLogic.mk_setT sum_sbd_listT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1098
    val bdTs = passiveAs @ replicate n sbdT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1099
    val to_sbd_maps = map4 mk_map_of_bnf Dss Ass (replicate n bdTs) bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1100
    val bdFTs = mk_FTs bdTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1101
    val sbdFT = mk_sumTN bdFTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1102
    val treeT = HOLogic.mk_prodT (sum_sbd_list_setT, sum_sbd_listT --> sbdFT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1103
    val treeQT = HOLogic.mk_setT treeT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1104
    val treeTs = passiveAs @ replicate n treeT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1105
    val treeQTs = passiveAs @ replicate n treeQT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1106
    val treeFTs = mk_FTs treeTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1107
    val tree_maps = map4 mk_map_of_bnf Dss (replicate n bdTs) (replicate n treeTs) bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1108
    val final_maps = map4 mk_map_of_bnf Dss (replicate n treeTs) (replicate n treeQTs) bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1109
    val tree_setss = mk_setss treeTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1110
    val isNode_setss = mk_setss (passiveAs @ replicate n sbdT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1111
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1112
    val root = HOLogic.mk_set sum_sbd_listT [HOLogic.mk_list sum_sbdT []];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1113
    val Zero = HOLogic.mk_tuple (map (fn U => absdummy U root) activeAs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1114
    val Lev_recT = fastype_of Zero;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1115
    val LevT = Library.foldr (op -->) (sTs, HOLogic.natT --> Lev_recT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1116
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1117
    val Nil = HOLogic.mk_tuple (map3 (fn i => fn z => fn z'=>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1118
      Term.absfree z' (mk_InN activeAs z i)) ks zs zs');
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1119
    val rv_recT = fastype_of Nil;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1120
    val rvT = Library.foldr (op -->) (sTs, sum_sbd_listT --> rv_recT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1121
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1122
    val (((((((((((sumx, sumx'), (kks, kks')), (kl, kl')), (kl_copy, kl'_copy)), (Kl, Kl')),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1123
      (lab, lab')), (Kl_lab, Kl_lab')), xs), (Lev_rec, Lev_rec')), (rv_rec, rv_rec')),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1124
      names_lthy) = names_lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1125
      |> yield_singleton (apfst (op ~~) oo mk_Frees' "sumx") sum_sbdT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1126
      ||>> mk_Frees' "k" sbdTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1127
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "kl") sum_sbd_listT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1128
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "kl") sum_sbd_listT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1129
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "Kl") sum_sbd_list_setT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1130
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "lab") (sum_sbd_listT --> sbdFT)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1131
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "Kl_lab") treeT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1132
      ||>> mk_Frees "x" bdFTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1133
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "rec") Lev_recT
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1134
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "rec") rv_recT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1135
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1136
    val (k, k') = (hd kks, hd kks')
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1137
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1138
    val timer = time (timer "Bounds");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1139
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1140
    (* tree coalgebra *)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1141
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1142
    fun isNode_bind i = Binding.suffix_name ("_" ^ isNodeN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1143
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1144
    val isNode_name = Binding.name_of o isNode_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1145
    val isNode_def_bind = rpair [] o Thm.def_binding o isNode_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1146
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1147
    val isNodeT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1148
      Library.foldr (op -->) (map fastype_of (As @ [Kl, lab, kl]), HOLogic.boolT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1149
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1150
    val Succs = map3 (fn i => fn k => fn k' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1151
      HOLogic.mk_Collect (fst k', snd k', HOLogic.mk_mem (mk_InN sbdTs k i, mk_Succ Kl kl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1152
      ks kks kks';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1153
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1154
    fun isNode_spec sets x i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1155
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1156
        val (passive_sets, active_sets) = chop m (map (fn set => set $ x) sets);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1157
        val lhs = Term.list_comb (Free (isNode_name i, isNodeT), As @ [Kl, lab, kl]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1158
        val rhs = list_exists_free [x]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1159
          (Library.foldr1 HOLogic.mk_conj (HOLogic.mk_eq (lab $ kl, mk_InN bdFTs x i) ::
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1160
          map2 mk_subset passive_sets As @ map2 (curry HOLogic.mk_eq) active_sets Succs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1161
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1162
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1163
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1164
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1165
    val ((isNode_frees, (_, isNode_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1166
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1167
      |> fold_map3 (fn i => fn x => fn sets => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1168
        (SOME (isNode_bind i, NONE, NoSyn), (isNode_def_bind i, isNode_spec sets x i)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1169
        ks xs isNode_setss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1170
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1171
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1172
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1173
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1174
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1175
    val isNode_defs = map (Morphism.thm phi) isNode_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1176
    val isNodes = map (fst o Term.dest_Const o Morphism.term phi) isNode_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1177
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1178
    fun mk_isNode As kl i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1179
      Term.list_comb (Const (nth isNodes (i - 1), isNodeT), As @ [Kl, lab, kl]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1180
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1181
    val isTree =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1182
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1183
        val empty = HOLogic.mk_mem (HOLogic.mk_list sum_sbdT [], Kl);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1184
        val Field = mk_subset Kl (mk_Field (mk_clists sum_sbd));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1185
        val prefCl = mk_prefCl Kl;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1186
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1187
        val tree = mk_Ball Kl (Term.absfree kl'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1188
          (HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1189
            (Library.foldr1 HOLogic.mk_disj (map (mk_isNode As kl) ks),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1190
            Library.foldr1 HOLogic.mk_conj (map4 (fn Succ => fn i => fn k => fn k' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1191
              mk_Ball Succ (Term.absfree k' (mk_isNode As
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1192
                (mk_append (kl, HOLogic.mk_list sum_sbdT [mk_InN sbdTs k i])) i)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1193
            Succs ks kks kks'))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1194
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1195
        val undef = list_all_free [kl] (HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1196
          (HOLogic.mk_not (HOLogic.mk_mem (kl, Kl)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1197
          HOLogic.mk_eq (lab $ kl, mk_undefined sbdFT)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1198
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1199
        Library.foldr1 HOLogic.mk_conj [empty, Field, prefCl, tree, undef]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1200
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1201
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1202
    fun carT_bind i = Binding.suffix_name ("_" ^ carTN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1203
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1204
    val carT_name = Binding.name_of o carT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1205
    val carT_def_bind = rpair [] o Thm.def_binding o carT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1206
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1207
    fun carT_spec i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1208
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1209
        val carTT = Library.foldr (op -->) (ATs, HOLogic.mk_setT treeT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1210
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1211
        val lhs = Term.list_comb (Free (carT_name i, carTT), As);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1212
        val rhs = HOLogic.mk_Collect (fst Kl_lab', snd Kl_lab', list_exists_free [Kl, lab]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1213
          (HOLogic.mk_conj (HOLogic.mk_eq (Kl_lab, HOLogic.mk_prod (Kl, lab)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1214
            HOLogic.mk_conj (isTree, mk_isNode As (HOLogic.mk_list sum_sbdT []) i))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1215
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1216
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1217
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1218
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1219
    val ((carT_frees, (_, carT_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1220
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1221
      |> fold_map (fn i => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1222
        (SOME (carT_bind i, NONE, NoSyn), (carT_def_bind i, carT_spec i))) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1223
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1224
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1225
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1226
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1227
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1228
    val carT_defs = map (Morphism.thm phi) carT_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1229
    val carTs = map (fst o Term.dest_Const o Morphism.term phi) carT_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1230
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1231
    fun mk_carT As i = Term.list_comb
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1232
      (Const (nth carTs (i - 1),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1233
         Library.foldr (op -->) (map fastype_of As, HOLogic.mk_setT treeT)), As);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1234
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1235
    fun strT_bind i = Binding.suffix_name ("_" ^ strTN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1236
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1237
    val strT_name = Binding.name_of o strT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1238
    val strT_def_bind = rpair [] o Thm.def_binding o strT_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1239
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1240
    fun strT_spec mapFT FT i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1241
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1242
        val strTT = treeT --> FT;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1243
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1244
        fun mk_f i k k' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1245
          let val in_k = mk_InN sbdTs k i;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1246
          in Term.absfree k' (HOLogic.mk_prod (mk_Shift Kl in_k, mk_shift lab in_k)) end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1247
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1248
        val f = Term.list_comb (mapFT, passive_ids @ map3 mk_f ks kks kks');
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1249
        val (fTs1, fTs2) = apsnd tl (chop (i - 1) (map (fn T => T --> FT) bdFTs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1250
        val fs = map mk_undefined fTs1 @ (f :: map mk_undefined fTs2);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1251
        val lhs = Free (strT_name i, strTT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1252
        val rhs = HOLogic.mk_split (Term.absfree Kl' (Term.absfree lab'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1253
          (mk_sum_caseN fs $ (lab $ HOLogic.mk_list sum_sbdT []))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1254
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1255
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1256
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1257
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1258
    val ((strT_frees, (_, strT_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1259
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1260
      |> fold_map3 (fn i => fn mapFT => fn FT => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1261
        (SOME (strT_bind i, NONE, NoSyn), (strT_def_bind i, strT_spec mapFT FT i)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1262
        ks tree_maps treeFTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1263
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1264
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1265
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1266
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1267
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1268
    val strT_defs = map ((fn def => trans OF [def RS fun_cong, @{thm prod.cases}]) o
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1269
      Morphism.thm phi) strT_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1270
    val strTs = map (fst o Term.dest_Const o Morphism.term phi) strT_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1271
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1272
    fun mk_strT FT i = Const (nth strTs (i - 1), treeT --> FT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1273
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1274
    val carTAs = map (mk_carT As) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1275
    val carTAs_copy = map (mk_carT As_copy) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1276
    val strTAs = map2 mk_strT treeFTs ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1277
    val hset_strTss = map (fn i => map2 (mk_hset strTAs i) ls passiveAs) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1278
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1279
    val coalgT_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1280
      Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1281
        (fold_rev Logic.all As (HOLogic.mk_Trueprop (mk_coalg As carTAs strTAs)))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1282
        (mk_coalgT_tac m (coalg_def :: isNode_defs @ carT_defs) strT_defs set_natural'ss)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1283
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1284
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1285
    val card_of_carT_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1286
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1287
        val lhs = mk_card_of
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1288
          (HOLogic.mk_Collect (fst Kl_lab', snd Kl_lab', list_exists_free [Kl, lab]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1289
            (HOLogic.mk_conj (HOLogic.mk_eq (Kl_lab, HOLogic.mk_prod (Kl, lab)), isTree))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1290
        val rhs = mk_cexp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1291
          (if m = 0 then ctwo else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1292
            (mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1293
            (mk_cexp sbd sbd);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1294
        val card_of_carT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1295
          Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1296
            (fold_rev Logic.all As (HOLogic.mk_Trueprop (mk_ordLeq lhs rhs)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1297
            (K (mk_card_of_carT_tac m isNode_defs sbd_sbd_thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1298
              sbd_card_order sbd_Card_order sbd_Cinfinite sbd_Cnotzero in_sbds))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1299
          |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1300
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1301
        map (fn def => @{thm ordLeq_transitive[OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1302
          card_of_mono1[OF ord_eq_le_trans[OF _ Collect_restrict']]]} OF [def, card_of_carT])
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1303
        carT_defs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1304
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1305
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1306
    val carT_set_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1307
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1308
        val Kl_lab = HOLogic.mk_prod (Kl, lab);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1309
        fun mk_goal carT strT set k i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1310
          fold_rev Logic.all (sumx :: Kl :: lab :: k :: kl :: As)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1311
            (Logic.list_implies (map HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1312
              [HOLogic.mk_mem (Kl_lab, carT), HOLogic.mk_mem (mk_Cons sumx kl, Kl),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1313
              HOLogic.mk_eq (sumx, mk_InN sbdTs k i)],
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1314
            HOLogic.mk_Trueprop (HOLogic.mk_mem
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1315
              (HOLogic.mk_prod (mk_Shift Kl sumx, mk_shift lab sumx),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1316
              set $ (strT $ Kl_lab)))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1317
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1318
        val goalss = map3 (fn carT => fn strT => fn sets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1319
          map3 (mk_goal carT strT) (drop m sets) kks ks) carTAs strTAs tree_setss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1320
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1321
        map6 (fn i => fn goals =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1322
            fn carT_def => fn strT_def => fn isNode_def => fn set_naturals =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1323
          map2 (fn goal => fn set_natural =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1324
            Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1325
              (mk_carT_set_tac n i carT_def strT_def isNode_def set_natural)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1326
            |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1327
          goals (drop m set_naturals))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1328
        ks goalss carT_defs strT_defs isNode_defs set_natural'ss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1329
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1330
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1331
    val carT_set_thmss' = transpose carT_set_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1332
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1333
    val isNode_hset_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1334
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1335
        val Kl_lab = HOLogic.mk_prod (Kl, lab);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1336
        fun mk_Kl_lab carT = HOLogic.mk_mem (Kl_lab, carT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1337
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1338
        val strT_hset_thmsss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1339
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1340
            val strT_hset_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1341
              let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1342
                fun mk_lab_kl i x = HOLogic.mk_eq (lab $ kl, mk_InN bdFTs x i);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1343
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1344
                fun mk_inner_conjunct j T i x set i' carT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1345
                  HOLogic.mk_imp (HOLogic.mk_conj (mk_Kl_lab carT, mk_lab_kl i x),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1346
                    mk_subset (set $ x) (mk_hset strTAs i' j T $ Kl_lab));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1347
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1348
                fun mk_conjunct j T i x set =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1349
                  Library.foldr1 HOLogic.mk_conj (map2 (mk_inner_conjunct j T i x set) ks carTAs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1350
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1351
                fun mk_concl j T = list_all_free (Kl :: lab :: xs @ As)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1352
                  (HOLogic.mk_imp (HOLogic.mk_mem (kl, Kl),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1353
                    Library.foldr1 HOLogic.mk_conj (map3 (mk_conjunct j T)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1354
                      ks xs (map (fn xs => nth xs (j - 1)) isNode_setss))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1355
                val concls = map2 mk_concl ls passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1356
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1357
                val cTs = [SOME (certifyT lthy sum_sbdT)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1358
                val arg_cong_cTs = map (SOME o certifyT lthy) treeFTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1359
                val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1360
                  map (fn phi => map (SOME o certify lthy) [Term.absfree kl' phi, kl]) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1361
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1362
                val goals = map HOLogic.mk_Trueprop concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1363
              in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1364
                map5 (fn j => fn goal => fn cts => fn set_incl_hsets => fn set_hset_incl_hsetss =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1365
                  singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1366
                    (Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1367
                      (K (mk_strT_hset_tac n m j arg_cong_cTs cTs cts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1368
                        carT_defs strT_defs isNode_defs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1369
                        set_incl_hsets set_hset_incl_hsetss coalg_set_thmss' carT_set_thmss'
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1370
                        coalgT_thm set_natural'ss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1371
                  |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1372
                ls goals ctss set_incl_hset_thmss' set_hset_incl_hset_thmsss''
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1373
              end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1374
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1375
            val strT_hset'_thms = map (fn thm => mk_specN (2 + n + m) thm RS mp) strT_hset_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1376
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1377
            map (fn thm => map (fn i => map (fn i' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1378
              thm RS mk_conjunctN n i RS mk_conjunctN n i' RS mp) ks) ks) strT_hset'_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1379
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1380
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1381
        val carT_prems = map (fn carT =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1382
          HOLogic.mk_Trueprop (HOLogic.mk_mem (Kl_lab, carT))) carTAs_copy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1383
        val prem = HOLogic.mk_Trueprop (HOLogic.mk_mem (kl, Kl));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1384
        val in_prems = map (fn hsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1385
          HOLogic.mk_Trueprop (HOLogic.mk_mem (Kl_lab, mk_in As hsets treeT))) hset_strTss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1386
        val isNode_premss = replicate n (map (HOLogic.mk_Trueprop o mk_isNode As_copy kl) ks);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1387
        val conclss = replicate n (map (HOLogic.mk_Trueprop o mk_isNode As kl) ks);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1388
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1389
        map5 (fn carT_prem => fn isNode_prems => fn in_prem => fn concls => fn strT_hset_thmss =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1390
          map4 (fn isNode_prem => fn concl => fn isNode_def => fn strT_hset_thms =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1391
            Skip_Proof.prove lthy [] []
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1392
              (fold_rev Logic.all (Kl :: lab :: kl :: As @ As_copy)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1393
                (Logic.list_implies ([carT_prem, prem, isNode_prem, in_prem], concl)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1394
              (mk_isNode_hset_tac n isNode_def strT_hset_thms)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1395
            |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1396
          isNode_prems concls isNode_defs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1397
          (if m = 0 then replicate n [] else transpose strT_hset_thmss))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1398
        carT_prems isNode_premss in_prems conclss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1399
        (if m = 0 then replicate n [] else transpose (map transpose strT_hset_thmsss))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1400
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1401
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1402
    val timer = time (timer "Tree coalgebra");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1403
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1404
    fun mk_to_sbd s x i i' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1405
      mk_toCard (nth (nth setssAs (i - 1)) (m + i' - 1) $ (s $ x)) sbd;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1406
    fun mk_from_sbd s x i i' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1407
      mk_fromCard (nth (nth setssAs (i - 1)) (m + i' - 1) $ (s $ x)) sbd;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1408
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1409
    fun mk_to_sbd_thmss thm = map (map (fn set_sbd =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1410
      thm OF [set_sbd, sbd_Card_order]) o drop m) set_sbdss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1411
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1412
    val to_sbd_inj_thmss = mk_to_sbd_thmss @{thm toCard_inj};
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1413
    val to_sbd_thmss = mk_to_sbd_thmss @{thm toCard};
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1414
    val from_to_sbd_thmss = mk_to_sbd_thmss @{thm fromCard_toCard};
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1415
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1416
    val Lev_bind = Binding.suffix_name ("_" ^ LevN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1417
    val Lev_name = Binding.name_of Lev_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1418
    val Lev_def_bind = rpair [] (Thm.def_binding Lev_bind);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1419
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1420
    val Lev_spec =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1421
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1422
        fun mk_Suc i s setsAs a a' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1423
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1424
            val sets = drop m setsAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1425
            fun mk_set i' set b =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1426
              let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1427
                val Cons = HOLogic.mk_eq (kl_copy,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1428
                  mk_Cons (mk_InN sbdTs (mk_to_sbd s a i i' $ b) i') kl)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1429
                val b_set = HOLogic.mk_mem (b, set $ (s $ a));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1430
                val kl_rec = HOLogic.mk_mem (kl, mk_nthN n Lev_rec i' $ b);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1431
              in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1432
                HOLogic.mk_Collect (fst kl'_copy, snd kl'_copy, list_exists_free [b, kl]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1433
                  (HOLogic.mk_conj (Cons, HOLogic.mk_conj (b_set, kl_rec))))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1434
              end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1435
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1436
            Term.absfree a' (Library.foldl1 mk_union (map3 mk_set ks sets zs_copy))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1437
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1438
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1439
        val Suc = Term.absdummy HOLogic.natT (Term.absfree Lev_rec'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1440
          (HOLogic.mk_tuple (map5 mk_Suc ks ss setssAs zs zs')));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1441
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1442
        val lhs = Term.list_comb (Free (Lev_name, LevT), ss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1443
        val rhs = mk_nat_rec Zero Suc;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1444
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1445
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1446
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1447
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1448
    val ((Lev_free, (_, Lev_def_free)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1449
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1450
      |> Specification.definition (SOME (Lev_bind, NONE, NoSyn), (Lev_def_bind, Lev_spec))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1451
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1452
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1453
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1454
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1455
    val Lev_def = Morphism.thm phi Lev_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1456
    val Lev = fst (Term.dest_Const (Morphism.term phi Lev_free));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1457
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1458
    fun mk_Lev ss nat i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1459
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1460
        val Ts = map fastype_of ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1461
        val LevT = Library.foldr (op -->) (Ts, HOLogic.natT -->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1462
          HOLogic.mk_tupleT (map (fn U => domain_type U --> sum_sbd_list_setT) Ts));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1463
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1464
        mk_nthN n (Term.list_comb (Const (Lev, LevT), ss) $ nat) i
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1465
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1466
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1467
    val Lev_0s = flat (mk_rec_simps n @{thm nat_rec_0} [Lev_def]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1468
    val Lev_Sucs = flat (mk_rec_simps n @{thm nat_rec_Suc} [Lev_def]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1469
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1470
    val rv_bind = Binding.suffix_name ("_" ^ rvN) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1471
    val rv_name = Binding.name_of rv_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1472
    val rv_def_bind = rpair [] (Thm.def_binding rv_bind);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1473
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1474
    val rv_spec =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1475
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1476
        fun mk_Cons i s b b' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1477
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1478
            fun mk_case i' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1479
              Term.absfree k' (mk_nthN n rv_rec i' $ (mk_from_sbd s b i i' $ k));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1480
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1481
            Term.absfree b' (mk_sum_caseN (map mk_case ks) $ sumx)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1482
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1483
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1484
        val Cons = Term.absfree sumx' (Term.absdummy sum_sbd_listT (Term.absfree rv_rec'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1485
          (HOLogic.mk_tuple (map4 mk_Cons ks ss zs zs'))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1486
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1487
        val lhs = Term.list_comb (Free (rv_name, rvT), ss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1488
        val rhs = mk_list_rec Nil Cons;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1489
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1490
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1491
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1492
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1493
    val ((rv_free, (_, rv_def_free)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1494
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1495
      |> Specification.definition (SOME (rv_bind, NONE, NoSyn), (rv_def_bind, rv_spec))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1496
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1497
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1498
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1499
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1500
    val rv_def = Morphism.thm phi rv_def_free;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1501
    val rv = fst (Term.dest_Const (Morphism.term phi rv_free));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1502
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1503
    fun mk_rv ss kl i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1504
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1505
        val Ts = map fastype_of ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1506
        val As = map domain_type Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1507
        val rvT = Library.foldr (op -->) (Ts, fastype_of kl -->
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1508
          HOLogic.mk_tupleT (map (fn U => U --> mk_sumTN As) As));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1509
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1510
        mk_nthN n (Term.list_comb (Const (rv, rvT), ss) $ kl) i
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1511
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1512
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1513
    val rv_Nils = flat (mk_rec_simps n @{thm list_rec_Nil} [rv_def]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1514
    val rv_Conss = flat (mk_rec_simps n @{thm list_rec_Cons} [rv_def]);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1515
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1516
    fun beh_bind i = Binding.suffix_name ("_" ^ behN ^ (if n = 1 then "" else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1517
      string_of_int i)) b;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1518
    val beh_name = Binding.name_of o beh_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1519
    val beh_def_bind = rpair [] o Thm.def_binding o beh_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1520
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1521
    fun beh_spec i z =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1522
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1523
        val mk_behT = Library.foldr (op -->) (map fastype_of (ss @ [z]), treeT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1524
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1525
        fun mk_case i to_sbd_map s k k' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1526
          Term.absfree k' (mk_InN bdFTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1527
            (Term.list_comb (to_sbd_map, passive_ids @ map (mk_to_sbd s k i) ks) $ (s $ k)) i);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1528
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1529
        val Lab = Term.absfree kl' (mk_If
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1530
          (HOLogic.mk_mem (kl, mk_Lev ss (mk_size kl) i $ z))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1531
          (mk_sum_caseN (map5 mk_case ks to_sbd_maps ss zs zs') $ (mk_rv ss kl i $ z))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1532
          (mk_undefined sbdFT));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1533
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1534
        val lhs = Term.list_comb (Free (beh_name i, mk_behT), ss) $ z;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1535
        val rhs = HOLogic.mk_prod (mk_UNION (HOLogic.mk_UNIV HOLogic.natT)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1536
          (Term.absfree nat' (mk_Lev ss nat i $ z)), Lab);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1537
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1538
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1539
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1540
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1541
    val ((beh_frees, (_, beh_def_frees)), (lthy, lthy_old)) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1542
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1543
      |> fold_map2 (fn i => fn z => Specification.definition
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1544
        (SOME (beh_bind i, NONE, NoSyn), (beh_def_bind i, beh_spec i z))) ks zs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1545
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1546
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1547
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1548
    val phi = Proof_Context.export_morphism lthy_old lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1549
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1550
    val beh_defs = map (Morphism.thm phi) beh_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1551
    val behs = map (fst o Term.dest_Const o Morphism.term phi) beh_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1552
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1553
    fun mk_beh ss i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1554
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1555
        val Ts = map fastype_of ss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1556
        val behT = Library.foldr (op -->) (Ts, nth activeAs (i - 1) --> treeT);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1557
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1558
        Term.list_comb (Const (nth behs (i - 1), behT), ss)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1559
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1560
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1561
    val Lev_sbd_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1562
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1563
        fun mk_conjunct i z = mk_subset (mk_Lev ss nat i $ z) (mk_Field (mk_clists sum_sbd));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1564
        val goal = list_all_free zs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1565
          (Library.foldr1 HOLogic.mk_conj (map2 mk_conjunct ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1566
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1567
        val cts = map (SOME o certify lthy) [Term.absfree nat' goal, nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1568
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1569
        val Lev_sbd = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1570
          (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1571
            (K (mk_Lev_sbd_tac cts Lev_0s Lev_Sucs to_sbd_thmss))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1572
          |> Thm.close_derivation);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1573
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1574
        val Lev_sbd' = mk_specN n Lev_sbd;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1575
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1576
        map (fn i => Lev_sbd' RS mk_conjunctN n i) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1577
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1578
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1579
    val (length_Lev_thms, length_Lev'_thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1580
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1581
        fun mk_conjunct i z = HOLogic.mk_imp (HOLogic.mk_mem (kl, mk_Lev ss nat i $ z),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1582
          HOLogic.mk_eq (mk_size kl, nat));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1583
        val goal = list_all_free (kl :: zs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1584
          (Library.foldr1 HOLogic.mk_conj (map2 mk_conjunct ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1585
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1586
        val cts = map (SOME o certify lthy) [Term.absfree nat' goal, nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1587
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1588
        val length_Lev = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1589
          (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1590
            (K (mk_length_Lev_tac cts Lev_0s Lev_Sucs))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1591
          |> Thm.close_derivation);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1592
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1593
        val length_Lev' = mk_specN (n + 1) length_Lev;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1594
        val length_Levs = map (fn i => length_Lev' RS mk_conjunctN n i RS mp) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1595
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1596
        fun mk_goal i z = fold_rev Logic.all (z :: kl :: nat :: ss) (Logic.mk_implies
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1597
            (HOLogic.mk_Trueprop (HOLogic.mk_mem (kl, mk_Lev ss nat i $ z)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1598
            HOLogic.mk_Trueprop (HOLogic.mk_mem (kl, mk_Lev ss (mk_size kl) i $ z))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1599
        val goals = map2 mk_goal ks zs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1600
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1601
        val length_Levs' = map2 (fn goal => fn length_Lev =>
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1602
          Skip_Proof.prove lthy [] [] goal (K (mk_length_Lev'_tac length_Lev))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1603
          |> Thm.close_derivation) goals length_Levs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1604
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1605
        (length_Levs, length_Levs')
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1606
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1607
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1608
    val prefCl_Lev_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1609
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1610
        fun mk_conjunct i z = HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1611
          (HOLogic.mk_conj (HOLogic.mk_mem (kl, mk_Lev ss nat i $ z), mk_subset kl_copy kl),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1612
          HOLogic.mk_mem (kl_copy, mk_Lev ss (mk_size kl_copy) i $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1613
        val goal = list_all_free (kl :: kl_copy :: zs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1614
          (Library.foldr1 HOLogic.mk_conj (map2 mk_conjunct ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1615
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1616
        val cts = map (SOME o certify lthy) [Term.absfree nat' goal, nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1617
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1618
        val prefCl_Lev = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1619
          (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1620
            (K (mk_prefCl_Lev_tac cts Lev_0s Lev_Sucs)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1621
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1622
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1623
        val prefCl_Lev' = mk_specN (n + 2) prefCl_Lev;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1624
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1625
        map (fn i => prefCl_Lev' RS mk_conjunctN n i RS mp) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1626
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1627
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1628
    val rv_last_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1629
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1630
        fun mk_conjunct i z i' z_copy = list_exists_free [z_copy]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1631
          (HOLogic.mk_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1632
            (mk_rv ss (mk_append (kl, HOLogic.mk_list sum_sbdT [mk_InN sbdTs k i'])) i $ z,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1633
            mk_InN activeAs z_copy i'));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1634
        val goal = list_all_free (k :: zs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1635
          (Library.foldr1 HOLogic.mk_conj (map2 (fn i => fn z =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1636
            Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1637
              (map2 (mk_conjunct i z) ks zs_copy)) ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1638
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1639
        val cTs = [SOME (certifyT lthy sum_sbdT)];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1640
        val cts = map (SOME o certify lthy) [Term.absfree kl' goal, kl];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1641
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1642
        val rv_last = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1643
          (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1644
            (K (mk_rv_last_tac cTs cts rv_Nils rv_Conss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1645
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1646
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1647
        val rv_last' = mk_specN (n + 1) rv_last;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1648
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1649
        map (fn i => map (fn i' => rv_last' RS mk_conjunctN n i RS mk_conjunctN n i') ks) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1650
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1651
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1652
    val set_rv_Lev_thmsss = if m = 0 then replicate n (replicate n []) else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1653
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1654
        fun mk_case s sets z z_free = Term.absfree z_free (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1655
          (map2 (fn set => fn A => mk_subset (set $ (s $ z)) A) (take m sets) As));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1656
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1657
        fun mk_conjunct i z B = HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1658
          (HOLogic.mk_conj (HOLogic.mk_mem (kl, mk_Lev ss nat i $ z), HOLogic.mk_mem (z, B)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1659
          mk_sum_caseN (map4 mk_case ss setssAs zs zs') $ (mk_rv ss kl i $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1660
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1661
        val goal = list_all_free (kl :: zs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1662
          (Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct ks zs Bs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1663
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1664
        val cts = map (SOME o certify lthy) [Term.absfree nat' goal, nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1665
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1666
        val set_rv_Lev = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1667
          (Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1668
            (Logic.mk_implies (coalg_prem, HOLogic.mk_Trueprop goal))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1669
            (K (mk_set_rv_Lev_tac m cts Lev_0s Lev_Sucs rv_Nils rv_Conss
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1670
              coalg_set_thmss from_to_sbd_thmss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1671
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1672
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1673
        val set_rv_Lev' = mk_specN (n + 1) set_rv_Lev;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1674
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1675
        map (fn i => map (fn i' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1676
          split_conj_thm (if n = 1 then set_rv_Lev' RS mk_conjunctN n i RS mp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1677
            else set_rv_Lev' RS mk_conjunctN n i RS mp RSN
49327
541d818d2ff3 put an underscore between names, for compatibility with old package (and also because it makes sense)
blanchet
parents: 49311
diff changeset
  1678
              (2, @{thm sum_case_weak_cong} RS @{thm subst[of _ _ "%x. x"]}) RS
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1679
              (mk_sum_casesN n i' RS @{thm subst[of _ _ "%x. x"]}))) ks) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1680
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1681
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1682
    val set_Lev_thmsss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1683
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1684
        fun mk_conjunct i z =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1685
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1686
            fun mk_conjunct' i' sets s z' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1687
              let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1688
                fun mk_conjunct'' i'' set z'' = HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1689
                  (HOLogic.mk_mem (z'', set $ (s $ z')),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1690
                    HOLogic.mk_mem (mk_append (kl,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1691
                      HOLogic.mk_list sum_sbdT [mk_InN sbdTs (mk_to_sbd s z' i' i'' $ z'') i'']),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1692
                      mk_Lev ss (HOLogic.mk_Suc nat) i $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1693
              in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1694
                HOLogic.mk_imp (HOLogic.mk_eq (mk_rv ss kl i $ z, mk_InN activeAs z' i'),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1695
                  (Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct'' ks (drop m sets) zs_copy2)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1696
              end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1697
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1698
            HOLogic.mk_imp (HOLogic.mk_mem (kl, mk_Lev ss nat i $ z),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1699
              Library.foldr1 HOLogic.mk_conj (map4 mk_conjunct' ks setssAs ss zs_copy))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1700
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1701
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1702
        val goal = list_all_free (kl :: zs @ zs_copy @ zs_copy2)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1703
          (Library.foldr1 HOLogic.mk_conj (map2 mk_conjunct ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1704
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1705
        val cts = map (SOME o certify lthy) [Term.absfree nat' goal, nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1706
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1707
        val set_Lev = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1708
          (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1709
            (K (mk_set_Lev_tac cts Lev_0s Lev_Sucs rv_Nils rv_Conss from_to_sbd_thmss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1710
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1711
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1712
        val set_Lev' = mk_specN (3 * n + 1) set_Lev;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1713
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1714
        map (fn i => map (fn i' => map (fn i'' => set_Lev' RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1715
          mk_conjunctN n i RS mp RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1716
          mk_conjunctN n i' RS mp RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1717
          mk_conjunctN n i'' RS mp) ks) ks) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1718
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1719
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1720
    val set_image_Lev_thmsss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1721
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1722
        fun mk_conjunct i z =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1723
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1724
            fun mk_conjunct' i' sets =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1725
              let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1726
                fun mk_conjunct'' i'' set s z'' = HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1727
                  (HOLogic.mk_eq (mk_rv ss kl i $ z, mk_InN activeAs z'' i''),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1728
                  HOLogic.mk_mem (k, mk_image (mk_to_sbd s z'' i'' i') $ (set $ (s $ z''))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1729
              in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1730
                HOLogic.mk_imp (HOLogic.mk_mem
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1731
                  (mk_append (kl, HOLogic.mk_list sum_sbdT [mk_InN sbdTs k i']),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1732
                    mk_Lev ss (HOLogic.mk_Suc nat) i $ z),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1733
                  (Library.foldr1 HOLogic.mk_conj (map4 mk_conjunct'' ks sets ss zs_copy)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1734
              end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1735
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1736
            HOLogic.mk_imp (HOLogic.mk_mem (kl, mk_Lev ss nat i $ z),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1737
              Library.foldr1 HOLogic.mk_conj (map2 mk_conjunct' ks (drop m setssAs')))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1738
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1739
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1740
        val goal = list_all_free (kl :: k :: zs @ zs_copy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1741
          (Library.foldr1 HOLogic.mk_conj (map2 mk_conjunct ks zs));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1742
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1743
        val cts = map (SOME o certify lthy) [Term.absfree nat' goal, nat];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1744
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1745
        val set_image_Lev = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1746
          (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1747
            (K (mk_set_image_Lev_tac cts Lev_0s Lev_Sucs rv_Nils rv_Conss
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1748
              from_to_sbd_thmss to_sbd_inj_thmss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1749
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1750
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1751
        val set_image_Lev' = mk_specN (2 * n + 2) set_image_Lev;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1752
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1753
        map (fn i => map (fn i' => map (fn i'' => set_image_Lev' RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1754
          mk_conjunctN n i RS mp RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1755
          mk_conjunctN n i'' RS mp RS
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1756
          mk_conjunctN n i' RS mp) ks) ks) ks
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1757
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1758
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1759
    val mor_beh_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1760
      Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1761
        (fold_rev Logic.all (As @ Bs @ ss) (Logic.mk_implies (coalg_prem,
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1762
          HOLogic.mk_Trueprop (mk_mor Bs ss carTAs strTAs (map (mk_beh ss) ks)))))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1763
        (mk_mor_beh_tac m mor_def mor_cong_thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1764
          beh_defs carT_defs strT_defs isNode_defs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1765
          to_sbd_inj_thmss from_to_sbd_thmss Lev_0s Lev_Sucs rv_Nils rv_Conss Lev_sbd_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1766
          length_Lev_thms length_Lev'_thms prefCl_Lev_thms rv_last_thmss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1767
          set_rv_Lev_thmsss set_Lev_thmsss set_image_Lev_thmsss
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1768
          set_natural'ss coalg_set_thmss map_comp_id_thms map_congs map_arg_cong_thms)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1769
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1770
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1771
    val timer = time (timer "Behavioral morphism");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1772
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1773
    fun mk_LSBIS As i = mk_lsbis As (map (mk_carT As) ks) strTAs i;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1774
    fun mk_car_final As i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1775
      mk_quotient (mk_carT As i) (mk_LSBIS As i);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1776
    fun mk_str_final As i =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1777
      mk_univ (HOLogic.mk_comp (Term.list_comb (nth final_maps (i - 1),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1778
        passive_ids @ map (mk_proj o mk_LSBIS As) ks), nth strTAs (i - 1)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1779
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1780
    val car_finalAs = map (mk_car_final As) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1781
    val str_finalAs = map (mk_str_final As) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1782
    val car_finals = map (mk_car_final passive_UNIVs) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1783
    val str_finals = map (mk_str_final passive_UNIVs) ks;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1784
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1785
    val coalgT_set_thmss = map (map (fn thm => coalgT_thm RS thm)) coalg_set_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1786
    val equiv_LSBIS_thms = map (fn thm => coalgT_thm RS thm) equiv_lsbis_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1787
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1788
    val congruent_str_final_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1789
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1790
        fun mk_goal R final_map strT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1791
          fold_rev Logic.all As (HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1792
            (mk_congruent R (HOLogic.mk_comp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1793
              (Term.list_comb (final_map, passive_ids @ map (mk_proj o mk_LSBIS As) ks), strT))));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1794
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1795
        val goals = map3 mk_goal (map (mk_LSBIS As) ks) final_maps strTAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1796
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1797
        map4 (fn goal => fn lsbisE => fn map_comp_id => fn map_cong =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1798
          Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1799
            (K (mk_congruent_str_final_tac m lsbisE map_comp_id map_cong equiv_LSBIS_thms))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1800
          |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1801
        goals lsbisE_thms map_comp_id_thms map_congs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1802
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1803
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1804
    val coalg_final_thm = Skip_Proof.prove lthy [] [] (fold_rev Logic.all As
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1805
      (HOLogic.mk_Trueprop (mk_coalg As car_finalAs str_finalAs)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1806
      (K (mk_coalg_final_tac m coalg_def congruent_str_final_thms equiv_LSBIS_thms
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1807
        set_natural'ss coalgT_set_thmss))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1808
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1809
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1810
    val mor_T_final_thm = Skip_Proof.prove lthy [] [] (fold_rev Logic.all As
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1811
      (HOLogic.mk_Trueprop (mk_mor carTAs strTAs car_finalAs str_finalAs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1812
        (map (mk_proj o mk_LSBIS As) ks))))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1813
      (K (mk_mor_T_final_tac mor_def congruent_str_final_thms equiv_LSBIS_thms))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1814
      |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1815
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1816
    val mor_final_thm = mor_comp_thm OF [mor_beh_thm, mor_T_final_thm];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1817
    val in_car_final_thms = map (fn mor_image' => mor_image' OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1818
      [tcoalg_thm RS mor_final_thm, UNIV_I]) mor_image'_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1819
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1820
    val timer = time (timer "Final coalgebra");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1821
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1822
    val ((T_names, (T_glob_infos, T_loc_infos)), lthy) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1823
      lthy
49169
937a0fadddfb honor mixfix specifications
blanchet
parents: 49134
diff changeset
  1824
      |> fold_map4 (fn b => fn mx => fn car_final => fn in_car_final =>
937a0fadddfb honor mixfix specifications
blanchet
parents: 49134
diff changeset
  1825
        typedef false NONE (b, params, mx) car_final NONE
937a0fadddfb honor mixfix specifications
blanchet
parents: 49134
diff changeset
  1826
          (EVERY' [rtac exI, rtac in_car_final] 1)) bs mixfixes car_finals in_car_final_thms
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1827
      |>> apsnd split_list o split_list;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1828
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1829
    val Ts = map (fn name => Type (name, params')) T_names;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1830
    fun mk_Ts passive = map (Term.typ_subst_atomic (passiveAs ~~ passive)) Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1831
    val Ts' = mk_Ts passiveBs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1832
    val Ts'' = mk_Ts passiveCs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1833
    val Rep_Ts = map2 (fn info => fn T => Const (#Rep_name info, T --> treeQT)) T_glob_infos Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1834
    val Abs_Ts = map2 (fn info => fn T => Const (#Abs_name info, treeQT --> T)) T_glob_infos Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1835
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1836
    val Reps = map #Rep T_loc_infos;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1837
    val Rep_injects = map #Rep_inject T_loc_infos;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1838
    val Rep_inverses = map #Rep_inverse T_loc_infos;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1839
    val Abs_inverses = map #Abs_inverse T_loc_infos;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1840
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1841
    val timer = time (timer "THE TYPEDEFs & Rep/Abs thms");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1842
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1843
    val UNIVs = map HOLogic.mk_UNIV Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1844
    val FTs = mk_FTs (passiveAs @ Ts);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1845
    val FTs' = mk_FTs (passiveBs @ Ts);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1846
    val prodTs = map (HOLogic.mk_prodT o `I) Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1847
    val prodFTs = mk_FTs (passiveAs @ prodTs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1848
    val FTs_setss = mk_setss (passiveAs @ Ts);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1849
    val prodFT_setss = mk_setss (passiveAs @ prodTs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1850
    val map_FTs = map2 (fn Ds => mk_map_of_bnf Ds treeQTs (passiveAs @ Ts)) Dss bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1851
    val map_FT_nths = map2 (fn Ds =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1852
      mk_map_of_bnf Ds (passiveAs @ prodTs) (passiveAs @ Ts)) Dss bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1853
    val fstsTs = map fst_const prodTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1854
    val sndsTs = map snd_const prodTs;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1855
    val dtorTs = map2 (curry (op -->)) Ts FTs;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1856
    val ctorTs = map2 (curry (op -->)) FTs Ts;
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1857
    val unfold_fTs = map2 (curry op -->) activeAs Ts;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1858
    val corec_sTs = map (Term.typ_subst_atomic (activeBs ~~ Ts)) sum_sTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1859
    val corec_maps = map (Term.subst_atomic_types (activeBs ~~ Ts)) map_Inls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1860
    val corec_maps_rev = map (Term.subst_atomic_types (activeBs ~~ Ts)) map_Inls_rev;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1861
    val corec_Inls = map (Term.subst_atomic_types (activeBs ~~ Ts)) Inls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1862
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1863
    val (((((((((((((Jzs, Jzs'), (Jz's, Jz's')), Jzs_copy), Jzs1), Jzs2), Jpairs),
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1864
      FJzs), TRs), unfold_fs), unfold_fs_copy), corec_ss), phis), names_lthy) = names_lthy
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1865
      |> mk_Frees' "z" Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1866
      ||>> mk_Frees' "z" Ts'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1867
      ||>> mk_Frees "z" Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1868
      ||>> mk_Frees "z1" Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1869
      ||>> mk_Frees "z2" Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1870
      ||>> mk_Frees "j" (map2 (curry HOLogic.mk_prodT) Ts Ts')
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1871
      ||>> mk_Frees "x" prodFTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1872
      ||>> mk_Frees "R" (map (mk_relT o `I) Ts)
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1873
      ||>> mk_Frees "f" unfold_fTs
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1874
      ||>> mk_Frees "g" unfold_fTs
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1875
      ||>> mk_Frees "s" corec_sTs
49463
83ac281bcdc2 provide predicator, define relator
blanchet
parents: 49460
diff changeset
  1876
      ||>> mk_Frees "P" (map2 mk_pred2T Ts Ts);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1877
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1878
    fun dtor_bind i = Binding.suffix_name ("_" ^ dtorN) (nth bs (i - 1));
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1879
    val dtor_name = Binding.name_of o dtor_bind;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1880
    val dtor_def_bind = rpair [] o Thm.def_binding o dtor_bind;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1881
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1882
    fun dtor_spec i rep str map_FT dtorT Jz Jz' =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1883
      let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1884
        val lhs = Free (dtor_name i, dtorT);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1885
        val rhs = Term.absfree Jz'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1886
          (Term.list_comb (map_FT, map HOLogic.id_const passiveAs @ Abs_Ts) $
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1887
            (str $ (rep $ Jz)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1888
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1889
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1890
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1891
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1892
    val ((dtor_frees, (_, dtor_def_frees)), (lthy, lthy_old)) =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1893
      lthy
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1894
      |> fold_map7 (fn i => fn rep => fn str => fn mapx => fn dtorT => fn Jz => fn Jz' =>
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1895
        Specification.definition (SOME (dtor_bind i, NONE, NoSyn),
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1896
          (dtor_def_bind i, dtor_spec i rep str mapx dtorT Jz Jz')))
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1897
        ks Rep_Ts str_finals map_FTs dtorTs Jzs Jzs'
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1898
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1899
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1900
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1901
    val phi = Proof_Context.export_morphism lthy_old lthy;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1902
    fun mk_dtors passive =
49185
073d7d1b7488 respect order of/additional type variables supplied by the user in fixed point constructions;
traytel
parents: 49176
diff changeset
  1903
      map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ (mk_params passive)) o
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1904
        Morphism.term phi) dtor_frees;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1905
    val dtors = mk_dtors passiveAs;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1906
    val dtor's = mk_dtors passiveBs;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1907
    val dtor_defs = map ((fn thm => thm RS fun_cong) o Morphism.thm phi) dtor_def_frees;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1908
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1909
    val coalg_final_set_thmss = map (map (fn thm => coalg_final_thm RS thm)) coalg_set_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1910
    val (mor_Rep_thm, mor_Abs_thm) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1911
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1912
        val mor_Rep =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1913
          Skip_Proof.prove lthy [] []
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1914
            (HOLogic.mk_Trueprop (mk_mor UNIVs dtors car_finals str_finals Rep_Ts))
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1915
            (mk_mor_Rep_tac m (mor_def :: dtor_defs) Reps Abs_inverses coalg_final_set_thmss
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1916
              map_comp_id_thms map_congL_thms)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1917
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1918
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1919
        val mor_Abs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1920
          Skip_Proof.prove lthy [] []
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1921
            (HOLogic.mk_Trueprop (mk_mor car_finals str_finals UNIVs dtors Abs_Ts))
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1922
            (mk_mor_Abs_tac (mor_def :: dtor_defs) Abs_inverses)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1923
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1924
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1925
        (mor_Rep, mor_Abs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1926
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1927
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1928
    val timer = time (timer "dtor definitions & thms");
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1929
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1930
    fun unfold_bind i = Binding.suffix_name ("_" ^ dtor_unfoldN) (nth bs (i - 1));
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1931
    val unfold_name = Binding.name_of o unfold_bind;
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1932
    val unfold_def_bind = rpair [] o Thm.def_binding o unfold_bind;
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1933
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1934
    fun unfold_spec i T AT abs f z z' =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1935
      let
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1936
        val unfoldT = Library.foldr (op -->) (sTs, AT --> T);
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1937
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1938
        val lhs = Term.list_comb (Free (unfold_name i, unfoldT), ss);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1939
        val rhs = Term.absfree z' (abs $ (f $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1940
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  1941
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1942
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1943
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1944
    val ((unfold_frees, (_, unfold_def_frees)), (lthy, lthy_old)) =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1945
      lthy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1946
      |> fold_map7 (fn i => fn T => fn AT => fn abs => fn f => fn z => fn z' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1947
        Specification.definition
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1948
          (SOME (unfold_bind i, NONE, NoSyn), (unfold_def_bind i, unfold_spec i T AT abs f z z')))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1949
          ks Ts activeAs Abs_Ts (map (fn i => HOLogic.mk_comp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1950
            (mk_proj (mk_LSBIS passive_UNIVs i), mk_beh ss i)) ks) zs zs'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1951
      |>> apsnd split_list o split_list
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1952
      ||> `Local_Theory.restore;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1953
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1954
    val phi = Proof_Context.export_morphism lthy_old lthy;
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1955
    val unfolds = map (Morphism.term phi) unfold_frees;
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1956
    val unfold_names = map (fst o dest_Const) unfolds;
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1957
    fun mk_unfold Ts ss i = Term.list_comb (Const (nth unfold_names (i - 1), Library.foldr (op -->)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1958
      (map fastype_of ss, domain_type (fastype_of (nth ss (i - 1))) --> nth Ts (i - 1))), ss);
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1959
    val unfold_defs = map ((fn thm => thm RS fun_cong) o Morphism.thm phi) unfold_def_frees;
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1960
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1961
    val mor_unfold_thm =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1962
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1963
        val Abs_inverses' = map2 (curry op RS) in_car_final_thms Abs_inverses;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1964
        val morEs' = map (fn thm =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1965
          (thm OF [tcoalg_thm RS mor_final_thm, UNIV_I]) RS sym) morE_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1966
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1967
        Skip_Proof.prove lthy [] []
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1968
          (fold_rev Logic.all ss
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1969
            (HOLogic.mk_Trueprop (mk_mor active_UNIVs ss UNIVs dtors (map (mk_unfold Ts ss) ks))))
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1970
          (K (mk_mor_unfold_tac m mor_UNIV_thm dtor_defs unfold_defs Abs_inverses' morEs'
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1971
            map_comp_id_thms map_congs))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1972
        |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1973
      end;
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1974
    val dtor_unfold_thms = map (fn thm => (thm OF [mor_unfold_thm, UNIV_I]) RS sym) morE_thms;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1976
    val (raw_coind_thms, raw_coind_thm) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1977
      let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  1978
        val prem = HOLogic.mk_Trueprop (mk_sbis passive_UNIVs UNIVs dtors TRs);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1979
        val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1980
          (map2 (fn R => fn T => mk_subset R (Id_const T)) TRs Ts));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1981
        val goal = fold_rev Logic.all TRs (Logic.mk_implies (prem, concl));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1982
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1983
        `split_conj_thm (Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1984
          (K (mk_raw_coind_tac bis_def bis_cong_thm bis_O_thm bis_converse_thm bis_Gr_thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1985
            tcoalg_thm coalgT_thm mor_T_final_thm sbis_lsbis_thm
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1986
            lsbis_incl_thms incl_lsbis_thms equiv_LSBIS_thms mor_Rep_thm Rep_injects))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  1987
          |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1988
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1989
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1990
    val unique_mor_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1991
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1992
        val prems = [HOLogic.mk_Trueprop (mk_coalg passive_UNIVs Bs ss), HOLogic.mk_Trueprop
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1993
          (HOLogic.mk_conj (mk_mor Bs ss UNIVs dtors unfold_fs,
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1994
            mk_mor Bs ss UNIVs dtors unfold_fs_copy))];
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1995
        fun mk_fun_eq B f g z = HOLogic.mk_imp
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1996
          (HOLogic.mk_mem (z, B), HOLogic.mk_eq (f $ z, g $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1997
        val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  1998
          (map4 mk_fun_eq Bs unfold_fs unfold_fs_copy zs));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  1999
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2000
        val unique_mor = Skip_Proof.prove lthy [] []
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2001
          (fold_rev Logic.all (Bs @ ss @ unfold_fs @ unfold_fs_copy @ zs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2002
            (Logic.list_implies (prems, unique)))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2003
          (K (mk_unique_mor_tac raw_coind_thms bis_image2_thm))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2004
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2005
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2006
        map (fn thm => conjI RSN (2, thm RS mp)) (split_conj_thm unique_mor)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2007
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2008
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2009
    val (unfold_unique_mor_thms, unfold_unique_mor_thm) =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2010
      let
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2011
        val prem = HOLogic.mk_Trueprop (mk_mor active_UNIVs ss UNIVs dtors unfold_fs);
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2012
        fun mk_fun_eq f i = HOLogic.mk_eq (f, mk_unfold Ts ss i);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2013
        val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2014
          (map2 mk_fun_eq unfold_fs ks));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2015
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2016
        val bis_thm = tcoalg_thm RSN (2, tcoalg_thm RS bis_image2_thm);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2017
        val mor_thm = mor_comp_thm OF [tcoalg_thm RS mor_final_thm, mor_Abs_thm];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2018
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2019
        val unique_mor = Skip_Proof.prove lthy [] []
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2020
          (fold_rev Logic.all (ss @ unfold_fs) (Logic.mk_implies (prem, unique)))
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2021
          (K (mk_unfold_unique_mor_tac raw_coind_thms bis_thm mor_thm unfold_defs))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2022
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2023
      in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2024
        `split_conj_thm unique_mor
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2025
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2026
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2027
    val (dtor_unfold_unique_thms, dtor_unfold_unique_thm) = `split_conj_thm (split_conj_prems n
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2028
      (mor_UNIV_thm RS @{thm ssubst[of _ _ "%x. x"]} RS unfold_unique_mor_thm));
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2029
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2030
    val unfold_dtor_thms = map (fn thm => mor_id_thm RS thm RS sym) unfold_unique_mor_thms;
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2031
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2032
    val unfold_o_dtor_thms =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2033
      let
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2034
        val mor = mor_comp_thm OF [mor_str_thm, mor_unfold_thm];
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2035
      in
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2036
        map2 (fn unique => fn unfold_ctor =>
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2037
          trans OF [mor RS unique, unfold_ctor]) unfold_unique_mor_thms unfold_dtor_thms
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2038
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2039
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2040
    val timer = time (timer "unfold definitions & thms");
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2041
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2042
    val map_dtors = map2 (fn Ds => fn bnf =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2043
      Term.list_comb (mk_map_of_bnf Ds (passiveAs @ Ts) (passiveAs @ FTs) bnf,
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2044
        map HOLogic.id_const passiveAs @ dtors)) Dss bnfs;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2045
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2046
    fun ctor_bind i = Binding.suffix_name ("_" ^ ctorN) (nth bs (i - 1));
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2047
    val ctor_name = Binding.name_of o ctor_bind;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2048
    val ctor_def_bind = rpair [] o Thm.def_binding o ctor_bind;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2049
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2050
    fun ctor_spec i ctorT =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2051
      let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2052
        val lhs = Free (ctor_name i, ctorT);
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2053
        val rhs = mk_unfold Ts map_dtors i;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2054
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  2055
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2056
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2057
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2058
    val ((ctor_frees, (_, ctor_def_frees)), (lthy, lthy_old)) =
49311
blanchet
parents: 49308
diff changeset
  2059
      lthy
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2060
      |> fold_map2 (fn i => fn ctorT =>
49311
blanchet
parents: 49308
diff changeset
  2061
        Specification.definition
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2062
          (SOME (ctor_bind i, NONE, NoSyn), (ctor_def_bind i, ctor_spec i ctorT))) ks ctorTs
49311
blanchet
parents: 49308
diff changeset
  2063
      |>> apsnd split_list o split_list
blanchet
parents: 49308
diff changeset
  2064
      ||> `Local_Theory.restore;
blanchet
parents: 49308
diff changeset
  2065
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2066
    val phi = Proof_Context.export_morphism lthy_old lthy;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2067
    fun mk_ctors params =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2068
      map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ params) o Morphism.term phi)
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2069
        ctor_frees;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2070
    val ctors = mk_ctors params';
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2071
    val ctor_defs = map (Morphism.thm phi) ctor_def_frees;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2072
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2073
    val ctor_o_dtor_thms = map2 (fold_thms lthy o single) ctor_defs unfold_o_dtor_thms;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2074
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2075
    val dtor_o_ctor_thms =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2076
      let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2077
        fun mk_goal dtor ctor FT =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2078
         mk_Trueprop_eq (HOLogic.mk_comp (dtor, ctor), HOLogic.id_const FT);
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2079
        val goals = map3 mk_goal dtors ctors FTs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2080
      in
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2081
        map5 (fn goal => fn ctor_def => fn unfold => fn map_comp_id => fn map_congL =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2082
          Skip_Proof.prove lthy [] [] goal
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2083
            (mk_dtor_o_ctor_tac ctor_def unfold map_comp_id map_congL unfold_o_dtor_thms)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2084
          |> Thm.close_derivation)
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2085
          goals ctor_defs dtor_unfold_thms map_comp_id_thms map_congL_thms
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2086
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2087
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2088
    val dtor_ctor_thms = map (fn thm => thm RS @{thm pointfree_idE}) dtor_o_ctor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2089
    val ctor_dtor_thms = map (fn thm => thm RS @{thm pointfree_idE}) ctor_o_dtor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2090
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2091
    val bij_dtor_thms =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2092
      map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) ctor_o_dtor_thms dtor_o_ctor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2093
    val inj_dtor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_dtor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2094
    val surj_dtor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_dtor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2095
    val dtor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_dtor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2096
    val dtor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_dtor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2097
    val dtor_exhaust_thms = map (fn thm => thm RS exE) dtor_nchotomy_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2098
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2099
    val bij_ctor_thms =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2100
      map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) dtor_o_ctor_thms ctor_o_dtor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2101
    val inj_ctor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_ctor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2102
    val surj_ctor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_ctor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2103
    val ctor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_ctor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2104
    val ctor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_ctor_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2105
    val ctor_exhaust_thms = map (fn thm => thm RS exE) ctor_nchotomy_thms;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2106
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2107
    fun mk_ctor_dtor_unfold_like_thm dtor_inject dtor_ctor unfold =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2108
      iffD1 OF [dtor_inject, trans OF [unfold, dtor_ctor RS sym]];
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2109
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2110
    val ctor_dtor_unfold_thms =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2111
      map3 mk_ctor_dtor_unfold_like_thm dtor_inject_thms dtor_ctor_thms dtor_unfold_thms;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2112
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2113
    val timer = time (timer "ctor definitions & thms");
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2114
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2115
    val corec_Inl_sum_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2116
      let
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2117
        val mor = mor_comp_thm OF [mor_sum_case_thm, mor_unfold_thm];
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2118
      in
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2119
        map2 (fn unique => fn unfold_dtor =>
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2120
          trans OF [mor RS unique, unfold_dtor]) unfold_unique_mor_thms unfold_dtor_thms
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2121
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2122
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2123
    fun corec_bind i = Binding.suffix_name ("_" ^ dtor_corecN) (nth bs (i - 1));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2124
    val corec_name = Binding.name_of o corec_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2125
    val corec_def_bind = rpair [] o Thm.def_binding o corec_bind;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2126
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2127
    fun corec_spec i T AT =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2128
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2129
        val corecT = Library.foldr (op -->) (corec_sTs, AT --> T);
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2130
        val maps = map3 (fn dtor => fn sum_s => fn mapx => mk_sum_case
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2131
            (HOLogic.mk_comp (Term.list_comb (mapx, passive_ids @ corec_Inls), dtor), sum_s))
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2132
          dtors corec_ss corec_maps;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2133
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2134
        val lhs = Term.list_comb (Free (corec_name i, corecT), corec_ss);
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2135
        val rhs = HOLogic.mk_comp (mk_unfold Ts maps i, Inr_const T AT);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2136
      in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  2137
        mk_Trueprop_eq (lhs, rhs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2138
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2139
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2140
    val ((corec_frees, (_, corec_def_frees)), (lthy, lthy_old)) =
49311
blanchet
parents: 49308
diff changeset
  2141
      lthy
blanchet
parents: 49308
diff changeset
  2142
      |> fold_map3 (fn i => fn T => fn AT =>
blanchet
parents: 49308
diff changeset
  2143
        Specification.definition
blanchet
parents: 49308
diff changeset
  2144
          (SOME (corec_bind i, NONE, NoSyn), (corec_def_bind i, corec_spec i T AT)))
blanchet
parents: 49308
diff changeset
  2145
          ks Ts activeAs
blanchet
parents: 49308
diff changeset
  2146
      |>> apsnd split_list o split_list
blanchet
parents: 49308
diff changeset
  2147
      ||> `Local_Theory.restore;
blanchet
parents: 49308
diff changeset
  2148
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2149
    val phi = Proof_Context.export_morphism lthy_old lthy;
49176
6d29d2db5f88 construct high-level iterator RHS
blanchet
parents: 49169
diff changeset
  2150
    val corecs = map (Morphism.term phi) corec_frees;
6d29d2db5f88 construct high-level iterator RHS
blanchet
parents: 49169
diff changeset
  2151
    val corec_names = map (fst o dest_Const) corecs;
6d29d2db5f88 construct high-level iterator RHS
blanchet
parents: 49169
diff changeset
  2152
    fun mk_corec ss i = Term.list_comb (Const (nth corec_names (i - 1), Library.foldr (op -->)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2153
      (map fastype_of ss, domain_type (fastype_of (nth ss (i - 1))) --> nth Ts (i - 1))), ss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2154
    val corec_defs = map (Morphism.thm phi) corec_def_frees;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2155
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2156
    val sum_cases =
49255
2ecc533d6697 use balanced sums for constructors (to gracefully handle 100 constructors or more)
blanchet
parents: 49231
diff changeset
  2157
      map2 (fn T => fn i => mk_sum_case (HOLogic.id_const T, mk_corec corec_ss i)) Ts ks;
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2158
    val dtor_corec_thms =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2159
      let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2160
        fun mk_goal i corec_s corec_map dtor z =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2161
          let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2162
            val lhs = dtor $ (mk_corec corec_ss i $ z);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2163
            val rhs = Term.list_comb (corec_map, passive_ids @ sum_cases) $ (corec_s $ z);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2164
          in
49123
263b0e330d8b more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents: 49121
diff changeset
  2165
            fold_rev Logic.all (z :: corec_ss) (mk_Trueprop_eq (lhs, rhs))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2166
          end;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2167
        val goals = map5 mk_goal ks corec_ss corec_maps_rev dtors zs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2168
      in
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2169
        map3 (fn goal => fn unfold => fn map_cong =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2170
          Skip_Proof.prove lthy [] [] goal
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2171
            (mk_corec_tac m corec_defs unfold map_cong corec_Inl_sum_thms)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2172
          |> Thm.close_derivation)
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2173
        goals dtor_unfold_thms map_congs
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2174
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2175
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2176
    val ctor_dtor_corec_thms =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2177
      map3 mk_ctor_dtor_unfold_like_thm dtor_inject_thms dtor_ctor_thms dtor_corec_thms;
49231
43d2df313559 generate "fld_unf_corecs" as well
blanchet
parents: 49228
diff changeset
  2178
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2179
    val timer = time (timer "corec definitions & thms");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2180
49507
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2181
    val (dtor_coinduct_thm, coinduct_params, srel_coinduct_thm, rel_coinduct_thm,
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2182
         dtor_strong_coinduct_thm, srel_strong_coinduct_thm, rel_strong_coinduct_thm) =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2183
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2184
        val zs = Jzs1 @ Jzs2;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2185
        val frees = phis @ zs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2186
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2187
        fun mk_Ids Id = if Id then map Id_const passiveAs else map mk_diag passive_UNIVs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2188
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2189
        fun mk_phi upto_eq phi z1 z2 = if upto_eq
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2190
          then Term.absfree (dest_Free z1) (Term.absfree (dest_Free z2)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2191
            (HOLogic.mk_disj (phi $ z1 $ z2, HOLogic.mk_eq (z1, z2))))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2192
          else phi;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2193
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2194
        fun phi_srels upto_eq = map4 (fn phi => fn T => fn z1 => fn z2 =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2195
          HOLogic.Collect_const (HOLogic.mk_prodT (T, T)) $
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2196
            HOLogic.mk_split (mk_phi upto_eq phi z1 z2)) phis Ts Jzs1 Jzs2;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2197
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2198
        val srels = map (Term.subst_atomic_types ((activeAs ~~ Ts) @ (activeBs ~~ Ts))) relsAsBs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2199
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2200
        fun mk_concl phi z1 z2 = HOLogic.mk_imp (phi $ z1 $ z2, HOLogic.mk_eq (z1, z2));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2201
        val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2202
          (map3 mk_concl phis Jzs1 Jzs2));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2203
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2204
        fun mk_srel_prem upto_eq phi dtor srel Jz Jz_copy =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2205
          let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2206
            val concl = HOLogic.mk_mem (HOLogic.mk_tuple [dtor $ Jz, dtor $ Jz_copy],
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2207
              Term.list_comb (srel, mk_Ids upto_eq @ phi_srels upto_eq));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2208
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2209
            HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2210
              (list_all_free [Jz, Jz_copy] (HOLogic.mk_imp (phi $ Jz $ Jz_copy, concl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2211
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2212
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2213
        val srel_prems = map5 (mk_srel_prem false) phis dtors srels Jzs Jzs_copy;
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2214
        val srel_upto_prems = map5 (mk_srel_prem true) phis dtors srels Jzs Jzs_copy;
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2215
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2216
        val srel_coinduct_goal = fold_rev Logic.all frees (Logic.list_implies (srel_prems, concl));
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2217
        val coinduct_params = rev (Term.add_tfrees srel_coinduct_goal []);
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2218
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2219
        val srel_coinduct = unfold_thms lthy @{thms diag_UNIV}
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2220
          (Skip_Proof.prove lthy [] [] srel_coinduct_goal
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2221
            (K (mk_srel_coinduct_tac ks raw_coind_thm bis_srel_thm))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2222
          |> Thm.close_derivation);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2223
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2224
        fun mk_dtor_prem upto_eq phi dtor map_nth sets Jz Jz_copy FJz =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2225
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2226
            val xs = [Jz, Jz_copy];
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2227
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2228
            fun mk_map_conjunct nths x =
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2229
              HOLogic.mk_eq (Term.list_comb (map_nth, passive_ids @ nths) $ FJz, dtor $ x);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2230
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2231
            fun mk_set_conjunct set phi z1 z2 =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2232
              list_all_free [z1, z2]
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2233
                (HOLogic.mk_imp (HOLogic.mk_mem (HOLogic.mk_prod (z1, z2), set $ FJz),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2234
                  mk_phi upto_eq phi z1 z2 $ z1 $ z2));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2235
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2236
            val concl = list_exists_free [FJz] (HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2237
              (Library.foldr1 HOLogic.mk_conj (map2 mk_map_conjunct [fstsTs, sndsTs] xs),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2238
              Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2239
                (map4 mk_set_conjunct (drop m sets) phis Jzs1 Jzs2)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2240
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2241
            fold_rev Logic.all xs (Logic.mk_implies
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2242
              (HOLogic.mk_Trueprop (Term.list_comb (phi, xs)), HOLogic.mk_Trueprop concl))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2243
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2244
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2245
        fun mk_dtor_prems upto_eq =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2246
          map7 (mk_dtor_prem upto_eq) phis dtors map_FT_nths prodFT_setss Jzs Jzs_copy FJzs;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2247
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2248
        val dtor_prems = mk_dtor_prems false;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2249
        val dtor_upto_prems = mk_dtor_prems true;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2250
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2251
        val dtor_coinduct_goal = fold_rev Logic.all frees (Logic.list_implies (dtor_prems, concl));
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2252
        val dtor_coinduct = Skip_Proof.prove lthy [] [] dtor_coinduct_goal
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2253
          (K (mk_dtor_coinduct_tac m ks raw_coind_thm bis_def))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2254
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2255
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2256
        val cTs = map (SOME o certifyT lthy o TFree) coinduct_params;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2257
        val cts = map3 (SOME o certify lthy ooo mk_phi true) phis Jzs1 Jzs2;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2258
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2259
        val srel_strong_coinduct = singleton (Proof_Context.export names_lthy lthy)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2260
          (Skip_Proof.prove lthy [] []
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2261
            (fold_rev Logic.all zs (Logic.list_implies (srel_upto_prems, concl)))
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2262
            (K (mk_srel_strong_coinduct_tac m cTs cts srel_coinduct srel_monos srel_Ids)))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2263
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2264
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2265
        val dtor_strong_coinduct = singleton (Proof_Context.export names_lthy lthy)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2266
          (Skip_Proof.prove lthy [] []
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2267
            (fold_rev Logic.all zs (Logic.list_implies (dtor_upto_prems, concl)))
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2268
            (K (mk_dtor_strong_coinduct_tac ks cTs cts dtor_coinduct bis_def
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2269
              (tcoalg_thm RS bis_diag_thm))))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2270
          |> Thm.close_derivation;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2271
49507
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2272
        val rel_of_srel_thms =
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2273
          srel_defs @ @{thms Id_def' mem_Collect_eq fst_conv snd_conv split_conv};
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2274
49507
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2275
        val rel_coinduct = unfold_thms lthy rel_of_srel_thms srel_coinduct;
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2276
        val rel_strong_coinduct = unfold_thms lthy rel_of_srel_thms srel_strong_coinduct;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2277
      in
49507
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2278
        (dtor_coinduct, rev (Term.add_tfrees dtor_coinduct_goal []), srel_coinduct, rel_coinduct,
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2279
         dtor_strong_coinduct, srel_strong_coinduct, rel_strong_coinduct)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2280
      end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2281
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2282
    val timer = time (timer "coinduction");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2283
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2284
    (*register new codatatypes as BNFs*)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2285
    val lthy = if m = 0 then lthy else
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2286
      let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2287
        val fTs = map2 (curry op -->) passiveAs passiveBs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2288
        val gTs = map2 (curry op -->) passiveBs passiveCs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2289
        val f1Ts = map2 (curry op -->) passiveAs passiveYs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2290
        val f2Ts = map2 (curry op -->) passiveBs passiveYs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2291
        val p1Ts = map2 (curry op -->) passiveXs passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2292
        val p2Ts = map2 (curry op -->) passiveXs passiveBs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2293
        val pTs = map2 (curry op -->) passiveXs passiveCs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2294
        val uTs = map2 (curry op -->) Ts Ts';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2295
        val JRTs = map2 (curry mk_relT) passiveAs passiveBs;
49463
83ac281bcdc2 provide predicator, define relator
blanchet
parents: 49460
diff changeset
  2296
        val JphiTs = map2 mk_pred2T passiveAs passiveBs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2297
        val prodTs = map2 (curry HOLogic.mk_prodT) Ts Ts';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2298
        val B1Ts = map HOLogic.mk_setT passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2299
        val B2Ts = map HOLogic.mk_setT passiveBs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2300
        val AXTs = map HOLogic.mk_setT passiveXs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2301
        val XTs = mk_Ts passiveXs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2302
        val YTs = mk_Ts passiveYs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2303
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2304
        val ((((((((((((((((((((fs, fs'), fs_copy), gs), us),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2305
          (Jys, Jys')), (Jys_copy, Jys'_copy)), set_induct_phiss), JRs), Jphis),
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2306
          B1s), B2s), AXs), f1s), f2s), p1s), p2s), ps), (ys, ys')), (ys_copy, ys'_copy)),
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2307
          names_lthy) = names_lthy
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2308
          |> mk_Frees' "f" fTs
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2309
          ||>> mk_Frees "f" fTs
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2310
          ||>> mk_Frees "g" gTs
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2311
          ||>> mk_Frees "u" uTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2312
          ||>> mk_Frees' "b" Ts'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2313
          ||>> mk_Frees' "b" Ts'
49463
83ac281bcdc2 provide predicator, define relator
blanchet
parents: 49460
diff changeset
  2314
          ||>> mk_Freess "P" (map (fn A => map (mk_pred2T A) Ts) passiveAs)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2315
          ||>> mk_Frees "R" JRTs
49362
1271aca16aed make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents: 49337
diff changeset
  2316
          ||>> mk_Frees "P" JphiTs
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2317
          ||>> mk_Frees "B1" B1Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2318
          ||>> mk_Frees "B2" B2Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2319
          ||>> mk_Frees "A" AXTs
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2320
          ||>> mk_Frees "f1" f1Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2321
          ||>> mk_Frees "f2" f2Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2322
          ||>> mk_Frees "p1" p1Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2323
          ||>> mk_Frees "p2" p2Ts
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2324
          ||>> mk_Frees "p" pTs
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2325
          ||>> mk_Frees' "y" passiveAs
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2326
          ||>> mk_Frees' "y" passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2327
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2328
        val map_FTFT's = map2 (fn Ds =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2329
          mk_map_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2330
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2331
        fun mk_maps ATs BTs Ts mk_T =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2332
          map2 (fn Ds => mk_map_of_bnf Ds (ATs @ Ts) (BTs @ map mk_T Ts)) Dss bnfs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2333
        fun mk_Fmap mk_const fs Ts Fmap = Term.list_comb (Fmap, fs @ map mk_const Ts);
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2334
        fun mk_map mk_const mk_T Ts fs Ts' dtors mk_maps =
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2335
          mk_unfold Ts' (map2 (fn dtor => fn Fmap =>
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2336
            HOLogic.mk_comp (mk_Fmap mk_const fs Ts Fmap, dtor)) dtors (mk_maps Ts mk_T));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2337
        val mk_map_id = mk_map HOLogic.id_const I;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2338
        val mk_mapsAB = mk_maps passiveAs passiveBs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2339
        val mk_mapsBC = mk_maps passiveBs passiveCs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2340
        val mk_mapsAC = mk_maps passiveAs passiveCs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2341
        val mk_mapsAY = mk_maps passiveAs passiveYs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2342
        val mk_mapsBY = mk_maps passiveBs passiveYs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2343
        val mk_mapsXA = mk_maps passiveXs passiveAs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2344
        val mk_mapsXB = mk_maps passiveXs passiveBs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2345
        val mk_mapsXC = mk_maps passiveXs passiveCs;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2346
        val fs_maps = map (mk_map_id Ts fs Ts' dtors mk_mapsAB) ks;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2347
        val fs_copy_maps = map (mk_map_id Ts fs_copy Ts' dtors mk_mapsAB) ks;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2348
        val gs_maps = map (mk_map_id Ts' gs Ts'' dtor's mk_mapsBC) ks;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2349
        val fgs_maps =
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2350
          map (mk_map_id Ts (map2 (curry HOLogic.mk_comp) gs fs) Ts'' dtors mk_mapsAC) ks;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2351
        val Xdtors = mk_dtors passiveXs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2352
        val UNIV's = map HOLogic.mk_UNIV Ts';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2353
        val CUNIVs = map HOLogic.mk_UNIV passiveCs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2354
        val UNIV''s = map HOLogic.mk_UNIV Ts'';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2355
        val fstsTsTs' = map fst_const prodTs;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2356
        val sndsTsTs' = map snd_const prodTs;
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2357
        val dtor''s = mk_dtors passiveCs;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2358
        val f1s_maps = map (mk_map_id Ts f1s YTs dtors mk_mapsAY) ks;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2359
        val f2s_maps = map (mk_map_id Ts' f2s YTs dtor's mk_mapsBY) ks;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2360
        val pid_maps = map (mk_map_id XTs ps Ts'' Xdtors mk_mapsXC) ks;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2361
        val pfst_Fmaps =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2362
          map (mk_Fmap fst_const p1s prodTs) (mk_mapsXA prodTs (fst o HOLogic.dest_prodT));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2363
        val psnd_Fmaps =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2364
          map (mk_Fmap snd_const p2s prodTs) (mk_mapsXB prodTs (snd o HOLogic.dest_prodT));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2365
        val p1id_Fmaps = map (mk_Fmap HOLogic.id_const p1s prodTs) (mk_mapsXA prodTs I);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2366
        val p2id_Fmaps = map (mk_Fmap HOLogic.id_const p2s prodTs) (mk_mapsXB prodTs I);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2367
        val pid_Fmaps = map (mk_Fmap HOLogic.id_const ps prodTs) (mk_mapsXC prodTs I);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2368
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2369
        val (map_simp_thms, map_thms) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2370
          let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2371
            fun mk_goal fs_map map dtor dtor' = fold_rev Logic.all fs
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2372
              (mk_Trueprop_eq (HOLogic.mk_comp (dtor', fs_map),
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2373
                HOLogic.mk_comp (Term.list_comb (map, fs @ fs_maps), dtor)));
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2374
            val goals = map4 mk_goal fs_maps map_FTFT's dtors dtor's;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2375
            val cTs = map (SOME o certifyT lthy) FTs';
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2376
            val maps =
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2377
              map5 (fn goal => fn cT => fn unfold => fn map_comp' => fn map_cong =>
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2378
                Skip_Proof.prove lthy [] [] goal
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2379
                  (K (mk_map_tac m n cT unfold map_comp' map_cong))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2380
                |> Thm.close_derivation)
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2381
              goals cTs dtor_unfold_thms map_comp's map_congs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2382
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2383
            map_split (fn thm => (thm RS @{thm pointfreeE}, thm)) maps
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2384
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2385
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2386
        val map_comp_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2387
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2388
            val goal = fold_rev Logic.all (fs @ gs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2389
              (HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2390
                (map3 (fn fmap => fn gmap => fn fgmap =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2391
                   HOLogic.mk_eq (HOLogic.mk_comp (gmap, fmap), fgmap))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2392
                fs_maps gs_maps fgs_maps)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2393
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2394
            split_conj_thm (Skip_Proof.prove lthy [] [] goal
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2395
              (K (mk_map_comp_tac m n map_thms map_comps map_congs dtor_unfold_unique_thm))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2396
              |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2397
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2398
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2399
        val map_unique_thm =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2400
          let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2401
            fun mk_prem u map dtor dtor' =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2402
              mk_Trueprop_eq (HOLogic.mk_comp (dtor', u),
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2403
                HOLogic.mk_comp (Term.list_comb (map, fs @ us), dtor));
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2404
            val prems = map4 mk_prem us map_FTFT's dtors dtor's;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2405
            val goal =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2406
              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2407
                (map2 (curry HOLogic.mk_eq) us fs_maps));
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2408
          in
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2409
            Skip_Proof.prove lthy [] []
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2410
              (fold_rev Logic.all (us @ fs) (Logic.list_implies (prems, goal)))
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2411
              (mk_map_unique_tac dtor_unfold_unique_thm map_comps)
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2412
              |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2413
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2414
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2415
        val timer = time (timer "map functions for the new codatatypes");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2416
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2417
        val bd = mk_ccexp sbd sbd;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2418
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2419
        val timer = time (timer "bounds for the new codatatypes");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2420
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2421
        val setss_by_bnf = map (fn i => map2 (mk_hset dtors i) ls passiveAs) ks;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2422
        val setss_by_bnf' = map (fn i => map2 (mk_hset dtor's i) ls passiveBs) ks;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2423
        val setss_by_range = transpose setss_by_bnf;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2424
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2425
        val set_simp_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2426
          let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2427
            fun mk_simp_goal relate pas_set act_sets sets dtor z set =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2428
              relate (set $ z, mk_union (pas_set $ (dtor $ z),
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2429
                 Library.foldl1 mk_union
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2430
                   (map2 (fn X => mk_UNION (X $ (dtor $ z))) act_sets sets)));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2431
            fun mk_goals eq =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2432
              map2 (fn i => fn sets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2433
                map4 (fn Fsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2434
                  mk_simp_goal eq (nth Fsets (i - 1)) (drop m Fsets) sets)
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2435
                FTs_setss dtors Jzs sets)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2436
              ls setss_by_range;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2437
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2438
            val le_goals = map
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2439
              (fold_rev Logic.all Jzs o HOLogic.mk_Trueprop o Library.foldr1 HOLogic.mk_conj)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2440
              (mk_goals (uncurry mk_subset));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2441
            val set_le_thmss = map split_conj_thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2442
              (map4 (fn goal => fn hset_minimal => fn set_hsets => fn set_hset_hsetss =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2443
                Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2444
                  (K (mk_set_le_tac n hset_minimal set_hsets set_hset_hsetss))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2445
                |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2446
              le_goals hset_minimal_thms set_hset_thmss' set_hset_hset_thmsss');
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2447
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2448
            val simp_goalss = map (map2 (fn z => fn goal =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2449
                Logic.all z (HOLogic.mk_Trueprop goal)) Jzs)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2450
              (mk_goals HOLogic.mk_eq);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2451
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2452
            map4 (map4 (fn goal => fn set_le => fn set_incl_hset => fn set_hset_incl_hsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2453
              Skip_Proof.prove lthy [] [] goal
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2454
                (K (mk_set_simp_tac n set_le set_incl_hset set_hset_incl_hsets))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2455
              |> Thm.close_derivation))
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2456
            simp_goalss set_le_thmss set_incl_hset_thmss' set_hset_incl_hset_thmsss'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2457
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2458
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2459
        val timer = time (timer "set functions for the new codatatypes");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2460
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2461
        val colss = map2 (fn j => fn T =>
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2462
          map (fn i => mk_hset_rec dtors nat i j T) ks) ls passiveAs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2463
        val colss' = map2 (fn j => fn T =>
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2464
          map (fn i => mk_hset_rec dtor's nat i j T) ks) ls passiveBs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2465
        val Xcolss = map2 (fn j => fn T =>
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2466
          map (fn i => mk_hset_rec Xdtors nat i j T) ks) ls passiveXs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2467
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2468
        val col_natural_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2469
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2470
            fun mk_col_natural f map z col col' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2471
              HOLogic.mk_eq (mk_image f $ (col $ z), col' $ (map $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2472
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2473
            fun mk_goal f cols cols' = list_all_free Jzs (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2474
              (map4 (mk_col_natural f) fs_maps Jzs cols cols'));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2475
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2476
            val goals = map3 mk_goal fs colss colss';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2477
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2478
            val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2479
              map (fn phi => map (SOME o certify lthy) [Term.absfree nat' phi, nat]) goals;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2480
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2481
            val thms =
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2482
              map4 (fn goal => fn cts => fn rec_0s => fn rec_Sucs =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2483
                singleton (Proof_Context.export names_lthy lthy)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2484
                  (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2485
                    (mk_col_natural_tac cts rec_0s rec_Sucs map_simp_thms set_natural'ss))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2486
                |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2487
              goals ctss hset_rec_0ss' hset_rec_Sucss';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2488
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2489
            map (split_conj_thm o mk_specN n) thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2490
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2491
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2492
        val col_bd_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2493
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2494
            fun mk_col_bd z col = mk_ordLeq (mk_card_of (col $ z)) sbd;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2495
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2496
            fun mk_goal cols = list_all_free Jzs (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2497
              (map2 mk_col_bd Jzs cols));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2498
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2499
            val goals = map mk_goal colss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2500
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2501
            val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2502
              map (fn phi => map (SOME o certify lthy) [Term.absfree nat' phi, nat]) goals;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2503
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2504
            val thms =
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2505
              map5 (fn j => fn goal => fn cts => fn rec_0s => fn rec_Sucs =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2506
                singleton (Proof_Context.export names_lthy lthy)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2507
                  (Skip_Proof.prove lthy [] [] (HOLogic.mk_Trueprop goal)
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2508
                    (K (mk_col_bd_tac m j cts rec_0s rec_Sucs
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2509
                      sbd_Card_order sbd_Cinfinite set_sbdss)))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2510
                |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2511
              ls goals ctss hset_rec_0ss' hset_rec_Sucss';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2512
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2513
            map (split_conj_thm o mk_specN n) thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2514
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2515
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2516
        val map_cong_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2517
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2518
            val cTs = map (SOME o certifyT lthy o
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2519
              Term.typ_subst_atomic (passiveAs ~~ passiveBs) o TFree) coinduct_params;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2520
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2521
            fun mk_prem z set f g y y' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2522
              mk_Ball (set $ z) (Term.absfree y' (HOLogic.mk_eq (f $ y, g $ y)));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2523
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2524
            fun mk_prems sets z =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2525
              Library.foldr1 HOLogic.mk_conj (map5 (mk_prem z) sets fs fs_copy ys ys')
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2526
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2527
            fun mk_map_cong sets z fmap gmap =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2528
              HOLogic.mk_imp (mk_prems sets z, HOLogic.mk_eq (fmap $ z, gmap $ z));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2529
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2530
            fun mk_coind_body sets (x, T) z fmap gmap y y_copy =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2531
              HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2532
                (HOLogic.mk_mem (z, HOLogic.mk_Collect (x, T, mk_prems sets z)),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2533
                  HOLogic.mk_conj (HOLogic.mk_eq (y, fmap $ z),
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2534
                    HOLogic.mk_eq (y_copy, gmap $ z)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2535
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2536
            fun mk_cphi sets (z' as (x, T)) z fmap gmap y' y y'_copy y_copy =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2537
              HOLogic.mk_exists (x, T, mk_coind_body sets z' z fmap gmap y y_copy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2538
              |> Term.absfree y'_copy
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2539
              |> Term.absfree y'
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2540
              |> certify lthy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2541
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2542
            val cphis =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2543
              map9 mk_cphi setss_by_bnf Jzs' Jzs fs_maps fs_copy_maps Jys' Jys Jys'_copy Jys_copy;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2544
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2545
            val coinduct = Drule.instantiate' cTs (map SOME cphis) dtor_coinduct_thm;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2546
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2547
            val goal =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2548
              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2549
                (map4 mk_map_cong setss_by_bnf Jzs fs_maps fs_copy_maps));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2550
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2551
            val thm = singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2552
              (Skip_Proof.prove lthy [] [] goal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2553
              (K (mk_mcong_tac m (rtac coinduct) map_comp's map_simp_thms map_congs set_natural'ss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2554
              set_hset_thmss set_hset_hset_thmsss)))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2555
              |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2556
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2557
            split_conj_thm thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2558
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2559
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2560
        val B1_ins = map2 (mk_in B1s) setss_by_bnf Ts;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2561
        val B2_ins = map2 (mk_in B2s) setss_by_bnf' Ts';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2562
        val thePulls = map4 mk_thePull B1_ins B2_ins f1s_maps f2s_maps;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2563
        val thePullTs = passiveXs @ map2 (curry HOLogic.mk_prodT) Ts Ts';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2564
        val thePull_ins = map2 (mk_in (AXs @ thePulls)) (mk_setss thePullTs) (mk_FTs thePullTs);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2565
        val pickFs = map5 mk_pickWP thePull_ins pfst_Fmaps psnd_Fmaps
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2566
          (map2 (curry (op $)) dtors Jzs) (map2 (curry (op $)) dtor's Jz's);
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2567
        val pickF_ss = map3 (fn pickF => fn z => fn z' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2568
          HOLogic.mk_split (Term.absfree z (Term.absfree z' pickF))) pickFs Jzs' Jz's';
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2569
        val picks = map (mk_unfold XTs pickF_ss) ks;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2570
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2571
        val wpull_prem = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2572
          (map8 mk_wpull AXs B1s B2s f1s f2s (replicate m NONE) p1s p2s));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2573
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2574
        val map_eq_thms = map2 (fn simp => fn diff => box_equals OF [diff RS iffD2, simp, simp])
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2575
          map_simp_thms dtor_inject_thms;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2576
        val map_wpull_thms = map (fn thm => thm OF
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2577
          (replicate m asm_rl @ replicate n @{thm wpull_thePull})) map_wpulls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2578
        val pickWP_assms_tacs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2579
          map3 mk_pickWP_assms_tac set_incl_hset_thmss set_incl_hin_thmss map_eq_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2580
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2581
        val coalg_thePull_thm =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2582
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2583
            val coalg = HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2584
              (mk_coalg CUNIVs thePulls (map2 (curry HOLogic.mk_comp) pid_Fmaps pickF_ss));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2585
            val goal = fold_rev Logic.all (AXs @ B1s @ B2s @ f1s @ f2s @ p1s @ p2s @ ps)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2586
              (Logic.mk_implies (wpull_prem, coalg));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2587
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2588
            Skip_Proof.prove lthy [] [] goal (mk_coalg_thePull_tac m coalg_def map_wpull_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2589
              set_natural'ss pickWP_assms_tacs)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2590
            |> Thm.close_derivation
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2591
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2592
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2593
        val (mor_thePull_fst_thm, mor_thePull_snd_thm, mor_thePull_pick_thm) =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2594
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2595
            val mor_fst = HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2596
              (mk_mor thePulls (map2 (curry HOLogic.mk_comp) p1id_Fmaps pickF_ss)
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2597
                UNIVs dtors fstsTsTs');
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2598
            val mor_snd = HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2599
              (mk_mor thePulls (map2 (curry HOLogic.mk_comp) p2id_Fmaps pickF_ss)
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2600
                UNIV's dtor's sndsTsTs');
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2601
            val mor_pick = HOLogic.mk_Trueprop
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2602
              (mk_mor thePulls (map2 (curry HOLogic.mk_comp) pid_Fmaps pickF_ss)
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2603
                UNIV''s dtor''s (map2 (curry HOLogic.mk_comp) pid_maps picks));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2604
49458
blanchet
parents: 49457
diff changeset
  2605
            val fst_goal = fold_rev Logic.all (AXs @ B1s @ B2s @ f1s @ f2s @ p1s @ p2s)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2606
              (Logic.mk_implies (wpull_prem, mor_fst));
49458
blanchet
parents: 49457
diff changeset
  2607
            val snd_goal = fold_rev Logic.all (AXs @ B1s @ B2s @ f1s @ f2s @ p1s @ p2s)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2608
              (Logic.mk_implies (wpull_prem, mor_snd));
49458
blanchet
parents: 49457
diff changeset
  2609
            val pick_goal = fold_rev Logic.all (AXs @ B1s @ B2s @ f1s @ f2s @ p1s @ p2s @ ps)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2610
              (Logic.mk_implies (wpull_prem, mor_pick));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2611
          in
49458
blanchet
parents: 49457
diff changeset
  2612
            (Skip_Proof.prove lthy [] [] fst_goal (mk_mor_thePull_fst_tac m mor_def map_wpull_thms
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2613
              map_comp's pickWP_assms_tacs) |> Thm.close_derivation,
49458
blanchet
parents: 49457
diff changeset
  2614
            Skip_Proof.prove lthy [] [] snd_goal (mk_mor_thePull_snd_tac m mor_def map_wpull_thms
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2615
              map_comp's pickWP_assms_tacs) |> Thm.close_derivation,
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2616
            Skip_Proof.prove lthy [] [] pick_goal (mk_mor_thePull_pick_tac mor_def dtor_unfold_thms
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2617
              map_comp's) |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2618
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2619
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2620
        val pick_col_thmss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2621
          let
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2622
            fun mk_conjunct AX Jpair pick thePull col =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2623
              HOLogic.mk_imp (HOLogic.mk_mem (Jpair, thePull), mk_subset (col $ (pick $ Jpair)) AX);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2624
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2625
            fun mk_concl AX cols =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2626
              list_all_free Jpairs (Library.foldr1 HOLogic.mk_conj
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2627
                (map4 (mk_conjunct AX) Jpairs picks thePulls cols));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2628
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2629
            val concls = map2 mk_concl AXs Xcolss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2630
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2631
            val ctss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2632
              map (fn phi => map (SOME o certify lthy) [Term.absfree nat' phi, nat]) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2633
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2634
            val goals =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2635
              map (fn concl => Logic.mk_implies (wpull_prem, HOLogic.mk_Trueprop concl)) concls;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2636
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2637
            val thms =
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2638
              map5 (fn j => fn goal => fn cts => fn rec_0s => fn rec_Sucs =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2639
                singleton (Proof_Context.export names_lthy lthy) (Skip_Proof.prove lthy [] [] goal
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2640
                  (mk_pick_col_tac m j cts rec_0s rec_Sucs dtor_unfold_thms set_natural'ss
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2641
                    map_wpull_thms pickWP_assms_tacs))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2642
                |> Thm.close_derivation)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2643
              ls goals ctss hset_rec_0ss' hset_rec_Sucss';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2644
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2645
            map (map (fn thm => thm RS mp) o split_conj_thm o mk_specN n) thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2646
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2647
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2648
        val timer = time (timer "helpers for BNF properties");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2649
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2650
        val map_id_tacs =
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2651
          map2 (K oo mk_map_id_tac map_thms) dtor_unfold_unique_thms unfold_dtor_thms;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2652
        val map_comp_tacs = map (fn thm => K (rtac (thm RS sym) 1)) map_comp_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2653
        val map_cong_tacs = map (mk_map_cong_tac m) map_cong_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2654
        val set_nat_tacss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2655
          map2 (map2 (K oo mk_set_natural_tac)) hset_defss (transpose col_natural_thmss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2656
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2657
        val bd_co_tacs = replicate n (K (mk_bd_card_order_tac sbd_card_order));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2658
        val bd_cinf_tacs = replicate n (K (mk_bd_cinfinite_tac sbd_Cinfinite));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2659
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2660
        val set_bd_tacss =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2661
          map2 (map2 (K oo mk_set_bd_tac sbd_Cinfinite)) hset_defss (transpose col_bd_thmss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2662
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2663
        val in_bd_tacs = map7 (fn i => fn isNode_hsets => fn carT_def =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2664
            fn card_of_carT => fn mor_image => fn Rep_inverse => fn mor_hsets =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2665
          K (mk_in_bd_tac (nth isNode_hsets (i - 1)) isNode_hsets carT_def
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2666
            card_of_carT mor_image Rep_inverse mor_hsets
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2667
            sbd_Cnotzero sbd_Card_order mor_Rep_thm coalgT_thm mor_T_final_thm tcoalg_thm))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2668
          ks isNode_hset_thmss carT_defs card_of_carT_thms
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2669
          mor_image'_thms Rep_inverses (transpose mor_hset_thmss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2670
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2671
        val map_wpull_tacs =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2672
          map3 (K ooo mk_wpull_tac m coalg_thePull_thm mor_thePull_fst_thm mor_thePull_snd_thm
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2673
            mor_thePull_pick_thm) unique_mor_thms (transpose pick_col_thmss) hset_defss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2674
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2675
        val srel_O_Gr_tacs = replicate n (simple_srel_O_Gr_tac o #context);
49456
fa8302c8dea1 adapted BNF composition to new relator approach
blanchet
parents: 49452
diff changeset
  2676
49460
4dd451a075ce fixed infinite loop with trivial rel_O_Gr + tuning
blanchet
parents: 49459
diff changeset
  2677
        val tacss = map10 zip_axioms map_id_tacs map_comp_tacs map_cong_tacs set_nat_tacss
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2678
          bd_co_tacs bd_cinf_tacs set_bd_tacss in_bd_tacs map_wpull_tacs srel_O_Gr_tacs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2679
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2680
        val (hset_dtor_incl_thmss, hset_hset_dtor_incl_thmsss, hset_induct_thms) =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2681
          let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2682
            fun tinst_of dtor =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2683
              map (SOME o certify lthy) (dtor :: remove (op =) dtor dtors);
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2684
            fun tinst_of' dtor = case tinst_of dtor of t :: ts => t :: NONE :: ts;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2685
            val Tinst = map (pairself (certifyT lthy))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2686
              (map Logic.varifyT_global (deads @ allAs) ~~ (deads @ passiveAs @ Ts));
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2687
            val set_incl_thmss =
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2688
              map2 (fn dtor => map (singleton (Proof_Context.export names_lthy lthy) o
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2689
                Drule.instantiate' [] (tinst_of' dtor) o
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2690
                Thm.instantiate (Tinst, []) o Drule.zero_var_indexes))
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2691
              dtors set_incl_hset_thmss;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2692
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2693
            val tinst = interleave (map (SOME o certify lthy) dtors) (replicate n NONE)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2694
            val set_minimal_thms =
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2695
              map (Drule.instantiate' [] tinst o Thm.instantiate (Tinst, []) o
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2696
                Drule.zero_var_indexes)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2697
              hset_minimal_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2698
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2699
            val set_set_incl_thmsss =
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2700
              map2 (fn dtor => map (map (singleton (Proof_Context.export names_lthy lthy) o
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2701
                Drule.instantiate' [] (NONE :: tinst_of' dtor) o
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2702
                Thm.instantiate (Tinst, []) o Drule.zero_var_indexes)))
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2703
              dtors set_hset_incl_hset_thmsss;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2704
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2705
            val set_set_incl_thmsss' = transpose (map transpose set_set_incl_thmsss);
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2706
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2707
            val incls =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2708
              maps (map (fn thm => thm RS @{thm subset_Collect_iff})) set_incl_thmss @
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2709
                @{thms subset_Collect_iff[OF subset_refl]};
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2710
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2711
            fun mk_induct_tinst phis jsets y y' =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2712
              map4 (fn phi => fn jset => fn Jz => fn Jz' =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2713
                SOME (certify lthy (Term.absfree Jz' (HOLogic.mk_Collect (fst y', snd y',
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2714
                  HOLogic.mk_conj (HOLogic.mk_mem (y, jset $ Jz), phi $ y $ Jz))))))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2715
              phis jsets Jzs Jzs';
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2716
            val set_induct_thms =
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2717
              map6 (fn set_minimal => fn set_set_inclss => fn jsets => fn y => fn y' => fn phis =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2718
                ((set_minimal
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2719
                  |> Drule.instantiate' [] (mk_induct_tinst phis jsets y y')
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2720
                  |> unfold_thms lthy incls) OF
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2721
                  (replicate n ballI @
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2722
                    maps (map (fn thm => thm RS @{thm subset_CollectI})) set_set_inclss))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2723
                |> singleton (Proof_Context.export names_lthy lthy)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2724
                |> rule_by_tactic lthy (ALLGOALS (TRY o etac asm_rl)))
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2725
              set_minimal_thms set_set_incl_thmsss' setss_by_range ys ys' set_induct_phiss
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2726
          in
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2727
            (set_incl_thmss, set_set_incl_thmsss, set_induct_thms)
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2728
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2729
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2730
        fun close_wit I wit = (I, fold_rev Term.absfree (map (nth ys') I) wit);
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2731
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2732
        val all_unitTs = replicate live HOLogic.unitT;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2733
        val unitTs = replicate n HOLogic.unitT;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2734
        val unit_funs = replicate n (Term.absdummy HOLogic.unitT HOLogic.unit);
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2735
        fun mk_map_args I =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2736
          map (fn i =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2737
            if member (op =) I i then Term.absdummy HOLogic.unitT (nth ys i)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2738
            else mk_undefined (HOLogic.unitT --> nth passiveAs i))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2739
          (0 upto (m - 1));
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2740
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2741
        fun mk_nat_wit Ds bnf (I, wit) () =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2742
          let
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2743
            val passiveI = filter (fn i => i < m) I;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2744
            val map_args = mk_map_args passiveI;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2745
          in
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2746
            Term.absdummy HOLogic.unitT (Term.list_comb
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2747
              (mk_map_of_bnf Ds all_unitTs (passiveAs @ unitTs) bnf, map_args @ unit_funs) $ wit)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2748
          end;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2749
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2750
        fun mk_dummy_wit Ds bnf I =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2751
          let
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2752
            val map_args = mk_map_args I;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2753
          in
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2754
            Term.absdummy HOLogic.unitT (Term.list_comb
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2755
              (mk_map_of_bnf Ds all_unitTs (passiveAs @ unitTs) bnf, map_args @ unit_funs) $
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2756
              mk_undefined (mk_T_of_bnf Ds all_unitTs bnf))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2757
          end;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2758
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2759
        val nat_witss =
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2760
          map2 (fn Ds => fn bnf => mk_wits_of_bnf (replicate (nwits_of_bnf bnf) Ds)
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2761
            (replicate (nwits_of_bnf bnf) (replicate live HOLogic.unitT)) bnf
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2762
            |> map (fn (I, wit) =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2763
              (I, Lazy.lazy (mk_nat_wit Ds bnf (I, Term.list_comb (wit, map (K HOLogic.unit) I))))))
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2764
          Dss bnfs;
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2765
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2766
        val nat_wit_thmss = map2 (curry op ~~) nat_witss (map wit_thmss_of_bnf bnfs)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2767
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2768
        val Iss = map (map fst) nat_witss;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2769
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2770
        fun filter_wits (I, wit) =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2771
          let val J = filter (fn i => i < m) I;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2772
          in (J, (length J < length I, wit)) end;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2773
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2774
        val wit_treess = map_index (fn (i, Is) =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2775
          map_index (finish Iss m [i+m] (i+m)) Is) Iss
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2776
          |> map (minimize_wits o map filter_wits o minimize_wits o flat);
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2777
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2778
        val coind_wit_argsss =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2779
          map (map (tree_to_coind_wits nat_wit_thmss o snd o snd) o filter (fst o snd)) wit_treess;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2780
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2781
        val nonredundant_coind_wit_argsss =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2782
          fold (fn i => fn argsss =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2783
            nth_map (i - 1) (filter_out (fn xs =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2784
              exists (fn ys =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2785
                let
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2786
                  val xs' = (map (fst o fst) xs, snd (fst (hd xs)));
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2787
                  val ys' = (map (fst o fst) ys, snd (fst (hd ys)));
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2788
                in
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2789
                  eq_pair (subset (op =)) (eq_set (op =)) (xs', ys') andalso not (fst xs' = fst ys')
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2790
                end)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2791
              (flat argsss)))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2792
            argsss)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2793
          ks coind_wit_argsss;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2794
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2795
        fun prepare_args args =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2796
          let
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2797
            val I = snd (fst (hd args));
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2798
            val (dummys, args') =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2799
              map_split (fn i =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2800
                (case find_first (fn arg => fst (fst arg) = i - 1) args of
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2801
                  SOME (_, ((_, wit), thms)) => (NONE, (Lazy.force wit, thms))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2802
                | NONE =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2803
                  (SOME (i - 1), (mk_dummy_wit (nth Dss (i - 1)) (nth bnfs (i - 1)) I, []))))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2804
              ks;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2805
          in
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2806
            ((I, dummys), apsnd flat (split_list args'))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2807
          end;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2808
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2809
        fun mk_coind_wits ((I, dummys), (args, thms)) =
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2810
          ((I, dummys), (map (fn i => mk_unfold Ts args i $ HOLogic.unit) ks, thms));
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2811
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2812
        val coind_witss =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2813
          maps (map (mk_coind_wits o prepare_args)) nonredundant_coind_wit_argsss;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2814
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2815
        fun mk_coind_wit_thms ((I, dummys), (wits, wit_thms)) =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2816
          let
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2817
            fun mk_goal sets y y_copy y'_copy j =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2818
              let
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2819
                fun mk_conjunct set z dummy wit =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2820
                  mk_Ball (set $ z) (Term.absfree y'_copy
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2821
                    (if dummy = NONE orelse member (op =) I (j - 1) then
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2822
                      HOLogic.mk_imp (HOLogic.mk_eq (z, wit),
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2823
                        if member (op =) I (j - 1) then HOLogic.mk_eq (y_copy, y)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2824
                        else @{term False})
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2825
                    else @{term True}));
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2826
              in
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2827
                fold_rev Logic.all (map (nth ys) I @ Jzs) (HOLogic.mk_Trueprop
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2828
                  (Library.foldr1 HOLogic.mk_conj (map4 mk_conjunct sets Jzs dummys wits)))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2829
              end;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2830
            val goals = map5 mk_goal setss_by_range ys ys_copy ys'_copy ls;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2831
          in
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2832
            map2 (fn goal => fn induct =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2833
              Skip_Proof.prove lthy [] [] goal
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2834
                (mk_coind_wit_tac induct dtor_unfold_thms (flat set_natural'ss) wit_thms)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2835
              |> Thm.close_derivation)
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2836
            goals hset_induct_thms
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2837
            |> map split_conj_thm
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2838
            |> transpose
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2839
            |> map (map_filter (try (fn thm => thm RS bspec RS mp)))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2840
            |> curry op ~~ (map_index Library.I (map (close_wit I) wits))
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2841
            |> filter (fn (_, thms) => length thms = m)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2842
          end;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2843
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2844
        val coind_wit_thms = maps mk_coind_wit_thms coind_witss;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2845
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2846
        val witss = map2 (fn Ds => fn bnf => mk_wits_of_bnf
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2847
          (replicate (nwits_of_bnf bnf) Ds)
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2848
          (replicate (nwits_of_bnf bnf) (passiveAs @ Ts)) bnf) Dss bnfs;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2849
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2850
        val ctor_witss =
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2851
          map (map (uncurry close_wit o tree_to_ctor_wit ys ctors witss o snd o snd) o
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2852
            filter_out (fst o snd)) wit_treess;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2853
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2854
        val all_witss =
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2855
          fold (fn ((i, wit), thms) => fn witss =>
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2856
            nth_map i (fn (thms', wits) => (thms @ thms', wit :: wits)) witss)
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2857
          coind_wit_thms (map (pair []) ctor_witss)
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2858
          |> map (apsnd (map snd o minimize_wits));
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2859
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2860
        val wit_tac = mk_wit_tac n dtor_ctor_thms (flat set_simp_thmss) (maps wit_thms_of_bnf bnfs);
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2861
49435
483007ddbdc2 bnf_note_all mode for "pre_"-BNFs
traytel
parents: 49434
diff changeset
  2862
        val policy = user_policy Derive_All_Facts_Note_Most;
483007ddbdc2 bnf_note_all mode for "pre_"-BNFs
traytel
parents: 49434
diff changeset
  2863
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2864
        val (Jbnfs, lthy) =
49458
blanchet
parents: 49457
diff changeset
  2865
          fold_map6 (fn tacs => fn b => fn mapx => fn sets => fn T => fn (thms, wits) => fn lthy =>
49435
483007ddbdc2 bnf_note_all mode for "pre_"-BNFs
traytel
parents: 49434
diff changeset
  2866
            bnf_def Dont_Inline policy I tacs (wit_tac thms) (SOME deads)
49459
3f8e2b5249ec adapted FP code to new relator approach
blanchet
parents: 49458
diff changeset
  2867
              (((((b, fold_rev Term.absfree fs' mapx), sets), absdummy T bd), wits), NONE) lthy
49434
433dc7e028c8 separated registration of BNFs from bnf_def (BNFs are now stored only for bnf_def and (co)data commands)
traytel
parents: 49362
diff changeset
  2868
            |> register_bnf (Local_Theory.full_name lthy b))
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2869
          tacss bs fs_maps setss_by_bnf Ts all_witss lthy;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2870
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2871
        val fold_maps = fold_thms lthy (map (fn bnf =>
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2872
          mk_unabs_def m (map_def_of_bnf bnf RS @{thm meta_eq_to_obj_eq})) Jbnfs);
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2873
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2874
        val fold_sets = fold_thms lthy (maps (fn bnf =>
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2875
         map (fn thm => thm RS @{thm meta_eq_to_obj_eq}) (set_defs_of_bnf bnf)) Jbnfs);
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2876
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2877
        val timer = time (timer "registered new codatatypes as BNFs");
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2878
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2879
        val set_incl_thmss = map (map fold_sets) hset_dtor_incl_thmss;
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2880
        val set_set_incl_thmsss = map (map (map fold_sets)) hset_hset_dtor_incl_thmsss;
49104
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2881
        val set_induct_thms = map fold_sets hset_induct_thms;
6defdacd595a generate coinductive witnesses for codatatypes
traytel
parents: 49074
diff changeset
  2882
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2883
        val srels = map2 (fn Ds => mk_srel_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs;
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2884
        val Jsrels = map (mk_srel_of_bnf deads passiveAs passiveBs) Jbnfs;
49507
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2885
        val rels = map2 (fn Ds => mk_rel_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs;
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2886
        val Jrels = map (mk_rel_of_bnf deads passiveAs passiveBs) Jbnfs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2887
49515
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2888
        val JsrelRs = map (fn Jsrel => Term.list_comb (Jsrel, JRs)) Jsrels;
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2889
        val srelRs = map (fn srel => Term.list_comb (srel, JRs @ JsrelRs)) srels;
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2890
        val Jrelphis = map (fn Jsrel => Term.list_comb (Jsrel, Jphis)) Jrels;
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2891
        val relphis = map (fn srel => Term.list_comb (srel, Jphis @ Jrelphis)) rels;
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2892
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2893
        val in_srels = map in_srel_of_bnf bnfs;
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2894
        val in_Jsrels = map in_srel_of_bnf Jbnfs;
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2895
        val Jsrel_defs = map srel_def_of_bnf Jbnfs;
49507
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2896
        val Jrel_defs = map rel_def_of_bnf Jbnfs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2897
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2898
        val folded_map_simp_thms = map fold_maps map_simp_thms;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2899
        val folded_set_simp_thmss = map (map fold_sets) set_simp_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2900
        val folded_set_simp_thmss' = transpose folded_set_simp_thmss;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2901
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2902
        val dtor_Jsrel_thms =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2903
          let
49515
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2904
            fun mk_goal Jz Jz' dtor dtor' JsrelR srelR = fold_rev Logic.all (Jz :: Jz' :: JRs)
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2905
              (mk_Trueprop_eq (HOLogic.mk_mem (HOLogic.mk_prod (Jz, Jz'), JsrelR),
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2906
                  HOLogic.mk_mem (HOLogic.mk_prod (dtor $ Jz, dtor' $ Jz'), srelR)));
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2907
            val goals = map6 mk_goal Jzs Jz's dtors dtor's JsrelRs srelRs;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2908
          in
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2909
            map12 (fn i => fn goal => fn in_srel => fn map_comp => fn map_cong =>
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2910
              fn map_simp => fn set_simps => fn dtor_inject => fn dtor_ctor =>
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2911
              fn set_naturals => fn set_incls => fn set_set_inclss =>
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2912
              Skip_Proof.prove lthy [] [] goal
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2913
                (K (mk_dtor_srel_tac in_Jsrels i in_srel map_comp map_cong map_simp set_simps
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2914
                  dtor_inject dtor_ctor set_naturals set_incls set_set_inclss))
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2915
              |> Thm.close_derivation)
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2916
            ks goals in_srels map_comp's map_congs folded_map_simp_thms folded_set_simp_thmss'
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2917
              dtor_inject_thms dtor_ctor_thms set_natural'ss set_incl_thmss set_set_incl_thmsss
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2918
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2919
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2920
        val dtor_Jrel_thms =
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2921
          let
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2922
            fun mk_goal Jz Jz' dtor dtor' Jpredphi predphi = fold_rev Logic.all (Jz :: Jz' :: Jphis)
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2923
              (mk_Trueprop_eq (Jpredphi $ Jz $ Jz', predphi $ (dtor $ Jz) $ (dtor' $ Jz')));
49515
191d9384966a fixed a few names that escaped the renaming
blanchet
parents: 49510
diff changeset
  2924
            val goals = map6 mk_goal Jzs Jz's dtors dtor's Jrelphis relphis;
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2925
          in
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2926
            map3 (fn goal => fn srel_def => fn dtor_Jsrel =>
49463
83ac281bcdc2 provide predicator, define relator
blanchet
parents: 49460
diff changeset
  2927
              Skip_Proof.prove lthy [] [] goal
49518
b377da40244b renamed LFP low-level rel property to have ctor not dtor in its name
blanchet
parents: 49516
diff changeset
  2928
                (mk_ctor_or_dtor_rel_tac srel_def Jrel_defs Jsrel_defs dtor_Jsrel)
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2929
              |> Thm.close_derivation)
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2930
            goals srel_defs dtor_Jsrel_thms
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2931
          end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2932
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2933
        val timer = time (timer "additional properties");
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2934
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2935
        val ls' = if m = 1 then [0] else ls;
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2936
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2937
        val Jbnf_common_notes =
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2938
          [(map_uniqueN, [fold_maps map_unique_thm])] @
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2939
          map2 (fn i => fn thm => (mk_set_inductN i, [thm])) ls' set_induct_thms
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2940
          |> map (fn (thmN, thms) =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2941
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2942
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2943
        val Jbnf_notes =
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2944
          [(dtor_relN, map single dtor_Jrel_thms),
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2945
          (dtor_srelN, map single dtor_Jsrel_thms),
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2946
          (map_simpsN, map single folded_map_simp_thms),
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2947
          (set_inclN, set_incl_thmss),
49516
d4859efc1096 renamed "rel_simp" to "dtor_rel" and similarly for "srel"
blanchet
parents: 49515
diff changeset
  2948
          (set_set_inclN, map flat set_set_incl_thmsss)] @
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2949
          map2 (fn i => fn thms => (mk_set_simpsN i, map single thms)) ls' folded_set_simp_thmss
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2950
          |> maps (fn (thmN, thmss) =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2951
            map2 (fn b => fn thms =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2952
              ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2953
            bs thmss)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2954
      in
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2955
        timer; lthy |> Local_Theory.notes (Jbnf_common_notes @ Jbnf_notes) |> snd
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2956
      end;
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2957
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2958
      val common_notes =
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2959
        [(dtor_coinductN, [dtor_coinduct_thm]),
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2960
        (dtor_strong_coinductN, [dtor_strong_coinduct_thm]),
49507
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2961
        (rel_coinductN, [rel_coinduct_thm]),
8826d5a4332b renamed "pred" to "rel" (relator)
blanchet
parents: 49506
diff changeset
  2962
        (rel_strong_coinductN, [rel_strong_coinduct_thm]),
49506
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2963
        (srel_coinductN, [srel_coinduct_thm]),
aeb0cc8889f2 renamed "rel" to "srel"
blanchet
parents: 49504
diff changeset
  2964
        (srel_strong_coinductN, [srel_strong_coinduct_thm])]
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2965
        |> map (fn (thmN, thms) =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2966
          ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2967
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2968
      val notes =
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2969
        [(ctor_dtorN, ctor_dtor_thms),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2970
        (ctor_dtor_unfoldsN, ctor_dtor_unfold_thms),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2971
        (ctor_dtor_corecsN, ctor_dtor_corec_thms),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2972
        (ctor_exhaustN, ctor_exhaust_thms),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2973
        (ctor_injectN, ctor_inject_thms),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2974
        (dtor_corecsN, dtor_corec_thms),
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2975
        (dtor_ctorN, dtor_ctor_thms),
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2976
        (dtor_exhaustN, dtor_exhaust_thms),
49501
acc9635a644a renamed "fld"/"unf" to "ctor"/"dtor"
blanchet
parents: 49499
diff changeset
  2977
        (dtor_injectN, dtor_inject_thms),
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2978
        (dtor_unfold_uniqueN, dtor_unfold_unique_thms),
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2979
        (dtor_unfoldsN, dtor_unfold_thms)]
49109
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2980
        |> map (apsnd (map single))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2981
        |> maps (fn (thmN, thmss) =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2982
          map2 (fn b => fn thms =>
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2983
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
0e5b859e1c91 no more aliases for Local_Theory.note; use Thm.close_derivation in internal theorems;
traytel
parents: 49105
diff changeset
  2984
          bs thmss)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2985
  in
49504
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2986
    ((dtors, ctors, unfolds, corecs, dtor_coinduct_thm, dtor_ctor_thms, ctor_dtor_thms,
df9b897fb254 renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents: 49501
diff changeset
  2987
      ctor_inject_thms, ctor_dtor_unfold_thms, ctor_dtor_corec_thms),
49205
674f04c737e0 implemented "mk_iter_or_rec_tac"
blanchet
parents: 49185
diff changeset
  2988
     lthy |> Local_Theory.notes (common_notes @ notes) |> snd)
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2989
  end;
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2990
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2991
val _ =
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2992
  Outer_Syntax.local_theory @{command_spec "codata_raw"}
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2993
    "define BNF-based coinductive datatypes (low-level)"
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2994
    (Parse.and_list1
49277
blanchet
parents: 49255
diff changeset
  2995
      ((Parse.binding --| @{keyword ":"}) -- (Parse.typ --| @{keyword "="} -- Parse.typ)) >>
49121
9e0acaa470ab more work on FP sugar
blanchet
parents: 49109
diff changeset
  2996
      (snd oo fp_bnf_cmd bnf_gfp o apsnd split_list o split_list));
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  2997
49308
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2998
val _ =
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  2999
  Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  3000
    (parse_datatype_cmd false bnf_gfp);
6190b701e4f4 reorganized dependencies so that the sugar does not depend on GFP -- this will be essential for bootstrapping
blanchet
parents: 49277
diff changeset
  3001
48975
7f79f94a432c added new (co)datatype package + theories of ordinals and cardinals (with Dmitriy and Andrei)
blanchet
parents:
diff changeset
  3002
end;