src/HOL/BNF/Tools/bnf_comp.ML
author traytel
Thu Oct 04 17:16:55 2012 +0200 (2012-10-04)
changeset 49713 3d07ddf70f8b
parent 49669 620fa6272c48
child 49714 2c7c32f34220
permissions -rw-r--r--
do not expose details of internal data structures for composition of BNFs
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(*  Title:      HOL/BNF/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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  val ID_bnf: BNF_Def.BNF
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  val DEADID_bnf: BNF_Def.BNF
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  type unfold_set
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  val empty_unfolds: unfold_set
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  val bnf_of_typ: BNF_Def.const_policy -> (binding -> binding) ->
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    ((string * sort) list list -> (string * sort) list) -> typ -> unfold_set * Proof.context ->
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    (BNF_Def.BNF * (typ list * typ list)) * (unfold_set * 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_set -> Proof.context ->
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    (int list list * ''a list) * (BNF_Def.BNF list * (unfold_set * Proof.context))
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  val seal_bnf: unfold_set -> 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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val ID_bnf = the (bnf_of @{context} "Basic_BNFs.ID");
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val DEADID_bnf = the (bnf_of @{context} "Basic_BNFs.DEADID");
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(* TODO: Replace by "BNF_Defs.defs list" *)
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type unfold_set = {
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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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  srel_unfolds: thm list
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};
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val empty_unfolds = {map_unfolds = [], set_unfoldss = [], rel_unfolds = [], srel_unfolds = []};
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fun add_to_thms thms new = thms |> not (Thm.is_reflexive new) ? insert Thm.eq_thm new;
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fun adds_to_thms thms news = insert (eq_set Thm.eq_thm) (no_reflexive news) thms;
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fun add_to_unfolds map sets rel srel
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  {map_unfolds, set_unfoldss, rel_unfolds, srel_unfolds} =
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  {map_unfolds = add_to_thms map_unfolds map,
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    set_unfoldss = adds_to_thms set_unfoldss sets,
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    rel_unfolds = add_to_thms rel_unfolds rel,
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    srel_unfolds = add_to_thms srel_unfolds srel};
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fun add_bnf_to_unfolds bnf =
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  add_to_unfolds (map_def_of_bnf bnf) (set_defs_of_bnf bnf) (rel_def_of_bnf bnf)
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    (srel_def_of_bnf bnf);
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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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(*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_set, 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', Qs'), Asets), xs), _(*names_lthy*)) = lthy
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      |> apfst snd o mk_Frees' "f" (map2 (curry (op -->)) As Bs)
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      ||>> apfst snd o mk_Frees' "Q" (map2 mk_pred2T 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 mapx = 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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    (*%Q1 ... Qn. outer.rel (inner_1.rel Q1 ... Qn) ... (inner_m.rel Q1 ... Qn)*)
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    val rel = fold_rev Term.abs Qs'
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      (Term.list_comb (mk_rel_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_rel_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_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 (sets, sets_alt) = map_split mk_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 bd = Term.absdummy CCA (mk_cprod (Library.foldr1 (uncurry mk_csum) inner_bds) outer_bd);
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    fun map_id_tac _ =
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      mk_comp_map_id_tac (map_id_of_bnf outer) (map_cong_of_bnf outer)
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        (map map_id_of_bnf inners);
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    fun 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_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 set_natural_tacs = map mk_single_set_natural_tac (0 upto ilive - 1);
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    fun 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 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 set_alt_thms =
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      if ! quick_and_dirty then
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        []
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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)) sets sets_alt);
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    fun map_cong_tac _ =
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      mk_comp_map_cong_tac set_alt_thms (map_cong_of_bnf outer) (map map_cong_of_bnf inners);
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    val set_bd_tacs =
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      if ! quick_and_dirty then
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        replicate ilive (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 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 single_set_bd_thm) (0 upto ilive - 1);
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        in
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          map2 (fn set_alt => fn single_set_bds => fn {context, ...} =>
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            mk_comp_set_bd_tac context set_alt single_set_bds)
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          set_alt_thms single_set_bd_thmss
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        end;
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    val in_alt_thm =
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      let
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        val inx = mk_in Asets sets CCA;
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        val 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 (inx, 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 set_alt_thms)
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        |> Thm.close_derivation
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      end;
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    fun in_bd_tac _ =
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      mk_comp_in_bd_tac 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 map_wpull_tac _ =
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      mk_map_wpull_tac in_alt_thm (map map_wpull_of_bnf inners) (map_wpull_of_bnf outer);
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    fun srel_O_Gr_tac _ =
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      let
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        val basic_thms = @{thms mem_Collect_eq fst_conv snd_conv}; (*TODO: tune*)
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        val outer_srel_Gr = srel_Gr_of_bnf outer RS sym;
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        val outer_srel_cong = srel_cong_of_bnf outer;
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        val thm =
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          (trans OF [in_alt_thm RS @{thm O_Gr_cong},
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             trans OF [@{thm arg_cong2[of _ _ _ _ relcomp]} OF
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               [trans OF [outer_srel_Gr RS @{thm arg_cong[of _ _ converse]},
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                 srel_converse_of_bnf outer RS sym], outer_srel_Gr],
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               trans OF [srel_O_of_bnf outer RS sym, outer_srel_cong OF
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                 (map (fn bnf => srel_O_Gr_of_bnf bnf RS sym) inners)]]] RS sym)
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          |> unfold_thms lthy (basic_thms @ srel_def_of_bnf outer :: map srel_def_of_bnf inners);
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      in
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        unfold_thms_tac lthy basic_thms THEN rtac thm 1
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      end;
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    val tacs = zip_axioms map_id_tac map_comp_tac map_cong_tac set_natural_tacs bd_card_order_tac
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      bd_cinfinite_tac set_bd_tacs in_bd_tac map_wpull_tac srel_O_Gr_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 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 Dont_Note) qualify tacs wit_tac (SOME (oDs @ flat Dss))
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        (((((b, mapx), sets), bd), wits), SOME rel) lthy;
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  in
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    (bnf', (add_bnf_to_unfolds bnf' unfold_set, lthy'))
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  end;
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(* Killing live variables *)
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fun kill_bnf qualify n bnf (unfold_set, lthy) = if n = 0 then (bnf, (unfold_set, lthy)) else
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  let
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    val b = Binding.suffix_name (mk_killN n) (name_of_bnf bnf);
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    val live = live_of_bnf bnf;
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    val dead = dead_of_bnf bnf;
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   276
    val nwits = nwits_of_bnf bnf;
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   277
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   278
    (* TODO: check 0 < n <= live *)
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   279
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   280
    val (Ds, lthy1) = apfst (map TFree)
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   281
      (Variable.invent_types (replicate dead HOLogic.typeS) lthy);
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   282
    val ((killedAs, As), lthy2) = apfst (`(take n) o map TFree)
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   283
      (Variable.invent_types (replicate live HOLogic.typeS) lthy1);
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   284
    val (Bs, _(*lthy3*)) = apfst (append killedAs o map TFree)
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   285
      (Variable.invent_types (replicate (live - n) HOLogic.typeS) lthy2);
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   286
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   287
    val ((Asets, lives), _(*names_lthy*)) = lthy
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   288
      |> mk_Frees "A" (map HOLogic.mk_setT (drop n As))
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   289
      ||>> mk_Frees "x" (drop n As);
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   290
    val xs = map (fn T => HOLogic.choice_const T $ absdummy T @{term True}) killedAs @ lives;
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   291
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   292
    val T = mk_T_of_bnf Ds As bnf;
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   293
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   294
    (*bnf.map id ... id*)
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   295
    val mapx = Term.list_comb (mk_map_of_bnf Ds As Bs bnf, map HOLogic.id_const killedAs);
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   296
    (*bnf.rel (op =) ... (op =)*)
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   297
    val rel = Term.list_comb (mk_rel_of_bnf Ds As Bs bnf, map HOLogic.eq_const killedAs);
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   298
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   299
    val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf;
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   300
    val sets = drop n bnf_sets;
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   301
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   302
    (*(|UNIV :: A1 set| +c ... +c |UNIV :: An set|) *c bnf.bd*)
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   303
    val bnf_bd = mk_bd_of_bnf Ds As bnf;
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   304
    val bd = mk_cprod
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   305
      (Library.foldr1 (uncurry mk_csum) (map (mk_card_of o HOLogic.mk_UNIV) killedAs)) bnf_bd;
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   306
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   307
    fun map_id_tac _ = rtac (map_id_of_bnf bnf) 1;
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   308
    fun map_comp_tac {context, ...} =
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   309
      unfold_thms_tac context ((map_comp_of_bnf bnf RS sym) :: @{thms o_assoc id_o o_id}) THEN
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   310
      rtac refl 1;
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   311
    fun map_cong_tac {context, ...} =
blanchet@49304
   312
      mk_kill_map_cong_tac context n (live - n) (map_cong_of_bnf bnf);
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   313
    val set_natural_tacs = map (fn thm => fn _ => rtac thm 1) (drop n (set_natural_of_bnf bnf));
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   314
    fun bd_card_order_tac _ = mk_kill_bd_card_order_tac n (bd_card_order_of_bnf bnf);
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   315
    fun bd_cinfinite_tac _ = mk_kill_bd_cinfinite_tac (bd_Cinfinite_of_bnf bnf);
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   316
    val set_bd_tacs =
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   317
      map (fn thm => fn _ => mk_kill_set_bd_tac (bd_Card_order_of_bnf bnf) thm)
blanchet@48975
   318
        (drop n (set_bd_of_bnf bnf));
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   319
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   320
    val in_alt_thm =
traytel@49155
   321
      let
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   322
        val inx = mk_in Asets sets T;
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   323
        val in_alt = mk_in (map HOLogic.mk_UNIV killedAs @ Asets) bnf_sets T;
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   324
        val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (inx, in_alt));
traytel@49155
   325
      in
blanchet@49304
   326
        Skip_Proof.prove lthy [] [] goal (K kill_in_alt_tac) |> Thm.close_derivation
traytel@49155
   327
      end;
blanchet@48975
   328
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   329
    fun in_bd_tac _ =
blanchet@49304
   330
      mk_kill_in_bd_tac n (live > n) in_alt_thm (in_bd_of_bnf bnf) (bd_Card_order_of_bnf bnf)
blanchet@49303
   331
        (bd_Cinfinite_of_bnf bnf) (bd_Cnotzero_of_bnf bnf);
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   332
    fun map_wpull_tac _ = mk_map_wpull_tac in_alt_thm [] (map_wpull_of_bnf bnf);
blanchet@48975
   333
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   334
    fun srel_O_Gr_tac _ =
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   335
      let
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   336
        val srel_Gr = srel_Gr_of_bnf bnf RS sym
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   337
        val thm =
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   338
          (trans OF [in_alt_thm RS @{thm O_Gr_cong},
blanchet@49463
   339
            trans OF [@{thm arg_cong2[of _ _ _ _ relcomp]} OF
blanchet@49506
   340
              [trans OF [srel_Gr RS @{thm arg_cong[of _ _ converse]},
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   341
                srel_converse_of_bnf bnf RS sym], srel_Gr],
blanchet@49506
   342
              trans OF [srel_O_of_bnf bnf RS sym, srel_cong_of_bnf bnf OF
blanchet@49463
   343
                (replicate n @{thm trans[OF Gr_UNIV_id[OF refl] Id_alt[symmetric]]} @
blanchet@49463
   344
                 replicate (live - n) @{thm Gr_fst_snd})]]] RS sym)
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   345
          |> unfold_thms lthy (srel_def_of_bnf bnf :: @{thms Id_def' mem_Collect_eq split_conv});
blanchet@49456
   346
      in
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   347
        rtac thm 1
blanchet@49456
   348
      end;
blanchet@49456
   349
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   350
    val tacs = zip_axioms map_id_tac map_comp_tac map_cong_tac set_natural_tacs bd_card_order_tac
blanchet@49506
   351
      bd_cinfinite_tac set_bd_tacs in_bd_tac map_wpull_tac srel_O_Gr_tac;
blanchet@48975
   352
blanchet@49303
   353
    val bnf_wits = mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf;
blanchet@48975
   354
blanchet@49303
   355
    val wits = map (fn t => fold absfree (Term.add_frees t []) t)
blanchet@49303
   356
      (map (fn (I, wit) => Term.list_comb (wit, map (nth xs) I)) bnf_wits);
blanchet@48975
   357
blanchet@48975
   358
    fun wit_tac _ = mk_simple_wit_tac (wit_thms_of_bnf bnf);
blanchet@48975
   359
blanchet@48975
   360
    val (bnf', lthy') =
blanchet@49538
   361
      bnf_def Smart_Inline (K Dont_Note) qualify tacs wit_tac (SOME (killedAs @ Ds))
blanchet@49507
   362
        (((((b, mapx), sets), Term.absdummy T bd), wits), SOME rel) lthy;
blanchet@48975
   363
  in
blanchet@49503
   364
    (bnf', (add_bnf_to_unfolds bnf' unfold_set, lthy'))
blanchet@48975
   365
  end;
blanchet@48975
   366
blanchet@48975
   367
(* Adding dummy live variables *)
blanchet@48975
   368
blanchet@49502
   369
fun lift_bnf qualify n bnf (unfold_set, lthy) = if n = 0 then (bnf, (unfold_set, lthy)) else
blanchet@48975
   370
  let
traytel@49425
   371
    val b = Binding.suffix_name (mk_liftN n) (name_of_bnf bnf);
blanchet@48975
   372
    val live = live_of_bnf bnf;
blanchet@48975
   373
    val dead = dead_of_bnf bnf;
blanchet@48975
   374
    val nwits = nwits_of_bnf bnf;
blanchet@48975
   375
blanchet@48975
   376
    (* TODO: check 0 < n *)
blanchet@48975
   377
blanchet@48975
   378
    val (Ds, lthy1) = apfst (map TFree)
blanchet@48975
   379
      (Variable.invent_types (replicate dead HOLogic.typeS) lthy);
blanchet@48975
   380
    val ((newAs, As), lthy2) = apfst (chop n o map TFree)
blanchet@48975
   381
      (Variable.invent_types (replicate (n + live) HOLogic.typeS) lthy1);
blanchet@48975
   382
    val ((newBs, Bs), _(*lthy3*)) = apfst (chop n o map TFree)
blanchet@48975
   383
      (Variable.invent_types (replicate (n + live) HOLogic.typeS) lthy2);
blanchet@48975
   384
blanchet@48975
   385
    val (Asets, _(*names_lthy*)) = lthy
blanchet@49456
   386
      |> mk_Frees "A" (map HOLogic.mk_setT (newAs @ As));
blanchet@48975
   387
blanchet@48975
   388
    val T = mk_T_of_bnf Ds As bnf;
blanchet@48975
   389
blanchet@48975
   390
    (*%f1 ... fn. bnf.map*)
blanchet@49303
   391
    val mapx =
blanchet@48975
   392
      fold_rev Term.absdummy (map2 (curry (op -->)) newAs newBs) (mk_map_of_bnf Ds As Bs bnf);
blanchet@49507
   393
    (*%Q1 ... Qn. bnf.rel*)
blanchet@49507
   394
    val rel = fold_rev Term.absdummy (map2 mk_pred2T newAs newBs) (mk_rel_of_bnf Ds As Bs bnf);
blanchet@48975
   395
blanchet@48975
   396
    val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf;
blanchet@49303
   397
    val sets = map (fn A => absdummy T (HOLogic.mk_set A [])) newAs @ bnf_sets;
blanchet@48975
   398
blanchet@49303
   399
    val bd = mk_bd_of_bnf Ds As bnf;
blanchet@48975
   400
blanchet@49303
   401
    fun map_id_tac _ = rtac (map_id_of_bnf bnf) 1;
blanchet@49303
   402
    fun map_comp_tac {context, ...} =
blanchet@49504
   403
      unfold_thms_tac context ((map_comp_of_bnf bnf RS sym) :: @{thms o_assoc id_o o_id}) THEN
blanchet@48975
   404
      rtac refl 1;
blanchet@49303
   405
    fun map_cong_tac {context, ...} =
blanchet@48975
   406
      rtac (map_cong_of_bnf bnf) 1 THEN REPEAT_DETERM_N live (Goal.assume_rule_tac context 1);
blanchet@49303
   407
    val set_natural_tacs =
blanchet@48975
   408
      if ! quick_and_dirty then
blanchet@48975
   409
        replicate (n + live) (K all_tac)
blanchet@48975
   410
      else
blanchet@48975
   411
        replicate n (K empty_natural_tac) @
blanchet@48975
   412
        map (fn thm => fn _ => rtac thm 1) (set_natural_of_bnf bnf);
blanchet@49303
   413
    fun bd_card_order_tac _ = rtac (bd_card_order_of_bnf bnf) 1;
blanchet@49303
   414
    fun bd_cinfinite_tac _ = rtac (bd_cinfinite_of_bnf bnf) 1;
blanchet@49303
   415
    val set_bd_tacs =
blanchet@48975
   416
      if ! quick_and_dirty then
blanchet@48975
   417
        replicate (n + live) (K all_tac)
blanchet@48975
   418
      else
blanchet@49304
   419
        replicate n (K (mk_lift_set_bd_tac (bd_Card_order_of_bnf bnf))) @
blanchet@48975
   420
        (map (fn thm => fn _ => rtac thm 1) (set_bd_of_bnf bnf));
blanchet@48975
   421
blanchet@49303
   422
    val in_alt_thm =
traytel@49155
   423
      let
blanchet@49303
   424
        val inx = mk_in Asets sets T;
blanchet@49303
   425
        val in_alt = mk_in (drop n Asets) bnf_sets T;
blanchet@49303
   426
        val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (inx, in_alt));
traytel@49155
   427
      in
blanchet@49304
   428
        Skip_Proof.prove lthy [] [] goal (K lift_in_alt_tac) |> Thm.close_derivation
traytel@49155
   429
      end;
blanchet@48975
   430
blanchet@49304
   431
    fun in_bd_tac _ = mk_lift_in_bd_tac n in_alt_thm (in_bd_of_bnf bnf) (bd_Card_order_of_bnf bnf);
blanchet@49303
   432
    fun map_wpull_tac _ = mk_map_wpull_tac in_alt_thm [] (map_wpull_of_bnf bnf);
blanchet@48975
   433
blanchet@49506
   434
    fun srel_O_Gr_tac _ =
blanchet@49506
   435
      mk_simple_srel_O_Gr_tac lthy (srel_def_of_bnf bnf) (srel_O_Gr_of_bnf bnf) in_alt_thm;
blanchet@49456
   436
blanchet@49460
   437
    val tacs = zip_axioms map_id_tac map_comp_tac map_cong_tac set_natural_tacs bd_card_order_tac
blanchet@49506
   438
      bd_cinfinite_tac set_bd_tacs in_bd_tac map_wpull_tac srel_O_Gr_tac;
blanchet@48975
   439
blanchet@49303
   440
    val wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf);
blanchet@48975
   441
blanchet@48975
   442
    fun wit_tac _ = mk_simple_wit_tac (wit_thms_of_bnf bnf);
blanchet@48975
   443
blanchet@48975
   444
    val (bnf', lthy') =
blanchet@49538
   445
      bnf_def Smart_Inline (K Dont_Note) qualify tacs wit_tac (SOME Ds)
blanchet@49507
   446
        (((((b, mapx), sets), Term.absdummy T bd), wits), SOME rel) lthy;
blanchet@48975
   447
blanchet@48975
   448
  in
blanchet@49503
   449
    (bnf', (add_bnf_to_unfolds bnf' unfold_set, lthy'))
blanchet@48975
   450
  end;
blanchet@48975
   451
blanchet@48975
   452
(* Changing the order of live variables *)
blanchet@48975
   453
blanchet@49502
   454
fun permute_bnf qualify src dest bnf (unfold_set, lthy) =
blanchet@49502
   455
  if src = dest then (bnf, (unfold_set, lthy)) else
blanchet@48975
   456
  let
traytel@49425
   457
    val b = Binding.suffix_name (mk_permuteN src dest) (name_of_bnf bnf);
blanchet@48975
   458
    val live = live_of_bnf bnf;
blanchet@48975
   459
    val dead = dead_of_bnf bnf;
blanchet@48975
   460
    val nwits = nwits_of_bnf bnf;
blanchet@48975
   461
    fun permute xs = mk_permute src dest xs;
blanchet@48975
   462
    fun permute_rev xs = mk_permute dest src xs;
blanchet@48975
   463
blanchet@48975
   464
    val (Ds, lthy1) = apfst (map TFree)
blanchet@48975
   465
      (Variable.invent_types (replicate dead HOLogic.typeS) lthy);
blanchet@48975
   466
    val (As, lthy2) = apfst (map TFree)
blanchet@48975
   467
      (Variable.invent_types (replicate live HOLogic.typeS) lthy1);
blanchet@48975
   468
    val (Bs, _(*lthy3*)) = apfst (map TFree)
blanchet@48975
   469
      (Variable.invent_types (replicate live HOLogic.typeS) lthy2);
blanchet@48975
   470
blanchet@48975
   471
    val (Asets, _(*names_lthy*)) = lthy
blanchet@49456
   472
      |> mk_Frees "A" (map HOLogic.mk_setT (permute As));
blanchet@48975
   473
blanchet@48975
   474
    val T = mk_T_of_bnf Ds As bnf;
blanchet@48975
   475
blanchet@48975
   476
    (*%f(1) ... f(n). bnf.map f\<sigma>(1) ... f\<sigma>(n)*)
blanchet@49303
   477
    val mapx = fold_rev Term.absdummy (permute (map2 (curry op -->) As Bs))
blanchet@49463
   478
      (Term.list_comb (mk_map_of_bnf Ds As Bs bnf, permute_rev (map Bound (live - 1 downto 0))));
blanchet@49507
   479
    (*%Q(1) ... Q(n). bnf.rel Q\<sigma>(1) ... Q\<sigma>(n)*)
blanchet@49507
   480
    val rel = fold_rev Term.absdummy (permute (map2 mk_pred2T As Bs))
blanchet@49507
   481
      (Term.list_comb (mk_rel_of_bnf Ds As Bs bnf, permute_rev (map Bound (live - 1 downto 0))));
blanchet@48975
   482
blanchet@48975
   483
    val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf;
blanchet@49303
   484
    val sets = permute bnf_sets;
blanchet@48975
   485
blanchet@49303
   486
    val bd = mk_bd_of_bnf Ds As bnf;
blanchet@48975
   487
blanchet@49303
   488
    fun map_id_tac _ = rtac (map_id_of_bnf bnf) 1;
blanchet@49303
   489
    fun map_comp_tac _ = rtac (map_comp_of_bnf bnf) 1;
blanchet@49303
   490
    fun map_cong_tac {context, ...} =
blanchet@48975
   491
      rtac (map_cong_of_bnf bnf) 1 THEN REPEAT_DETERM_N live (Goal.assume_rule_tac context 1);
blanchet@49303
   492
    val set_natural_tacs = permute (map (fn thm => fn _ => rtac thm 1) (set_natural_of_bnf bnf));
blanchet@49303
   493
    fun bd_card_order_tac _ = rtac (bd_card_order_of_bnf bnf) 1;
blanchet@49303
   494
    fun bd_cinfinite_tac _ = rtac (bd_cinfinite_of_bnf bnf) 1;
blanchet@49303
   495
    val set_bd_tacs = permute (map (fn thm => fn _ => rtac thm 1) (set_bd_of_bnf bnf));
blanchet@48975
   496
blanchet@49303
   497
    val in_alt_thm =
traytel@49155
   498
      let
blanchet@49303
   499
        val inx = mk_in Asets sets T;
blanchet@49303
   500
        val in_alt = mk_in (permute_rev Asets) bnf_sets T;
blanchet@49303
   501
        val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (inx, in_alt));
traytel@49155
   502
      in
traytel@49155
   503
        Skip_Proof.prove lthy [] [] goal (K (mk_permute_in_alt_tac src dest))
traytel@49155
   504
        |> Thm.close_derivation
traytel@49155
   505
      end;
blanchet@48975
   506
blanchet@49303
   507
    fun in_bd_tac _ =
blanchet@49303
   508
      mk_permute_in_bd_tac src dest in_alt_thm (in_bd_of_bnf bnf) (bd_Card_order_of_bnf bnf);
blanchet@49303
   509
    fun map_wpull_tac _ = mk_map_wpull_tac in_alt_thm [] (map_wpull_of_bnf bnf);
blanchet@48975
   510
blanchet@49506
   511
    fun srel_O_Gr_tac _ =
blanchet@49506
   512
      mk_simple_srel_O_Gr_tac lthy (srel_def_of_bnf bnf) (srel_O_Gr_of_bnf bnf) in_alt_thm;
blanchet@49456
   513
blanchet@49460
   514
    val tacs = zip_axioms map_id_tac map_comp_tac map_cong_tac set_natural_tacs bd_card_order_tac
blanchet@49506
   515
      bd_cinfinite_tac set_bd_tacs in_bd_tac map_wpull_tac srel_O_Gr_tac;
blanchet@48975
   516
blanchet@49303
   517
    val wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf);
blanchet@48975
   518
blanchet@48975
   519
    fun wit_tac _ = mk_simple_wit_tac (wit_thms_of_bnf bnf);
blanchet@48975
   520
blanchet@48975
   521
    val (bnf', lthy') =
blanchet@49538
   522
      bnf_def Smart_Inline (K Dont_Note) qualify tacs wit_tac (SOME Ds)
blanchet@49507
   523
        (((((b, mapx), sets), Term.absdummy T bd), wits), SOME rel) lthy;
blanchet@48975
   524
  in
blanchet@49503
   525
    (bnf', (add_bnf_to_unfolds bnf' unfold_set, lthy'))
blanchet@48975
   526
  end;
blanchet@48975
   527
blanchet@49014
   528
(* Composition pipeline *)
blanchet@49014
   529
blanchet@49014
   530
fun permute_and_kill qualify n src dest bnf =
blanchet@49014
   531
  bnf
blanchet@49014
   532
  |> permute_bnf qualify src dest
blanchet@49304
   533
  #> uncurry (kill_bnf qualify n);
blanchet@49014
   534
blanchet@49014
   535
fun lift_and_permute qualify n src dest bnf =
blanchet@49014
   536
  bnf
blanchet@49304
   537
  |> lift_bnf qualify n
blanchet@49014
   538
  #> uncurry (permute_bnf qualify src dest);
blanchet@49014
   539
blanchet@49502
   540
fun normalize_bnfs qualify Ass Ds sort bnfs unfold_set lthy =
blanchet@49014
   541
  let
blanchet@49014
   542
    val before_kill_src = map (fn As => 0 upto (length As - 1)) Ass;
blanchet@49014
   543
    val kill_poss = map (find_indices Ds) Ass;
blanchet@49014
   544
    val live_poss = map2 (subtract (op =)) kill_poss before_kill_src;
blanchet@49014
   545
    val before_kill_dest = map2 append kill_poss live_poss;
blanchet@49014
   546
    val kill_ns = map length kill_poss;
blanchet@49502
   547
    val (inners', (unfold_set', lthy')) =
blanchet@49014
   548
      fold_map5 (fn i => permute_and_kill (qualify i))
blanchet@49014
   549
        (if length bnfs = 1 then [0] else (1 upto length bnfs))
blanchet@49502
   550
        kill_ns before_kill_src before_kill_dest bnfs (unfold_set, lthy);
blanchet@49014
   551
blanchet@49014
   552
    val Ass' = map2 (map o nth) Ass live_poss;
blanchet@49014
   553
    val As = sort Ass';
blanchet@49014
   554
    val after_lift_dest = replicate (length Ass') (0 upto (length As - 1));
blanchet@49014
   555
    val old_poss = map (map (fn x => find_index (fn y => x = y) As)) Ass';
blanchet@49014
   556
    val new_poss = map2 (subtract (op =)) old_poss after_lift_dest;
blanchet@49014
   557
    val after_lift_src = map2 append new_poss old_poss;
blanchet@49014
   558
    val lift_ns = map (fn xs => length As - length xs) Ass';
blanchet@49014
   559
  in
blanchet@49014
   560
    ((kill_poss, As), fold_map5 (fn i => lift_and_permute (qualify i))
blanchet@49014
   561
      (if length bnfs = 1 then [0] else (1 upto length bnfs))
blanchet@49502
   562
      lift_ns after_lift_src after_lift_dest inners' (unfold_set', lthy'))
blanchet@49014
   563
  end;
blanchet@49014
   564
blanchet@49014
   565
fun default_comp_sort Ass =
blanchet@49014
   566
  Library.sort (Term_Ord.typ_ord o pairself TFree) (fold (fold (insert (op =))) Ass []);
blanchet@49014
   567
blanchet@49502
   568
fun compose_bnf const_policy qualify sort outer inners oDs Dss tfreess (unfold_set, lthy) =
blanchet@49014
   569
  let
traytel@49425
   570
    val b = name_of_bnf outer;
blanchet@49014
   571
blanchet@49121
   572
    val Ass = map (map Term.dest_TFree) tfreess;
blanchet@49014
   573
    val Ds = fold (fold Term.add_tfreesT) (oDs :: Dss) [];
blanchet@49014
   574
blanchet@49502
   575
    val ((kill_poss, As), (inners', (unfold_set', lthy'))) =
blanchet@49502
   576
      normalize_bnfs qualify Ass Ds sort inners unfold_set lthy;
blanchet@49014
   577
blanchet@49014
   578
    val Ds = oDs @ flat (map3 (append oo map o nth) tfreess kill_poss Dss);
blanchet@49014
   579
    val As = map TFree As;
blanchet@49014
   580
  in
traytel@49425
   581
    apfst (rpair (Ds, As))
blanchet@49502
   582
      (clean_compose_bnf const_policy (qualify 0) b outer inners' (unfold_set', lthy'))
blanchet@49014
   583
  end;
blanchet@49014
   584
blanchet@48975
   585
(* Hide the type of the bound (optimization) and unfold the definitions (nicer to the user) *)
blanchet@48975
   586
blanchet@49502
   587
fun seal_bnf unfold_set b Ds bnf lthy =
blanchet@48975
   588
  let
blanchet@48975
   589
    val live = live_of_bnf bnf;
blanchet@48975
   590
    val nwits = nwits_of_bnf bnf;
blanchet@48975
   591
blanchet@48975
   592
    val (As, lthy1) = apfst (map TFree)
blanchet@48975
   593
      (Variable.invent_types (replicate live HOLogic.typeS) (fold Variable.declare_typ Ds lthy));
blanchet@48975
   594
    val (Bs, _) = apfst (map TFree)
blanchet@48975
   595
      (Variable.invent_types (replicate live HOLogic.typeS) lthy1);
blanchet@48975
   596
traytel@49713
   597
    val map_unfolds = #map_unfolds unfold_set;
traytel@49713
   598
    val set_unfoldss = #set_unfoldss unfold_set;
traytel@49713
   599
    val rel_unfolds = #rel_unfolds unfold_set;
traytel@49713
   600
    val srel_unfolds = #srel_unfolds unfold_set;
blanchet@48975
   601
blanchet@49507
   602
    val expand_maps =
blanchet@49507
   603
      fold expand_term_const (map (single o Logic.dest_equals o Thm.prop_of) map_unfolds);
blanchet@49507
   604
    val expand_sets =
blanchet@49507
   605
      fold expand_term_const (map (map (Logic.dest_equals o Thm.prop_of)) set_unfoldss);
blanchet@49507
   606
    val expand_rels =
blanchet@49507
   607
      fold expand_term_const (map (single o Logic.dest_equals o Thm.prop_of) rel_unfolds);
blanchet@49504
   608
    val unfold_maps = fold (unfold_thms lthy o single) map_unfolds;
blanchet@49504
   609
    val unfold_sets = fold (unfold_thms lthy) set_unfoldss;
blanchet@49507
   610
    val unfold_rels = unfold_thms lthy rel_unfolds;
blanchet@49506
   611
    val unfold_srels = unfold_thms lthy srel_unfolds;
blanchet@49507
   612
    val unfold_all = unfold_sets o unfold_maps o unfold_rels o unfold_srels;
blanchet@48975
   613
    val bnf_map = expand_maps (mk_map_of_bnf Ds As Bs bnf);
blanchet@48975
   614
    val bnf_sets = map (expand_maps o expand_sets)
blanchet@48975
   615
      (mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf);
blanchet@48975
   616
    val bnf_bd = mk_bd_of_bnf Ds As bnf;
blanchet@49507
   617
    val bnf_rel = expand_rels (mk_rel_of_bnf Ds As Bs bnf);
blanchet@48975
   618
    val T = mk_T_of_bnf Ds As bnf;
blanchet@48975
   619
blanchet@48975
   620
    (*bd should only depend on dead type variables!*)
blanchet@48975
   621
    val bd_repT = fst (dest_relT (fastype_of bnf_bd));
blanchet@48975
   622
    val bdT_bind = Binding.suffix_name ("_" ^ bdTN) b;
blanchet@48975
   623
    val params = fold Term.add_tfreesT Ds [];
traytel@49185
   624
    val deads = map TFree params;
blanchet@48975
   625
traytel@49228
   626
    val ((bdT_name, (bdT_glob_info, bdT_loc_info)), lthy) =
traytel@49228
   627
      typedef false NONE (bdT_bind, params, NoSyn)
traytel@49228
   628
        (HOLogic.mk_UNIV bd_repT) NONE (EVERY' [rtac exI, rtac UNIV_I] 1) lthy;
blanchet@48975
   629
blanchet@48975
   630
    val bnf_bd' = mk_dir_image bnf_bd
traytel@49185
   631
      (Const (#Abs_name bdT_glob_info, bd_repT --> Type (bdT_name, deads)))
blanchet@48975
   632
traytel@49228
   633
    val Abs_bdT_inj = mk_Abs_inj_thm (#Abs_inject bdT_loc_info);
traytel@49228
   634
    val Abs_bdT_bij = mk_Abs_bij_thm lthy Abs_bdT_inj (#Abs_cases bdT_loc_info);
blanchet@48975
   635
blanchet@48975
   636
    val bd_ordIso = @{thm dir_image} OF [Abs_bdT_inj, bd_Card_order_of_bnf bnf];
blanchet@48975
   637
    val bd_card_order =
blanchet@48975
   638
      @{thm card_order_dir_image} OF [Abs_bdT_bij, bd_card_order_of_bnf bnf];
blanchet@48975
   639
    val bd_cinfinite =
blanchet@48975
   640
      (@{thm Cinfinite_cong} OF [bd_ordIso, bd_Cinfinite_of_bnf bnf]) RS conjunct1;
blanchet@48975
   641
blanchet@48975
   642
    val set_bds =
blanchet@48975
   643
      map (fn thm => @{thm ordLeq_ordIso_trans} OF [thm, bd_ordIso]) (set_bd_of_bnf bnf);
blanchet@48975
   644
    val in_bd =
blanchet@48975
   645
      @{thm ordLeq_ordIso_trans} OF [in_bd_of_bnf bnf,
blanchet@48975
   646
        @{thm cexp_cong2_Cnotzero} OF [bd_ordIso, if live = 0 then
blanchet@48975
   647
          @{thm ctwo_Cnotzero} else @{thm ctwo_Cnotzero} RS @{thm csum_Cnotzero2},
blanchet@48975
   648
            bd_Card_order_of_bnf bnf]];
blanchet@48975
   649
blanchet@49463
   650
    fun mk_tac thm {context = ctxt, prems = _} =
blanchet@49463
   651
      (rtac (unfold_all thm) THEN'
blanchet@48975
   652
      SOLVE o REPEAT_DETERM o (atac ORELSE' Goal.assume_rule_tac ctxt)) 1;
blanchet@49456
   653
blanchet@49460
   654
    val tacs = zip_axioms (mk_tac (map_id_of_bnf bnf)) (mk_tac (map_comp_of_bnf bnf))
blanchet@49456
   655
      (mk_tac (map_cong_of_bnf bnf)) (map mk_tac (set_natural_of_bnf bnf))
blanchet@49456
   656
      (K (rtac bd_card_order 1)) (K (rtac bd_cinfinite 1)) (map mk_tac set_bds) (mk_tac in_bd)
blanchet@49463
   657
      (mk_tac (map_wpull_of_bnf bnf))
blanchet@49506
   658
      (mk_tac (unfold_thms lthy [srel_def_of_bnf bnf] (srel_O_Gr_of_bnf bnf)));
blanchet@48975
   659
blanchet@48975
   660
    val bnf_wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf);
blanchet@48975
   661
blanchet@49463
   662
    fun wit_tac _ = mk_simple_wit_tac (map unfold_all (wit_thms_of_bnf bnf));
blanchet@48975
   663
blanchet@49538
   664
    val (bnf', lthy') = bnf_def Hardly_Inline (user_policy Dont_Note) I tacs wit_tac (SOME deads)
blanchet@49507
   665
      (((((b, bnf_map), bnf_sets), Term.absdummy T bnf_bd'), bnf_wits), SOME bnf_rel) lthy;
blanchet@48975
   666
  in
blanchet@49456
   667
    ((bnf', deads), lthy')
blanchet@48975
   668
  end;
blanchet@48975
   669
blanchet@49456
   670
fun bnf_of_typ _ _ _ (T as TFree _) accum = ((ID_bnf, ([], [T])), accum)
traytel@49425
   671
  | bnf_of_typ _ _ _ (TVar _) _ = error "Unexpected schematic variable"
blanchet@49502
   672
  | bnf_of_typ const_policy qualify' sort (T as Type (C, Ts)) (unfold_set, lthy) =
traytel@49186
   673
    let
traytel@49186
   674
      val tfrees = Term.add_tfreesT T [];
traytel@49236
   675
      val bnf_opt = if null tfrees then NONE else bnf_of lthy C;
blanchet@48975
   676
    in
traytel@49186
   677
      (case bnf_opt of
blanchet@49502
   678
        NONE => ((DEADID_bnf, ([T], [])), (unfold_set, lthy))
traytel@49186
   679
      | SOME bnf =>
traytel@49186
   680
        if forall (can Term.dest_TFree) Ts andalso length Ts = length tfrees then
traytel@49186
   681
          let
traytel@49186
   682
            val T' = T_of_bnf bnf;
traytel@49186
   683
            val deads = deads_of_bnf bnf;
traytel@49186
   684
            val lives = lives_of_bnf bnf;
traytel@49186
   685
            val tvars' = Term.add_tvarsT T' [];
traytel@49186
   686
            val deads_lives =
traytel@49186
   687
              pairself (map (Term.typ_subst_TVars (map fst tvars' ~~ map TFree tfrees)))
traytel@49186
   688
                (deads, lives);
blanchet@49502
   689
          in ((bnf, deads_lives), (unfold_set, lthy)) end
traytel@49186
   690
        else
traytel@49186
   691
          let
traytel@49425
   692
            val name = Long_Name.base_name C;
traytel@49425
   693
            fun qualify i =
traytel@49425
   694
              let val namei = name ^ nonzero_string_of_int i;
traytel@49425
   695
              in qualify' o Binding.qualify true namei end;
traytel@49186
   696
            val odead = dead_of_bnf bnf;
traytel@49186
   697
            val olive = live_of_bnf bnf;
traytel@49186
   698
            val oDs_pos = find_indices [TFree ("dead", [])] (snd (Term.dest_Type
traytel@49186
   699
              (mk_T_of_bnf (replicate odead (TFree ("dead", []))) (replicate olive dummyT) bnf)));
traytel@49186
   700
            val oDs = map (nth Ts) oDs_pos;
traytel@49186
   701
            val Ts' = map (nth Ts) (subtract (op =) oDs_pos (0 upto length Ts - 1));
blanchet@49502
   702
            val ((inners, (Dss, Ass)), (unfold_set', lthy')) =
traytel@49186
   703
              apfst (apsnd split_list o split_list)
traytel@49425
   704
                (fold_map2 (fn i => bnf_of_typ Smart_Inline (qualify i) sort)
blanchet@49502
   705
                (if length Ts' = 1 then [0] else (1 upto length Ts')) Ts' (unfold_set, lthy));
traytel@49186
   706
          in
blanchet@49502
   707
            compose_bnf const_policy qualify sort bnf inners oDs Dss Ass (unfold_set', lthy')
traytel@49186
   708
          end)
blanchet@48975
   709
    end;
blanchet@48975
   710
blanchet@48975
   711
end;