src/HOL/Codatatype/Tools/bnf_comp.ML
author traytel
Sun Sep 09 10:58:11 2012 +0200 (2012-09-09)
changeset 49228 e43910ccee74
parent 49186 4b5fa9d5e330
child 49236 632f68beff2a
permissions -rw-r--r--
open typedefs everywhere in the package
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(*  Title:      HOL/Codatatype/Tools/bnf_comp.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Composition of bounded natural functors.
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*)
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signature BNF_COMP =
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sig
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  type unfold_thms
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  val empty_unfold: unfold_thms
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  val map_unfolds_of: unfold_thms -> thm list
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  val set_unfoldss_of: unfold_thms -> thm list list
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  val rel_unfolds_of: unfold_thms -> thm list
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  val pred_unfolds_of: unfold_thms -> thm list
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  val bnf_of_typ: BNF_Def.const_policy -> binding -> (binding -> binding) ->
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    ((string * sort) list list -> (string * sort) list) -> typ -> unfold_thms * Proof.context ->
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    (BNF_Def.BNF * (typ list * typ list)) * (unfold_thms * Proof.context)
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  val default_comp_sort: (string * sort) list list -> (string * sort) list
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  val normalize_bnfs: (int -> binding -> binding) -> ''a list list -> ''a list ->
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    (''a list list -> ''a list) -> BNF_Def.BNF list -> unfold_thms -> Proof.context ->
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    (int list list * ''a list) * (BNF_Def.BNF list * (unfold_thms * Proof.context))
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  val seal_bnf: unfold_thms -> binding -> typ list -> BNF_Def.BNF -> Proof.context ->
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    (BNF_Def.BNF * typ list) * local_theory
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end;
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structure BNF_Comp : BNF_COMP =
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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_Comp_Tactics
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type unfold_thms = {
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  map_unfolds: thm list,
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  set_unfoldss: thm list list,
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  rel_unfolds: thm list,
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  pred_unfolds: thm list
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};
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fun add_to_thms thms NONE = thms
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  | add_to_thms thms (SOME new) = if Thm.is_reflexive new then thms else insert Thm.eq_thm new thms;
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fun adds_to_thms thms NONE = thms
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  | adds_to_thms thms (SOME news) = insert (eq_set Thm.eq_thm) (filter_refl news) thms;
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fun mk_unfold_thms maps setss rels preds =
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  {map_unfolds = maps, set_unfoldss = setss, rel_unfolds = rels, pred_unfolds = preds};
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val empty_unfold = mk_unfold_thms [] [] [] [];
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fun add_to_unfold_opt map_opt sets_opt rel_opt pred_opt
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  {map_unfolds = maps, set_unfoldss = setss, rel_unfolds = rels, pred_unfolds = preds} = {
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    map_unfolds = add_to_thms maps map_opt,
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    set_unfoldss = adds_to_thms setss sets_opt,
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    rel_unfolds = add_to_thms rels rel_opt,
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    pred_unfolds = add_to_thms preds pred_opt};
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fun add_to_unfold map sets rel pred =
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  add_to_unfold_opt (SOME map) (SOME sets) (SOME rel) (SOME pred);
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val map_unfolds_of = #map_unfolds;
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val set_unfoldss_of = #set_unfoldss;
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val rel_unfolds_of = #rel_unfolds;
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val pred_unfolds_of = #pred_unfolds;
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val bdTN = "bdT";
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fun mk_killN n = "kill" ^ string_of_int n ^ "_";
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fun mk_liftN n = "lift" ^ string_of_int n ^ "_";
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fun mk_permuteN src dest =
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  "permute_" ^ implode (map string_of_int src) ^ "_" ^ implode (map string_of_int dest) ^ "_";
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val no_thm = refl;
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val Collect_split_box_equals = box_equals RS @{thm Collect_split_cong};
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val abs_pred_sym = sym RS @{thm abs_pred_def};
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val abs_pred_sym_pred_abs = abs_pred_sym RS @{thm pred_def_abs};
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(*copied from Envir.expand_term_free*)
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fun expand_term_const defs =
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  let
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    val eqs = map ((fn ((x, U), u) => (x, (U, u))) o apfst dest_Const) defs;
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    val get = fn Const (x, _) => AList.lookup (op =) eqs x | _ => NONE;
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  in Envir.expand_term get end;
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fun clean_compose_bnf const_policy qualify b outer inners (unfold, lthy) =
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  let
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    val olive = live_of_bnf outer;
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    val onwits = nwits_of_bnf outer;
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    val odead = dead_of_bnf outer;
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    val inner = hd inners;
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    val ilive = live_of_bnf inner;
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    val ideads = map dead_of_bnf inners;
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    val inwitss = map nwits_of_bnf inners;
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    (* TODO: check olive = length inners > 0,
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                   forall inner from inners. ilive = live,
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                   forall inner from inners. idead = dead  *)
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    val (oDs, lthy1) = apfst (map TFree)
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      (Variable.invent_types (replicate odead HOLogic.typeS) lthy);
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    val (Dss, lthy2) = apfst (map (map TFree))
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        (fold_map Variable.invent_types (map (fn n => replicate n HOLogic.typeS) ideads) lthy1);
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    val (Ass, lthy3) = apfst (replicate ilive o map TFree)
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      (Variable.invent_types (replicate ilive HOLogic.typeS) lthy2);
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    val As = if ilive > 0 then hd Ass else [];
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    val Ass_repl = replicate olive As;
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    val (Bs, _(*lthy4*)) = apfst (map TFree)
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      (Variable.invent_types (replicate ilive HOLogic.typeS) lthy3);
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    val Bss_repl = replicate olive Bs;
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    val (((fs', Asets), xs), _(*names_lthy*)) = lthy
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      |> apfst snd o mk_Frees' "f" (map2 (curry (op -->)) As Bs)
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      ||>> mk_Frees "A" (map (HOLogic.mk_setT) As)
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      ||>> mk_Frees "x" As;
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    val CAs = map3 mk_T_of_bnf Dss Ass_repl inners;
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    val CCA = mk_T_of_bnf oDs CAs outer;
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    val CBs = map3 mk_T_of_bnf Dss Bss_repl inners;
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    val outer_sets = mk_sets_of_bnf (replicate olive oDs) (replicate olive CAs) outer;
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    val inner_setss = map3 mk_sets_of_bnf (map (replicate ilive) Dss) (replicate olive Ass) inners;
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    val inner_bds = map3 mk_bd_of_bnf Dss Ass_repl inners;
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    val outer_bd = mk_bd_of_bnf oDs CAs outer;
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    (*%f1 ... fn. outer.map (inner_1.map f1 ... fn) ... (inner_m.map f1 ... fn)*)
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    val comp_map = fold_rev Term.abs fs'
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      (Term.list_comb (mk_map_of_bnf oDs CAs CBs outer,
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        map2 (fn Ds => (fn f => Term.list_comb (f, map Bound ((ilive - 1) downto 0))) o
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          mk_map_of_bnf Ds As Bs) Dss inners));
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    (*Union o collect {outer.set_1 ... outer.set_m} o outer.map inner_1.set_i ... inner_m.set_i*)
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    (*Union o collect {image inner_1.set_i o outer.set_1 ... image inner_m.set_i o outer.set_m}*)
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    fun mk_comp_set i =
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      let
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        val (setTs, T) = `(replicate olive o HOLogic.mk_setT) (nth As i);
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        val outer_set = mk_collect
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          (mk_sets_of_bnf (replicate olive oDs) (replicate olive setTs) outer)
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          (mk_T_of_bnf oDs setTs outer --> HOLogic.mk_setT T);
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        val inner_sets = map (fn sets => nth sets i) inner_setss;
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        val outer_map = mk_map_of_bnf oDs CAs setTs outer;
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        val map_inner_sets = Term.list_comb (outer_map, inner_sets);
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        val collect_image = mk_collect
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          (map2 (fn f => fn set => HOLogic.mk_comp (mk_image f, set)) inner_sets outer_sets)
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          (CCA --> HOLogic.mk_setT T);
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      in
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        (Library.foldl1 HOLogic.mk_comp [mk_Union T, outer_set, map_inner_sets],
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        HOLogic.mk_comp (mk_Union T, collect_image))
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      end;
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    val (comp_sets, comp_sets_alt) = map_split mk_comp_set (0 upto ilive - 1);
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    (*(inner_1.bd +c ... +c inner_m.bd) *c outer.bd*)
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    val comp_bd = Term.absdummy CCA (mk_cprod
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      (Library.foldr1 (uncurry mk_csum) inner_bds) outer_bd);
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    fun comp_map_id_tac {context = ctxt, ...} =
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      let
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        (*order the theorems by reverse size to prevent bad interaction with nonconfluent rewrite
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          rules*)
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        val thms = (map map_id_of_bnf inners
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          |> map (`(Term.size_of_term o Thm.prop_of))
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          |> sort (rev_order o int_ord o pairself fst)
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          |> map snd) @ [map_id_of_bnf outer];
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      in
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        (EVERY' (map (fn thm => subst_tac ctxt [thm]) thms) THEN' rtac refl) 1
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      end;
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    fun comp_map_comp_tac _ =
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      mk_comp_map_comp_tac (map_comp_of_bnf outer) (map_cong_of_bnf outer)
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        (map map_comp_of_bnf inners);
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    fun mk_single_comp_set_natural_tac i _ =
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      mk_comp_set_natural_tac (map_comp_of_bnf outer) (map_cong_of_bnf outer)
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        (collect_set_natural_of_bnf outer)
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        (map ((fn thms => nth thms i) o set_natural_of_bnf) inners);
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    val comp_set_natural_tacs = map mk_single_comp_set_natural_tac (0 upto ilive - 1);
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    fun comp_bd_card_order_tac _ =
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      mk_comp_bd_card_order_tac (map bd_card_order_of_bnf inners) (bd_card_order_of_bnf outer);
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    fun comp_bd_cinfinite_tac _ =
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      mk_comp_bd_cinfinite_tac (bd_cinfinite_of_bnf inner) (bd_cinfinite_of_bnf outer);
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    val comp_set_alt_thms =
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      if ! quick_and_dirty then
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        replicate ilive no_thm
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      else
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        map (fn goal =>
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          Skip_Proof.prove lthy [] [] goal
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            (fn {context, ...} => (mk_comp_set_alt_tac context (collect_set_natural_of_bnf outer)))
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          |> Thm.close_derivation)
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        (map2 (curry (HOLogic.mk_Trueprop o HOLogic.mk_eq)) comp_sets comp_sets_alt);
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    fun comp_map_cong_tac _ =
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      mk_comp_map_cong_tac comp_set_alt_thms (map_cong_of_bnf outer) (map map_cong_of_bnf inners);
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    val comp_set_bd_tacs =
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      if ! quick_and_dirty then
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        replicate (length comp_set_alt_thms) (K all_tac)
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      else
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        let
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          val outer_set_bds = set_bd_of_bnf outer;
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          val inner_set_bdss = map set_bd_of_bnf inners;
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          val inner_bd_Card_orders = map bd_Card_order_of_bnf inners;
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          fun comp_single_set_bd_thm i j =
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            @{thm comp_single_set_bd} OF [nth inner_bd_Card_orders j, nth (nth inner_set_bdss j) i,
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              nth outer_set_bds j]
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          val single_set_bd_thmss =
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            map ((fn f => map f (0 upto olive - 1)) o comp_single_set_bd_thm) (0 upto ilive - 1);
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        in
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          map2 (fn comp_set_alt => fn single_set_bds => fn {context, ...} =>
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            mk_comp_set_bd_tac context comp_set_alt single_set_bds)
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          comp_set_alt_thms single_set_bd_thmss
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        end;
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    val comp_in_alt_thm =
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      let
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        val comp_in = mk_in Asets comp_sets CCA;
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        val comp_in_alt = mk_in (map2 (mk_in Asets) inner_setss CAs) outer_sets CCA;
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        val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (comp_in, comp_in_alt));
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      in
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        Skip_Proof.prove lthy [] [] goal
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          (fn {context, ...} => mk_comp_in_alt_tac context comp_set_alt_thms)
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        |> Thm.close_derivation
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      end;
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    fun comp_in_bd_tac _ =
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      mk_comp_in_bd_tac comp_in_alt_thm (map in_bd_of_bnf inners) (in_bd_of_bnf outer)
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        (map bd_Cinfinite_of_bnf inners) (bd_Card_order_of_bnf outer);
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    fun comp_map_wpull_tac _ =
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      mk_map_wpull_tac comp_in_alt_thm (map map_wpull_of_bnf inners) (map_wpull_of_bnf outer);
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    val tacs = [comp_map_id_tac, comp_map_comp_tac, comp_map_cong_tac] @ comp_set_natural_tacs @
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      [comp_bd_card_order_tac, comp_bd_cinfinite_tac] @ comp_set_bd_tacs @
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      [comp_in_bd_tac, comp_map_wpull_tac];
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    val outer_wits = mk_wits_of_bnf (replicate onwits oDs) (replicate onwits CAs) outer;
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    val inner_witss = map (map (fn (I, wit) => Term.list_comb (wit, map (nth xs) I)))
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      (map3 (fn Ds => fn n => mk_wits_of_bnf (replicate n Ds) (replicate n As))
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        Dss inwitss inners);
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    val inner_witsss = map (map (nth inner_witss) o fst) outer_wits;
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    val comp_wits = (inner_witsss, (map (single o snd) outer_wits))
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      |-> map2 (fold (map_product (fn iwit => fn owit => owit $ iwit)))
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      |> flat
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      |> map (`(fn t => Term.add_frees t []))
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      |> minimize_wits
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      |> map (fn (frees, t) => fold absfree frees t);
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    fun wit_tac {context = ctxt, ...} =
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      mk_comp_wit_tac ctxt (wit_thms_of_bnf outer) (collect_set_natural_of_bnf outer)
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        (maps wit_thms_of_bnf inners);
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    val (bnf', lthy') =
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      bnf_def const_policy (K Derive_Some_Facts) qualify tacs wit_tac (SOME (oDs @ flat Dss))
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        ((((b, comp_map), comp_sets), comp_bd), comp_wits) lthy;
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    val outer_rel_Gr = rel_Gr_of_bnf outer RS sym;
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    val outer_rel_cong = rel_cong_of_bnf outer;
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    val comp_rel_unfold_thm =
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      trans OF [rel_def_of_bnf bnf',
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        trans OF [comp_in_alt_thm RS @{thm subst_rel_def},
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          trans OF [@{thm arg_cong2[of _ _ _ _ relcomp]} OF
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            [trans OF [outer_rel_Gr RS @{thm arg_cong[of _ _ converse]},
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              rel_converse_of_bnf outer RS sym], outer_rel_Gr],
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            trans OF [rel_O_of_bnf outer RS sym, outer_rel_cong OF
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              (map (fn bnf => rel_def_of_bnf bnf RS sym) inners)]]]];
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    val comp_pred_unfold_thm = Collect_split_box_equals OF [comp_rel_unfold_thm,
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      pred_def_of_bnf bnf' RS abs_pred_sym,
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   278
        trans OF [outer_rel_cong OF (map (fn bnf => pred_def_of_bnf bnf RS abs_pred_sym) inners),
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   279
          pred_def_of_bnf outer RS abs_pred_sym]];
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   280
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   281
    val unfold' = add_to_unfold (map_def_of_bnf bnf') (set_defs_of_bnf bnf')
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   282
      comp_rel_unfold_thm comp_pred_unfold_thm unfold;
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   283
  in
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   284
    (bnf', (unfold', lthy'))
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   285
  end;
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   286
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(* Killing live variables *)
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   288
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   289
fun killN_bnf qualify n bnf (unfold, lthy) = if n = 0 then (bnf, (unfold, lthy)) else
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   290
  let
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   291
    val b = Binding.prefix_name (mk_killN n) (name_of_bnf bnf);
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   292
    val live = live_of_bnf bnf;
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   293
    val dead = dead_of_bnf bnf;
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   294
    val nwits = nwits_of_bnf bnf;
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   295
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   296
    (* TODO: check 0 < n <= live *)
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   297
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   298
    val (Ds, lthy1) = apfst (map TFree)
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   299
      (Variable.invent_types (replicate dead HOLogic.typeS) lthy);
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   300
    val ((killedAs, As), lthy2) = apfst (`(take n) o map TFree)
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   301
      (Variable.invent_types (replicate live HOLogic.typeS) lthy1);
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   302
    val (Bs, _(*lthy3*)) = apfst (append killedAs o map TFree)
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   303
      (Variable.invent_types (replicate (live - n) HOLogic.typeS) lthy2);
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   304
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   305
    val ((Asets, lives), _(*names_lthy*)) = lthy
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   306
      |> mk_Frees "A" (map (HOLogic.mk_setT) (drop n As))
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   307
      ||>> mk_Frees "x" (drop n As);
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   308
    val xs = map (fn T => HOLogic.choice_const T $ absdummy T @{term True}) killedAs @ lives;
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   309
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   310
    val T = mk_T_of_bnf Ds As bnf;
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   311
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   312
    (*bnf.map id ... id*)
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   313
    val killN_map = Term.list_comb (mk_map_of_bnf Ds As Bs bnf, map HOLogic.id_const killedAs);
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   314
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   315
    val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf;
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   316
    val killN_sets = drop n bnf_sets;
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   317
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   318
    (*(|UNIV :: A1 set| +c ... +c |UNIV :: An set|) *c bnf.bd*)
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   319
    val bnf_bd = mk_bd_of_bnf Ds As bnf;
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   320
    val killN_bd = mk_cprod
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   321
      (Library.foldr1 (uncurry mk_csum) (map (mk_card_of o HOLogic.mk_UNIV) killedAs)) bnf_bd;
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   322
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   323
    fun killN_map_id_tac _ = rtac (map_id_of_bnf bnf) 1;
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   324
    fun killN_map_comp_tac {context, ...} =
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   325
      Local_Defs.unfold_tac context ((map_comp_of_bnf bnf RS sym) :: @{thms o_assoc id_o o_id}) THEN
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   326
      rtac refl 1;
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   327
    fun killN_map_cong_tac {context, ...} =
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   328
      mk_killN_map_cong_tac context n (live - n) (map_cong_of_bnf bnf);
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   329
    val killN_set_natural_tacs =
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   330
      map (fn thm => fn _ => rtac thm 1) (drop n (set_natural_of_bnf bnf));
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   331
    fun killN_bd_card_order_tac _ = mk_killN_bd_card_order_tac n (bd_card_order_of_bnf bnf);
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   332
    fun killN_bd_cinfinite_tac _ = mk_killN_bd_cinfinite_tac (bd_Cinfinite_of_bnf bnf);
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   333
    val killN_set_bd_tacs =
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   334
      map (fn thm => fn _ => mk_killN_set_bd_tac (bd_Card_order_of_bnf bnf) thm)
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   335
        (drop n (set_bd_of_bnf bnf));
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   336
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   337
    val killN_in_alt_thm =
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   338
      let
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   339
        val killN_in = mk_in Asets killN_sets T;
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   340
        val killN_in_alt = mk_in (map HOLogic.mk_UNIV killedAs @ Asets) bnf_sets T;
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   341
        val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (killN_in, killN_in_alt));
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   342
      in
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   343
        Skip_Proof.prove lthy [] [] goal (K killN_in_alt_tac) |> Thm.close_derivation
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   344
      end;
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   345
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   346
    fun killN_in_bd_tac _ =
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   347
      mk_killN_in_bd_tac n (live > n) killN_in_alt_thm (in_bd_of_bnf bnf)
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   348
         (bd_Card_order_of_bnf bnf) (bd_Cinfinite_of_bnf bnf) (bd_Cnotzero_of_bnf bnf);
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   349
    fun killN_map_wpull_tac _ =
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   350
      mk_map_wpull_tac killN_in_alt_thm [] (map_wpull_of_bnf bnf);
blanchet@48975
   351
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   352
    val tacs = [killN_map_id_tac, killN_map_comp_tac, killN_map_cong_tac] @ killN_set_natural_tacs @
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   353
      [killN_bd_card_order_tac, killN_bd_cinfinite_tac] @ killN_set_bd_tacs @
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   354
      [killN_in_bd_tac, killN_map_wpull_tac];
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   355
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   356
    val wits = mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf;
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   357
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   358
    val killN_wits = map (fn t => fold absfree (Term.add_frees t []) t)
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   359
      (map (fn (I, wit) => Term.list_comb (wit, map (nth xs) I)) wits);
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   360
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   361
    fun wit_tac _ = mk_simple_wit_tac (wit_thms_of_bnf bnf);
blanchet@48975
   362
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   363
    val (bnf', lthy') =
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   364
      bnf_def Smart_Inline (K Derive_Some_Facts) qualify tacs wit_tac (SOME (killedAs @ Ds))
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   365
        ((((b, killN_map), killN_sets), Term.absdummy T killN_bd), killN_wits) lthy;
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   366
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   367
    val rel_Gr = rel_Gr_of_bnf bnf RS sym;
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   368
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   369
    val killN_rel_unfold_thm =
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   370
      trans OF [rel_def_of_bnf bnf',
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   371
        trans OF [killN_in_alt_thm RS @{thm subst_rel_def},
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   372
          trans OF [@{thm arg_cong2[of _ _ _ _ relcomp]} OF
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   373
            [trans OF [rel_Gr RS @{thm arg_cong[of _ _ converse]}, rel_converse_of_bnf bnf RS sym],
blanchet@48975
   374
              rel_Gr],
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   375
            trans OF [rel_O_of_bnf bnf RS sym, rel_cong_of_bnf bnf OF
blanchet@48975
   376
              (replicate n @{thm trans[OF Gr_UNIV_id[OF refl] Id_alt[symmetric]]} @
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   377
               replicate (live - n) @{thm Gr_fst_snd})]]]];
blanchet@48975
   378
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   379
    val killN_pred_unfold_thm = Collect_split_box_equals OF
blanchet@48975
   380
      [Local_Defs.unfold lthy' @{thms Id_def'} killN_rel_unfold_thm,
blanchet@48975
   381
        pred_def_of_bnf bnf' RS abs_pred_sym, pred_def_of_bnf bnf RS abs_pred_sym];
blanchet@48975
   382
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   383
    val unfold' = add_to_unfold (map_def_of_bnf bnf') (set_defs_of_bnf bnf')
blanchet@48975
   384
      killN_rel_unfold_thm killN_pred_unfold_thm unfold;
blanchet@48975
   385
  in
blanchet@48975
   386
    (bnf', (unfold', lthy'))
blanchet@48975
   387
  end;
blanchet@48975
   388
blanchet@48975
   389
(* Adding dummy live variables *)
blanchet@48975
   390
blanchet@48975
   391
fun liftN_bnf qualify n bnf (unfold, lthy) = if n = 0 then (bnf, (unfold, lthy)) else
blanchet@48975
   392
  let
blanchet@48975
   393
    val b = Binding.prefix_name (mk_liftN n) (name_of_bnf bnf);
blanchet@48975
   394
    val live = live_of_bnf bnf;
blanchet@48975
   395
    val dead = dead_of_bnf bnf;
blanchet@48975
   396
    val nwits = nwits_of_bnf bnf;
blanchet@48975
   397
blanchet@48975
   398
    (* TODO: check 0 < n *)
blanchet@48975
   399
blanchet@48975
   400
    val (Ds, lthy1) = apfst (map TFree)
blanchet@48975
   401
      (Variable.invent_types (replicate dead HOLogic.typeS) lthy);
blanchet@48975
   402
    val ((newAs, As), lthy2) = apfst (chop n o map TFree)
blanchet@48975
   403
      (Variable.invent_types (replicate (n + live) HOLogic.typeS) lthy1);
blanchet@48975
   404
    val ((newBs, Bs), _(*lthy3*)) = apfst (chop n o map TFree)
blanchet@48975
   405
      (Variable.invent_types (replicate (n + live) HOLogic.typeS) lthy2);
blanchet@48975
   406
blanchet@48975
   407
    val (Asets, _(*names_lthy*)) = lthy
blanchet@48975
   408
      |> mk_Frees "A" (map (HOLogic.mk_setT) (newAs @ As));
blanchet@48975
   409
blanchet@48975
   410
    val T = mk_T_of_bnf Ds As bnf;
blanchet@48975
   411
blanchet@48975
   412
    (*%f1 ... fn. bnf.map*)
blanchet@48975
   413
    val liftN_map =
blanchet@48975
   414
      fold_rev Term.absdummy (map2 (curry (op -->)) newAs newBs) (mk_map_of_bnf Ds As Bs bnf);
blanchet@48975
   415
blanchet@48975
   416
    val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf;
blanchet@48975
   417
    val liftN_sets = map (fn A => absdummy T (HOLogic.mk_set A [])) newAs @ bnf_sets;
blanchet@48975
   418
blanchet@48975
   419
    val liftN_bd = mk_bd_of_bnf Ds As bnf;
blanchet@48975
   420
blanchet@48975
   421
    fun liftN_map_id_tac _ = rtac (map_id_of_bnf bnf) 1;
blanchet@48975
   422
    fun liftN_map_comp_tac {context, ...} =
blanchet@48975
   423
      Local_Defs.unfold_tac context ((map_comp_of_bnf bnf RS sym) :: @{thms o_assoc id_o o_id}) THEN
blanchet@48975
   424
      rtac refl 1;
blanchet@48975
   425
    fun liftN_map_cong_tac {context, ...} =
blanchet@48975
   426
      rtac (map_cong_of_bnf bnf) 1 THEN REPEAT_DETERM_N live (Goal.assume_rule_tac context 1);
blanchet@48975
   427
    val liftN_set_natural_tacs =
blanchet@48975
   428
      if ! quick_and_dirty then
blanchet@48975
   429
        replicate (n + live) (K all_tac)
blanchet@48975
   430
      else
blanchet@48975
   431
        replicate n (K empty_natural_tac) @
blanchet@48975
   432
        map (fn thm => fn _ => rtac thm 1) (set_natural_of_bnf bnf);
blanchet@48975
   433
    fun liftN_bd_card_order_tac _ = rtac (bd_card_order_of_bnf bnf) 1;
blanchet@48975
   434
    fun liftN_bd_cinfinite_tac _ = rtac (bd_cinfinite_of_bnf bnf) 1;
blanchet@48975
   435
    val liftN_set_bd_tacs =
blanchet@48975
   436
      if ! quick_and_dirty then
blanchet@48975
   437
        replicate (n + live) (K all_tac)
blanchet@48975
   438
      else
blanchet@48975
   439
        replicate n (K (mk_liftN_set_bd_tac (bd_Card_order_of_bnf bnf))) @
blanchet@48975
   440
        (map (fn thm => fn _ => rtac thm 1) (set_bd_of_bnf bnf));
blanchet@48975
   441
blanchet@48975
   442
    val liftN_in_alt_thm =
traytel@49155
   443
      let
traytel@49155
   444
        val liftN_in = mk_in Asets liftN_sets T;
traytel@49155
   445
        val liftN_in_alt = mk_in (drop n Asets) bnf_sets T;
traytel@49155
   446
        val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (liftN_in, liftN_in_alt));
traytel@49155
   447
      in
traytel@49155
   448
        Skip_Proof.prove lthy [] [] goal (K liftN_in_alt_tac) |> Thm.close_derivation
traytel@49155
   449
      end;
blanchet@48975
   450
blanchet@48975
   451
    fun liftN_in_bd_tac _ =
blanchet@48975
   452
      mk_liftN_in_bd_tac n liftN_in_alt_thm (in_bd_of_bnf bnf) (bd_Card_order_of_bnf bnf);
blanchet@48975
   453
    fun liftN_map_wpull_tac _ =
blanchet@48975
   454
      mk_map_wpull_tac liftN_in_alt_thm [] (map_wpull_of_bnf bnf);
blanchet@48975
   455
blanchet@48975
   456
    val tacs = [liftN_map_id_tac, liftN_map_comp_tac, liftN_map_cong_tac] @ liftN_set_natural_tacs @
blanchet@48975
   457
      [liftN_bd_card_order_tac, liftN_bd_cinfinite_tac] @ liftN_set_bd_tacs @
blanchet@48975
   458
      [liftN_in_bd_tac, liftN_map_wpull_tac];
blanchet@48975
   459
blanchet@48975
   460
    val liftN_wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf);
blanchet@48975
   461
blanchet@48975
   462
    fun wit_tac _ = mk_simple_wit_tac (wit_thms_of_bnf bnf);
blanchet@48975
   463
blanchet@48975
   464
    val (bnf', lthy') =
blanchet@49018
   465
      bnf_def Smart_Inline (K Derive_Some_Facts) qualify tacs wit_tac (SOME Ds)
blanchet@48975
   466
        ((((b, liftN_map), liftN_sets), Term.absdummy T liftN_bd), liftN_wits) lthy;
blanchet@48975
   467
blanchet@48975
   468
    val liftN_rel_unfold_thm =
blanchet@48975
   469
      trans OF [rel_def_of_bnf bnf',
blanchet@48975
   470
        trans OF [liftN_in_alt_thm RS @{thm subst_rel_def}, rel_def_of_bnf bnf RS sym]];
blanchet@48975
   471
blanchet@48975
   472
    val liftN_pred_unfold_thm = Collect_split_box_equals OF [liftN_rel_unfold_thm,
blanchet@48975
   473
      pred_def_of_bnf bnf' RS abs_pred_sym, pred_def_of_bnf bnf RS abs_pred_sym];
blanchet@48975
   474
blanchet@48975
   475
    val unfold' = add_to_unfold (map_def_of_bnf bnf') (set_defs_of_bnf bnf')
blanchet@48975
   476
      liftN_rel_unfold_thm liftN_pred_unfold_thm unfold;
blanchet@48975
   477
  in
blanchet@48975
   478
    (bnf', (unfold', lthy'))
blanchet@48975
   479
  end;
blanchet@48975
   480
blanchet@48975
   481
(* Changing the order of live variables *)
blanchet@48975
   482
blanchet@48975
   483
fun permute_bnf qualify src dest bnf (unfold, lthy) = if src = dest then (bnf, (unfold, lthy)) else
blanchet@48975
   484
  let
blanchet@48975
   485
    val b = Binding.prefix_name (mk_permuteN src dest) (name_of_bnf bnf);
blanchet@48975
   486
    val live = live_of_bnf bnf;
blanchet@48975
   487
    val dead = dead_of_bnf bnf;
blanchet@48975
   488
    val nwits = nwits_of_bnf bnf;
blanchet@48975
   489
    fun permute xs = mk_permute src dest xs;
blanchet@48975
   490
    fun permute_rev xs = mk_permute dest src xs;
blanchet@48975
   491
blanchet@48975
   492
    val (Ds, lthy1) = apfst (map TFree)
blanchet@48975
   493
      (Variable.invent_types (replicate dead HOLogic.typeS) lthy);
blanchet@48975
   494
    val (As, lthy2) = apfst (map TFree)
blanchet@48975
   495
      (Variable.invent_types (replicate live HOLogic.typeS) lthy1);
blanchet@48975
   496
    val (Bs, _(*lthy3*)) = apfst (map TFree)
blanchet@48975
   497
      (Variable.invent_types (replicate live HOLogic.typeS) lthy2);
blanchet@48975
   498
blanchet@48975
   499
    val (Asets, _(*names_lthy*)) = lthy
blanchet@48975
   500
      |> mk_Frees "A" (map (HOLogic.mk_setT) (permute As));
blanchet@48975
   501
blanchet@48975
   502
    val T = mk_T_of_bnf Ds As bnf;
blanchet@48975
   503
blanchet@48975
   504
    (*%f(1) ... f(n). bnf.map f\<sigma>(1) ... f\<sigma>(n)*)
blanchet@48975
   505
    val permute_map = fold_rev Term.absdummy (permute (map2 (curry op -->) As Bs))
blanchet@48975
   506
      (Term.list_comb (mk_map_of_bnf Ds As Bs bnf,
blanchet@48975
   507
        permute_rev (map Bound ((live - 1) downto 0))));
blanchet@48975
   508
blanchet@48975
   509
    val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf;
blanchet@48975
   510
    val permute_sets = permute bnf_sets;
blanchet@48975
   511
blanchet@48975
   512
    val permute_bd = mk_bd_of_bnf Ds As bnf;
blanchet@48975
   513
blanchet@48975
   514
    fun permute_map_id_tac _ = rtac (map_id_of_bnf bnf) 1;
blanchet@48975
   515
    fun permute_map_comp_tac _ = rtac (map_comp_of_bnf bnf) 1;
blanchet@48975
   516
    fun permute_map_cong_tac {context, ...} =
blanchet@48975
   517
      rtac (map_cong_of_bnf bnf) 1 THEN REPEAT_DETERM_N live (Goal.assume_rule_tac context 1);
blanchet@48975
   518
    val permute_set_natural_tacs =
blanchet@48975
   519
      permute (map (fn thm => fn _ => rtac thm 1) (set_natural_of_bnf bnf));
blanchet@48975
   520
    fun permute_bd_card_order_tac _ = rtac (bd_card_order_of_bnf bnf) 1;
blanchet@48975
   521
    fun permute_bd_cinfinite_tac _ = rtac (bd_cinfinite_of_bnf bnf) 1;
blanchet@48975
   522
    val permute_set_bd_tacs = permute (map (fn thm => fn _ => rtac thm 1) (set_bd_of_bnf bnf));
blanchet@48975
   523
blanchet@48975
   524
    val permute_in_alt_thm =
traytel@49155
   525
      let
traytel@49155
   526
        val permute_in = mk_in Asets permute_sets T;
traytel@49155
   527
        val permute_in_alt = mk_in (permute_rev Asets) bnf_sets T;
traytel@49155
   528
        val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (permute_in, permute_in_alt));
traytel@49155
   529
      in
traytel@49155
   530
        Skip_Proof.prove lthy [] [] goal (K (mk_permute_in_alt_tac src dest))
traytel@49155
   531
        |> Thm.close_derivation
traytel@49155
   532
      end;
blanchet@48975
   533
blanchet@48975
   534
    fun permute_in_bd_tac _ =
blanchet@48975
   535
      mk_permute_in_bd_tac src dest permute_in_alt_thm (in_bd_of_bnf bnf)
blanchet@48975
   536
        (bd_Card_order_of_bnf bnf);
blanchet@48975
   537
    fun permute_map_wpull_tac _ =
blanchet@48975
   538
      mk_map_wpull_tac permute_in_alt_thm [] (map_wpull_of_bnf bnf);
blanchet@48975
   539
blanchet@48975
   540
    val tacs = [permute_map_id_tac, permute_map_comp_tac, permute_map_cong_tac] @
blanchet@48975
   541
      permute_set_natural_tacs @ [permute_bd_card_order_tac, permute_bd_cinfinite_tac] @
blanchet@48975
   542
      permute_set_bd_tacs @ [permute_in_bd_tac, permute_map_wpull_tac];
blanchet@48975
   543
blanchet@48975
   544
    val permute_wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf);
blanchet@48975
   545
blanchet@48975
   546
    fun wit_tac _ = mk_simple_wit_tac (wit_thms_of_bnf bnf);
blanchet@48975
   547
blanchet@48975
   548
    val (bnf', lthy') =
blanchet@49018
   549
      bnf_def Smart_Inline (K Derive_Some_Facts) qualify tacs wit_tac (SOME Ds)
blanchet@48975
   550
        ((((b, permute_map), permute_sets), Term.absdummy T permute_bd), permute_wits) lthy;
blanchet@48975
   551
blanchet@48975
   552
    val permute_rel_unfold_thm =
blanchet@48975
   553
      trans OF [rel_def_of_bnf bnf',
blanchet@48975
   554
        trans OF [permute_in_alt_thm RS @{thm subst_rel_def}, rel_def_of_bnf bnf RS sym]];
blanchet@48975
   555
blanchet@48975
   556
    val permute_pred_unfold_thm = Collect_split_box_equals OF [permute_rel_unfold_thm,
blanchet@48975
   557
      pred_def_of_bnf bnf' RS abs_pred_sym, pred_def_of_bnf bnf RS abs_pred_sym];
blanchet@48975
   558
blanchet@48975
   559
    val unfold' = add_to_unfold (map_def_of_bnf bnf') (set_defs_of_bnf bnf')
blanchet@48975
   560
      permute_rel_unfold_thm permute_pred_unfold_thm unfold;
blanchet@48975
   561
  in
blanchet@48975
   562
    (bnf', (unfold', lthy'))
blanchet@48975
   563
  end;
blanchet@48975
   564
blanchet@49014
   565
(* Composition pipeline *)
blanchet@49014
   566
blanchet@49014
   567
fun permute_and_kill qualify n src dest bnf =
blanchet@49014
   568
  bnf
blanchet@49014
   569
  |> permute_bnf qualify src dest
blanchet@49014
   570
  #> uncurry (killN_bnf qualify n);
blanchet@49014
   571
blanchet@49014
   572
fun lift_and_permute qualify n src dest bnf =
blanchet@49014
   573
  bnf
blanchet@49014
   574
  |> liftN_bnf qualify n
blanchet@49014
   575
  #> uncurry (permute_bnf qualify src dest);
blanchet@49014
   576
blanchet@49014
   577
fun normalize_bnfs qualify Ass Ds sort bnfs unfold lthy =
blanchet@49014
   578
  let
blanchet@49014
   579
    val before_kill_src = map (fn As => 0 upto (length As - 1)) Ass;
blanchet@49014
   580
    val kill_poss = map (find_indices Ds) Ass;
blanchet@49014
   581
    val live_poss = map2 (subtract (op =)) kill_poss before_kill_src;
blanchet@49014
   582
    val before_kill_dest = map2 append kill_poss live_poss;
blanchet@49014
   583
    val kill_ns = map length kill_poss;
blanchet@49014
   584
    val (inners', (unfold', lthy')) =
blanchet@49014
   585
      fold_map5 (fn i => permute_and_kill (qualify i))
blanchet@49014
   586
        (if length bnfs = 1 then [0] else (1 upto length bnfs))
blanchet@49014
   587
        kill_ns before_kill_src before_kill_dest bnfs (unfold, lthy);
blanchet@49014
   588
blanchet@49014
   589
    val Ass' = map2 (map o nth) Ass live_poss;
blanchet@49014
   590
    val As = sort Ass';
blanchet@49014
   591
    val after_lift_dest = replicate (length Ass') (0 upto (length As - 1));
blanchet@49014
   592
    val old_poss = map (map (fn x => find_index (fn y => x = y) As)) Ass';
blanchet@49014
   593
    val new_poss = map2 (subtract (op =)) old_poss after_lift_dest;
blanchet@49014
   594
    val after_lift_src = map2 append new_poss old_poss;
blanchet@49014
   595
    val lift_ns = map (fn xs => length As - length xs) Ass';
blanchet@49014
   596
  in
blanchet@49014
   597
    ((kill_poss, As), fold_map5 (fn i => lift_and_permute (qualify i))
blanchet@49014
   598
      (if length bnfs = 1 then [0] else (1 upto length bnfs))
blanchet@49014
   599
      lift_ns after_lift_src after_lift_dest inners' (unfold', lthy'))
blanchet@49014
   600
  end;
blanchet@49014
   601
blanchet@49014
   602
fun default_comp_sort Ass =
blanchet@49014
   603
  Library.sort (Term_Ord.typ_ord o pairself TFree) (fold (fold (insert (op =))) Ass []);
blanchet@49014
   604
blanchet@49014
   605
fun compose_bnf const_policy qualify' b sort outer inners oDs Dss tfreess (unfold, lthy) =
blanchet@49014
   606
  let
blanchet@49014
   607
    val name = Binding.name_of b;
blanchet@49014
   608
    fun qualify i bind =
blanchet@49014
   609
      let val namei = if i > 0 then name ^ string_of_int i else name;
blanchet@49014
   610
      in
blanchet@49014
   611
        if member (op =) (#2 (Binding.dest bind)) (namei, true) then qualify' bind
blanchet@49014
   612
        else qualify' (Binding.prefix_name namei bind)
blanchet@49014
   613
      end;
blanchet@49014
   614
blanchet@49121
   615
    val Ass = map (map Term.dest_TFree) tfreess;
blanchet@49014
   616
    val Ds = fold (fold Term.add_tfreesT) (oDs :: Dss) [];
blanchet@49014
   617
blanchet@49014
   618
    val ((kill_poss, As), (inners', (unfold', lthy'))) =
blanchet@49014
   619
      normalize_bnfs qualify Ass Ds sort inners unfold lthy;
blanchet@49014
   620
blanchet@49014
   621
    val Ds = oDs @ flat (map3 (append oo map o nth) tfreess kill_poss Dss);
blanchet@49014
   622
    val As = map TFree As;
blanchet@49014
   623
  in
blanchet@49014
   624
    apfst (rpair (Ds, As)) (clean_compose_bnf const_policy I b outer inners' (unfold', lthy'))
blanchet@49014
   625
  end;
blanchet@49014
   626
blanchet@48975
   627
(* Hide the type of the bound (optimization) and unfold the definitions (nicer to the user) *)
blanchet@48975
   628
blanchet@48975
   629
fun seal_bnf unfold b Ds bnf lthy =
blanchet@48975
   630
  let
blanchet@48975
   631
    val live = live_of_bnf bnf;
blanchet@48975
   632
    val nwits = nwits_of_bnf bnf;
blanchet@48975
   633
blanchet@48975
   634
    val (As, lthy1) = apfst (map TFree)
blanchet@48975
   635
      (Variable.invent_types (replicate live HOLogic.typeS) (fold Variable.declare_typ Ds lthy));
blanchet@48975
   636
    val (Bs, _) = apfst (map TFree)
blanchet@48975
   637
      (Variable.invent_types (replicate live HOLogic.typeS) lthy1);
blanchet@48975
   638
blanchet@48975
   639
    val map_unfolds = filter_refl (map_unfolds_of unfold);
blanchet@48975
   640
    val set_unfoldss = map filter_refl (set_unfoldss_of unfold);
blanchet@48975
   641
blanchet@48975
   642
    val expand_maps = fold expand_term_const (map (single o Logic.dest_equals o Thm.prop_of)
blanchet@48975
   643
      map_unfolds);
blanchet@48975
   644
    val expand_sets = fold expand_term_const (map (map (Logic.dest_equals o Thm.prop_of))
blanchet@48975
   645
      set_unfoldss);
blanchet@48975
   646
    val unfold_maps = fold (Local_Defs.unfold lthy o single) map_unfolds;
blanchet@48975
   647
    val unfold_sets = fold (Local_Defs.unfold lthy) set_unfoldss;
blanchet@48975
   648
    val unfold_defs = unfold_sets o unfold_maps;
blanchet@48975
   649
    val bnf_map = expand_maps (mk_map_of_bnf Ds As Bs bnf);
blanchet@48975
   650
    val bnf_sets = map (expand_maps o expand_sets)
blanchet@48975
   651
      (mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf);
blanchet@48975
   652
    val bnf_bd = mk_bd_of_bnf Ds As bnf;
blanchet@48975
   653
    val T = mk_T_of_bnf Ds As bnf;
blanchet@48975
   654
blanchet@48975
   655
    (*bd should only depend on dead type variables!*)
blanchet@48975
   656
    val bd_repT = fst (dest_relT (fastype_of bnf_bd));
blanchet@48975
   657
    val bdT_bind = Binding.suffix_name ("_" ^ bdTN) b;
blanchet@48975
   658
    val params = fold Term.add_tfreesT Ds [];
traytel@49185
   659
    val deads = map TFree params;
blanchet@48975
   660
traytel@49228
   661
    val ((bdT_name, (bdT_glob_info, bdT_loc_info)), lthy) =
traytel@49228
   662
      typedef false NONE (bdT_bind, params, NoSyn)
traytel@49228
   663
        (HOLogic.mk_UNIV bd_repT) NONE (EVERY' [rtac exI, rtac UNIV_I] 1) lthy;
blanchet@48975
   664
blanchet@48975
   665
    val bnf_bd' = mk_dir_image bnf_bd
traytel@49185
   666
      (Const (#Abs_name bdT_glob_info, bd_repT --> Type (bdT_name, deads)))
blanchet@48975
   667
traytel@49228
   668
    val Abs_bdT_inj = mk_Abs_inj_thm (#Abs_inject bdT_loc_info);
traytel@49228
   669
    val Abs_bdT_bij = mk_Abs_bij_thm lthy Abs_bdT_inj (#Abs_cases bdT_loc_info);
blanchet@48975
   670
blanchet@48975
   671
    val bd_ordIso = @{thm dir_image} OF [Abs_bdT_inj, bd_Card_order_of_bnf bnf];
blanchet@48975
   672
    val bd_card_order =
blanchet@48975
   673
      @{thm card_order_dir_image} OF [Abs_bdT_bij, bd_card_order_of_bnf bnf];
blanchet@48975
   674
    val bd_cinfinite =
blanchet@48975
   675
      (@{thm Cinfinite_cong} OF [bd_ordIso, bd_Cinfinite_of_bnf bnf]) RS conjunct1;
blanchet@48975
   676
blanchet@48975
   677
    val set_bds =
blanchet@48975
   678
      map (fn thm => @{thm ordLeq_ordIso_trans} OF [thm, bd_ordIso]) (set_bd_of_bnf bnf);
blanchet@48975
   679
    val in_bd =
blanchet@48975
   680
      @{thm ordLeq_ordIso_trans} OF [in_bd_of_bnf bnf,
blanchet@48975
   681
        @{thm cexp_cong2_Cnotzero} OF [bd_ordIso, if live = 0 then
blanchet@48975
   682
          @{thm ctwo_Cnotzero} else @{thm ctwo_Cnotzero} RS @{thm csum_Cnotzero2},
blanchet@48975
   683
            bd_Card_order_of_bnf bnf]];
blanchet@48975
   684
blanchet@48975
   685
    fun mk_tac thm {context = ctxt, prems = _} = (rtac (unfold_defs thm) THEN'
blanchet@48975
   686
      SOLVE o REPEAT_DETERM o (atac ORELSE' Goal.assume_rule_tac ctxt)) 1;
blanchet@48975
   687
    val tacs =
blanchet@48975
   688
      map mk_tac ([map_id_of_bnf bnf, map_comp_of_bnf bnf, map_cong_of_bnf bnf] @
blanchet@48975
   689
        set_natural_of_bnf bnf) @
blanchet@48975
   690
      map K [rtac bd_card_order 1, rtac bd_cinfinite 1] @
blanchet@48975
   691
      map mk_tac (set_bds @ [in_bd, map_wpull_of_bnf bnf]);
blanchet@48975
   692
blanchet@48975
   693
    val bnf_wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf);
blanchet@48975
   694
blanchet@48975
   695
    fun wit_tac _ = mk_simple_wit_tac (map unfold_defs (wit_thms_of_bnf bnf));
blanchet@48975
   696
traytel@49185
   697
    val (bnf', lthy') = bnf_def Hardly_Inline (K Derive_All_Facts) I tacs wit_tac (SOME deads)
traytel@49185
   698
      ((((b, bnf_map), bnf_sets), Term.absdummy T bnf_bd'), bnf_wits) lthy;
blanchet@48975
   699
blanchet@48975
   700
    val defs' = filter_refl (map_def_of_bnf bnf' :: set_defs_of_bnf bnf');
blanchet@48975
   701
    val unfold_defs' = unfold_defs o Local_Defs.unfold lthy' defs';
blanchet@48975
   702
blanchet@48975
   703
    val rel_def = unfold_defs' (rel_def_of_bnf bnf');
blanchet@48975
   704
    val rel_unfold = Local_Defs.unfold lthy'
blanchet@48975
   705
      (map unfold_defs (filter_refl (rel_unfolds_of unfold))) rel_def;
blanchet@48975
   706
blanchet@49015
   707
    val unfold_defs'' = unfold_defs' o Local_Defs.unfold lthy' (filter_refl [rel_def_of_bnf bnf']);
blanchet@48975
   708
blanchet@48975
   709
    val pred_def = unfold_defs'' (pred_def_of_bnf bnf' RS abs_pred_sym_pred_abs);
blanchet@48975
   710
    val pred_unfold = Local_Defs.unfold lthy'
blanchet@48975
   711
      (map unfold_defs (filter_refl (pred_unfolds_of unfold))) pred_def;
blanchet@48975
   712
traytel@49109
   713
    val notes =
traytel@49109
   714
      [(rel_unfoldN, [rel_unfold]),
traytel@49109
   715
      (pred_unfoldN, [pred_unfold])]
traytel@49109
   716
      |> map (fn (thmN, thms) =>
traytel@49109
   717
        ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
blanchet@48975
   718
  in
traytel@49185
   719
    ((bnf', deads), lthy' |> Local_Theory.notes notes |> snd)
blanchet@48975
   720
  end;
blanchet@48975
   721
blanchet@48975
   722
fun bnf_of_typ _ _ _ _ (T as TFree _) (unfold, lthy) =
blanchet@48975
   723
    ((Basic_BNFs.ID_bnf, ([], [T])), (add_to_unfold_opt NONE NONE
blanchet@48975
   724
      (SOME Basic_BNFs.ID_rel_def) (SOME Basic_BNFs.ID_pred_def) unfold, lthy))
blanchet@48975
   725
  | bnf_of_typ _ _ _ _ (TVar _) _ = error "Unexpected schematic variable"
blanchet@48975
   726
  | bnf_of_typ const_policy b qualify' sort (T as Type (C, Ts)) (unfold, lthy) =
traytel@49186
   727
    let
traytel@49186
   728
      val tfrees = Term.add_tfreesT T [];
traytel@49186
   729
      val bnf_opt = if null tfrees then NONE else bnf_of lthy (Long_Name.base_name C);
blanchet@48975
   730
    in
traytel@49186
   731
      (case bnf_opt of
traytel@49186
   732
        NONE => ((Basic_BNFs.DEADID_bnf, ([T], [])), (unfold, lthy))
traytel@49186
   733
      | SOME bnf =>
traytel@49186
   734
        if forall (can Term.dest_TFree) Ts andalso length Ts = length tfrees then
traytel@49186
   735
          let
traytel@49186
   736
            val T' = T_of_bnf bnf;
traytel@49186
   737
            val deads = deads_of_bnf bnf;
traytel@49186
   738
            val lives = lives_of_bnf bnf;
traytel@49186
   739
            val tvars' = Term.add_tvarsT T' [];
traytel@49186
   740
            val deads_lives =
traytel@49186
   741
              pairself (map (Term.typ_subst_TVars (map fst tvars' ~~ map TFree tfrees)))
traytel@49186
   742
                (deads, lives);
traytel@49186
   743
            val rel_def = rel_def_of_bnf bnf;
traytel@49186
   744
            val unfold' = add_to_unfold_opt NONE NONE (SOME (rel_def RS sym))
traytel@49186
   745
              (SOME (Local_Defs.unfold lthy [rel_def] (pred_def_of_bnf bnf) RS sym)) unfold;
traytel@49186
   746
          in ((bnf, deads_lives), (unfold', lthy)) end
traytel@49186
   747
        else
traytel@49186
   748
          let
traytel@49186
   749
            (* FIXME: we should allow several BNFs with the same base name *)
traytel@49186
   750
            val Tname = Long_Name.base_name C;
traytel@49186
   751
            val name = Binding.name_of b ^ "_" ^ Tname;
traytel@49186
   752
            fun qualify i bind =
traytel@49186
   753
              let val namei = if i > 0 then name ^ string_of_int i else name;
traytel@49186
   754
              in
traytel@49186
   755
                if member (op =) (#2 (Binding.dest bind)) (namei, true) then qualify' bind
traytel@49186
   756
                else qualify' (Binding.prefix_name namei bind)
traytel@49186
   757
              end;
traytel@49186
   758
            val odead = dead_of_bnf bnf;
traytel@49186
   759
            val olive = live_of_bnf bnf;
traytel@49186
   760
            val oDs_pos = find_indices [TFree ("dead", [])] (snd (Term.dest_Type
traytel@49186
   761
              (mk_T_of_bnf (replicate odead (TFree ("dead", []))) (replicate olive dummyT) bnf)));
traytel@49186
   762
            val oDs = map (nth Ts) oDs_pos;
traytel@49186
   763
            val Ts' = map (nth Ts) (subtract (op =) oDs_pos (0 upto length Ts - 1));
traytel@49186
   764
            val ((inners, (Dss, Ass)), (unfold', lthy')) =
traytel@49186
   765
              apfst (apsnd split_list o split_list)
traytel@49186
   766
                (fold_map2 (fn i =>
blanchet@48975
   767
                  bnf_of_typ Smart_Inline (Binding.name (name ^ string_of_int i)) (qualify i) sort)
traytel@49186
   768
                (if length Ts' = 1 then [0] else (1 upto length Ts')) Ts' (unfold, lthy));
traytel@49186
   769
          in
traytel@49186
   770
            compose_bnf const_policy (qualify 0) b sort bnf inners oDs Dss Ass (unfold', lthy')
traytel@49186
   771
          end)
blanchet@48975
   772
    end;
blanchet@48975
   773
blanchet@48975
   774
end;