--- a/src/HOL/BNF/Tools/bnf_lfp.ML Mon Jan 20 18:24:55 2014 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1881 +0,0 @@
-(* Title: HOL/BNF/Tools/bnf_lfp.ML
- Author: Dmitriy Traytel, TU Muenchen
- Author: Andrei Popescu, TU Muenchen
- Copyright 2012
-
-Datatype construction.
-*)
-
-signature BNF_LFP =
-sig
- val construct_lfp: mixfix list -> binding list -> binding list -> binding list list ->
- binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list ->
- local_theory -> BNF_FP_Util.fp_result * local_theory
-end;
-
-structure BNF_LFP : BNF_LFP =
-struct
-
-open BNF_Def
-open BNF_Util
-open BNF_Tactics
-open BNF_Comp
-open BNF_FP_Util
-open BNF_FP_Def_Sugar
-open BNF_LFP_Rec_Sugar
-open BNF_LFP_Util
-open BNF_LFP_Tactics
-
-(*all BNFs have the same lives*)
-fun construct_lfp mixfixes map_bs rel_bs set_bss0 bs resBs (resDs, Dss) bnfs lthy =
- let
- val time = time lthy;
- val timer = time (Timer.startRealTimer ());
-
- val live = live_of_bnf (hd bnfs);
- val n = length bnfs; (*active*)
- val ks = 1 upto n;
- val m = live - n; (*passive, if 0 don't generate a new BNF*)
-
- val note_all = Config.get lthy bnf_note_all;
- val b_names = map Binding.name_of bs;
- val b_name = mk_common_name b_names;
- val b = Binding.name b_name;
- val mk_internal_b = Binding.name #> Binding.prefix true b_name #> Binding.conceal;
- fun mk_internal_bs name =
- map (fn b =>
- Binding.prefix true b_name (Binding.prefix_name (name ^ "_") b) |> Binding.conceal) bs;
- val external_bs = map2 (Binding.prefix false) b_names bs
- |> note_all = false ? map Binding.conceal;
-
- (* TODO: check if m, n, etc., are sane *)
-
- val deads = fold (union (op =)) Dss resDs;
- val names_lthy = fold Variable.declare_typ deads lthy;
- val passives = map fst (subtract (op = o apsnd TFree) deads resBs);
-
- (* tvars *)
- val (((((passiveAs, activeAs), passiveBs), activeBs), passiveCs), activeCs) =
- names_lthy
- |> variant_tfrees passives
- ||>> mk_TFrees n
- ||>> variant_tfrees passives
- ||>> mk_TFrees n
- ||>> variant_tfrees passives
- ||>> mk_TFrees n
- |> fst;
-
- val allAs = passiveAs @ activeAs;
- val allBs' = passiveBs @ activeBs;
- val Ass = replicate n allAs;
- val allBs = passiveAs @ activeBs;
- val Bss = replicate n allBs;
- val allCs = passiveAs @ activeCs;
- val allCs' = passiveBs @ activeCs;
- val Css' = replicate n allCs';
-
- (* types *)
- val dead_poss =
- map (fn x => if member (op =) deads (TFree x) then SOME (TFree x) else NONE) resBs;
- fun mk_param NONE passive = (hd passive, tl passive)
- | mk_param (SOME a) passive = (a, passive);
- val mk_params = fold_map mk_param dead_poss #> fst;
-
- fun mk_FTs Ts = map2 (fn Ds => mk_T_of_bnf Ds Ts) Dss bnfs;
- val (params, params') = `(map Term.dest_TFree) (mk_params passiveAs);
- val FTsAs = mk_FTs allAs;
- val FTsBs = mk_FTs allBs;
- val FTsCs = mk_FTs allCs;
- val ATs = map HOLogic.mk_setT passiveAs;
- val BTs = map HOLogic.mk_setT activeAs;
- val B'Ts = map HOLogic.mk_setT activeBs;
- val B''Ts = map HOLogic.mk_setT activeCs;
- val sTs = map2 (curry op -->) FTsAs activeAs;
- val s'Ts = map2 (curry op -->) FTsBs activeBs;
- val s''Ts = map2 (curry op -->) FTsCs activeCs;
- val fTs = map2 (curry op -->) activeAs activeBs;
- val inv_fTs = map2 (curry op -->) activeBs activeAs;
- val self_fTs = map2 (curry op -->) activeAs activeAs;
- val gTs = map2 (curry op -->) activeBs activeCs;
- val all_gTs = map2 (curry op -->) allBs allCs';
- val prodBsAs = map2 (curry HOLogic.mk_prodT) activeBs activeAs;
- val prodFTs = mk_FTs (passiveAs @ prodBsAs);
- val prod_sTs = map2 (curry op -->) prodFTs activeAs;
-
- (* terms *)
- val mapsAsAs = map4 mk_map_of_bnf Dss Ass Ass bnfs;
- val mapsAsBs = map4 mk_map_of_bnf Dss Ass Bss bnfs;
- val mapsBsAs = map4 mk_map_of_bnf Dss Bss Ass bnfs;
- val mapsBsCs' = map4 mk_map_of_bnf Dss Bss Css' bnfs;
- val mapsAsCs' = map4 mk_map_of_bnf Dss Ass Css' bnfs;
- val map_fsts = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ prodBsAs)) Bss bnfs;
- val map_fsts_rev = map4 mk_map_of_bnf Dss Bss (replicate n (passiveAs @ prodBsAs)) bnfs;
- fun mk_setss Ts = map3 mk_sets_of_bnf (map (replicate live) Dss)
- (map (replicate live) (replicate n Ts)) bnfs;
- val setssAs = mk_setss allAs;
- val bd0s = map3 mk_bd_of_bnf Dss Ass bnfs;
- val bds =
- map3 (fn bd0 => fn Ds => fn bnf => mk_csum bd0
- (mk_card_of (HOLogic.mk_UNIV
- (mk_T_of_bnf Ds (replicate live (fst (dest_relT (fastype_of bd0)))) bnf))))
- bd0s Dss bnfs;
- val witss = map wits_of_bnf bnfs;
-
- val (((((((((((((((((((zs, zs'), As), Bs), Bs_copy), B's), B''s), ss), prod_ss), s's), s''s),
- fs), fs_copy), inv_fs), self_fs), gs), all_gs), (xFs, xFs')), (yFs, yFs')),
- names_lthy) = lthy
- |> mk_Frees' "z" activeAs
- ||>> mk_Frees "A" ATs
- ||>> mk_Frees "B" BTs
- ||>> mk_Frees "B" BTs
- ||>> mk_Frees "B'" B'Ts
- ||>> mk_Frees "B''" B''Ts
- ||>> mk_Frees "s" sTs
- ||>> mk_Frees "prods" prod_sTs
- ||>> mk_Frees "s'" s'Ts
- ||>> mk_Frees "s''" s''Ts
- ||>> mk_Frees "f" fTs
- ||>> mk_Frees "f" fTs
- ||>> mk_Frees "f" inv_fTs
- ||>> mk_Frees "f" self_fTs
- ||>> mk_Frees "g" gTs
- ||>> mk_Frees "g" all_gTs
- ||>> mk_Frees' "x" FTsAs
- ||>> mk_Frees' "y" FTsBs;
-
- val passive_UNIVs = map HOLogic.mk_UNIV passiveAs;
- val active_UNIVs = map HOLogic.mk_UNIV activeAs;
- val prod_UNIVs = map HOLogic.mk_UNIV prodBsAs;
- val passive_ids = map HOLogic.id_const passiveAs;
- val active_ids = map HOLogic.id_const activeAs;
- val fsts = map fst_const prodBsAs;
-
- (* thms *)
- val bd0_card_orders = map bd_card_order_of_bnf bnfs;
- val bd0_Card_orders = map bd_Card_order_of_bnf bnfs;
- val bd0_Cinfinites = map bd_Cinfinite_of_bnf bnfs;
- val set_bd0ss = map set_bd_of_bnf bnfs;
-
- val bd_card_orders =
- map (fn thm => @{thm card_order_csum} OF [thm, @{thm card_of_card_order_on}]) bd0_card_orders;
- val bd_Card_order = @{thm Card_order_csum};
- val bd_Card_orders = replicate n bd_Card_order;
- val bd_Cinfinites = map (fn thm => thm RS @{thm Cinfinite_csum1}) bd0_Cinfinites;
- val bd_Cnotzeros = map (fn thm => thm RS @{thm Cinfinite_Cnotzero}) bd_Cinfinites;
- val bd_Cinfinite = hd bd_Cinfinites;
- val bd_Cnotzero = hd bd_Cnotzeros;
- val set_bdss =
- map2 (fn set_bd0s => fn bd0_Card_order =>
- map (fn thm => ctrans OF [thm, bd0_Card_order RS @{thm ordLeq_csum1}]) set_bd0s)
- set_bd0ss bd0_Card_orders;
- val in_bds = map in_bd_of_bnf bnfs;
- val sym_map_comps = map (fn bnf => map_comp0_of_bnf bnf RS sym) bnfs;
- val map_comps = map map_comp_of_bnf bnfs;
- val map_cong0s = map map_cong0_of_bnf bnfs;
- val map_id0s = map map_id0_of_bnf bnfs;
- val map_ids = map map_id_of_bnf bnfs;
- val set_mapss = map set_map_of_bnf bnfs;
- val rel_mono_strongs = map rel_mono_strong_of_bnf bnfs;
- val rel_OOs = map rel_OO_of_bnf bnfs;
-
- val timer = time (timer "Extracted terms & thms");
-
- (* nonemptiness check *)
- fun new_wit X (wit: nonemptiness_witness) = subset (op =) (#I wit, (0 upto m - 1) @ map snd X);
-
- val all = m upto m + n - 1;
-
- fun enrich X = map_filter (fn i =>
- (case find_first (fn (_, i') => i = i') X of
- NONE =>
- (case find_index (new_wit X) (nth witss (i - m)) of
- ~1 => NONE
- | j => SOME (j, i))
- | SOME ji => SOME ji)) all;
- val reachable = fixpoint (op =) enrich [];
- val _ = (case subtract (op =) (map snd reachable) all of
- [] => ()
- | i :: _ => error ("Cannot define empty datatype " ^ quote (Binding.name_of (nth bs (i - m)))));
-
- val wit_thms = flat (map2 (fn bnf => fn (j, _) => nth (wit_thmss_of_bnf bnf) j) bnfs reachable);
-
- val timer = time (timer "Checked nonemptiness");
-
- (* derived thms *)
-
- (*map g1 ... gm g(m+1) ... g(m+n) (map id ... id f(m+1) ... f(m+n) x) =
- map g1 ... gm (g(m+1) o f(m+1)) ... (g(m+n) o f(m+n)) x*)
- fun mk_map_comp_id x mapAsBs mapBsCs mapAsCs map_comp0 =
- let
- val lhs = Term.list_comb (mapBsCs, all_gs) $
- (Term.list_comb (mapAsBs, passive_ids @ fs) $ x);
- val rhs = Term.list_comb (mapAsCs,
- take m all_gs @ map HOLogic.mk_comp (drop m all_gs ~~ fs)) $ x;
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (x :: fs @ all_gs) (mk_Trueprop_eq (lhs, rhs)))
- (K (mk_map_comp_id_tac map_comp0))
- |> Thm.close_derivation
- end;
-
- val map_comp_id_thms = map5 mk_map_comp_id xFs mapsAsBs mapsBsCs' mapsAsCs' map_comps;
-
- (*forall a : set(m+1) x. f(m+1) a = a; ...; forall a : set(m+n) x. f(m+n) a = a ==>
- map id ... id f(m+1) ... f(m+n) x = x*)
- fun mk_map_cong0L x mapAsAs sets map_cong0 map_id =
- let
- fun mk_prem set f z z' = HOLogic.mk_Trueprop
- (mk_Ball (set $ x) (Term.absfree z' (HOLogic.mk_eq (f $ z, z))));
- val prems = map4 mk_prem (drop m sets) self_fs zs zs';
- val goal = mk_Trueprop_eq (Term.list_comb (mapAsAs, passive_ids @ self_fs) $ x, x);
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (x :: self_fs) (Logic.list_implies (prems, goal)))
- (K (mk_map_cong0L_tac m map_cong0 map_id))
- |> Thm.close_derivation
- end;
-
- val map_cong0L_thms = map5 mk_map_cong0L xFs mapsAsAs setssAs map_cong0s map_ids;
- val in_mono'_thms = map (fn bnf => in_mono_of_bnf bnf OF (replicate m subset_refl)) bnfs;
- val in_cong'_thms = map (fn bnf => in_cong_of_bnf bnf OF (replicate m refl)) bnfs;
-
- val timer = time (timer "Derived simple theorems");
-
- (* algebra *)
-
- val alg_bind = mk_internal_b algN;
- val alg_name = Binding.name_of alg_bind;
- val alg_def_bind = (Thm.def_binding alg_bind, []);
-
- (*forall i = 1 ... n: (\<forall>x \<in> Fi_in A1 .. Am B1 ... Bn. si x \<in> Bi)*)
- val alg_spec =
- let
- val algT = Library.foldr (op -->) (ATs @ BTs @ sTs, HOLogic.boolT);
-
- val ins = map3 mk_in (replicate n (As @ Bs)) setssAs FTsAs;
- fun mk_alg_conjunct B s X x x' =
- mk_Ball X (Term.absfree x' (HOLogic.mk_mem (s $ x, B)));
-
- val lhs = Term.list_comb (Free (alg_name, algT), As @ Bs @ ss);
- val rhs = Library.foldr1 HOLogic.mk_conj (map5 mk_alg_conjunct Bs ss ins xFs xFs')
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((alg_free, (_, alg_def_free)), (lthy, lthy_old)) =
- lthy
- |> Specification.definition (SOME (alg_bind, NONE, NoSyn), (alg_def_bind, alg_spec))
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- val alg = fst (Term.dest_Const (Morphism.term phi alg_free));
- val alg_def = Morphism.thm phi alg_def_free;
-
- fun mk_alg As Bs ss =
- let
- val args = As @ Bs @ ss;
- val Ts = map fastype_of args;
- val algT = Library.foldr (op -->) (Ts, HOLogic.boolT);
- in
- Term.list_comb (Const (alg, algT), args)
- end;
-
- val alg_set_thms =
- let
- val alg_prem = HOLogic.mk_Trueprop (mk_alg As Bs ss);
- fun mk_prem x set B = HOLogic.mk_Trueprop (mk_leq (set $ x) B);
- fun mk_concl s x B = HOLogic.mk_Trueprop (HOLogic.mk_mem (s $ x, B));
- val premss = map2 ((fn x => fn sets => map2 (mk_prem x) sets (As @ Bs))) xFs setssAs;
- val concls = map3 mk_concl ss xFs Bs;
- val goals = map3 (fn x => fn prems => fn concl =>
- fold_rev Logic.all (x :: As @ Bs @ ss)
- (Logic.list_implies (alg_prem :: prems, concl))) xFs premss concls;
- in
- map (fn goal =>
- Goal.prove_sorry lthy [] [] goal (K (mk_alg_set_tac alg_def)) |> Thm.close_derivation)
- goals
- end;
-
- fun mk_talg ATs BTs = mk_alg (map HOLogic.mk_UNIV ATs) (map HOLogic.mk_UNIV BTs);
-
- val talg_thm =
- let
- val goal = fold_rev Logic.all ss
- (HOLogic.mk_Trueprop (mk_talg passiveAs activeAs ss))
- in
- Goal.prove_sorry lthy [] [] goal
- (K (stac alg_def 1 THEN CONJ_WRAP (K (EVERY' [rtac ballI, rtac UNIV_I] 1)) ss))
- |> Thm.close_derivation
- end;
-
- val timer = time (timer "Algebra definition & thms");
-
- val alg_not_empty_thms =
- let
- val alg_prem =
- HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss);
- val concls = map (HOLogic.mk_Trueprop o mk_not_empty) Bs;
- val goals =
- map (fn concl =>
- fold_rev Logic.all (Bs @ ss) (Logic.mk_implies (alg_prem, concl))) concls;
- in
- map2 (fn goal => fn alg_set =>
- Goal.prove_sorry lthy [] []
- goal (K (mk_alg_not_empty_tac lthy alg_set alg_set_thms wit_thms))
- |> Thm.close_derivation)
- goals alg_set_thms
- end;
-
- val timer = time (timer "Proved nonemptiness");
-
- (* morphism *)
-
- val mor_bind = mk_internal_b morN;
- val mor_name = Binding.name_of mor_bind;
- val mor_def_bind = (Thm.def_binding mor_bind, []);
-
- (*fbetw) forall i = 1 ... n: (\<forall>x \<in> Bi. f x \<in> B'i)*)
- (*mor) forall i = 1 ... n: (\<forall>x \<in> Fi_in UNIV ... UNIV B1 ... Bn.
- f (s1 x) = s1' (Fi_map id ... id f1 ... fn x))*)
- val mor_spec =
- let
- val morT = Library.foldr (op -->) (BTs @ sTs @ B'Ts @ s'Ts @ fTs, HOLogic.boolT);
-
- fun mk_fbetw f B1 B2 z z' =
- mk_Ball B1 (Term.absfree z' (HOLogic.mk_mem (f $ z, B2)));
- fun mk_mor sets mapAsBs f s s' T x x' =
- mk_Ball (mk_in (passive_UNIVs @ Bs) sets T)
- (Term.absfree x' (HOLogic.mk_eq (f $ (s $ x), s' $
- (Term.list_comb (mapAsBs, passive_ids @ fs) $ x))));
- val lhs = Term.list_comb (Free (mor_name, morT), Bs @ ss @ B's @ s's @ fs);
- val rhs = HOLogic.mk_conj
- (Library.foldr1 HOLogic.mk_conj (map5 mk_fbetw fs Bs B's zs zs'),
- Library.foldr1 HOLogic.mk_conj
- (map8 mk_mor setssAs mapsAsBs fs ss s's FTsAs xFs xFs'))
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((mor_free, (_, mor_def_free)), (lthy, lthy_old)) =
- lthy
- |> Specification.definition (SOME (mor_bind, NONE, NoSyn), (mor_def_bind, mor_spec))
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- val mor = fst (Term.dest_Const (Morphism.term phi mor_free));
- val mor_def = Morphism.thm phi mor_def_free;
-
- fun mk_mor Bs1 ss1 Bs2 ss2 fs =
- let
- val args = Bs1 @ ss1 @ Bs2 @ ss2 @ fs;
- val Ts = map fastype_of (Bs1 @ ss1 @ Bs2 @ ss2 @ fs);
- val morT = Library.foldr (op -->) (Ts, HOLogic.boolT);
- in
- Term.list_comb (Const (mor, morT), args)
- end;
-
- val (mor_image_thms, morE_thms) =
- let
- val prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs);
- fun mk_image_goal f B1 B2 = fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs)
- (Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_leq (mk_image f $ B1) B2)));
- val image_goals = map3 mk_image_goal fs Bs B's;
- fun mk_elim_prem sets x T = HOLogic.mk_Trueprop
- (HOLogic.mk_mem (x, mk_in (passive_UNIVs @ Bs) sets T));
- fun mk_elim_goal sets mapAsBs f s s' x T =
- fold_rev Logic.all (x :: Bs @ ss @ B's @ s's @ fs)
- (Logic.list_implies ([prem, mk_elim_prem sets x T],
- mk_Trueprop_eq (f $ (s $ x), s' $ Term.list_comb (mapAsBs, passive_ids @ fs @ [x]))));
- val elim_goals = map7 mk_elim_goal setssAs mapsAsBs fs ss s's xFs FTsAs;
- fun prove goal =
- Goal.prove_sorry lthy [] [] goal (K (mk_mor_elim_tac mor_def)) |> Thm.close_derivation;
- in
- (map prove image_goals, map prove elim_goals)
- end;
-
- val mor_incl_thm =
- let
- val prems = map2 (HOLogic.mk_Trueprop oo mk_leq) Bs Bs_copy;
- val concl = HOLogic.mk_Trueprop (mk_mor Bs ss Bs_copy ss active_ids);
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ Bs_copy) (Logic.list_implies (prems, concl)))
- (K (mk_mor_incl_tac mor_def map_ids))
- |> Thm.close_derivation
- end;
-
- val mor_comp_thm =
- let
- val prems =
- [HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs),
- HOLogic.mk_Trueprop (mk_mor B's s's B''s s''s gs)];
- val concl =
- HOLogic.mk_Trueprop (mk_mor Bs ss B''s s''s (map2 (curry HOLogic.mk_comp) gs fs));
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ B's @ s's @ B''s @ s''s @ fs @ gs)
- (Logic.list_implies (prems, concl)))
- (K (mk_mor_comp_tac mor_def set_mapss map_comp_id_thms))
- |> Thm.close_derivation
- end;
-
- val mor_inv_thm =
- let
- fun mk_inv_prem f inv_f B B' = HOLogic.mk_conj (mk_leq (mk_image inv_f $ B') B,
- HOLogic.mk_conj (mk_inver inv_f f B, mk_inver f inv_f B'));
- val prems = map HOLogic.mk_Trueprop
- ([mk_mor Bs ss B's s's fs,
- mk_alg passive_UNIVs Bs ss,
- mk_alg passive_UNIVs B's s's] @
- map4 mk_inv_prem fs inv_fs Bs B's);
- val concl = HOLogic.mk_Trueprop (mk_mor B's s's Bs ss inv_fs);
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs @ inv_fs)
- (Logic.list_implies (prems, concl)))
- (K (mk_mor_inv_tac alg_def mor_def set_mapss morE_thms map_comp_id_thms map_cong0L_thms))
- |> Thm.close_derivation
- end;
-
- val mor_cong_thm =
- let
- val prems = map HOLogic.mk_Trueprop
- (map2 (curry HOLogic.mk_eq) fs_copy fs @ [mk_mor Bs ss B's s's fs])
- val concl = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs_copy);
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs @ fs_copy)
- (Logic.list_implies (prems, concl)))
- (K ((hyp_subst_tac lthy THEN' atac) 1))
- |> Thm.close_derivation
- end;
-
- val mor_str_thm =
- let
- val maps = map2 (fn Ds => fn bnf => Term.list_comb
- (mk_map_of_bnf Ds (passiveAs @ FTsAs) allAs bnf, passive_ids @ ss)) Dss bnfs;
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all ss (HOLogic.mk_Trueprop
- (mk_mor (map HOLogic.mk_UNIV FTsAs) maps active_UNIVs ss ss)))
- (K (mk_mor_str_tac ks mor_def))
- |> Thm.close_derivation
- end;
-
- val mor_convol_thm =
- let
- val maps = map3 (fn s => fn prod_s => fn mapx =>
- mk_convol (HOLogic.mk_comp (s, Term.list_comb (mapx, passive_ids @ fsts)), prod_s))
- s's prod_ss map_fsts;
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (s's @ prod_ss) (HOLogic.mk_Trueprop
- (mk_mor prod_UNIVs maps (map HOLogic.mk_UNIV activeBs) s's fsts)))
- (K (mk_mor_convol_tac ks mor_def))
- |> Thm.close_derivation
- end;
-
- val mor_UNIV_thm =
- let
- fun mk_conjunct mapAsBs f s s' = HOLogic.mk_eq
- (HOLogic.mk_comp (f, s),
- HOLogic.mk_comp (s', Term.list_comb (mapAsBs, passive_ids @ fs)));
- val lhs = mk_mor active_UNIVs ss (map HOLogic.mk_UNIV activeBs) s's fs;
- val rhs = Library.foldr1 HOLogic.mk_conj (map4 mk_conjunct mapsAsBs fs ss s's);
- in
- Goal.prove_sorry lthy [] [] (fold_rev Logic.all (ss @ s's @ fs) (mk_Trueprop_eq (lhs, rhs)))
- (K (mk_mor_UNIV_tac m morE_thms mor_def))
- |> Thm.close_derivation
- end;
-
- val timer = time (timer "Morphism definition & thms");
-
- (* isomorphism *)
-
- (*mor Bs1 ss1 Bs2 ss2 fs \<and> (\<exists>gs. mor Bs2 ss2 Bs1 ss1 fs \<and>
- forall i = 1 ... n. (inver gs[i] fs[i] Bs1[i] \<and> inver fs[i] gs[i] Bs2[i]))*)
- fun mk_iso Bs1 ss1 Bs2 ss2 fs gs =
- let
- val ex_inv_mor = list_exists_free gs
- (HOLogic.mk_conj (mk_mor Bs2 ss2 Bs1 ss1 gs,
- Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_conj)
- (map3 mk_inver gs fs Bs1) (map3 mk_inver fs gs Bs2))));
- in
- HOLogic.mk_conj (mk_mor Bs1 ss1 Bs2 ss2 fs, ex_inv_mor)
- end;
-
- val iso_alt_thm =
- let
- val prems = map HOLogic.mk_Trueprop
- [mk_alg passive_UNIVs Bs ss,
- mk_alg passive_UNIVs B's s's]
- val concl = mk_Trueprop_eq (mk_iso Bs ss B's s's fs inv_fs,
- HOLogic.mk_conj (mk_mor Bs ss B's s's fs,
- Library.foldr1 HOLogic.mk_conj (map3 mk_bij_betw fs Bs B's)));
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs) (Logic.list_implies (prems, concl)))
- (K (mk_iso_alt_tac mor_image_thms mor_inv_thm))
- |> Thm.close_derivation
- end;
-
- val timer = time (timer "Isomorphism definition & thms");
-
- (* algebra copies *)
-
- val (copy_alg_thm, ex_copy_alg_thm) =
- let
- val prems = map HOLogic.mk_Trueprop
- (mk_alg passive_UNIVs Bs ss :: map3 mk_bij_betw inv_fs B's Bs);
- val inver_prems = map HOLogic.mk_Trueprop
- (map3 mk_inver inv_fs fs Bs @ map3 mk_inver fs inv_fs B's);
- val all_prems = prems @ inver_prems;
- fun mk_s f s mapT y y' = Term.absfree y' (f $ (s $
- (Term.list_comb (mapT, passive_ids @ inv_fs) $ y)));
-
- val alg = HOLogic.mk_Trueprop
- (mk_alg passive_UNIVs B's (map5 mk_s fs ss mapsBsAs yFs yFs'));
- val copy_str_thm = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs)
- (Logic.list_implies (all_prems, alg)))
- (K (mk_copy_str_tac set_mapss alg_def alg_set_thms))
- |> Thm.close_derivation;
-
- val iso = HOLogic.mk_Trueprop
- (mk_iso B's (map5 mk_s fs ss mapsBsAs yFs yFs') Bs ss inv_fs fs_copy);
- val copy_alg_thm = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs)
- (Logic.list_implies (all_prems, iso)))
- (K (mk_copy_alg_tac set_mapss alg_set_thms mor_def iso_alt_thm copy_str_thm))
- |> Thm.close_derivation;
-
- val ex = HOLogic.mk_Trueprop
- (list_exists_free s's
- (HOLogic.mk_conj (mk_alg passive_UNIVs B's s's,
- mk_iso B's s's Bs ss inv_fs fs_copy)));
- val ex_copy_alg_thm = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs)
- (Logic.list_implies (prems, ex)))
- (K (mk_ex_copy_alg_tac n copy_str_thm copy_alg_thm))
- |> Thm.close_derivation;
- in
- (copy_alg_thm, ex_copy_alg_thm)
- end;
-
- val timer = time (timer "Copy thms");
-
-
- (* bounds *)
-
- val sum_Card_order = if n = 1 then bd_Card_order else @{thm Card_order_csum};
- val sum_Cnotzero = if n = 1 then bd_Cnotzero else bd_Cnotzero RS @{thm csum_Cnotzero1};
- val sum_Cinfinite = if n = 1 then bd_Cinfinite else bd_Cinfinite RS @{thm Cinfinite_csum1};
- fun mk_set_bd_sums i bd_Card_order bds =
- if n = 1 then bds
- else map (fn thm => bd_Card_order RS mk_ordLeq_csum n i thm) bds;
- val set_bd_sumss = map3 mk_set_bd_sums ks bd_Card_orders set_bdss;
-
- fun mk_in_bd_sum i Co Cnz bd =
- if n = 1 then bd
- else Cnz RS ((Co RS mk_ordLeq_csum n i (Co RS @{thm ordLeq_refl})) RS
- (bd RS @{thm ordLeq_transitive[OF _ cexp_mono2_Cnotzero[OF _ Card_order_csum]]}));
- val in_bd_sums = map4 mk_in_bd_sum ks bd_Card_orders bd_Cnotzeros in_bds;
-
- val sum_bd = Library.foldr1 (uncurry mk_csum) bds;
- val suc_bd = mk_cardSuc sum_bd;
- val field_suc_bd = mk_Field suc_bd;
- val suc_bdT = fst (dest_relT (fastype_of suc_bd));
- fun mk_Asuc_bd [] = mk_cexp ctwo suc_bd
- | mk_Asuc_bd As =
- mk_cexp (mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo) suc_bd;
-
- val suc_bd_Card_order = if n = 1 then bd_Card_order RS @{thm cardSuc_Card_order}
- else @{thm cardSuc_Card_order[OF Card_order_csum]};
- val suc_bd_Cinfinite = if n = 1 then bd_Cinfinite RS @{thm Cinfinite_cardSuc}
- else bd_Cinfinite RS @{thm Cinfinite_cardSuc[OF Cinfinite_csum1]};
- val suc_bd_Cnotzero = suc_bd_Cinfinite RS @{thm Cinfinite_Cnotzero};
- val suc_bd_worel = suc_bd_Card_order RS @{thm Card_order_wo_rel}
- val basis_Asuc = if m = 0 then @{thm ordLeq_refl[OF Card_order_ctwo]}
- else @{thm ordLeq_csum2[OF Card_order_ctwo]};
- val Asuc_bd_Cinfinite = suc_bd_Cinfinite RS (basis_Asuc RS @{thm Cinfinite_cexp});
-
- val suc_bd_Asuc_bd = @{thm ordLess_ordLeq_trans[OF ordLess_ctwo_cexp cexp_mono1]} OF
- [suc_bd_Card_order, basis_Asuc, suc_bd_Card_order];
-
- val Asuc_bdT = fst (dest_relT (fastype_of (mk_Asuc_bd As)));
- val II_BTs = replicate n (HOLogic.mk_setT Asuc_bdT);
- val II_sTs = map2 (fn Ds => fn bnf =>
- mk_T_of_bnf Ds (passiveAs @ replicate n Asuc_bdT) bnf --> Asuc_bdT) Dss bnfs;
-
- val (((((((idxs, Asi_name), (idx, idx')), (jdx, jdx')), II_Bs), II_ss), Asuc_fs),
- names_lthy) = names_lthy
- |> mk_Frees "i" (replicate n suc_bdT)
- ||>> (fn ctxt => apfst the_single (mk_fresh_names ctxt 1 "Asi"))
- ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") suc_bdT
- ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "j") suc_bdT
- ||>> mk_Frees "IIB" II_BTs
- ||>> mk_Frees "IIs" II_sTs
- ||>> mk_Frees "f" (map (fn T => Asuc_bdT --> T) activeAs);
-
- val suc_bd_limit_thm =
- let
- val prem = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map (fn idx => HOLogic.mk_mem (idx, field_suc_bd)) idxs));
- fun mk_conjunct idx = HOLogic.mk_conj (mk_not_eq idx jdx,
- HOLogic.mk_mem (HOLogic.mk_prod (idx, jdx), suc_bd));
- val concl = HOLogic.mk_Trueprop (mk_Bex field_suc_bd
- (Term.absfree jdx' (Library.foldr1 HOLogic.mk_conj (map mk_conjunct idxs))));
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all idxs (Logic.list_implies ([prem], concl)))
- (K (mk_bd_limit_tac n suc_bd_Cinfinite))
- |> Thm.close_derivation
- end;
-
- val timer = time (timer "Bounds");
-
-
- (* minimal algebra *)
-
- fun mk_minG Asi i k = mk_UNION (mk_underS suc_bd $ i)
- (Term.absfree jdx' (mk_nthN n (Asi $ jdx) k));
-
- fun mk_minH_component As Asi i sets Ts s k =
- HOLogic.mk_binop @{const_name "sup"}
- (mk_minG Asi i k, mk_image s $ mk_in (As @ map (mk_minG Asi i) ks) sets Ts);
-
- fun mk_min_algs As ss =
- let
- val BTs = map (range_type o fastype_of) ss;
- val Ts = map (HOLogic.dest_setT o fastype_of) As @ BTs;
- val (Asi, Asi') = `Free (Asi_name, suc_bdT -->
- Library.foldr1 HOLogic.mk_prodT (map HOLogic.mk_setT BTs));
- in
- mk_worec suc_bd (Term.absfree Asi' (Term.absfree idx' (HOLogic.mk_tuple
- (map4 (mk_minH_component As Asi idx) (mk_setss Ts) (mk_FTs Ts) ss ks))))
- end;
-
- val (min_algs_thms, min_algs_mono_thms, card_of_min_algs_thm, least_min_algs_thm) =
- let
- val i_field = HOLogic.mk_mem (idx, field_suc_bd);
- val min_algs = mk_min_algs As ss;
- val min_algss = map (fn k => mk_nthN n (min_algs $ idx) k) ks;
-
- val concl = HOLogic.mk_Trueprop
- (HOLogic.mk_eq (min_algs $ idx, HOLogic.mk_tuple
- (map4 (mk_minH_component As min_algs idx) setssAs FTsAs ss ks)));
- val goal = fold_rev Logic.all (idx :: As @ ss)
- (Logic.mk_implies (HOLogic.mk_Trueprop i_field, concl));
-
- val min_algs_thm = Goal.prove_sorry lthy [] [] goal
- (K (mk_min_algs_tac suc_bd_worel in_cong'_thms))
- |> Thm.close_derivation;
-
- val min_algs_thms = map (fn k => min_algs_thm RS mk_nthI n k) ks;
-
- fun mk_mono_goal min_alg =
- fold_rev Logic.all (As @ ss) (HOLogic.mk_Trueprop (mk_relChain suc_bd
- (Term.absfree idx' min_alg)));
-
- val monos =
- map2 (fn goal => fn min_algs =>
- Goal.prove_sorry lthy [] [] goal (K (mk_min_algs_mono_tac lthy min_algs))
- |> Thm.close_derivation)
- (map mk_mono_goal min_algss) min_algs_thms;
-
- val Asuc_bd = mk_Asuc_bd As;
-
- fun mk_card_conjunct min_alg = mk_ordLeq (mk_card_of min_alg) Asuc_bd;
- val card_conjunction = Library.foldr1 HOLogic.mk_conj (map mk_card_conjunct min_algss);
- val card_cT = certifyT lthy suc_bdT;
- val card_ct = certify lthy (Term.absfree idx' card_conjunction);
-
- val card_of = singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] []
- (HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, card_conjunction)))
- (K (mk_min_algs_card_of_tac card_cT card_ct
- m suc_bd_worel min_algs_thms in_bd_sums
- sum_Card_order sum_Cnotzero suc_bd_Card_order suc_bd_Cinfinite suc_bd_Cnotzero
- suc_bd_Asuc_bd Asuc_bd_Cinfinite)))
- |> Thm.close_derivation;
-
- val least_prem = HOLogic.mk_Trueprop (mk_alg As Bs ss);
- val least_conjunction = Library.foldr1 HOLogic.mk_conj (map2 mk_leq min_algss Bs);
- val least_cT = certifyT lthy suc_bdT;
- val least_ct = certify lthy (Term.absfree idx' least_conjunction);
-
- val least = singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] []
- (Logic.mk_implies (least_prem,
- HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, least_conjunction))))
- (K (mk_min_algs_least_tac least_cT least_ct
- suc_bd_worel min_algs_thms alg_set_thms)))
- |> Thm.close_derivation;
- in
- (min_algs_thms, monos, card_of, least)
- end;
-
- val timer = time (timer "min_algs definition & thms");
-
- val min_alg_binds = mk_internal_bs min_algN;
- fun min_alg_bind i = nth min_alg_binds (i - 1);
- fun min_alg_name i = Binding.name_of (min_alg_bind i);
- val min_alg_def_bind = rpair [] o Thm.def_binding o min_alg_bind;
-
- fun min_alg_spec i =
- let
- val min_algT =
- Library.foldr (op -->) (ATs @ sTs, HOLogic.mk_setT (nth activeAs (i - 1)));
-
- val lhs = Term.list_comb (Free (min_alg_name i, min_algT), As @ ss);
- val rhs = mk_UNION (field_suc_bd)
- (Term.absfree idx' (mk_nthN n (mk_min_algs As ss $ idx) i));
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((min_alg_frees, (_, min_alg_def_frees)), (lthy, lthy_old)) =
- lthy
- |> fold_map (fn i => Specification.definition
- (SOME (min_alg_bind i, NONE, NoSyn), (min_alg_def_bind i, min_alg_spec i))) ks
- |>> apsnd split_list o split_list
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- val min_algs = map (fst o Term.dest_Const o Morphism.term phi) min_alg_frees;
- val min_alg_defs = map (Morphism.thm phi) min_alg_def_frees;
-
- fun mk_min_alg As ss i =
- let
- val T = HOLogic.mk_setT (range_type (fastype_of (nth ss (i - 1))))
- val args = As @ ss;
- val Ts = map fastype_of args;
- val min_algT = Library.foldr (op -->) (Ts, T);
- in
- Term.list_comb (Const (nth min_algs (i - 1), min_algT), args)
- end;
-
- val (alg_min_alg_thm, card_of_min_alg_thms, least_min_alg_thms, mor_incl_min_alg_thm) =
- let
- val min_algs = map (mk_min_alg As ss) ks;
-
- val goal = fold_rev Logic.all (As @ ss) (HOLogic.mk_Trueprop (mk_alg As min_algs ss));
- val alg_min_alg = Goal.prove_sorry lthy [] [] goal
- (K (mk_alg_min_alg_tac m alg_def min_alg_defs suc_bd_limit_thm sum_Cinfinite
- set_bd_sumss min_algs_thms min_algs_mono_thms))
- |> Thm.close_derivation;
-
- val Asuc_bd = mk_Asuc_bd As;
- fun mk_card_of_thm min_alg def = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (As @ ss)
- (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of min_alg) Asuc_bd)))
- (K (mk_card_of_min_alg_tac def card_of_min_algs_thm
- suc_bd_Card_order suc_bd_Asuc_bd Asuc_bd_Cinfinite))
- |> Thm.close_derivation;
-
- val least_prem = HOLogic.mk_Trueprop (mk_alg As Bs ss);
- fun mk_least_thm min_alg B def = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (As @ Bs @ ss)
- (Logic.mk_implies (least_prem, HOLogic.mk_Trueprop (mk_leq min_alg B))))
- (K (mk_least_min_alg_tac def least_min_algs_thm))
- |> Thm.close_derivation;
-
- val leasts = map3 mk_least_thm min_algs Bs min_alg_defs;
-
- val incl_prem = HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss);
- val incl_min_algs = map (mk_min_alg passive_UNIVs ss) ks;
- val incl = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss)
- (Logic.mk_implies (incl_prem,
- HOLogic.mk_Trueprop (mk_mor incl_min_algs ss Bs ss active_ids))))
- (K (EVERY' (rtac mor_incl_thm :: map etac leasts) 1))
- |> Thm.close_derivation;
- in
- (alg_min_alg, map2 mk_card_of_thm min_algs min_alg_defs, leasts, incl)
- end;
-
- val timer = time (timer "Minimal algebra definition & thms");
-
- val II_repT = HOLogic.mk_prodT (HOLogic.mk_tupleT II_BTs, HOLogic.mk_tupleT II_sTs);
- val IIT_bind = mk_internal_b IITN;
-
- val ((IIT_name, (IIT_glob_info, IIT_loc_info)), lthy) =
- typedef (IIT_bind, params, NoSyn)
- (HOLogic.mk_UNIV II_repT) NONE (EVERY' [rtac exI, rtac UNIV_I] 1) lthy;
-
- val IIT = Type (IIT_name, params');
- val Abs_IIT = Const (#Abs_name IIT_glob_info, II_repT --> IIT);
- val Rep_IIT = Const (#Rep_name IIT_glob_info, IIT --> II_repT);
- val Abs_IIT_inverse_thm = UNIV_I RS #Abs_inverse IIT_loc_info;
-
- val initT = IIT --> Asuc_bdT;
- val active_initTs = replicate n initT;
- val init_FTs = map2 (fn Ds => mk_T_of_bnf Ds (passiveAs @ active_initTs)) Dss bnfs;
- val init_fTs = map (fn T => initT --> T) activeAs;
-
- val (((((((iidx, iidx'), init_xs), (init_xFs, init_xFs')),
- init_fs), init_fs_copy), init_phis), names_lthy) = names_lthy
- |> yield_singleton (apfst (op ~~) oo mk_Frees' "i") IIT
- ||>> mk_Frees "ix" active_initTs
- ||>> mk_Frees' "x" init_FTs
- ||>> mk_Frees "f" init_fTs
- ||>> mk_Frees "f" init_fTs
- ||>> mk_Frees "P" (replicate n (mk_pred1T initT));
-
- val II = HOLogic.mk_Collect (fst iidx', IIT, list_exists_free (II_Bs @ II_ss)
- (HOLogic.mk_conj (HOLogic.mk_eq (iidx,
- Abs_IIT $ (HOLogic.mk_prod (HOLogic.mk_tuple II_Bs, HOLogic.mk_tuple II_ss))),
- mk_alg passive_UNIVs II_Bs II_ss)));
-
- val select_Bs = map (mk_nthN n (HOLogic.mk_fst (Rep_IIT $ iidx))) ks;
- val select_ss = map (mk_nthN n (HOLogic.mk_snd (Rep_IIT $ iidx))) ks;
-
- val str_init_binds = mk_internal_bs str_initN;
- fun str_init_bind i = nth str_init_binds (i - 1);
- val str_init_name = Binding.name_of o str_init_bind;
- val str_init_def_bind = rpair [] o Thm.def_binding o str_init_bind;
-
- fun str_init_spec i =
- let
- val T = nth init_FTs (i - 1);
- val init_xF = nth init_xFs (i - 1)
- val select_s = nth select_ss (i - 1);
- val map = mk_map_of_bnf (nth Dss (i - 1))
- (passiveAs @ active_initTs) (passiveAs @ replicate n Asuc_bdT)
- (nth bnfs (i - 1));
- val map_args = passive_ids @ replicate n (mk_rapp iidx Asuc_bdT);
- val str_initT = T --> IIT --> Asuc_bdT;
-
- val lhs = Term.list_comb (Free (str_init_name i, str_initT), [init_xF, iidx]);
- val rhs = select_s $ (Term.list_comb (map, map_args) $ init_xF);
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((str_init_frees, (_, str_init_def_frees)), (lthy, lthy_old)) =
- lthy
- |> fold_map (fn i => Specification.definition
- (SOME (str_init_bind i, NONE, NoSyn), (str_init_def_bind i, str_init_spec i))) ks
- |>> apsnd split_list o split_list
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- val str_inits =
- map (Term.subst_atomic_types (map (`(Morphism.typ phi)) params') o Morphism.term phi)
- str_init_frees;
-
- val str_init_defs = map (Morphism.thm phi) str_init_def_frees;
-
- val car_inits = map (mk_min_alg passive_UNIVs str_inits) ks;
-
- (*TODO: replace with instantiate? (problem: figure out right type instantiation)*)
- val alg_init_thm = Goal.prove_sorry lthy [] []
- (HOLogic.mk_Trueprop (mk_alg passive_UNIVs car_inits str_inits))
- (K (rtac alg_min_alg_thm 1))
- |> Thm.close_derivation;
-
- val alg_select_thm = Goal.prove_sorry lthy [] []
- (HOLogic.mk_Trueprop (mk_Ball II
- (Term.absfree iidx' (mk_alg passive_UNIVs select_Bs select_ss))))
- (mk_alg_select_tac Abs_IIT_inverse_thm)
- |> Thm.close_derivation;
-
- val mor_select_thm =
- let
- val alg_prem = HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss);
- val i_prem = HOLogic.mk_Trueprop (HOLogic.mk_mem (iidx, II));
- val mor_prem = HOLogic.mk_Trueprop (mk_mor select_Bs select_ss Bs ss Asuc_fs);
- val prems = [alg_prem, i_prem, mor_prem];
- val concl = HOLogic.mk_Trueprop
- (mk_mor car_inits str_inits Bs ss
- (map (fn f => HOLogic.mk_comp (f, mk_rapp iidx Asuc_bdT)) Asuc_fs));
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (iidx :: Bs @ ss @ Asuc_fs) (Logic.list_implies (prems, concl)))
- (K (mk_mor_select_tac mor_def mor_cong_thm mor_comp_thm mor_incl_min_alg_thm alg_def
- alg_select_thm alg_set_thms set_mapss str_init_defs))
- |> Thm.close_derivation
- end;
-
- val (init_ex_mor_thm, init_unique_mor_thms) =
- let
- val prem = HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss);
- val concl = HOLogic.mk_Trueprop
- (list_exists_free init_fs (mk_mor car_inits str_inits Bs ss init_fs));
- val ex_mor = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (Bs @ ss) (Logic.mk_implies (prem, concl)))
- (mk_init_ex_mor_tac Abs_IIT_inverse_thm ex_copy_alg_thm alg_min_alg_thm
- card_of_min_alg_thms mor_comp_thm mor_select_thm mor_incl_min_alg_thm)
- |> Thm.close_derivation;
-
- val prems = map2 (HOLogic.mk_Trueprop oo curry HOLogic.mk_mem) init_xs car_inits
- val mor_prems = map HOLogic.mk_Trueprop
- [mk_mor car_inits str_inits Bs ss init_fs,
- mk_mor car_inits str_inits Bs ss init_fs_copy];
- fun mk_fun_eq f g x = HOLogic.mk_eq (f $ x, g $ x);
- val unique = HOLogic.mk_Trueprop
- (Library.foldr1 HOLogic.mk_conj (map3 mk_fun_eq init_fs init_fs_copy init_xs));
- val unique_mor = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (init_xs @ Bs @ ss @ init_fs @ init_fs_copy)
- (Logic.list_implies (prems @ mor_prems, unique)))
- (K (mk_init_unique_mor_tac m alg_def alg_init_thm least_min_alg_thms
- in_mono'_thms alg_set_thms morE_thms map_cong0s))
- |> Thm.close_derivation;
- in
- (ex_mor, split_conj_thm unique_mor)
- end;
-
- val init_setss = mk_setss (passiveAs @ active_initTs);
- val active_init_setss = map (drop m) init_setss;
- val init_ins = map2 (fn sets => mk_in (passive_UNIVs @ car_inits) sets) init_setss init_FTs;
-
- fun mk_closed phis =
- let
- fun mk_conjunct phi str_init init_sets init_in x x' =
- let
- val prem = Library.foldr1 HOLogic.mk_conj
- (map2 (fn set => mk_Ball (set $ x)) init_sets phis);
- val concl = phi $ (str_init $ x);
- in
- mk_Ball init_in (Term.absfree x' (HOLogic.mk_imp (prem, concl)))
- end;
- in
- Library.foldr1 HOLogic.mk_conj
- (map6 mk_conjunct phis str_inits active_init_setss init_ins init_xFs init_xFs')
- end;
-
- val init_induct_thm =
- let
- val prem = HOLogic.mk_Trueprop (mk_closed init_phis);
- val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map2 mk_Ball car_inits init_phis));
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all init_phis (Logic.mk_implies (prem, concl)))
- (K (mk_init_induct_tac m alg_def alg_init_thm least_min_alg_thms alg_set_thms))
- |> Thm.close_derivation
- end;
-
- val timer = time (timer "Initiality definition & thms");
-
- val ((T_names, (T_glob_infos, T_loc_infos)), lthy) =
- lthy
- |> fold_map3 (fn b => fn mx => fn car_init =>
- typedef (Binding.conceal b, params, mx) car_init NONE
- (EVERY' [rtac ssubst, rtac @{thm ex_in_conv}, resolve_tac alg_not_empty_thms,
- rtac alg_init_thm] 1)) bs mixfixes car_inits
- |>> apsnd split_list o split_list;
-
- val Ts = map (fn name => Type (name, params')) T_names;
- fun mk_Ts passive = map (Term.typ_subst_atomic (passiveAs ~~ passive)) Ts;
- val Ts' = mk_Ts passiveBs;
- val Rep_Ts = map2 (fn info => fn T => Const (#Rep_name info, T --> initT)) T_glob_infos Ts;
- val Abs_Ts = map2 (fn info => fn T => Const (#Abs_name info, initT --> T)) T_glob_infos Ts;
-
- val type_defs = map #type_definition T_loc_infos;
- val Reps = map #Rep T_loc_infos;
- val Rep_casess = map #Rep_cases T_loc_infos;
- val Rep_injects = map #Rep_inject T_loc_infos;
- val Rep_inverses = map #Rep_inverse T_loc_infos;
- val Abs_inverses = map #Abs_inverse T_loc_infos;
-
- fun mk_inver_thm mk_tac rep abs X thm =
- Goal.prove_sorry lthy [] []
- (HOLogic.mk_Trueprop (mk_inver rep abs X))
- (K (EVERY' [rtac ssubst, rtac @{thm inver_def}, rtac ballI, mk_tac thm] 1))
- |> Thm.close_derivation;
-
- val inver_Reps = map4 (mk_inver_thm rtac) Abs_Ts Rep_Ts (map HOLogic.mk_UNIV Ts) Rep_inverses;
- val inver_Abss = map4 (mk_inver_thm etac) Rep_Ts Abs_Ts car_inits Abs_inverses;
-
- val timer = time (timer "THE TYPEDEFs & Rep/Abs thms");
-
- val UNIVs = map HOLogic.mk_UNIV Ts;
- val FTs = mk_FTs (passiveAs @ Ts);
- val FTs' = mk_FTs (passiveBs @ Ts');
- fun mk_set_Ts T = passiveAs @ replicate n (HOLogic.mk_setT T);
- val setFTss = map (mk_FTs o mk_set_Ts) passiveAs;
- val FTs_setss = mk_setss (passiveAs @ Ts);
- val FTs'_setss = mk_setss (passiveBs @ Ts');
- val map_FT_inits = map2 (fn Ds =>
- mk_map_of_bnf Ds (passiveAs @ Ts) (passiveAs @ active_initTs)) Dss bnfs;
- val fTs = map2 (curry op -->) Ts activeAs;
- val foldT = Library.foldr1 HOLogic.mk_prodT (map2 (curry op -->) Ts activeAs);
- val rec_sTs = map (Term.typ_subst_atomic (activeBs ~~ Ts)) prod_sTs;
- val rec_maps = map (Term.subst_atomic_types (activeBs ~~ Ts)) map_fsts;
- val rec_maps_rev = map (Term.subst_atomic_types (activeBs ~~ Ts)) map_fsts_rev;
- val rec_fsts = map (Term.subst_atomic_types (activeBs ~~ Ts)) fsts;
- val rec_UNIVs = map2 (HOLogic.mk_UNIV oo curry HOLogic.mk_prodT) Ts activeAs;
-
- val (((((((((Izs1, Izs1'), (Izs2, Izs2')), (xFs, xFs')), yFs), (AFss, AFss')),
- (fold_f, fold_f')), fs), rec_ss), names_lthy) = names_lthy
- |> mk_Frees' "z1" Ts
- ||>> mk_Frees' "z2" Ts'
- ||>> mk_Frees' "x" FTs
- ||>> mk_Frees "y" FTs'
- ||>> mk_Freess' "z" setFTss
- ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "f") foldT
- ||>> mk_Frees "f" fTs
- ||>> mk_Frees "s" rec_sTs;
-
- val Izs = map2 retype_free Ts zs;
- val phis = map2 retype_free (map mk_pred1T Ts) init_phis;
- val phi2s = map2 retype_free (map2 mk_pred2T Ts Ts') init_phis;
-
- fun ctor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctorN ^ "_");
- val ctor_name = Binding.name_of o ctor_bind;
- val ctor_def_bind = rpair [] o Binding.conceal o Thm.def_binding o ctor_bind;
-
- fun ctor_spec i abs str map_FT_init x x' =
- let
- val ctorT = nth FTs (i - 1) --> nth Ts (i - 1);
-
- val lhs = Free (ctor_name i, ctorT);
- val rhs = Term.absfree x' (abs $ (str $
- (Term.list_comb (map_FT_init, map HOLogic.id_const passiveAs @ Rep_Ts) $ x)));
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((ctor_frees, (_, ctor_def_frees)), (lthy, lthy_old)) =
- lthy
- |> fold_map6 (fn i => fn abs => fn str => fn mapx => fn x => fn x' =>
- Specification.definition
- (SOME (ctor_bind i, NONE, NoSyn), (ctor_def_bind i, ctor_spec i abs str mapx x x')))
- ks Abs_Ts str_inits map_FT_inits xFs xFs'
- |>> apsnd split_list o split_list
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- fun mk_ctors passive =
- map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ (mk_params passive)) o
- Morphism.term phi) ctor_frees;
- val ctors = mk_ctors passiveAs;
- val ctor's = mk_ctors passiveBs;
- val ctor_defs = map (Morphism.thm phi) ctor_def_frees;
-
- val (mor_Rep_thm, mor_Abs_thm) =
- let
- val copy = alg_init_thm RS copy_alg_thm;
- fun mk_bij inj Rep cases = @{thm bij_betwI'} OF [inj, Rep, cases];
- val bijs = map3 mk_bij Rep_injects Reps Rep_casess;
- val mor_Rep =
- Goal.prove_sorry lthy [] []
- (HOLogic.mk_Trueprop (mk_mor UNIVs ctors car_inits str_inits Rep_Ts))
- (mk_mor_Rep_tac ctor_defs copy bijs inver_Abss inver_Reps)
- |> Thm.close_derivation;
-
- val inv = mor_inv_thm OF [mor_Rep, talg_thm, alg_init_thm];
- val mor_Abs =
- Goal.prove_sorry lthy [] []
- (HOLogic.mk_Trueprop (mk_mor car_inits str_inits UNIVs ctors Abs_Ts))
- (K (mk_mor_Abs_tac inv inver_Abss inver_Reps))
- |> Thm.close_derivation;
- in
- (mor_Rep, mor_Abs)
- end;
-
- val timer = time (timer "ctor definitions & thms");
-
- val fold_fun = Term.absfree fold_f'
- (mk_mor UNIVs ctors active_UNIVs ss (map (mk_nthN n fold_f) ks));
- val foldx = HOLogic.choice_const foldT $ fold_fun;
-
- fun fold_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctor_foldN ^ "_");
- val fold_name = Binding.name_of o fold_bind;
- val fold_def_bind = rpair [] o Binding.conceal o Thm.def_binding o fold_bind;
-
- fun fold_spec i T AT =
- let
- val foldT = Library.foldr (op -->) (sTs, T --> AT);
-
- val lhs = Term.list_comb (Free (fold_name i, foldT), ss);
- val rhs = mk_nthN n foldx i;
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((fold_frees, (_, fold_def_frees)), (lthy, lthy_old)) =
- lthy
- |> fold_map3 (fn i => fn T => fn AT =>
- Specification.definition
- (SOME (fold_bind i, NONE, NoSyn), (fold_def_bind i, fold_spec i T AT)))
- ks Ts activeAs
- |>> apsnd split_list o split_list
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- val folds = map (Morphism.term phi) fold_frees;
- val fold_names = map (fst o dest_Const) folds;
- fun mk_folds passives actives =
- map3 (fn name => fn T => fn active =>
- Const (name, Library.foldr (op -->)
- (map2 (curry op -->) (mk_FTs (passives @ actives)) actives, T --> active)))
- fold_names (mk_Ts passives) actives;
- fun mk_fold Ts ss i = Term.list_comb (Const (nth fold_names (i - 1), Library.foldr (op -->)
- (map fastype_of ss, nth Ts (i - 1) --> range_type (fastype_of (nth ss (i - 1))))), ss);
- val fold_defs = map (Morphism.thm phi) fold_def_frees;
-
- val mor_fold_thm =
- let
- val ex_mor = talg_thm RS init_ex_mor_thm;
- val mor_cong = mor_cong_thm OF (map (mk_nth_conv n) ks);
- val mor_comp = mor_Rep_thm RS mor_comp_thm;
- val cT = certifyT lthy foldT;
- val ct = certify lthy fold_fun
- in
- singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] []
- (HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss (map (mk_fold Ts ss) ks)))
- (K (mk_mor_fold_tac cT ct fold_defs ex_mor (mor_comp RS mor_cong))))
- |> Thm.close_derivation
- end;
-
- val ctor_fold_thms = map (fn morE => rule_by_tactic lthy
- ((rtac CollectI THEN' CONJ_WRAP' (K (rtac @{thm subset_UNIV})) (1 upto m + n)) 1)
- (mor_fold_thm RS morE)) morE_thms;
-
- val (fold_unique_mor_thms, fold_unique_mor_thm) =
- let
- val prem = HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss fs);
- fun mk_fun_eq f i = HOLogic.mk_eq (f, mk_fold Ts ss i);
- val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_fun_eq fs ks));
- val unique_mor = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (ss @ fs) (Logic.mk_implies (prem, unique)))
- (K (mk_fold_unique_mor_tac type_defs init_unique_mor_thms Reps
- mor_comp_thm mor_Abs_thm mor_fold_thm))
- |> Thm.close_derivation;
- in
- `split_conj_thm unique_mor
- end;
-
- val (ctor_fold_unique_thms, ctor_fold_unique_thm) =
- `split_conj_thm (mk_conjIN n RS
- (mor_UNIV_thm RS iffD2 RS fold_unique_mor_thm))
-
- val fold_ctor_thms =
- map (fn thm => (mor_incl_thm OF replicate n @{thm subset_UNIV}) RS thm RS sym)
- fold_unique_mor_thms;
-
- val ctor_o_fold_thms =
- let
- val mor = mor_comp_thm OF [mor_fold_thm, mor_str_thm];
- in
- map2 (fn unique => fn fold_ctor =>
- trans OF [mor RS unique, fold_ctor]) fold_unique_mor_thms fold_ctor_thms
- end;
-
- val timer = time (timer "fold definitions & thms");
-
- val map_ctors = map2 (fn Ds => fn bnf =>
- Term.list_comb (mk_map_of_bnf Ds (passiveAs @ FTs) (passiveAs @ Ts) bnf,
- map HOLogic.id_const passiveAs @ ctors)) Dss bnfs;
-
- fun dtor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (dtorN ^ "_");
- val dtor_name = Binding.name_of o dtor_bind;
- val dtor_def_bind = rpair [] o Binding.conceal o Thm.def_binding o dtor_bind;
-
- fun dtor_spec i FT T =
- let
- val dtorT = T --> FT;
-
- val lhs = Free (dtor_name i, dtorT);
- val rhs = mk_fold Ts map_ctors i;
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((dtor_frees, (_, dtor_def_frees)), (lthy, lthy_old)) =
- lthy
- |> fold_map3 (fn i => fn FT => fn T =>
- Specification.definition
- (SOME (dtor_bind i, NONE, NoSyn), (dtor_def_bind i, dtor_spec i FT T))) ks FTs Ts
- |>> apsnd split_list o split_list
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- fun mk_dtors params =
- map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ params) o Morphism.term phi)
- dtor_frees;
- val dtors = mk_dtors params';
- val dtor_defs = map (Morphism.thm phi) dtor_def_frees;
-
- val ctor_o_dtor_thms = map2 (fold_thms lthy o single) dtor_defs ctor_o_fold_thms;
-
- val dtor_o_ctor_thms =
- let
- fun mk_goal dtor ctor FT =
- mk_Trueprop_eq (HOLogic.mk_comp (dtor, ctor), HOLogic.id_const FT);
- val goals = map3 mk_goal dtors ctors FTs;
- in
- map5 (fn goal => fn dtor_def => fn foldx => fn map_comp_id => fn map_cong0L =>
- Goal.prove_sorry lthy [] [] goal
- (K (mk_dtor_o_ctor_tac dtor_def foldx map_comp_id map_cong0L ctor_o_fold_thms))
- |> Thm.close_derivation)
- goals dtor_defs ctor_fold_thms map_comp_id_thms map_cong0L_thms
- end;
-
- val dtor_ctor_thms = map (fn thm => thm RS @{thm pointfree_idE}) dtor_o_ctor_thms;
- val ctor_dtor_thms = map (fn thm => thm RS @{thm pointfree_idE}) ctor_o_dtor_thms;
-
- val bij_dtor_thms =
- map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) ctor_o_dtor_thms dtor_o_ctor_thms;
- val inj_dtor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_dtor_thms;
- val surj_dtor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_dtor_thms;
- val dtor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_dtor_thms;
- val dtor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_dtor_thms;
- val dtor_exhaust_thms = map (fn thm => thm RS exE) dtor_nchotomy_thms;
-
- val bij_ctor_thms =
- map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) dtor_o_ctor_thms ctor_o_dtor_thms;
- val inj_ctor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_ctor_thms;
- val surj_ctor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_ctor_thms;
- val ctor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_ctor_thms;
- val ctor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_ctor_thms;
- val ctor_exhaust_thms = map (fn thm => thm RS exE) ctor_nchotomy_thms;
-
- val timer = time (timer "dtor definitions & thms");
-
- val fst_rec_pair_thms =
- let
- val mor = mor_comp_thm OF [mor_fold_thm, mor_convol_thm];
- in
- map2 (fn unique => fn fold_ctor =>
- trans OF [mor RS unique, fold_ctor]) fold_unique_mor_thms fold_ctor_thms
- end;
-
- fun rec_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctor_recN ^ "_");
- val rec_name = Binding.name_of o rec_bind;
- val rec_def_bind = rpair [] o Binding.conceal o Thm.def_binding o rec_bind;
-
- val rec_strs =
- map3 (fn ctor => fn prod_s => fn mapx =>
- mk_convol (HOLogic.mk_comp (ctor, Term.list_comb (mapx, passive_ids @ rec_fsts)), prod_s))
- ctors rec_ss rec_maps;
-
- fun rec_spec i T AT =
- let
- val recT = Library.foldr (op -->) (rec_sTs, T --> AT);
-
- val lhs = Term.list_comb (Free (rec_name i, recT), rec_ss);
- val rhs = HOLogic.mk_comp (snd_const (HOLogic.mk_prodT (T, AT)), mk_fold Ts rec_strs i);
- in
- mk_Trueprop_eq (lhs, rhs)
- end;
-
- val ((rec_frees, (_, rec_def_frees)), (lthy, lthy_old)) =
- lthy
- |> fold_map3 (fn i => fn T => fn AT =>
- Specification.definition
- (SOME (rec_bind i, NONE, NoSyn), (rec_def_bind i, rec_spec i T AT)))
- ks Ts activeAs
- |>> apsnd split_list o split_list
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy_old lthy;
- val recs = map (Morphism.term phi) rec_frees;
- val rec_names = map (fst o dest_Const) recs;
- fun mk_rec ss i = Term.list_comb (Const (nth rec_names (i - 1), Library.foldr (op -->)
- (map fastype_of ss, nth Ts (i - 1) --> range_type (fastype_of (nth ss (i - 1))))), ss);
- val rec_defs = map (Morphism.thm phi) rec_def_frees;
-
- val convols = map2 (fn T => fn i => mk_convol (HOLogic.id_const T, mk_rec rec_ss i)) Ts ks;
- val ctor_rec_thms =
- let
- fun mk_goal i rec_s rec_map ctor x =
- let
- val lhs = mk_rec rec_ss i $ (ctor $ x);
- val rhs = rec_s $ (Term.list_comb (rec_map, passive_ids @ convols) $ x);
- in
- fold_rev Logic.all (x :: rec_ss) (mk_Trueprop_eq (lhs, rhs))
- end;
- val goals = map5 mk_goal ks rec_ss rec_maps_rev ctors xFs;
- in
- map2 (fn goal => fn foldx =>
- Goal.prove_sorry lthy [] [] goal (mk_rec_tac rec_defs foldx fst_rec_pair_thms)
- |> Thm.close_derivation)
- goals ctor_fold_thms
- end;
-
- val rec_unique_mor_thm =
- let
- val id_fs = map2 (fn T => fn f => mk_convol (HOLogic.id_const T, f)) Ts fs;
- val prem = HOLogic.mk_Trueprop (mk_mor UNIVs ctors rec_UNIVs rec_strs id_fs);
- fun mk_fun_eq f i = HOLogic.mk_eq (f, mk_rec rec_ss i);
- val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_fun_eq fs ks));
- in
- Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (rec_ss @ fs) (Logic.mk_implies (prem, unique)))
- (mk_rec_unique_mor_tac rec_defs fst_rec_pair_thms fold_unique_mor_thm)
- |> Thm.close_derivation
- end;
-
- val (ctor_rec_unique_thms, ctor_rec_unique_thm) =
- `split_conj_thm (split_conj_prems n
- (mor_UNIV_thm RS iffD2 RS rec_unique_mor_thm)
- |> Local_Defs.unfold lthy (@{thms convol_o o_id id_o o_assoc[symmetric] fst_convol} @
- map_id0s @ sym_map_comps) OF replicate n @{thm arg_cong2[of _ _ _ _ convol, OF refl]});
-
- val timer = time (timer "rec definitions & thms");
-
- val (ctor_induct_thm, induct_params) =
- let
- fun mk_prem phi ctor sets x =
- let
- fun mk_IH phi set z =
- let
- val prem = HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set $ x));
- val concl = HOLogic.mk_Trueprop (phi $ z);
- in
- Logic.all z (Logic.mk_implies (prem, concl))
- end;
-
- val IHs = map3 mk_IH phis (drop m sets) Izs;
- val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x));
- in
- Logic.all x (Logic.list_implies (IHs, concl))
- end;
-
- val prems = map4 mk_prem phis ctors FTs_setss xFs;
-
- fun mk_concl phi z = phi $ z;
- val concl =
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_concl phis Izs));
-
- val goal = Logic.list_implies (prems, concl);
- in
- (Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (phis @ Izs) goal)
- (K (mk_ctor_induct_tac lthy m set_mapss init_induct_thm morE_thms mor_Abs_thm
- Rep_inverses Abs_inverses Reps))
- |> Thm.close_derivation,
- rev (Term.add_tfrees goal []))
- end;
-
- val cTs = map (SOME o certifyT lthy o TFree) induct_params;
-
- val weak_ctor_induct_thms =
- let fun insts i = (replicate (i - 1) TrueI) @ (asm_rl :: replicate (n - i) TrueI);
- in map (fn i => (ctor_induct_thm OF insts i) RS mk_conjunctN n i) ks end;
-
- val (ctor_induct2_thm, induct2_params) =
- let
- fun mk_prem phi ctor ctor' sets sets' x y =
- let
- fun mk_IH phi set set' z1 z2 =
- let
- val prem1 = HOLogic.mk_Trueprop (HOLogic.mk_mem (z1, (set $ x)));
- val prem2 = HOLogic.mk_Trueprop (HOLogic.mk_mem (z2, (set' $ y)));
- val concl = HOLogic.mk_Trueprop (phi $ z1 $ z2);
- in
- fold_rev Logic.all [z1, z2] (Logic.list_implies ([prem1, prem2], concl))
- end;
-
- val IHs = map5 mk_IH phi2s (drop m sets) (drop m sets') Izs1 Izs2;
- val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x) $ (ctor' $ y));
- in
- fold_rev Logic.all [x, y] (Logic.list_implies (IHs, concl))
- end;
-
- val prems = map7 mk_prem phi2s ctors ctor's FTs_setss FTs'_setss xFs yFs;
-
- fun mk_concl phi z1 z2 = phi $ z1 $ z2;
- val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map3 mk_concl phi2s Izs1 Izs2));
- fun mk_t phi (z1, z1') (z2, z2') =
- Term.absfree z1' (HOLogic.mk_all (fst z2', snd z2', phi $ z1 $ z2));
- val cts = map3 (SOME o certify lthy ooo mk_t) phi2s (Izs1 ~~ Izs1') (Izs2 ~~ Izs2');
- val goal = Logic.list_implies (prems, concl);
- in
- (singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] [] goal
- (mk_ctor_induct2_tac cTs cts ctor_induct_thm weak_ctor_induct_thms))
- |> Thm.close_derivation,
- rev (Term.add_tfrees goal []))
- end;
-
- val timer = time (timer "induction");
-
- fun mk_ctor_map_DEADID_thm ctor_inject map_id0 =
- trans OF [id_apply, iffD2 OF [ctor_inject, map_id0 RS sym]];
-
- fun mk_ctor_Irel_DEADID_thm ctor_inject bnf =
- trans OF [ctor_inject, rel_eq_of_bnf bnf RS @{thm predicate2_eqD} RS sym];
-
- val IphiTs = map2 mk_pred2T passiveAs passiveBs;
- val Ipsi1Ts = map2 mk_pred2T passiveAs passiveCs;
- val Ipsi2Ts = map2 mk_pred2T passiveCs passiveBs;
- val activephiTs = map2 mk_pred2T activeAs activeBs;
- val activeIphiTs = map2 mk_pred2T Ts Ts';
- val (((((Iphis, Ipsi1s), Ipsi2s), activephis), activeIphis), names_lthy) = names_lthy
- |> mk_Frees "R" IphiTs
- ||>> mk_Frees "R" Ipsi1Ts
- ||>> mk_Frees "Q" Ipsi2Ts
- ||>> mk_Frees "S" activephiTs
- ||>> mk_Frees "IR" activeIphiTs;
- val rels = map2 (fn Ds => mk_rel_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs;
-
- (*register new datatypes as BNFs*)
- val (timer, Ibnfs, (ctor_Imap_o_thms, ctor_Imap_thms), ctor_Iset_thmss',
- ctor_Irel_thms, Ibnf_notes, lthy) =
- if m = 0 then
- (timer, replicate n DEADID_bnf,
- map_split (`(mk_pointfree lthy)) (map2 mk_ctor_map_DEADID_thm ctor_inject_thms map_ids),
- replicate n [], map2 mk_ctor_Irel_DEADID_thm ctor_inject_thms bnfs, [], lthy)
- else let
- val fTs = map2 (curry op -->) passiveAs passiveBs;
- val uTs = map2 (curry op -->) Ts Ts';
-
- val (((((fs, fs'), fs_copy), us), (ys, ys')),
- names_lthy) = names_lthy
- |> mk_Frees' "f" fTs
- ||>> mk_Frees "f" fTs
- ||>> mk_Frees "u" uTs
- ||>> mk_Frees' "y" passiveAs;
-
- val map_FTFT's = map2 (fn Ds =>
- mk_map_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs;
- fun mk_passive_maps ATs BTs Ts =
- map2 (fn Ds => mk_map_of_bnf Ds (ATs @ Ts) (BTs @ Ts)) Dss bnfs;
- fun mk_map_fold_arg fs Ts ctor fmap =
- HOLogic.mk_comp (ctor, Term.list_comb (fmap, fs @ map HOLogic.id_const Ts));
- fun mk_map Ts fs Ts' ctors mk_maps =
- mk_fold Ts (map2 (mk_map_fold_arg fs Ts') ctors (mk_maps Ts'));
- val pmapsABT' = mk_passive_maps passiveAs passiveBs;
- val fs_maps = map (mk_map Ts fs Ts' ctor's pmapsABT') ks;
-
- val ls = 1 upto m;
- val setsss = map (mk_setss o mk_set_Ts) passiveAs;
-
- fun mk_col l T z z' sets =
- let
- fun mk_UN set = mk_Union T $ (set $ z);
- in
- Term.absfree z'
- (mk_union (nth sets (l - 1) $ z,
- Library.foldl1 mk_union (map mk_UN (drop m sets))))
- end;
-
- val colss = map5 (fn l => fn T => map3 (mk_col l T)) ls passiveAs AFss AFss' setsss;
- val setss_by_range = map (fn cols => map (mk_fold Ts cols) ks) colss;
- val setss_by_bnf = transpose setss_by_range;
-
- val set_bss =
- map (flat o map2 (fn B => fn b =>
- if member (op =) resDs (TFree B) then [] else [b]) resBs) set_bss0;
-
- val ctor_witss =
- let
- val witss = map2 (fn Ds => fn bnf => mk_wits_of_bnf
- (replicate (nwits_of_bnf bnf) Ds)
- (replicate (nwits_of_bnf bnf) (passiveAs @ Ts)) bnf) Dss bnfs;
- fun close_wit (I, wit) = fold_rev Term.absfree (map (nth ys') I) wit;
- fun wit_apply (arg_I, arg_wit) (fun_I, fun_wit) =
- (union (op =) arg_I fun_I, fun_wit $ arg_wit);
-
- fun gen_arg support i =
- if i < m then [([i], nth ys i)]
- else maps (mk_wit support (nth ctors (i - m)) (i - m)) (nth support (i - m))
- and mk_wit support ctor i (I, wit) =
- let val args = map (gen_arg (nth_map i (remove (op =) (I, wit)) support)) I;
- in
- (args, [([], wit)])
- |-> fold (map_product wit_apply)
- |> map (apsnd (fn t => ctor $ t))
- |> minimize_wits
- end;
- in
- map3 (fn ctor => fn i => map close_wit o minimize_wits o maps (mk_wit witss ctor i))
- ctors (0 upto n - 1) witss
- end;
-
- val (Ibnf_consts, lthy) =
- fold_map8 (fn b => fn map_b => fn rel_b => fn set_bs => fn mapx => fn sets => fn wits =>
- fn T => fn lthy =>
- define_bnf_consts Dont_Inline (user_policy Note_Some lthy) (SOME deads)
- map_b rel_b set_bs
- ((((((b, T), fold_rev Term.absfree fs' mapx), sets), sum_bd), wits), NONE) lthy)
- bs map_bs rel_bs set_bss fs_maps setss_by_bnf ctor_witss Ts lthy;
-
- val (_, Iconsts, Iconst_defs, mk_Iconsts) = split_list4 Ibnf_consts;
- val (_, Isetss, Ibds_Ds, Iwitss_Ds, _) = split_list5 Iconsts;
- val (Imap_defs, Iset_defss, Ibd_defs, Iwit_defss, Irel_defs) = split_list5 Iconst_defs;
- val (mk_Imaps_Ds, mk_It_Ds, _, mk_Irels_Ds, _) = split_list5 mk_Iconsts;
-
- val Irel_unabs_defs = map (fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) Irel_defs;
- val Iset_defs = flat Iset_defss;
-
- fun mk_Imaps As Bs = map (fn mk => mk deads As Bs) mk_Imaps_Ds;
- fun mk_Isetss As = map2 (fn mk => fn Isets => map (mk deads As) Isets) mk_It_Ds Isetss;
- val Ibds = map2 (fn mk => mk deads passiveAs) mk_It_Ds Ibds_Ds;
- val Iwitss =
- map2 (fn mk => fn Iwits => map (mk deads passiveAs o snd) Iwits) mk_It_Ds Iwitss_Ds;
- fun mk_Irels As Bs = map (fn mk => mk deads As Bs) mk_Irels_Ds;
-
- val Imaps = mk_Imaps passiveAs passiveBs;
- val fs_Imaps = map (fn m => Term.list_comb (m, fs)) Imaps;
- val fs_copy_Imaps = map (fn m => Term.list_comb (m, fs_copy)) Imaps;
- val (Isetss_by_range, Isetss_by_bnf) = `transpose (mk_Isetss passiveAs);
-
- val map_setss = map (fn T => map2 (fn Ds =>
- mk_map_of_bnf Ds (passiveAs @ Ts) (mk_set_Ts T)) Dss bnfs) passiveAs;
-
- val timer = time (timer "bnf constants for the new datatypes");
-
- val (ctor_Imap_thms, ctor_Imap_o_thms) =
- let
- fun mk_goal fs_map map ctor ctor' = fold_rev Logic.all fs
- (mk_Trueprop_eq (HOLogic.mk_comp (fs_map, ctor),
- HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ fs_Imaps))));
- val goals = map4 mk_goal fs_Imaps map_FTFT's ctors ctor's;
- val maps =
- map4 (fn goal => fn foldx => fn map_comp_id => fn map_cong0 =>
- Goal.prove_sorry lthy [] [] goal
- (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN
- mk_map_tac m n foldx map_comp_id map_cong0)
- |> Thm.close_derivation)
- goals ctor_fold_thms map_comp_id_thms map_cong0s;
- in
- `(map (fn thm => thm RS @{thm comp_eq_dest})) maps
- end;
-
- val (ctor_Imap_unique_thms, ctor_Imap_unique_thm) =
- let
- fun mk_prem u map ctor ctor' =
- mk_Trueprop_eq (HOLogic.mk_comp (u, ctor),
- HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ us)));
- val prems = map4 mk_prem us map_FTFT's ctors ctor's;
- val goal =
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map2 (curry HOLogic.mk_eq) us fs_Imaps));
- val unique = Goal.prove_sorry lthy [] []
- (fold_rev Logic.all (us @ fs) (Logic.list_implies (prems, goal)))
- (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN
- mk_ctor_map_unique_tac ctor_fold_unique_thm sym_map_comps ctxt)
- |> Thm.close_derivation;
- in
- `split_conj_thm unique
- end;
-
- val timer = time (timer "map functions for the new datatypes");
-
- val ctor_Iset_thmss =
- let
- fun mk_goal sets ctor set col map =
- mk_Trueprop_eq (HOLogic.mk_comp (set, ctor),
- HOLogic.mk_comp (col, Term.list_comb (map, passive_ids @ sets)));
- val goalss =
- map3 (fn sets => map4 (mk_goal sets) ctors sets) Isetss_by_range colss map_setss;
- val setss = map (map2 (fn foldx => fn goal =>
- Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} =>
- unfold_thms_tac ctxt Iset_defs THEN mk_set_tac foldx)
- |> Thm.close_derivation)
- ctor_fold_thms) goalss;
-
- fun mk_simp_goal pas_set act_sets sets ctor z set =
- Logic.all z (mk_Trueprop_eq (set $ (ctor $ z),
- mk_union (pas_set $ z,
- Library.foldl1 mk_union (map2 (fn X => mk_UNION (X $ z)) act_sets sets))));
- val simp_goalss =
- map2 (fn i => fn sets =>
- map4 (fn Fsets => mk_simp_goal (nth Fsets (i - 1)) (drop m Fsets) sets)
- FTs_setss ctors xFs sets)
- ls Isetss_by_range;
-
- val ctor_setss = map3 (fn i => map3 (fn set_nats => fn goal => fn set =>
- Goal.prove_sorry lthy [] [] goal
- (K (mk_ctor_set_tac set (nth set_nats (i - 1)) (drop m set_nats)))
- |> Thm.close_derivation)
- set_mapss) ls simp_goalss setss;
- in
- ctor_setss
- end;
-
- fun mk_set_thms ctor_set = (@{thm xt1(3)} OF [ctor_set, @{thm Un_upper1}]) ::
- map (fn i => (@{thm xt1(3)} OF [ctor_set, @{thm Un_upper2}]) RS
- (mk_Un_upper n i RS subset_trans) RSN
- (2, @{thm UN_upper} RS subset_trans))
- (1 upto n);
- val set_Iset_thmsss = transpose (map (map mk_set_thms) ctor_Iset_thmss);
-
- val timer = time (timer "set functions for the new datatypes");
-
- val cxs = map (SOME o certify lthy) Izs;
- val Isetss_by_range' =
- map (map (Term.subst_atomic_types (passiveAs ~~ passiveBs))) Isetss_by_range;
-
- val Iset_Imap0_thmss =
- let
- fun mk_set_map0 f map z set set' =
- HOLogic.mk_eq (mk_image f $ (set $ z), set' $ (map $ z));
-
- fun mk_cphi f map z set set' = certify lthy
- (Term.absfree (dest_Free z) (mk_set_map0 f map z set set'));
-
- val csetss = map (map (certify lthy)) Isetss_by_range';
-
- val cphiss = map3 (fn f => fn sets => fn sets' =>
- (map4 (mk_cphi f) fs_Imaps Izs sets sets')) fs Isetss_by_range Isetss_by_range';
-
- val inducts = map (fn cphis =>
- Drule.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm) cphiss;
-
- val goals =
- map3 (fn f => fn sets => fn sets' =>
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map4 (mk_set_map0 f) fs_Imaps Izs sets sets')))
- fs Isetss_by_range Isetss_by_range';
-
- fun mk_tac induct = mk_set_nat_tac m (rtac induct) set_mapss ctor_Imap_thms;
- val thms =
- map5 (fn goal => fn csets => fn ctor_sets => fn induct => fn i =>
- singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] [] goal (mk_tac induct csets ctor_sets i))
- |> Thm.close_derivation)
- goals csetss ctor_Iset_thmss inducts ls;
- in
- map split_conj_thm thms
- end;
-
- val Iset_bd_thmss =
- let
- fun mk_set_bd z bd set = mk_ordLeq (mk_card_of (set $ z)) bd;
-
- fun mk_cphi z set = certify lthy (Term.absfree (dest_Free z) (mk_set_bd z sum_bd set));
-
- val cphiss = map (map2 mk_cphi Izs) Isetss_by_range;
-
- val inducts = map (fn cphis =>
- Drule.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm) cphiss;
-
- val goals =
- map (fn sets =>
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map3 mk_set_bd Izs Ibds sets))) Isetss_by_range;
-
- fun mk_tac induct = mk_set_bd_tac m (rtac induct) sum_Cinfinite set_bd_sumss;
- val thms =
- map4 (fn goal => fn ctor_sets => fn induct => fn i =>
- singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] [] goal
- (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Ibd_defs THEN
- mk_tac induct ctor_sets i ctxt))
- |> Thm.close_derivation)
- goals ctor_Iset_thmss inducts ls;
- in
- map split_conj_thm thms
- end;
-
- val Imap_cong0_thms =
- let
- fun mk_prem z set f g y y' =
- mk_Ball (set $ z) (Term.absfree y' (HOLogic.mk_eq (f $ y, g $ y)));
-
- fun mk_map_cong0 sets z fmap gmap =
- HOLogic.mk_imp
- (Library.foldr1 HOLogic.mk_conj (map5 (mk_prem z) sets fs fs_copy ys ys'),
- HOLogic.mk_eq (fmap $ z, gmap $ z));
-
- fun mk_cphi sets z fmap gmap =
- certify lthy (Term.absfree (dest_Free z) (mk_map_cong0 sets z fmap gmap));
-
- val cphis = map4 mk_cphi Isetss_by_bnf Izs fs_Imaps fs_copy_Imaps;
-
- val induct = Drule.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm;
-
- val goal =
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map4 mk_map_cong0 Isetss_by_bnf Izs fs_Imaps fs_copy_Imaps));
-
- val thm = singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] [] goal
- (mk_mcong_tac (rtac induct) set_Iset_thmsss map_cong0s ctor_Imap_thms))
- |> Thm.close_derivation;
- in
- split_conj_thm thm
- end;
-
- val in_rels = map in_rel_of_bnf bnfs;
- val in_Irels = map (fn def => trans OF [def, @{thm OO_Grp_alt}] RS @{thm predicate2_eqD})
- Irel_unabs_defs;
-
- val ctor_Iset_incl_thmss = map (map hd) set_Iset_thmsss;
- val ctor_set_Iset_incl_thmsss = map (transpose o map tl) set_Iset_thmsss;
- val ctor_Iset_thmss' = transpose ctor_Iset_thmss;
-
- val Irels = mk_Irels passiveAs passiveBs;
- val Irelphis = map (fn rel => Term.list_comb (rel, Iphis)) Irels;
- val relphis = map (fn rel => Term.list_comb (rel, Iphis @ Irelphis)) rels;
- val Irelpsi1s = map (fn rel => Term.list_comb (rel, Ipsi1s)) (mk_Irels passiveAs passiveCs);
- val Irelpsi2s = map (fn rel => Term.list_comb (rel, Ipsi2s)) (mk_Irels passiveCs passiveBs);
- val Irelpsi12s = map (fn rel =>
- Term.list_comb (rel, map2 (curry mk_rel_compp) Ipsi1s Ipsi2s)) Irels;
-
- val ctor_Irel_thms =
- let
- fun mk_goal xF yF ctor ctor' Irelphi relphi = fold_rev Logic.all (xF :: yF :: Iphis)
- (mk_Trueprop_eq (Irelphi $ (ctor $ xF) $ (ctor' $ yF), relphi $ xF $ yF));
- val goals = map6 mk_goal xFs yFs ctors ctor's Irelphis relphis;
- in
- map12 (fn i => fn goal => fn in_rel => fn map_comp0 => fn map_cong0 =>
- fn ctor_map => fn ctor_sets => fn ctor_inject => fn ctor_dtor =>
- fn set_map0s => fn ctor_set_incls => fn ctor_set_set_inclss =>
- Goal.prove_sorry lthy [] [] goal
- (K (mk_ctor_rel_tac lthy in_Irels i in_rel map_comp0 map_cong0 ctor_map ctor_sets
- ctor_inject ctor_dtor set_map0s ctor_set_incls ctor_set_set_inclss))
- |> Thm.close_derivation)
- ks goals in_rels map_comps map_cong0s ctor_Imap_thms ctor_Iset_thmss'
- ctor_inject_thms ctor_dtor_thms set_mapss ctor_Iset_incl_thmss
- ctor_set_Iset_incl_thmsss
- end;
-
- val le_Irel_OO_thm =
- let
- fun mk_le_Irel_OO Irelpsi1 Irelpsi2 Irelpsi12 Iz1 Iz2 =
- HOLogic.mk_imp (mk_rel_compp (Irelpsi1, Irelpsi2) $ Iz1 $ Iz2,
- Irelpsi12 $ Iz1 $ Iz2);
- val goals = map5 mk_le_Irel_OO Irelpsi1s Irelpsi2s Irelpsi12s Izs1 Izs2;
-
- val cTs = map (SOME o certifyT lthy o TFree) induct2_params;
- val cxs = map (SOME o certify lthy) (splice Izs1 Izs2);
- fun mk_cphi z1 z2 goal = SOME (certify lthy (Term.absfree z1 (Term.absfree z2 goal)));
- val cphis = map3 mk_cphi Izs1' Izs2' goals;
- val induct = Drule.instantiate' cTs (cphis @ cxs) ctor_induct2_thm;
-
- val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj goals);
- in
- singleton (Proof_Context.export names_lthy lthy)
- (Goal.prove_sorry lthy [] [] goal
- (mk_le_rel_OO_tac m induct ctor_nchotomy_thms ctor_Irel_thms rel_mono_strongs
- rel_OOs))
- |> Thm.close_derivation
- end;
-
- val timer = time (timer "helpers for BNF properties");
-
- val map_id0_tacs = map (K o mk_map_id0_tac map_id0s) ctor_Imap_unique_thms;
- val map_comp0_tacs =
- map2 (K oo mk_map_comp0_tac map_comps ctor_Imap_thms) ctor_Imap_unique_thms ks;
- val map_cong0_tacs = map (mk_map_cong0_tac m) Imap_cong0_thms;
- val set_map0_tacss = map (map (K o mk_set_map0_tac)) (transpose Iset_Imap0_thmss);
- val bd_co_tacs = replicate n (fn {context = ctxt, prems = _} =>
- unfold_thms_tac ctxt Ibd_defs THEN mk_bd_card_order_tac bd_card_orders);
- val bd_cinf_tacs = replicate n (fn {context = ctxt, prems = _} =>
- unfold_thms_tac ctxt Ibd_defs THEN rtac (sum_Cinfinite RS conjunct1) 1);
- val set_bd_tacss = map (map (fn thm => K (rtac thm 1))) (transpose Iset_bd_thmss);
- val le_rel_OO_tacs = map (fn i =>
- K ((rtac @{thm predicate2I} THEN' etac (le_Irel_OO_thm RS mk_conjunctN n i RS mp)) 1)) ks;
-
- val rel_OO_Grp_tacs = map (fn def => K (rtac def 1)) Irel_unabs_defs;
-
- val tacss = map9 zip_axioms map_id0_tacs map_comp0_tacs map_cong0_tacs set_map0_tacss
- bd_co_tacs bd_cinf_tacs set_bd_tacss le_rel_OO_tacs rel_OO_Grp_tacs;
-
- fun wit_tac {context = ctxt, prems = _} = unfold_thms_tac ctxt (flat Iwit_defss) THEN
- mk_wit_tac ctxt n (flat ctor_Iset_thmss) (maps wit_thms_of_bnf bnfs);
-
- val (Ibnfs, lthy) =
- fold_map5 (fn tacs => fn map_b => fn rel_b => fn set_bs => fn consts => fn lthy =>
- bnf_def Do_Inline (user_policy Note_Some) I tacs wit_tac (SOME deads)
- map_b rel_b set_bs consts lthy
- |> register_bnf (Local_Theory.full_name lthy b))
- tacss map_bs rel_bs set_bss
- ((((((bs ~~ Ts) ~~ Imaps) ~~ Isetss_by_bnf) ~~ Ibds) ~~ Iwitss) ~~ map SOME Irels)
- lthy;
-
- val timer = time (timer "registered new datatypes as BNFs");
-
- val ls' = if m = 1 then [0] else ls
-
- val Ibnf_common_notes =
- [(ctor_map_uniqueN, [ctor_Imap_unique_thm])]
- |> map (fn (thmN, thms) =>
- ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
-
- val Ibnf_notes =
- [(ctor_mapN, map single ctor_Imap_thms),
- (ctor_relN, map single ctor_Irel_thms),
- (ctor_set_inclN, ctor_Iset_incl_thmss),
- (ctor_set_set_inclN, map flat ctor_set_Iset_incl_thmsss)] @
- map2 (fn i => fn thms => (mk_ctor_setN i, map single thms)) ls' ctor_Iset_thmss
- |> maps (fn (thmN, thmss) =>
- map2 (fn b => fn thms =>
- ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
- bs thmss)
- in
- (timer, Ibnfs, (ctor_Imap_o_thms, ctor_Imap_thms), ctor_Iset_thmss',
- ctor_Irel_thms, Ibnf_common_notes @ Ibnf_notes, lthy)
- end;
-
- val ctor_fold_o_Imap_thms = mk_xtor_un_fold_o_map_thms Least_FP false m ctor_fold_unique_thm
- ctor_Imap_o_thms (map (mk_pointfree lthy) ctor_fold_thms) sym_map_comps map_cong0s;
- val ctor_rec_o_Imap_thms = mk_xtor_un_fold_o_map_thms Least_FP true m ctor_rec_unique_thm
- ctor_Imap_o_thms (map (mk_pointfree lthy) ctor_rec_thms) sym_map_comps map_cong0s;
-
- val Irels = if m = 0 then map HOLogic.eq_const Ts
- else map (mk_rel_of_bnf deads passiveAs passiveBs) Ibnfs;
- val Irel_induct_thm =
- mk_rel_xtor_co_induct_thm Least_FP rels activeIphis Irels Iphis xFs yFs ctors ctor's
- (mk_rel_induct_tac m ctor_induct2_thm ks ctor_Irel_thms rel_mono_strongs) lthy;
-
- val rels = map2 (fn Ds => mk_rel_of_bnf Ds allAs allBs') Dss bnfs;
- val ctor_fold_transfer_thms =
- mk_un_fold_transfer_thms Least_FP rels activephis Irels Iphis
- (mk_folds passiveAs activeAs) (mk_folds passiveBs activeBs)
- (mk_fold_transfer_tac m Irel_induct_thm (map map_transfer_of_bnf bnfs) ctor_fold_thms)
- lthy;
-
- val timer = time (timer "relator induction");
-
- val common_notes =
- [(ctor_inductN, [ctor_induct_thm]),
- (ctor_induct2N, [ctor_induct2_thm]),
- (rel_inductN, [Irel_induct_thm]),
- (ctor_fold_transferN, ctor_fold_transfer_thms)]
- |> map (fn (thmN, thms) =>
- ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
-
- val notes =
- [(ctor_dtorN, ctor_dtor_thms),
- (ctor_exhaustN, ctor_exhaust_thms),
- (ctor_foldN, ctor_fold_thms),
- (ctor_fold_uniqueN, ctor_fold_unique_thms),
- (ctor_rec_uniqueN, ctor_rec_unique_thms),
- (ctor_fold_o_mapN, ctor_fold_o_Imap_thms),
- (ctor_rec_o_mapN, ctor_rec_o_Imap_thms),
- (ctor_injectN, ctor_inject_thms),
- (ctor_recN, ctor_rec_thms),
- (dtor_ctorN, dtor_ctor_thms),
- (dtor_exhaustN, dtor_exhaust_thms),
- (dtor_injectN, dtor_inject_thms)]
- |> map (apsnd (map single))
- |> maps (fn (thmN, thmss) =>
- map2 (fn b => fn thms =>
- ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
- bs thmss);
-
- (*FIXME: once the package exports all the necessary high-level characteristic theorems,
- those should not only be concealed but rather not noted at all*)
- val maybe_conceal_notes = note_all = false ? map (apfst (apfst Binding.conceal));
- in
- timer;
- ({Ts = Ts, bnfs = Ibnfs, ctors = ctors, dtors = dtors, xtor_co_iterss = transpose [folds, recs],
- xtor_co_induct = ctor_induct_thm, dtor_ctors = dtor_ctor_thms, ctor_dtors = ctor_dtor_thms,
- ctor_injects = ctor_inject_thms, dtor_injects = dtor_inject_thms,
- xtor_map_thms = ctor_Imap_thms, xtor_set_thmss = ctor_Iset_thmss',
- xtor_rel_thms = ctor_Irel_thms,
- xtor_co_iter_thmss = transpose [ctor_fold_thms, ctor_rec_thms],
- xtor_co_iter_o_map_thmss = transpose [ctor_fold_o_Imap_thms, ctor_rec_o_Imap_thms],
- rel_xtor_co_induct_thm = Irel_induct_thm},
- lthy |> Local_Theory.notes (maybe_conceal_notes (common_notes @ notes @ Ibnf_notes)) |> snd)
- end;
-
-val _ =
- Outer_Syntax.local_theory @{command_spec "datatype_new"} "define new-style inductive datatypes"
- (parse_co_datatype_cmd Least_FP construct_lfp);
-
-val _ = Outer_Syntax.local_theory @{command_spec "primrec_new"}
- "define primitive recursive functions"
- (Parse.fixes -- Parse_Spec.where_alt_specs >> (snd oo uncurry add_primrec_cmd));
-
-end;