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(* Title: HOL/Tools/BNF/bnf_comp.ML
Author: Dmitriy Traytel, TU Muenchen Author: Jasmin Blanchette, TU Muenchen Copyright 2012 Composition of bounded natural functors. *) signature BNF_COMP = sig val typedef_threshold: int Config.T val with_typedef_threshold: int -> (Proof.context -> Proof.context) -> Proof.context -> Proof.context val with_typedef_threshold_yield: int -> (Proof.context -> 'a * Proof.context) -> Proof. 'a * Proof.context val ID_bnf: BNF_Def.bnf val DEADID_bnf: BNF_Def.bnf type comp_cache type unfold_set = {map_unfolds: thm list, set_unfoldss: thm list list, rel_unfolds: thm list, pred_unfolds: thm list} val empty_comp_cache: comp_cache val empty_unfolds: unfold_set exception BAD_DEAD of typ * typ val bnf_of_typ: bool -> BNF_Def.inline_policy -> (binding -> binding) -> ((string * sort) list list -> (string * sort) list) -> (string * sort) list -> (string * sort) list -> typ -> (comp_cache * unfold_set) * local_theory -> (BNF_Def.bnf * (typ list * typ list)) * ((comp_cache * unfold_set) * local_theory) val default_comp_sort: (string * sort) list list -> (string * sort) list val clean_compose_bnf: BNF_Def.inline_policy -> (binding -> binding) -> binding -> BNF_Def.bnf BNF_Def.bnf list -> unfold_set * local_theory -> BNF_Def.bnf * (unfold_set * local_theory) val kill_bnf: (binding -> binding) -> int -> BNF_Def.bnf -> (comp_cache * unfold_set) * local_theory -> BNF_Def.bnf * ((comp_cache * unfold_set) * local_theory) val lift_bnf: (binding -> binding) -> int -> BNF_Def.bnf -> (comp_cache * unfold_set) * local_theory -> BNF_Def.bnf * ((comp_cache * unfold_set) * local_theory) val permute_bnf: (binding -> binding) -> int list -> int list -> BNF_Def.bnf -> (comp_cache * unfold_set) * local_theory -> BNF_Def.bnf * ((comp_cache * unfold_set) * local_theory) val permute_and_kill_bnf: (binding -> binding) -> int -> int list -> int list -> BNF_Def.bnf -> (comp_cache * unfold_set) * local_theory -> BNF_Def.bnf * ((comp_cache * unfold_set) * local_theory) val lift_and_permute_bnf: (binding -> binding) -> int -> int list -> int list -> BNF_Def.bnf -> (comp_cache * unfold_set) * local_theory -> BNF_Def.bnf * ((comp_cache * unfold_set) * local_theory) val normalize_bnfs: (int -> binding -> binding) -> ''a list list -> ''a list -> (''a list list -> ''a list) -> BNF_Def.bnf list -> (comp_cache * unfold_set) * local_theory -> (int list list * ''a list) * (BNF_Def.bnf list * ((comp_cache * unfold_set) * local_theory)) val compose_bnf: BNF_Def.inline_policy -> (int -> binding -> binding) -> ((string * sort) list list -> (string * sort) list) -> BNF_Def.bnf -> BNF_Def.bnf list -> typ list -> typ list list -> typ list list -> (comp_cache * unfold_set) * local_theory -> (BNF_Def.bnf * (typ list * typ list)) * ((comp_cache * unfold_set) * local_theory) type absT_info = {absT: typ, repT: typ, abs: term, rep: term, abs_inject: thm, abs_inverse: thm, type_definition: thm} val morph_absT_info: morphism -> absT_info -> absT_info val mk_absT: theory -> typ -> typ -> typ -> typ val mk_repT: typ -> typ -> typ -> typ val mk_abs: typ -> term -> term val mk_rep: typ -> term -> term val seal_bnf: (binding -> binding) -> unfold_set -> binding -> bool -> typ list -> typ list -> BNF_Def.bnf -> local_theory -> (BNF_Def.bnf * (typ list * absT_info)) * local_theory end; structure BNF_Comp : BNF_COMP = struct open BNF_Def open BNF_Util open BNF_Tactics open BNF_Comp_Tactics val typedef_threshold = Attrib.setup_config_int \<^binding>\<open>bnf_typedef_threshold\< fun with_typedef_threshold threshold f lthy = lthy |> Config.put typedef_threshold threshold |> f |> Config.put typedef_threshold (Config.get lthy typedef_threshold); fun with_typedef_threshold_yield threshold f lthy = lthy |> Config.put typedef_threshold threshold |> f ||> Config.put typedef_threshold (Config.get lthy typedef_threshold); val ID_bnf = the (bnf_of \<^context> "BNF_Composition.ID"); val DEADID_bnf = the (bnf_of \<^context> "BNF_Composition.DEADID"); type comp_cache = (bnf * (typ list * typ list)) Typtab.table; fun key_of_types s Ts = Type (s, Ts); fun key_of_typess s = key_of_types s o map (key_of_types ""); fun typ_of_int n = Type (string_of_int n, []); fun typ_of_bnf bnf = key_of_typess "" [[T_of_bnf bnf], lives_of_bnf bnf, sort Term_Ord.typ_ord (deads_of_bnf b fun key_of_kill n bnf = key_of_types "k" [typ_of_int n, typ_of_bnf bnf]; fun key_of_lift n bnf = key_of_types "l" [typ_of_int n, typ_of_bnf bnf]; fun key_of_permute src dest bnf = key_of_types "p" (map typ_of_int src @ map typ_of_int dest @ [typ_of_bnf bnf]); fun key_of_compose oDs Dss Ass outer inners = key_of_types "c" (map (key_of_typess "") [[oDs], Dss, Ass, [map typ_of_bnf (outer :: inners) fun cache_comp_simple key cache (bnf, (unfold_set, lthy)) = (bnf, ((Typtab.update (key, (bnf, ([], []))) cache, unfold_set), lthy)); fun cache_comp key (bnf_Ds_As, ((cache, unfold_set), lthy)) = (bnf_Ds_As, ((Typtab.update (key, bnf_Ds_As) cache, unfold_set), lthy)); type unfold_set = { map_unfolds: thm list, set_unfoldss: thm list list, rel_unfolds: thm list, pred_unfolds: thm list }; val empty_comp_cache = Typtab.empty; val empty_unfolds = {map_unfolds = [], set_unfoldss = [], rel_unfolds = [], pred_unfolds = []} fun add_to_thms thms new = thms |> not (Thm.is_reflexive new) ? insert Thm.eq_thm new; fun adds_to_thms thms news = insert (eq_set Thm.eq_thm) (no_reflexive news) thms; fun add_to_unfolds map sets rel pred {map_unfolds, set_unfoldss, rel_unfolds, pred_unfolds} = {map_unfolds = add_to_thms map_unfolds map, set_unfoldss = adds_to_thms set_unfoldss sets, rel_unfolds = add_to_thms rel_unfolds rel, pred_unfolds = add_to_thms pred_unfolds pred}; fun add_bnf_to_unfolds bnf = add_to_unfolds (map_def_of_bnf bnf) (set_defs_of_bnf bnf) (rel_def_of_bnf bnf) (pred_de val bdTN = "bdT"; fun mk_killN n = "_kill" ^ string_of_int n; fun mk_liftN n = "_lift" ^ string_of_int n; fun mk_permuteN src dest = "_permute_" ^ implode (map string_of_int src) ^ "_" ^ implode (map string_of_int dest); (*copied from Envir.expand_term_free*) fun expand_term_const defs = let val eqs = map ((fn ((x, U), u) => (x, (U, u))) o apfst dest_Const) defs; val get = fn Const (x, _) => AList.lookup (op =) eqs x | _ => NONE; in Envir.expand_term get end; val id_bnf_def = @{thm id_bnf_def}; val expand_id_bnf_def = expand_term_const [Thm.prop_of id_bnf_def |> Logic.dest_equals]; fun is_sum_prod_natLeq (Const (\<^const_name>\<open>csum\<close>, _) $ t $ u) = forall is_sum_pro | is_sum_prod_natLeq (Const (\<^const_name>\<open>cprod\<close>, _) $ t $ u) = forall is_sum_prod | is_sum_prod_natLeq t = t aconv \<^term>\<open>natLeq\<close>; fun clean_compose_bnf const_policy qualify b outer inners (unfold_set, lthy) = let val olive = live_of_bnf outer; val onwits = nwits_of_bnf outer; val odeads = deads_of_bnf outer; val inner = hd inners; val ilive = live_of_bnf inner; val ideadss = map deads_of_bnf inners; val inwitss = map nwits_of_bnf inners; (* TODO: check olive = length inners > 0, forall inner from inners. ilive = live, forall inner from inners. idead = dead *) val (oDs, lthy1) = apfst (map TFree) (Variable.invent_types (map Type.sort_of_atyp odeads) lthy); val (Dss, lthy2) = apfst (map (map TFree)) (fold_map Variable.invent_types (map (map Type.sort_of_atyp) ideadss) lthy1); val (Ass, lthy3) = apfst (replicate ilive o map TFree) (Variable.invent_types (replicate ilive \<^sort>\<open>type\<close>) lthy2); val As = if ilive > 0 then hd Ass else []; val Ass_repl = replicate olive As; val (Bs, names_lthy) = apfst (map TFree) (Variable.invent_types (replicate ilive \<^sort>\<open>type\<close>) lthy3); val Bss_repl = replicate olive Bs; val (((((fs', Qs'), Ps'), Asets), xs), _) = names_lthy |> apfst snd o mk_Frees' "f" (map2 (curry op -->) As Bs) ||>> apfst snd o mk_Frees' "Q" (map2 mk_pred2T As Bs) ||>> apfst snd o mk_Frees' "P" (map mk_pred1T As) ||>> mk_Frees "A" (map HOLogic.mk_setT As) ||>> mk_Frees "x" As; val CAs = @{map 3} mk_T_of_bnf Dss Ass_repl inners; val CCA = mk_T_of_bnf oDs CAs outer; val CBs = @{map 3} mk_T_of_bnf Dss Bss_repl inners; val outer_sets = mk_sets_of_bnf (replicate olive oDs) (replicate olive CAs) outer; val inner_setss = @{map 3} mk_sets_of_bnf (map (replicate ilive) Dss) (replicate olive Ass) inners; val inner_bds = @{map 3} mk_bd_of_bnf Dss Ass_repl inners; val outer_bd = mk_bd_of_bnf oDs CAs outer; (*%f1 ... fn. outer.map (inner_1.map f1 ... fn) ... (inner_m.map f1 ... fn)*) val mapx = fold_rev Term.abs fs' (Term.list_comb (mk_map_of_bnf oDs CAs CBs outer, map2 (fn Ds => (fn f => Term.list_comb (f, map Bound (ilive - 1 downto 0))) o mk_map_of_bnf Ds As Bs) Dss inners)); (*%Q1 ... Qn. outer.rel (inner_1.rel Q1 ... Qn) ... (inner_m.rel Q1 ... Qn)*) val rel = fold_rev Term.abs Qs' (Term.list_comb (mk_rel_of_bnf oDs CAs CBs outer, map2 (fn Ds => (fn f => Term.list_comb (f, map Bound (ilive - 1 downto 0))) o mk_rel_of_bnf Ds As Bs) Dss inners)); (*%P1 ... Pn. outer.pred (inner_1.pred P1 ... Pn) ... (inner_m.pred P1 ... Pn)*) val pred = fold_rev Term.abs Ps' (Term.list_comb (mk_pred_of_bnf oDs CAs outer, map2 (fn Ds => (fn f => Term.list_comb (f, map Bound (ilive - 1 downto 0))) o mk_pred_of_bnf Ds As) Dss inners)); (*Union o collect {outer.set_1 ... outer.set_m} o outer.map inner_1.set_i ... inner_m.set_ (*Union o collect {image inner_1.set_i o outer.set_1 ... image inner_m.set_i o outer.set_m} fun mk_set i = let val (setTs, T) = `(replicate olive o HOLogic.mk_setT) (nth As i); val outer_set = mk_collect (mk_sets_of_bnf (replicate olive oDs) (replicate olive setTs) outer) (mk_T_of_bnf oDs setTs outer --> HOLogic.mk_setT T); val inner_sets = map (fn sets => nth sets i) inner_setss; val outer_map = mk_map_of_bnf oDs CAs setTs outer; val map_inner_sets = Term.list_comb (outer_map, inner_sets); val collect_image = mk_collect (map2 (fn f => fn set => HOLogic.mk_comp (mk_image f, set)) inner_sets outer_sets) (CCA --> HOLogic.mk_setT T); in (Library.foldl1 HOLogic.mk_comp [mk_Union T, outer_set, map_inner_sets], HOLogic.mk_comp (mk_Union T, collect_image)) end; val (sets, sets_alt) = map_split mk_set (0 upto ilive - 1); fun mk_simplified_set set = let val setT = fastype_of set; val var_set' = Const (\<^const_name>\ val goal = mk_Trueprop_eq (var_set', set); fun tac {context = ctxt, prems = _} = mk_simplified_set_tac ctxt (collect_set_map_of_bnf outer); val set'_eq_set = Goal.prove (*no sorry*) names_lthy [] [] goal tac |> Thm.close_derivation \<^here>; val set' = fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (Thm.prop_of set'_eq_set)) in (set', set'_eq_set) end; val (sets', set'_eq_sets) = map_split mk_simplified_set sets ||> Proof_Context.export names_lthy lthy; (*(inner_1.bd +c ... +c inner_m.bd) *c outer.bd*) val bd = mk_cprod (Library.foldr1 (uncurry mk_csum) inner_bds) outer_bd; val (bd', bd_ordIso_natLeq_thm_opt) = if is_sum_prod_natLeq bd then let val bd' = \<^term>\ val bd_bd' = HOLogic.mk_prod (bd, bd'); val ordIso = Const (\<^const_name>\<open>ordIso\<close>, HOLogic.mk_setT (fastype_of bd_bd')) val goal = mk_Trueprop_mem (bd_bd', ordIso); in (bd', SOME (Goal.prove_sorry lthy [] [] goal (bd_ordIso_natLeq_tac o #context) |> Thm.close_derivation \<^here>)) end else (bd, NONE); fun map_id0_tac ctxt = mk_comp_map_id0_tac ctxt (map_id0_of_bnf outer) (map_cong0_of_bnf outer) (map map_id0_of_bnf inners); fun map_comp0_tac ctxt = mk_comp_map_comp0_tac ctxt (map_comp0_of_bnf outer) (map_cong0_of_bnf outer) (map map_comp0_of_bnf inners); fun mk_single_set_map0_tac i ctxt = mk_comp_set_map0_tac ctxt (nth set'_eq_sets i) (map_comp0_of_bnf outer) (map_cong0_of_bnf outer) (collect_set_map_of_bnf outer) (map ((fn thms => nth thms i) o set_map0_of_bnf) inners); val set_map0_tacs = map mk_single_set_map0_tac (0 upto ilive - 1); fun bd_card_order_tac ctxt = mk_comp_bd_card_order_tac ctxt (map bd_card_order_of_bnf inners) (bd_card_order_of_bn fun bd_cinfinite_tac ctxt = mk_comp_bd_cinfinite_tac ctxt (bd_cinfinite_of_bnf inner) (bd_cinfinite_of_bnf outer) val set_alt_thms = if Config.get lthy quick_and_dirty then [] else map (fn goal => Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => mk_comp_set_alt_tac ctxt (collect_set_map_of_bnf outer)) |> Thm.close_derivation \<^here>) (map2 (curry mk_Trueprop_eq) sets sets_alt); fun map_cong0_tac ctxt = mk_comp_map_cong0_tac ctxt set'_eq_sets set_alt_thms (map_cong0_of_bnf outer) (map map_cong0_of_bnf inners); val set_bd_tacs = if Config.get lthy quick_and_dirty then replicate ilive (K all_tac) else let val outer_set_bds = set_bd_of_bnf outer; val inner_set_bdss = map set_bd_of_bnf inners; val inner_bd_Card_orders = map bd_Card_order_of_bnf inners; fun single_set_bd_thm i j = @{thm comp_single_set_bd} OF [nth inner_bd_Card_orders j, nth (nth inner_set_bdss j) i, nth outer_set_bds j] val single_set_bd_thmss = map ((fn f => map f (0 upto olive - 1)) o single_set_bd_thm) (0 upto ilive - 1); in @{map 3} (fn set'_eq_set => fn set_alt => fn single_set_bds => fn ctxt => mk_comp_set_bd_tac ctxt set'_eq_set bd_ordIso_natLeq_thm_opt set_alt single_set_bd set'_eq_sets set_alt_thms single_set_bd_thmss end; val in_alt_thm = let val inx = mk_in Asets sets CCA; val in_alt = mk_in (map2 (mk_in Asets) inner_setss CAs) outer_sets CCA; val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (inx, in_alt)); in Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => mk_comp_in_alt_tac ctxt set_alt_thms) |> Thm.close_derivation \<^here> end; fun le_rel_OO_tac ctxt = mk_le_rel_OO_tac ctxt (le_rel_OO_of_bnf outer) (rel_mono_of_bnf (map le_rel_OO_of_bnf inners); fun rel_OO_Grp_tac ctxt = let val outer_rel_Grp = rel_Grp_of_bnf outer RS sym; val thm = trans OF [in_alt_thm RS @{thm OO_Grp_cong}, trans OF [@{thm arg_cong2[of _ _ _ _ relcompp]} OF [trans OF [outer_rel_Grp RS @{thm arg_cong[of _ _ conversep]}, rel_conversep_of_bnf outer RS sym], outer_rel_Grp], trans OF [rel_OO_of_bnf outer RS sym, rel_cong0_of_bnf outer OF (map (fn bnf => rel_OO_Grp_of_bnf bnf RS sym) inners)]]] RS sym; in unfold_thms_tac ctxt set'_eq_sets THEN rtac ctxt thm 1 end; fun pred_set_tac ctxt = let val pred_alt = unfold_thms ctxt @{thms Ball_Collect} (trans OF [pred_cong0_of_bnf outer OF map pred_set_of_bnf inners, pred_set_of_bnf outer]) val in_alt = in_alt_thm RS @{thm Collect_inj} RS sym; in unfold_thms_tac ctxt (@{thm Ball_Collect} :: set'_eq_sets) THEN HEADGOAL (rtac ctxt (trans OF [pred_alt, in_alt])) end val tacs = zip_axioms map_id0_tac map_comp0_tac map_cong0_tac set_map0_tacs bd_card_orde bd_cinfinite_tac set_bd_tacs le_rel_OO_tac rel_OO_Grp_tac pred_set_tac; val outer_wits = mk_wits_of_bnf (replicate onwits oDs) (replicate onwits CAs) outer; val inner_witss = map (map (fn (I, wit) => Term.list_comb (wit, map (nth xs) I))) (@{map 3} (fn Ds => fn n => mk_wits_of_bnf (replicate n Ds) (replicate n As)) Dss inwitss inners); val inner_witsss = map (map (nth inner_witss) o fst) outer_wits; val wits = (inner_witsss, (map (single o snd) outer_wits)) |-> map2 (fold (map_product (fn iwit => fn owit => owit $ iwit))) |> flat |> map (`(fn t => Term.add_frees t [])) |> minimize_wits |> map (fn (frees, t) => fold absfree frees t); fun wit_tac ctxt = mk_comp_wit_tac ctxt set'_eq_sets (wit_thms_of_bnf outer) (collect_set_map_of_bnf (maps wit_thms_of_bnf inners); val (bnf', lthy') = bnf_def const_policy (K Dont_Note) true qualify tacs wit_tac (SOME (oDs @ flat Dss)) Binding.empty Binding.empty Binding.empty [] (((((((b, CCA), mapx), sets'), bd'), wits), SOME rel), SOME pred) lthy; val phi = Morphism.thm_morphism "BNF" (unfold_thms lthy' [id_bnf_def]) $> Morphism.term_morphism "BNF" expand_id_bnf_def; val bnf'' = morph_bnf phi bnf'; in (bnf'', (add_bnf_to_unfolds bnf'' unfold_set, lthy')) end; (* Killing live variables *) fun raw_kill_bnf qualify n bnf (accum as (unfold_set, lthy)) = if n = 0 then (bnf, accum) else let val b = Binding.suffix_name (mk_killN n) (name_of_bnf bnf); val live = live_of_bnf bnf; val deads = deads_of_bnf bnf; val nwits = nwits_of_bnf bnf; (* TODO: check 0 < n <= live *) val (Ds, lthy1) = apfst (map TFree) (Variable.invent_types (map Type.sort_of_atyp deads) lthy); val ((killedAs, As), lthy2) = apfst (`(take n) o map TFree) (Variable.invent_types (replicate live \<^sort>\<open>type\<close>) lthy1); val (Bs, _(*lthy3*)) = apfst (append killedAs o map TFree) (Variable.invent_types (replicate (live - n) \<^sort>\<open>type\<close>) lthy2); val ((Asets, lives), _(*names_lthy*)) = lthy |> mk_Frees "A" (map HOLogic.mk_setT (drop n As)) ||>> mk_Frees "x" (drop n As); val xs = map (fn T => Const (\<^const_name>\<open>undefined\<close>, T)) killedAs @ lives; val T = mk_T_of_bnf Ds As bnf; (*bnf.map id ... id*) val mapx = Term.list_comb (mk_map_of_bnf Ds As Bs bnf, map HOLogic.id_const killedAs); (*bnf.rel (op =) ... (op =)*) val rel = Term.list_comb (mk_rel_of_bnf Ds As Bs bnf, map HOLogic.eq_const killedAs); (*bnf.pred (%_. True) ... (%_ True)*) val pred = Term.list_comb (mk_pred_of_bnf Ds As bnf, map (fn T => Term.absdummy T \<^term>\<open>True\<close>) killedAs); val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf; val sets = drop n bnf_sets; val bd = mk_bd_of_bnf Ds As bnf; fun map_id0_tac ctxt = rtac ctxt (map_id0_of_bnf bnf) 1; fun map_comp0_tac ctxt = unfold_thms_tac ctxt ((map_comp0_of_bnf bnf RS sym) :: @{thms comp_assoc id_comp comp_id}) THEN rtac ctxt refl 1; fun map_cong0_tac ctxt = mk_kill_map_cong0_tac ctxt n (live - n) (map_cong0_of_bnf bnf); val set_map0_tacs = map (fn thm => fn ctxt => rtac ctxt thm 1) (drop n (set_map0_of_bnf bnf)); fun bd_card_order_tac ctxt = rtac ctxt (bd_card_order_of_bnf bnf) 1; fun bd_cinfinite_tac ctxt = rtac ctxt (bd_cinfinite_of_bnf bnf) 1; val set_bd_tacs = map (fn thm => fn ctxt => rtac ctxt thm 1) (drop n (set_bd_of_bnf bnf)); val in_alt_thm = let val inx = mk_in Asets sets T; val in_alt = mk_in (map HOLogic.mk_UNIV killedAs @ Asets) bnf_sets T; val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (inx, in_alt)); in Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => kill_in_alt_tac ctxt) |> Thm.close_derivation \<^here> end; fun le_rel_OO_tac ctxt = EVERY' [rtac ctxt @{thm ord_le_eq_trans}, rtac ctxt (le_rel_OO_of_bnf bnf)] 1 TH unfold_thms_tac ctxt @{thms eq_OO} THEN rtac ctxt refl 1; fun rel_OO_Grp_tac ctxt = let val rel_Grp = rel_Grp_of_bnf bnf RS sym val thm = (trans OF [in_alt_thm RS @{thm OO_Grp_cong}, trans OF [@{thm arg_cong2[of _ _ _ _ relcompp]} OF [trans OF [rel_Grp RS @{thm arg_cong[of _ _ conversep]}, rel_conversep_of_bnf bnf RS sym], rel_Grp], trans OF [rel_OO_of_bnf bnf RS sym, rel_cong0_of_bnf bnf OF (replicate n @{thm trans[OF Grp_UNIV_id[OF refl] eq_alt[symmetric]]} @ replicate (live - n) @{thm Grp_fst_snd})]]] RS sym); in rtac ctxt thm 1 end; fun pred_set_tac ctxt = mk_simple_pred_set_tac ctxt (pred_set_of_bnf bnf) in_alt_thm; val tacs = zip_axioms map_id0_tac map_comp0_tac map_cong0_tac set_map0_tacs bd_card_orde bd_cinfinite_tac set_bd_tacs le_rel_OO_tac rel_OO_Grp_tac pred_set_tac; val bnf_wits = mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf; val wits = map (fn t => fold absfree (Term.add_frees t []) t) (map (fn (I, wit) => Term.list_comb (wit, map (nth xs) I)) bnf_wits); fun wit_tac ctxt = mk_simple_wit_tac ctxt (wit_thms_of_bnf bnf); val (bnf', lthy') = bnf_def Smart_Inline (K Dont_Note) true qualify tacs wit_tac (SOME (Ds @ killedAs)) Binding.empty Binding.empty Binding.empty [] (((((((b, T), mapx), sets), bd), wits), SOME rel), SOME pred) lthy; in (bnf', (add_bnf_to_unfolds bnf' unfold_set, lthy')) end; fun kill_bnf qualify n bnf (accum as ((cache, unfold_set), lthy)) = let val key = key_of_kill n bnf in (case Typtab.lookup cache key of SOME (bnf, _) => (bnf, accum) | NONE => cache_comp_simple key cache (raw_kill_bnf qualify n bnf (unfold_set, lthy))) end; (* Adding dummy live variables *) fun raw_lift_bnf qualify n bnf (accum as (unfold_set, lthy)) = if n = 0 then (bnf, accum) else let val b = Binding.suffix_name (mk_liftN n) (name_of_bnf bnf); val live = live_of_bnf bnf; val deads = deads_of_bnf bnf; val nwits = nwits_of_bnf bnf; (* TODO: check 0 < n *) val (Ds, lthy1) = apfst (map TFree) (Variable.invent_types (map Type.sort_of_atyp deads) lthy); val ((newAs, As), lthy2) = apfst (chop n o map TFree) (Variable.invent_types (replicate (n + live) \<^sort>\<open>type\<close>) lthy1); val ((newBs, Bs), _(*lthy3*)) = apfst (chop n o map TFree) (Variable.invent_types (replicate (n + live) \<^sort>\<open>type\<close>) lthy2); val (Asets, _(*names_lthy*)) = lthy |> mk_Frees "A" (map HOLogic.mk_setT (newAs @ As)); val T = mk_T_of_bnf Ds As bnf; (*%f1 ... fn. bnf.map*) val mapx = fold_rev Term.absdummy (map2 (curry op -->) newAs newBs) (mk_map_of_bnf Ds As Bs bnf); (*%Q1 ... Qn. bnf.rel*) val rel = fold_rev Term.absdummy (map2 mk_pred2T newAs newBs) (mk_rel_of_bnf Ds As Bs bnf); (*%P1 ... Pn. bnf.pred*) val pred = fold_rev Term.absdummy (map mk_pred1T newAs) (mk_pred_of_bnf Ds As bnf); val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf; val sets = map (fn A => absdummy T (HOLogic.mk_set A [])) newAs @ bnf_sets; val bd = mk_bd_of_bnf Ds As bnf; fun map_id0_tac ctxt = rtac ctxt (map_id0_of_bnf bnf) 1; fun map_comp0_tac ctxt = unfold_thms_tac ctxt ((map_comp0_of_bnf bnf RS sym) :: @{thms comp_assoc id_comp comp_id}) THEN rtac ctxt refl 1; fun map_cong0_tac ctxt = rtac ctxt (map_cong0_of_bnf bnf) 1 THEN REPEAT_DETERM_N live (Goal.assume_rule_tac ctxt 1) val set_map0_tacs = if Config.get lthy quick_and_dirty then replicate (n + live) (K all_tac) else replicate n empty_natural_tac @ map (fn thm => fn ctxt => rtac ctxt thm 1) (set_map0_of_bnf bnf); fun bd_card_order_tac ctxt = rtac ctxt (bd_card_order_of_bnf bnf) 1; fun bd_cinfinite_tac ctxt = rtac ctxt (bd_cinfinite_of_bnf bnf) 1; val set_bd_tacs = if Config.get lthy quick_and_dirty then replicate (n + live) (K all_tac) else replicate n (fn ctxt => mk_lift_set_bd_tac ctxt (bd_Card_order_of_bnf bnf)) @ (map (fn thm => fn ctxt => rtac ctxt thm 1) (set_bd_of_bnf bnf)); val in_alt_thm = let val inx = mk_in Asets sets T; val in_alt = mk_in (drop n Asets) bnf_sets T; val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (inx, in_alt)); in Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => lift_in_alt_tac ctxt) |> Thm.close_derivation \<^here> end; fun le_rel_OO_tac ctxt = rtac ctxt (le_rel_OO_of_bnf bnf) 1; fun rel_OO_Grp_tac ctxt = mk_simple_rel_OO_Grp_tac ctxt (rel_OO_Grp_of_bnf bnf) in_alt_t fun pred_set_tac ctxt = mk_simple_pred_set_tac ctxt (pred_set_of_bnf bnf) in_alt_thm; val tacs = zip_axioms map_id0_tac map_comp0_tac map_cong0_tac set_map0_tacs bd_card_orde bd_cinfinite_tac set_bd_tacs le_rel_OO_tac rel_OO_Grp_tac pred_set_tac; val wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf); fun wit_tac ctxt = mk_simple_wit_tac ctxt (wit_thms_of_bnf bnf); val (bnf', lthy') = bnf_def Smart_Inline (K Dont_Note) true qualify tacs wit_tac (SOME Ds) Binding.empty Binding.empty Binding.empty [] (((((((b, T), mapx), sets), bd), wits), SOME rel), SOME pred) lthy; in (bnf', (add_bnf_to_unfolds bnf' unfold_set, lthy')) end; fun lift_bnf qualify n bnf (accum as ((cache, unfold_set), lthy)) = let val key = key_of_lift n bnf in (case Typtab.lookup cache key of SOME (bnf, _) => (bnf, accum) | NONE => cache_comp_simple key cache (raw_lift_bnf qualify n bnf (unfold_set, lthy))) end; (* Changing the order of live variables *) fun raw_permute_bnf qualify src dest bnf (accum as (unfold_set, lthy)) = if src = dest then (bnf, accum) else let val b = Binding.suffix_name (mk_permuteN src dest) (name_of_bnf bnf) |> Binding.reset_pos; val live = live_of_bnf bnf; val deads = deads_of_bnf bnf; val nwits = nwits_of_bnf bnf; fun permute xs = permute_like_unique (op =) src dest xs; fun unpermute xs = permute_like_unique (op =) dest src xs; val (Ds, lthy1) = apfst (map TFree) (Variable.invent_types (map Type.sort_of_atyp deads) lthy); val (As, lthy2) = apfst (map TFree) (Variable.invent_types (replicate live \<^sort>\<open>type\<close>) lthy1); val (Bs, _(*lthy3*)) = apfst (map TFree) (Variable.invent_types (replicate live \<^sort>\<open>type\<close>) lthy2); val (Asets, _(*names_lthy*)) = lthy |> mk_Frees "A" (map HOLogic.mk_setT (permute As)); val T = mk_T_of_bnf Ds As bnf; (*%f(1) ... f(n). bnf.map f\<sigma>(1) ... f\<sigma>(n)*) val mapx = fold_rev Term.absdummy (permute (map2 (curry op -->) As Bs)) (Term.list_comb (mk_map_of_bnf Ds As Bs bnf, unpermute (map Bound (live - 1 downto 0)))); (*%Q(1) ... Q(n). bnf.rel Q\<sigma>(1) ... Q\<sigma>(n)*) val rel = fold_rev Term.absdummy (permute (map2 mk_pred2T As Bs)) (Term.list_comb (mk_rel_of_bnf Ds As Bs bnf, unpermute (map Bound (live - 1 downto 0)))); (*%P(1) ... P(n). bnf.pred P\<sigma>(1) ... P\<sigma>(n)*) val pred = fold_rev Term.absdummy (permute (map mk_pred1T As)) (Term.list_comb (mk_pred_of_bnf Ds As bnf, unpermute (map Bound (live - 1 downto 0)))); val bnf_sets = mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf; val sets = permute bnf_sets; val bd = mk_bd_of_bnf Ds As bnf; fun map_id0_tac ctxt = rtac ctxt (map_id0_of_bnf bnf) 1; fun map_comp0_tac ctxt = rtac ctxt (map_comp0_of_bnf bnf) 1; fun map_cong0_tac ctxt = rtac ctxt (map_cong0_of_bnf bnf) 1 THEN REPEAT_DETERM_N live (Goal.assume_rule_tac ctxt 1) val set_map0_tacs = permute (map (fn thm => fn ctxt => rtac ctxt thm 1) (set_map0_of_bnf bnf)); fun bd_card_order_tac ctxt = rtac ctxt (bd_card_order_of_bnf bnf) 1; fun bd_cinfinite_tac ctxt = rtac ctxt (bd_cinfinite_of_bnf bnf) 1; val set_bd_tacs = permute (map (fn thm => fn ctxt => rtac ctxt thm 1) (set_bd_of_bnf bnf)); val in_alt_thm = let val inx = mk_in Asets sets T; val in_alt = mk_in (unpermute Asets) bnf_sets T; val goal = fold_rev Logic.all Asets (mk_Trueprop_eq (inx, in_alt)); in Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => mk_permute_in_alt_tac ctxt src dest) |> Thm.close_derivation \<^here> end; fun le_rel_OO_tac ctxt = rtac ctxt (le_rel_OO_of_bnf bnf) 1; fun rel_OO_Grp_tac ctxt = mk_simple_rel_OO_Grp_tac ctxt (rel_OO_Grp_of_bnf bnf) in_alt_t fun pred_set_tac ctxt = mk_simple_pred_set_tac ctxt (pred_set_of_bnf bnf) in_alt_thm; val tacs = zip_axioms map_id0_tac map_comp0_tac map_cong0_tac set_map0_tacs bd_card_orde bd_cinfinite_tac set_bd_tacs le_rel_OO_tac rel_OO_Grp_tac pred_set_tac; val wits = map snd (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf); fun wit_tac ctxt = mk_simple_wit_tac ctxt (wit_thms_of_bnf bnf); val (bnf', lthy') = bnf_def Smart_Inline (K Dont_Note) true qualify tacs wit_tac (SOME Ds) Binding.empty Binding.empty Binding.empty [] (((((((b, T), mapx), sets), bd), wits), SOME rel), SOME pred) lthy; in (bnf', (add_bnf_to_unfolds bnf' unfold_set, lthy')) end; fun permute_bnf qualify src dest bnf (accum as ((cache, unfold_set), lthy)) = let val key = key_of_permute src dest bnf in (case Typtab.lookup cache key of SOME (bnf, _) => (bnf, accum) | NONE => cache_comp_simple key cache (raw_permute_bnf qualify src dest bnf (unfold_set, lthy end; (* Composition pipeline *) fun permute_and_kill_bnf qualify n src dest bnf = permute_bnf qualify src dest bnf #> uncurry (kill_bnf qualify n); fun lift_and_permute_bnf qualify n src dest bnf = lift_bnf qualify n bnf #> uncurry (permute_bnf qualify src dest); fun normalize_bnfs qualify Ass Ds flatten_tyargs bnfs accum = let val before_kill_src = map (fn As => 0 upto (length As - 1)) Ass; val kill_poss = map (find_indices op = Ds) Ass; val live_poss = map2 (subtract op =) kill_poss before_kill_src; val before_kill_dest = map2 append kill_poss live_poss; val kill_ns = map length kill_poss; val (inners', accum') = @{fold_map 5} (permute_and_kill_bnf o qualify) (if length bnfs = 1 then [0] else 1 upto length bnfs) kill_ns before_kill_src before_kill_dest bnfs accum; val Ass' = map2 (map o nth) Ass live_poss; val As = flatten_tyargs Ass'; val after_lift_dest = replicate (length Ass') (0 upto (length As - 1)); val old_poss = map (map (fn x => find_index (fn y => x = y) As)) Ass'; val new_poss = map2 (subtract op =) old_poss after_lift_dest; val after_lift_src = map2 append new_poss old_poss; val lift_ns = map (fn xs => length As - length xs) Ass'; in ((kill_poss, As), @{fold_map 5} (lift_and_permute_bnf o qualify) (if length bnfs = 1 then [0] else 1 upto length bnfs) lift_ns after_lift_src after_lift_dest inners' accum') end; fun default_comp_sort Ass = Library.sort (Term_Ord.typ_ord o apply2 TFree) (fold (fold (insert (op =))) Ass []); fun raw_compose_bnf const_policy qualify flatten_tyargs outer inners oDs Dss tfreess accum let val b = name_of_bnf outer; val Ass = map (map Term.dest_TFree) tfreess; val Ds = fold (fold Term.add_tfreesT) (oDs :: Dss) []; val ((kill_poss, As), (inners', ((cache', unfold_set'), lthy'))) = normalize_bnfs qualify Ass Ds flatten_tyargs inners accum; val Ds = oDs @ flat (@{map 3} (uncurry append oo curry swap oo map o nth) tfreess kill_poss Dss); val As = map TFree As; in apfst (rpair (Ds, As)) (apsnd (apfst (pair cache')) (clean_compose_bnf const_policy (qualify 0) b outer inners' (unfold_set', lthy'))) end; fun compose_bnf const_policy qualify flatten_tyargs outer inners oDs Dss tfreess (accum as ((cache, _), _)) = let val key = key_of_compose oDs Dss tfreess outer inners in (case Typtab.lookup cache key of SOME bnf_Ds_As => (bnf_Ds_As, accum) | NONE => cache_comp key (raw_compose_bnf const_policy qualify flatten_tyargs outer inners oDs Dss tfreess accum)) end; (* Hide the type of the bound (optimization) and unfold the definitions (nicer to the user) *) type absT_info = {absT: typ, repT: typ, abs: term, rep: term, abs_inject: thm, abs_inverse: thm, type_definition: thm}; fun morph_absT_info phi {absT, repT, abs, rep, abs_inject, abs_inverse, type_definition} = {absT = Morphism.typ phi absT, repT = Morphism.typ phi repT, abs = Morphism.term phi abs, rep = Morphism.term phi rep, abs_inject = Morphism.thm phi abs_inject, abs_inverse = Morphism.thm phi abs_inverse, type_definition = Morphism.thm phi type_definition}; fun mk_absT thy repT absT repU = let val rho = Vartab.fold (cons o apsnd snd) (Sign.typ_match thy (repT, repU) Vartab.empty) []; in Term.typ_subst_TVars rho absT end handle Type.TYPE_MATCH => raise Term.TYPE ("mk_absT", [repT, absT, repU], []); fun mk_repT absT repT absU = if absT = repT then absU else (case (absT, absU) of (Type (C, Ts), Type (C', Us)) => if C = C' then Term.typ_subst_atomic (Ts ~~ Us) repT else raise Term.TYPE ("mk_repT", [absT, repT, absU], []) | _ => raise Term.TYPE ("mk_repT", [absT, repT, absU], [])); fun mk_abs_or_rep _ absU (Const (\<^const_name>\<open>id_bnf\<close>, _)) = Const (\<^const_name>\<open>id_bnf\<close>, absU --> absU) | mk_abs_or_rep getT (Type (_, Us)) abs = let val Ts = snd (dest_Type (getT (fastype_of abs))) in Term.subst_atomic_types (Ts ~~ Us) abs end; val mk_abs = mk_abs_or_rep range_type; val mk_rep = mk_abs_or_rep domain_type; fun maybe_typedef force_out_of_line (b, As, mx) set opt_morphs tac lthy = let val threshold = Config.get lthy typedef_threshold; val repT = HOLogic.dest_setT (fastype_of set); val out_of_line = force_out_of_line orelse (threshold >= 0 andalso Term.size_of_typ repT >= threshold); in if out_of_line then typedef (b, As, mx) set opt_morphs tac lthy |>> (fn (T_name, ({Rep_name, Abs_name, ...}, {type_definition, Abs_inverse, Abs_inject, Abs_cases, ...}) : Typedef.info) => (Type (T_name, map TFree As), (Rep_name, Abs_name, type_definition, Abs_inverse, Abs_inject, Abs_cases))) else ((repT, (\<^const_name>\<open>id_bnf\<close>, \<^const_name>\<open>id_bnf\<close>, @{thm type_definition_id_bnf_UNIV}, @{thm type_definition.Abs_inverse[OF type_definition_id_bnf_UNIV]}, @{thm type_definition.Abs_inject[OF type_definition_id_bnf_UNIV]}, @{thm type_definition.Abs_cases[OF type_definition_id_bnf_UNIV]})), lthy) end; fun seal_bnf qualify (unfold_set : unfold_set) b force_out_of_line Ds all_Ds bnf lthy = let val live = live_of_bnf bnf; val nwits = nwits_of_bnf bnf; val ((As, As'), lthy1) = apfst (`(map TFree)) (Variable.invent_types (replicate live \<^sort>\<open>type\<close>) (fold Variable.declare_ val (Bs, _) = apfst (map TFree) (Variable.invent_types (replicate live \<^sort>\<open>type\<clo val ((((fs, fs'), (Rs, Rs')), (Ps, Ps')), _(*names_lthy*)) = lthy |> mk_Frees' "f" (map2 (curry op -->) As Bs) ||>> mk_Frees' "R" (map2 mk_pred2T As Bs) ||>> mk_Frees' "P" (map mk_pred1T As); val repTA = mk_T_of_bnf Ds As bnf; val T_bind = qualify b; val repTA_tfrees = Term.add_tfreesT repTA []; val all_TA_params_in_order = fold_rev Term.add_tfreesT all_Ds As'; val TA_params = (if force_out_of_line then all_TA_params_in_order else inter (op =) repTA_tfrees all_TA_params_in_order); val ((TA, (Rep_name, Abs_name, type_definition, Abs_inverse, Abs_inject, _)), lthy) = maybe_typedef force_out_of_line (T_bind, TA_params, NoSyn) (HOLogic.mk_UNIV repTA) NONE (fn ctxt => EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) lthy; val repTB = mk_T_of_bnf Ds Bs bnf; val TB = Term.typ_subst_atomic (As ~~ Bs) TA; val RepA = Const (Rep_name, TA --> repTA); val RepB = Const (Rep_name, TB --> repTB); val AbsA = Const (Abs_name, repTA --> TA); val AbsB = Const (Abs_name, repTB --> TB); val Abs_inject' = Abs_inject OF @{thms UNIV_I UNIV_I}; val Abs_inverse' = Abs_inverse OF @{thms UNIV_I}; val absT_info = {absT = TA, repT = repTA, abs = AbsA, rep = RepA, abs_inject = Abs_inject', abs_inverse = Abs_inverse', type_definition = type_definition}; val bnf_map = fold_rev Term.absfree fs' (HOLogic.mk_comp (HOLogic.mk_comp (AbsB, Term.list_comb (mk_map_of_bnf Ds As Bs bnf, fs)), RepA)); val bnf_sets = map ((fn t => HOLogic.mk_comp (t, RepA))) (mk_sets_of_bnf (replicate live Ds) (replicate live As) bnf); val bnf_bd = mk_bd_of_bnf Ds As bnf; val bnf_rel = fold_rev Term.absfree Rs' (mk_vimage2p RepA RepB $ (Term.list_comb (mk_rel_of_bnf Ds As Bs bnf, Rs))); val bnf_pred = fold_rev Term.absfree Ps' (HOLogic.mk_comp (Term.list_comb (mk_pred_of_bnf Ds As bnf, Ps), RepA)); (*bd may depend only on dead type variables*) val bd_repT = fst (dest_relT (fastype_of bnf_bd)); val bdT_bind = qualify (Binding.suffix_name ("_" ^ bdTN) b); val params = Term.add_tfreesT bd_repT []; val all_deads = map TFree (fold_rev Term.add_tfreesT all_Ds []); val ((bdT, (_, Abs_bd_name, _, _, Abs_bdT_inject, Abs_bdT_cases)), lthy) = maybe_typedef false (bdT_bind, params, NoSyn) (HOLogic.mk_UNIV bd_repT) NONE (fn ctxt => EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) lthy; val (bnf_bd', bd_ordIso, bd_card_order, bd_cinfinite) = if bdT = bd_repT then (bnf_bd, bd_Card_order_of_bnf bnf RS @{thm ordIso_refl}, bd_card_order_of_bnf bnf, bd_cinfinite_of_bnf bnf) else let val bnf_bd' = mk_dir_image bnf_bd (Const (Abs_bd_name, bd_repT --> bdT)); val Abs_bdT_inj = mk_Abs_inj_thm Abs_bdT_inject; val Abs_bdT_bij = mk_Abs_bij_thm lthy Abs_bdT_inj Abs_bdT_cases; val bd_ordIso = @{thm dir_image} OF [Abs_bdT_inj, bd_Card_order_of_bnf bnf]; val bd_card_order = @{thm card_order_dir_image} OF [Abs_bdT_bij, bd_card_order_of_bnf bnf]; val bd_cinfinite = (@{thm Cinfinite_cong} OF [bd_ordIso, bd_Cinfinite_of_bnf bnf]) RS conjunct1; in (bnf_bd', bd_ordIso, bd_card_order, bd_cinfinite) end; fun map_id0_tac ctxt = rtac ctxt (@{thm type_copy_map_id0} OF [type_definition, map_id0_of_bnf bnf]) 1; fun map_comp0_tac ctxt = rtac ctxt (@{thm type_copy_map_comp0} OF [type_definition, map_comp0_of_bnf bnf]) 1; fun map_cong0_tac ctxt = EVERY' (rtac ctxt @{thm type_copy_map_cong0} :: rtac ctxt (map_cong0_of_bnf bnf) map (fn i => EVERY' [select_prem_tac ctxt live (dtac ctxt meta_spec) i, etac ctxt met etac ctxt (o_apply RS equalityD2 RS set_mp)]) (1 upto live)) 1; fun set_map0_tac thm ctxt = rtac ctxt (@{thm type_copy_set_map0} OF [type_definition, thm]) 1; val set_bd_tacs = map (fn thm => fn ctxt => rtac ctxt (@{thm ordLeq_ordIso_trans} OF [thm, bd_ordIso] RS @{thm type_copy_set_bd}) 1) (set_bd_of_bnf bnf); fun le_rel_OO_tac ctxt = rtac ctxt (le_rel_OO_of_bnf bnf RS @{thm vimage2p_relcompp_mono}) 1; fun rel_OO_Grp_tac ctxt = (rtac ctxt (rel_OO_Grp_of_bnf bnf RS @{thm vimage2p_cong} RS trans) THEN' (if force_out_of_line then subst_tac ctxt NONE else SELECT_GOAL o unfold_thms_tac ctxt) [type_definition RS @{thm vimage2p_relcompp_converse}] THEN' SELECT_GOAL (unfold_thms_tac ctxt [o_apply, type_definition RS @{thm type_copy_vimage2p_Grp_Rep}, type_definition RS @{thm vimage2p_relcompp_converse}]) THEN' rtac ctxt refl) 1; fun pred_set_tac ctxt = HEADGOAL (EVERY' [rtac ctxt (pred_set_of_bnf bnf RS @{thm arg_cong[of _ _ "\ SELECT_GOAL (unfold_thms_tac ctxt (@{thms Ball_comp_iff conj_comp_iff})), rtac ctxt refl val tacs = zip_axioms map_id0_tac map_comp0_tac map_cong0_tac (map set_map0_tac (set_map0_of_bnf bnf)) (fn ctxt => rtac ctxt bd_card_order 1) (fn ctxt => rtac ctxt bd_cinfinite 1) set_bd_tacs le_rel_OO_tac rel_OO_Grp_tac pred_set_tac; val bnf_wits = map (fn (I, t) => fold Term.absdummy (map (nth As) I) (AbsA $ Term.list_comb (t, map Bound (0 upto length I - 1)))) (mk_wits_of_bnf (replicate nwits Ds) (replicate nwits As) bnf); fun wit_tac ctxt = ALLGOALS (dtac ctxt (type_definition RS @{thm type_copy_wit})) THEN mk_simple_wit_tac ctxt (wit_thms_of_bnf bnf); val (bnf', lthy') = bnf_def Hardly_Inline (user_policy Dont_Note) true qualify tacs wit_tac (SOME all_deads) Binding.empty Binding.empty Binding.empty [] (((((((b, TA), bnf_map), bnf_sets), bnf_bd'), bnf_wits), SOME bnf_rel), SOME bnf_pre val unfolds = @{thm id_bnf_apply} :: (#map_unfolds unfold_set @ flat (#set_unfoldss unfold_set) @ #rel_unfolds unfold_set @ #pred_unfolds unfold_set); val bnf'' = bnf' |> morph_bnf_defs (Morphism.thm_morphism "BNF" (unfold_thms lthy' u val map_def = map_def_of_bnf bnf''; val set_defs = set_defs_of_bnf bnf''; val rel_def = rel_def_of_bnf bnf''; val bnf_b = qualify b; val def_qualify = Thm.def_binding o Binding.concealed o Binding.qualify false (Binding.name_of bnf_b); fun mk_prefix_binding pre = Binding.prefix_name (pre ^ "_") bnf_b; val map_b = def_qualify (mk_prefix_binding mapN); val rel_b = def_qualify (mk_prefix_binding relN); val set_bs = if live = 1 then [def_qualify (mk_prefix_binding setN)] else map (def_qualify o mk_prefix_binding o mk_setN) (1 upto live); val notes = (map_b, map_def) :: (rel_b, rel_def) :: (set_bs ~~ set_defs) |> map (fn (b, def) => ((b, []), [([def], [])])) val (noted, lthy'') = lthy' |> Local_Theory.notes notes ||> (if repTA = TA then I else register_bnf_raw (fst (dest_Type TA)) bnf'') in ((morph_bnf (substitute_noted_thm noted) bnf'', (all_deads, absT_info)), lthy'') end; exception BAD_DEAD of typ * typ; fun bnf_of_typ _ _ _ _ _ Ds0 (T as TFree T') accum = (if member (op =) Ds0 T' then (DEADID_bnf, ([T], [])) else (ID_bnf, ([], [T])), accum | bnf_of_typ _ _ _ _ _ _ (TVar _) _ = error "Unexpected schematic variable" | bnf_of_typ optim const_policy qualify' flatten_tyargs Xs Ds0 (T as Type (C, Ts)) (accum as (_, lthy)) = let fun check_bad_dead ((_, (deads, _)), _) = let val Ds = fold Term.add_tfreesT deads [] in (case Library.inter (op =) Ds Xs of [] => () | X :: _ => raise BAD_DEAD (TFree X, T)) end; val tfrees = subtract (op =) Ds0 (Term.add_tfreesT T []); val bnf_opt = if null tfrees then NONE else bnf_of lthy C; in (case bnf_opt of NONE => ((DEADID_bnf, ([T], [])), accum) | SOME bnf => if optim andalso forall (can Term.dest_TFree) Ts andalso length Ts = length tfrees then let val T' = T_of_bnf bnf; val deads = deads_of_bnf bnf; val lives = lives_of_bnf bnf; val tvars' = Term.add_tvarsT T' []; val Ds_As = apply2 (map (Term.typ_subst_TVars (map fst tvars' ~~ map TFree tfrees))) (deads, lives); in ((bnf, Ds_As), accum) end else let val name = Long_Name.base_name C; fun qualify i = let val namei = name ^ nonzero_string_of_int i; in qualify' o Binding.qualify true namei end; val odead = dead_of_bnf bnf; val olive = live_of_bnf bnf; val Ds = map (fn i => TFree (string_of_int i, [])) (1 upto odead); val Us = snd (Term.dest_Type (mk_T_of_bnf Ds (replicate olive dummyT) bnf)); val oDs_pos = map (fn x => find_index (fn y => x = y) Us) Ds |> filter (fn x => x >= 0); val oDs = map (nth Ts) oDs_pos; val Ts' = map (nth Ts) (subtract (op =) oDs_pos (0 upto length Ts - 1)); val ((inners, (Dss, Ass)), (accum', lthy')) = apfst (apsnd split_list o split_list) (@{fold_map 2} (fn i => bnf_of_typ optim Smart_Inline (qualify i) flatten_tyargs Xs Ds0) (if length Ts' = 1 then [0] else 1 upto length Ts') Ts' accum); in compose_bnf const_policy qualify flatten_tyargs bnf inners oDs Dss Ass (accum', lthy') end) |> tap check_bad_dead end; end; [ Dauer der Verarbeitung: 0.124 Sekunden (vorverarbeitet) ] |