| products/Sources/formale Sprachen/Isabelle/HOL/Tools/BNF/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: Sprache: SMLOriginal von: Isabelle© |
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(* Title: HOL/Tools/BNF/bnf_lfp.ML
Author: Dmitriy Traytel, TU Muenchen Author: Andrei Popescu, TU Muenchen Copyright 2012 Datatype construction. *) signature BNF_LFP = sig val construct_lfp: mixfix list -> binding list -> binding list -> binding list -> binding list list -> binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory -> BNF_FP_Util.fp_result * local_theory end; structure BNF_LFP : BNF_LFP = struct open BNF_Def open BNF_Util open BNF_Tactics open BNF_Comp open BNF_FP_Util open BNF_FP_Def_Sugar open BNF_LFP_Util open BNF_LFP_Tactics (*all BNFs have the same lives*) fun construct_lfp mixfixes map_bs rel_bs pred_bs set_bss0 bs resBs (resDs, Dss) bnfs absT_in lthy = let val time = time lthy; val timer = time (Timer.startRealTimer ()); val live = live_of_bnf (hd bnfs); val n = length bnfs; (*active*) val ks = 1 upto n; val m = live - n; (*passive, if 0 don't generate a new BNF*) val internals = Config.get lthy bnf_internals; val b_names = map Binding.name_of bs; val b_name = mk_common_name b_names; val b = Binding.name b_name; fun mk_internal_of_b name = Binding.prefix_name (name ^ "_") #> Binding.prefix true b_name #> Binding.concealed; fun mk_internal_b name = mk_internal_of_b name b; fun mk_internal_bs name = map (mk_internal_of_b name) bs; val external_bs = map2 (Binding.prefix false) b_names bs |> not internals ? map Binding.concealed; val deads = fold (union (op =)) Dss resDs; val names_lthy = fold Variable.declare_typ deads lthy; val passives = map fst (subtract (op = o apsnd TFree) deads resBs); (* tvars *) val (((((passiveAs, activeAs), passiveBs), activeBs), passiveCs), activeCs) = names_lthy |> variant_tfrees passives ||>> mk_TFrees n ||>> variant_tfrees passives ||>> mk_TFrees n ||>> variant_tfrees passives ||>> mk_TFrees n |> fst; val allAs = passiveAs @ activeAs; val allBs' = passiveBs @ activeBs; val Ass = replicate n allAs; val allBs = passiveAs @ activeBs; val Bss = replicate n allBs; val allCs = passiveAs @ activeCs; val allCs' = passiveBs @ activeCs; val Css' = replicate n allCs'; (* types *) val dead_poss = map (fn x => if member (op =) deads (TFree x) then SOME (TFree x) else NONE) resBs; fun mk_param NONE passive = (hd passive, tl passive) | mk_param (SOME a) passive = (a, passive); val mk_params = fold_map mk_param dead_poss #> fst; fun mk_FTs Ts = map2 (fn Ds => mk_T_of_bnf Ds Ts) Dss bnfs; val (params, params') = `(map Term.dest_TFree) (mk_params passiveAs); val FTsAs = mk_FTs allAs; val FTsBs = mk_FTs allBs; val FTsCs = mk_FTs allCs; val BTs = map HOLogic.mk_setT activeAs; val B'Ts = map HOLogic.mk_setT activeBs; val B''Ts = map HOLogic.mk_setT activeCs; val sTs = map2 (curry op -->) FTsAs activeAs; val s'Ts = map2 (curry op -->) FTsBs activeBs; val s''Ts = map2 (curry op -->) FTsCs activeCs; val fTs = map2 (curry op -->) activeAs activeBs; val inv_fTs = map2 (curry op -->) activeBs activeAs; val self_fTs = map2 (curry op -->) activeAs activeAs; val gTs = map2 (curry op -->) activeBs activeCs; val all_gTs = map2 (curry op -->) allBs allCs'; (* terms *) val mapsAsAs = @{map 4} mk_map_of_bnf Dss Ass Ass bnfs; val mapsAsBs = @{map 4} mk_map_of_bnf Dss Ass Bss bnfs; val mapsBsCs' = @{map 4} mk_map_of_bnf Dss Bss Css' bnfs; val mapsAsCs' = @{map 4} mk_map_of_bnf Dss Ass Css' bnfs; fun mk_setss Ts = @{map 3} mk_sets_of_bnf (map (replicate live) Dss) (map (replicate live) (replicate n Ts)) bnfs; val setssAs = mk_setss allAs; val bd0s = @{map 3} mk_bd_of_bnf Dss Ass bnfs; val bds = @{map 3} (fn bd0 => fn Ds => fn bnf => mk_csum bd0 (mk_card_of (HOLogic.mk_UNIV (mk_T_of_bnf Ds (replicate live (fst (dest_relT (fastype_of bd0)))) bnf)))) bd0s Dss bnfs; val witss = map wits_of_bnf bnfs; val ((((((((zs, zs'), Bs), ss), fs), self_fs), all_gs), (xFs, xFs')), _) = lthy |> mk_Frees' "z" activeAs ||>> mk_Frees "B" BTs ||>> mk_Frees "s" sTs ||>> mk_Frees "f" fTs ||>> mk_Frees "f" self_fTs ||>> mk_Frees "g" all_gTs ||>> mk_Frees' "x" FTsAs; val passive_UNIVs = map HOLogic.mk_UNIV passiveAs; val active_UNIVs = map HOLogic.mk_UNIV activeAs; val passive_ids = map HOLogic.id_const passiveAs; val active_ids = map HOLogic.id_const activeAs; (* thms *) val bd0_card_orders = map bd_card_order_of_bnf bnfs; val bd0_Card_orders = map bd_Card_order_of_bnf bnfs; val bd0_Cinfinites = map bd_Cinfinite_of_bnf bnfs; val set_bd0ss = map set_bd_of_bnf bnfs; val bd_Card_order = @{thm Card_order_csum}; val bd_Card_orders = replicate n bd_Card_order; val bd_Cinfinites = map (fn thm => thm RS @{thm Cinfinite_csum1}) bd0_Cinfinites; val bd_Cnotzeros = map (fn thm => thm RS @{thm Cinfinite_Cnotzero}) bd_Cinfinites; val bd_Cinfinite = hd bd_Cinfinites; val set_bdss = map2 (fn set_bd0s => fn bd0_Card_order => map (fn thm => ctrans OF [thm, bd0_Card_order RS @{thm ordLeq_csum1}]) set_bd0s) set_bd0ss bd0_Card_orders; val in_bds = map in_bd_of_bnf bnfs; val sym_map_comps = map (fn bnf => map_comp0_of_bnf bnf RS sym) bnfs; val map_comps = map map_comp_of_bnf bnfs; val map_cong0s = map map_cong0_of_bnf bnfs; val map_id0s = map map_id0_of_bnf bnfs; val map_ids = map map_id_of_bnf bnfs; val set_mapss = map set_map_of_bnf bnfs; val rel_mono_strong0s = map rel_mono_strong0_of_bnf bnfs; val le_rel_OOs = map le_rel_OO_of_bnf bnfs; val timer = time (timer "Extracted terms & thms"); (* nonemptiness check *) fun new_wit X (wit: nonemptiness_witness) = subset (op =) (#I wit, (0 upto m - 1) @ map snd X); val all = m upto m + n - 1; fun enrich X = map_filter (fn i => (case find_first (fn (_, i') => i = i') X of NONE => (case find_index (new_wit X) (nth witss (i - m)) of ~1 => NONE | j => SOME (j, i)) | SOME ji => SOME ji)) all; val reachable = fixpoint (op =) enrich []; val _ = (case subtract (op =) (map snd reachable) all of [] => () | i :: _ => raise EMPTY_DATATYPE (Binding.name_of (nth bs (i - m)))); val wit_thms = flat (map2 (fn bnf => fn (j, _) => nth (wit_thmss_of_bnf bnf) j) bnfs reachable); val timer = time (timer "Checked nonemptiness"); (* derived thms *) (*map g1 ... gm g(m+1) ... g(m+n) (map id ... id f(m+1) ... f(m+n) x) = map g1 ... gm (g(m+1) o f(m+1)) ... (g(m+n) o f(m+n)) x*) fun mk_map_comp_id x mapAsBs mapBsCs mapAsCs map_comp0 = let val lhs = Term.list_comb (mapBsCs, all_gs) $ (Term.list_comb (mapAsBs, passive_ids @ fs) $ x); val rhs = Term.list_comb (mapAsCs, take m all_gs @ map HOLogic.mk_comp (drop m all_gs ~~ fs)) $ x; val vars = fold (Variable.add_free_names lthy) [lhs, rhs] []; in Goal.prove_sorry lthy vars [] (mk_Trueprop_eq (lhs, rhs)) (fn {context = ctxt, prems = _} => mk_map_comp_id_tac ctxt map_comp0) |> Thm.close_derivation \<^here> end; val map_comp_id_thms = @{map 5} mk_map_comp_id xFs mapsAsBs mapsBsCs' mapsAsCs' map_comps (*forall a : set(m+1) x. f(m+1) a = a; ...; forall a : set(m+n) x. f(m+n) a = a ==> map id ... id f(m+1) ... f(m+n) x = x*) fun mk_map_cong0L x mapAsAs sets map_cong0 map_id = let fun mk_prem set f z z' = HOLogic.mk_Trueprop (mk_Ball (set $ x) (Term.absfree z' (HOLogic.mk_eq (f $ z, z)))); val prems = @{map 4} mk_prem (drop m sets) self_fs zs zs'; val goal = mk_Trueprop_eq (Term.list_comb (mapAsAs, passive_ids @ self_fs) $ x, x); val vars = fold (Variable.add_free_names lthy) (goal :: prems) []; in Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, goal)) (fn {context = ctxt, prems = _} => mk_map_cong0L_tac ctxt m map_cong0 map_id) |> Thm.close_derivation \<^here> end; val map_cong0L_thms = @{map 5} mk_map_cong0L xFs mapsAsAs setssAs map_cong0s map_ids; val in_mono'_thms = map (fn bnf => in_mono_of_bnf bnf OF (replicate m subset_refl val in_cong'_thms = map (fn bnf => in_cong_of_bnf bnf OF (replicate m refl)) bnfs val timer = time (timer "Derived simple theorems"); (* algebra *) val alg_bind = mk_internal_b algN; val alg_def_bind = (Thm.def_binding alg_bind, []); (*forall i = 1 ... n: (\<forall>x \<in> Fi_in UNIV .. UNIV B1 ... Bn. si x \<in> Bi)*) val alg_spec = let val ins = @{map 3} mk_in (replicate n (passive_UNIVs @ Bs)) setssAs FTsAs; fun mk_alg_conjunct B s X x x' = mk_Ball X (Term.absfree x' (HOLogic.mk_mem (s $ x, B))); val rhs = Library.foldr1 HOLogic.mk_conj (@{map 5} mk_alg_conjunct Bs ss ins xFs xFs') in fold_rev (Term.absfree o Term.dest_Free) (Bs @ ss) rhs end; val ((alg_free, (_, alg_def_free)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> Local_Theory.define ((alg_bind, NoSyn), (alg_def_bind, alg_spec)) ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val alg = fst (Term.dest_Const (Morphism.term phi alg_free)); val alg_def = mk_unabs_def (2 * n) (HOLogic.mk_obj_eq (Morphism.thm phi alg_def_free)); fun mk_alg Bs ss = let val args = Bs @ ss; val Ts = map fastype_of args; val algT = Library.foldr (op -->) (Ts, HOLogic.boolT); in Term.list_comb (Const (alg, algT), args) end; val ((((((((zs, zs'), Bs), B's), ss), s's), fs), (xFs, xFs')), _) = lthy |> mk_Frees' "z" activeAs ||>> mk_Frees "B" BTs ||>> mk_Frees "B'" B'Ts ||>> mk_Frees "s" sTs ||>> mk_Frees "s'" s'Ts ||>> mk_Frees "f" fTs ||>> mk_Frees' "x" FTsAs; val alg_set_thms = let val alg_prem = HOLogic.mk_Trueprop (mk_alg Bs ss); fun mk_prem x set B = HOLogic.mk_Trueprop (mk_leq (set $ x) B); fun mk_concl s x B = mk_Trueprop_mem (s $ x, B); val premss = map2 ((fn x => fn sets => map2 (mk_prem x) (drop m sets) Bs)) xFs setssAs; val concls = @{map 3} mk_concl ss xFs Bs; val goals = map2 (fn prems => fn concl => Logic.list_implies (alg_prem :: prems, concl)) premss concls; in map (fn goal => Variable.add_free_names lthy goal [] |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_alg_set_tac ctxt alg_def)) |> Thm.close_derivation \<^here>) goals end; val timer = time (timer "Algebra definition & thms"); val alg_not_empty_thms = let val alg_prem = HOLogic.mk_Trueprop (mk_alg Bs ss); val concls = map (HOLogic.mk_Trueprop o mk_not_empty) Bs; val goals = map (fn concl => Logic.mk_implies (alg_prem, concl)) concls; in map2 (fn goal => fn alg_set => Variable.add_free_names lthy goal [] |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_alg_not_empty_tac ctxt alg_set alg_set_thms wit_thms)) |> Thm.close_derivation \<^here>) goals alg_set_thms end; val timer = time (timer "Proved nonemptiness"); (* morphism *) val mor_bind = mk_internal_b morN; val mor_def_bind = (Thm.def_binding mor_bind, []); (*fbetw) forall i = 1 ... n: (\<forall>x \<in> Bi. f x \<in> B'i)*) (*mor) forall i = 1 ... n: (\<forall>x \<in> Fi_in UNIV ... UNIV B1 ... Bn. f (s1 x) = s1' (Fi_map id ... id f1 ... fn x))*) val mor_spec = let fun mk_fbetw f B1 B2 z z' = mk_Ball B1 (Term.absfree z' (HOLogic.mk_mem (f $ z, B2))); fun mk_mor sets mapAsBs f s s' T x x' = mk_Ball (mk_in (passive_UNIVs @ Bs) sets T) (Term.absfree x' (HOLogic.mk_eq (f $ (s $ x), s' $ (Term.list_comb (mapAsBs, passive_ids @ fs) $ x)))); val rhs = HOLogic.mk_conj (Library.foldr1 HOLogic.mk_conj (@{map 5} mk_fbetw fs Bs B's zs zs'), Library.foldr1 HOLogic.mk_conj (@{map 8} mk_mor setssAs mapsAsBs fs ss s's FTsAs xFs xFs')) in fold_rev (Term.absfree o Term.dest_Free) (Bs @ ss @ B's @ s's @ fs) rhs end; val ((mor_free, (_, mor_def_free)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> Local_Theory.define ((mor_bind, NoSyn), (mor_def_bind, mor_spec)) ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val mor = fst (Term.dest_Const (Morphism.term phi mor_free)); val mor_def = mk_unabs_def (5 * n) (HOLogic.mk_obj_eq (Morphism.thm phi mor_def_free)); fun mk_mor Bs1 ss1 Bs2 ss2 fs = let val args = Bs1 @ ss1 @ Bs2 @ ss2 @ fs; val Ts = map fastype_of (Bs1 @ ss1 @ Bs2 @ ss2 @ fs); val morT = Library.foldr (op -->) (Ts, HOLogic.boolT); in Term.list_comb (Const (mor, morT), args) end; val (((((((((((Bs, Bs_copy), B's), B''s), ss), s's), s''s), fs), fs_copy), gs), xFs), _) = lthy |> mk_Frees "B" BTs ||>> mk_Frees "B" BTs ||>> mk_Frees "B'" B'Ts ||>> mk_Frees "B''" B''Ts ||>> mk_Frees "s" sTs ||>> mk_Frees "s'" s'Ts ||>> mk_Frees "s''" s''Ts ||>> mk_Frees "f" fTs ||>> mk_Frees "f" fTs ||>> mk_Frees "g" gTs ||>> mk_Frees "x" FTsAs; val morE_thms = let val prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs); fun mk_elim_prem sets x T = HOLogic.mk_Trueprop (HOLogic.mk_mem (x, mk_in (passive_UNIVs @ Bs) sets T)); fun mk_elim_goal sets mapAsBs f s s' x T = Logic.list_implies ([prem, mk_elim_prem sets x T], mk_Trueprop_eq (f $ (s $ x), s' $ Term.list_comb (mapAsBs, passive_ids @ fs @ [x]))); val elim_goals = @{map 7} mk_elim_goal setssAs mapsAsBs fs ss s's xFs FTsAs; fun prove goal = Variable.add_free_names lthy goal [] |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_mor_elim_tac ctxt mor_def)) |> Thm.close_derivation \<^here>; in map prove elim_goals end; val mor_incl_thm = let val prems = map2 (HOLogic.mk_Trueprop oo mk_leq) Bs Bs_copy; val concl = HOLogic.mk_Trueprop (mk_mor Bs ss Bs_copy ss active_ids); val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; in Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) (fn {context = ctxt, prems = _} => mk_mor_incl_tac ctxt mor_def map_ids) |> Thm.close_derivation \<^here> end; val mor_comp_thm = let val prems = [HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs), HOLogic.mk_Trueprop (mk_mor B's s's B''s s''s gs)]; val concl = HOLogic.mk_Trueprop (mk_mor Bs ss B''s s''s (map2 (curry HOLogic.mk_comp) gs fs)); val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; in Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) (fn {context = ctxt, prems = _} => mk_mor_comp_tac ctxt mor_def set_mapss map_comp_id_thms) |> Thm.close_derivation \<^here> end; val mor_cong_thm = let val prems = map HOLogic.mk_Trueprop (map2 (curry HOLogic.mk_eq) fs_copy fs @ [mk_mor Bs ss B's s's fs]) val concl = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs_copy); val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; in Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) (fn {context = ctxt, prems = _} => (hyp_subst_tac ctxt THEN' assume_tac ctxt) 1) |> Thm.close_derivation \<^here> end; val mor_str_thm = let val maps = map2 (fn Ds => fn bnf => Term.list_comb (mk_map_of_bnf Ds (passiveAs @ FTsAs) allAs bnf, passive_ids @ ss)) Dss bnfs; val goal = HOLogic.mk_Trueprop (mk_mor (map HOLogic.mk_UNIV FTsAs) maps active_UNIVs ss ss); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_mor_str_tac ctxt ks mor_def) |> Thm.close_derivation \<^here> end; val mor_UNIV_thm = let fun mk_conjunct mapAsBs f s s' = HOLogic.mk_eq (HOLogic.mk_comp (f, s), HOLogic.mk_comp (s', Term.list_comb (mapAsBs, passive_ids @ fs))); val lhs = mk_mor active_UNIVs ss (map HOLogic.mk_UNIV activeBs) s's fs; val rhs = Library.foldr1 HOLogic.mk_conj (@{map 4} mk_conjunct mapsAsBs fs ss s's); val vars = fold (Variable.add_free_names lthy) [lhs, rhs] []; in Goal.prove_sorry lthy vars [] (mk_Trueprop_eq (lhs, rhs)) (fn {context = ctxt, prems = _} => mk_mor_UNIV_tac ctxt m morE_thms mor_def) |> Thm.close_derivation \<^here> end; val timer = time (timer "Morphism definition & thms"); (* bounds *) val sum_bd = Library.foldr1 (uncurry mk_csum) bds; val sum_bdT = fst (dest_relT (fastype_of sum_bd)); val (sum_bdT_params, sum_bdT_params') = `(map TFree) (Term.add_tfreesT sum_bdT []) val (lthy, sbd, sbd_Cinfinite, sbd_Card_order, set_sbdss, in_sbds) = if n = 1 then (lthy, sum_bd, bd_Cinfinite, bd_Card_order, set_bdss, in_bds) else let val sbdT_bind = mk_internal_b sum_bdTN; val ((sbdT_name, (sbdT_glob_info, sbdT_loc_info)), lthy) = typedef (sbdT_bind, sum_bdT_params', NoSyn) (HOLogic.mk_UNIV sum_bdT) NONE (fn ctxt => EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) lthy; val sbdT = Type (sbdT_name, sum_bdT_params); val Abs_sbdT = Const (#Abs_name sbdT_glob_info, sum_bdT --> sbdT); val sbd_bind = mk_internal_b sum_bdN; val sbd_def_bind = (Thm.def_binding sbd_bind, []); val sbd_spec = mk_dir_image sum_bd Abs_sbdT; val ((sbd_free, (_, sbd_def_free)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> Local_Theory.define ((sbd_bind, NoSyn), (sbd_def_bind, sbd_spec)) ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val sbd_def = HOLogic.mk_obj_eq (Morphism.thm phi sbd_def_free); val sbd = Const (fst (Term.dest_Const (Morphism.term phi sbd_free)), mk_relT (`I sbdT)); val Abs_sbdT_inj = mk_Abs_inj_thm (#Abs_inject sbdT_loc_info); val sum_Cinfinite = mk_sum_Cinfinite bd_Cinfinites; val sum_Card_order = sum_Cinfinite RS conjunct2; val sbd_ordIso = @{thm ssubst_Pair_rhs} OF [@{thm dir_image} OF [Abs_sbdT_inj, sum_Card_order], sbd_def]; val sbd_Cinfinite = @{thm Cinfinite_cong} OF [sbd_ordIso, sum_Cinfinite]; val sbd_Card_order = sbd_Cinfinite RS conjunct2; fun mk_set_sbd i bd_Card_order bds = map (fn thm => @{thm ordLeq_ordIso_trans} OF [bd_Card_order RS mk_ordLeq_csum n i thm, sbd_ordIso]) bds; val set_sbdss = @{map 3} mk_set_sbd ks bd_Card_orders set_bdss; fun mk_in_bd_sum i Co Cnz bd = Cnz RS ((@{thm ordLeq_ordIso_trans} OF [Co RS mk_ordLeq_csum n i (Co RS @{thm ordLeq_refl}), sbd_ordIso]) RS (bd RS @{thm ordLeq_transitive[OF _ cexp_mono2_Cnotzero[OF _ Card_order_csum]]})); val in_sbds = @{map 4} mk_in_bd_sum ks bd_Card_orders bd_Cnotzeros in_bds; in (lthy, sbd, sbd_Cinfinite, sbd_Card_order, set_sbdss, in_sbds) end; val sbd_Cnotzero = sbd_Cinfinite RS @{thm Cinfinite_Cnotzero}; val suc_bd = mk_cardSuc sbd; val field_suc_bd = mk_Field suc_bd; val suc_bdT = fst (dest_relT (fastype_of suc_bd)); fun mk_Asuc_bd [] = mk_cexp ctwo suc_bd | mk_Asuc_bd As = mk_cexp (mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo) suc_bd; val suc_bd_Card_order = sbd_Card_order RS @{thm cardSuc_Card_order}; val suc_bd_Cinfinite = sbd_Cinfinite RS @{thm Cinfinite_cardSuc}; val suc_bd_Cnotzero = suc_bd_Cinfinite RS @{thm Cinfinite_Cnotzero}; val suc_bd_worel = suc_bd_Card_order RS @{thm Card_order_wo_rel} val basis_Asuc = if m = 0 then @{thm ordLeq_refl[OF Card_order_ctwo]} else @{thm ordLeq_csum2[OF Card_order_ctwo]}; val Asuc_bd_Cinfinite = suc_bd_Cinfinite RS (basis_Asuc RS @{thm Cinfinite_cexp}); val suc_bd_Asuc_bd = @{thm ordLess_ordLeq_trans[OF ordLess_ctwo_cexp cexp_mono1]} OF [suc_bd_Card_order, basis_Asuc, suc_bd_Card_order]; val Asuc_bd = mk_Asuc_bd passive_UNIVs; val Asuc_bdT = fst (dest_relT (fastype_of Asuc_bd)); val II_BTs = replicate n (HOLogic.mk_setT Asuc_bdT); val II_sTs = map2 (fn Ds => fn bnf => mk_T_of_bnf Ds (passiveAs @ replicate n Asuc_bdT) bnf --> Asuc_bdT) Dss bnfs; val ((((((Bs, ss), idxs), Asi_name), (idx, idx')), (jdx, jdx')), _) = lthy |> mk_Frees "B" BTs ||>> mk_Frees "s" sTs ||>> mk_Frees "i" (replicate n suc_bdT) ||>> (fn ctxt => apfst the_single (mk_fresh_names ctxt 1 "Asi")) ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") suc_bdT ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "j") suc_bdT; val suc_bd_limit_thm = let val prem = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map (fn idx => HOLogic.mk_mem (idx, field_suc_bd)) idxs)); fun mk_conjunct idx = HOLogic.mk_conj (mk_not_eq idx jdx, HOLogic.mk_mem (HOLogic.mk_prod (idx, jdx), suc_bd)); val concl = HOLogic.mk_Trueprop (mk_Bex field_suc_bd (Term.absfree jdx' (Library.foldr1 HOLogic.mk_conj (map mk_conjunct idxs)))); val vars = fold (Variable.add_free_names lthy) [prem, concl] []; in Goal.prove_sorry lthy vars [] (Logic.list_implies ([prem], concl)) (fn {context = ctxt, prems = _} => mk_bd_limit_tac ctxt n suc_bd_Cinfinite) |> Thm.close_derivation \<^here> end; val timer = time (timer "Bounds"); (* minimal algebra *) fun mk_minG Asi i k = mk_UNION (mk_underS suc_bd $ i) (Term.absfree jdx' (mk_nthN n (Asi $ jdx) k)); fun mk_minH_component Asi i sets Ts s k = HOLogic.mk_binop \<^const_name>\<open>sup\<close> (mk_minG Asi i k, mk_image s $ mk_in (passive_UNIVs @ map (mk_minG Asi i) ks) sets Ts); fun mk_min_algs ss = let val BTs = map (range_type o fastype_of) ss; val Ts = passiveAs @ BTs; val (Asi, Asi') = `Free (Asi_name, suc_bdT --> Library.foldr1 HOLogic.mk_prodT (map HOLogic.mk_setT BTs)); in mk_worec suc_bd (Term.absfree Asi' (Term.absfree idx' (HOLogic.mk_tuple (@{map 4} (mk_minH_component Asi idx) (mk_setss Ts) (mk_FTs Ts) ss ks)))) end; val (min_algs_thms, min_algs_mono_thms, card_of_min_algs_thm, least_min_algs_thm) = let val i_field = HOLogic.mk_mem (idx, field_suc_bd); val min_algs = mk_min_algs ss; val min_algss = map (fn k => mk_nthN n (min_algs $ idx) k) ks; val concl = HOLogic.mk_Trueprop (HOLogic.mk_eq (min_algs $ idx, HOLogic.mk_tuple (@{map 4} (mk_minH_component min_algs idx) setssAs FTsAs ss ks))); val goal = Logic.mk_implies (HOLogic.mk_Trueprop i_field, concl); val vars = Variable.add_free_names lthy goal []; val min_algs_thm = Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_min_algs_tac ctxt suc_bd_worel in_cong'_thms) |> Thm.close_derivation \<^here>; val min_algs_thms = map (fn k => min_algs_thm RS mk_nthI n k) ks; fun mk_mono_goal min_alg = HOLogic.mk_Trueprop (mk_relChain suc_bd (Term.absfree idx' min_alg)); val monos = map2 (fn goal => fn min_algs => Variable.add_free_names lthy goal [] |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_min_algs_mono_tac ctxt min_algs)) |> Thm.close_derivation \<^here>) (map mk_mono_goal min_algss) min_algs_thms; fun mk_card_conjunct min_alg = mk_ordLeq (mk_card_of min_alg) Asuc_bd; val card_conjunction = Library.foldr1 HOLogic.mk_conj (map mk_card_conjunct min_algss); val card_cT = Thm.ctyp_of lthy suc_bdT; val card_ct = Thm.cterm_of lthy (Term.absfree idx' card_conjunction); val card_of = let val goal = HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, card_conjunction)); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_min_algs_card_of_tac ctxt card_cT card_ct m suc_bd_worel min_algs_thms in_sbds sbd_Card_order sbd_Cnotzero suc_bd_Card_order suc_bd_Cinfinite suc_bd_Cnotzero suc_bd_Asuc_bd Asuc_bd_Cinfinite) |> Thm.close_derivation \<^here> end; val least_prem = HOLogic.mk_Trueprop (mk_alg Bs ss); val least_conjunction = Library.foldr1 HOLogic.mk_conj (map2 mk_leq min_algss Bs); val least_cT = Thm.ctyp_of lthy suc_bdT; val least_ct = Thm.cterm_of lthy (Term.absfree idx' least_conjunction); val least = let val goal = Logic.mk_implies (least_prem, HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, least_conjunction))); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_min_algs_least_tac ctxt least_cT least_ct suc_bd_worel min_algs_thms alg_set_thms) |> Thm.close_derivation \<^here> end; in (min_algs_thms, monos, card_of, least) end; val timer = time (timer "min_algs definition & thms"); val min_alg_binds = mk_internal_bs min_algN; fun min_alg_bind i = nth min_alg_binds (i - 1); val min_alg_def_bind = rpair [] o Thm.def_binding o min_alg_bind; fun min_alg_spec i = let val rhs = mk_UNION (field_suc_bd) (Term.absfree idx' (mk_nthN n (mk_min_algs ss $ idx) i)); in fold_rev (Term.absfree o Term.dest_Free) ss rhs end; val ((min_alg_frees, (_, min_alg_def_frees)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> fold_map (fn i => Local_Theory.define ((min_alg_bind i, NoSyn), (min_alg_def_bind i, min_alg_spec i))) ks |>> apsnd split_list o split_list ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val min_algs = map (fst o Term.dest_Const o Morphism.term phi) min_alg_frees; val min_alg_defs = map (fn def => mk_unabs_def n (HOLogic.mk_obj_eq (Morphism.thm phi def))) min_alg_def_frees; fun mk_min_alg ss i = let val T = HOLogic.mk_setT (range_type (fastype_of (nth ss (i - 1)))) val Ts = map fastype_of ss; val min_algT = Library.foldr (op -->) (Ts, T); in Term.list_comb (Const (nth min_algs (i - 1), min_algT), ss) end; val min_algs = map (mk_min_alg ss) ks; val ((Bs, ss), _) = lthy |> mk_Frees "B" BTs ||>> mk_Frees "s" sTs; val (alg_min_alg_thm, card_of_min_alg_thms, least_min_alg_thms, mor_incl_min_alg_thm let val alg_min_alg = let val goal = HOLogic.mk_Trueprop (mk_alg min_algs ss); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_alg_min_alg_tac ctxt m alg_def min_alg_defs suc_bd_limit_thm sbd_Cinfinite set_sbdss min_algs_thms min_algs_mono_thms) |> Thm.close_derivation \<^here> end; fun mk_card_of_thm min_alg def = let val goal = HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of min_alg) Asuc_bd); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_card_of_min_alg_tac ctxt def card_of_min_algs_thm suc_bd_Card_order suc_bd_Asuc_bd Asuc_bd_Cinfinite) |> Thm.close_derivation \<^here> end; fun mk_least_thm min_alg B def = let val prem = HOLogic.mk_Trueprop (mk_alg Bs ss); val goal = Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_leq min_alg B)); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_least_min_alg_tac ctxt def least_min_algs_thm) |> Thm.close_derivation \<^here> end; val leasts = @{map 3} mk_least_thm min_algs Bs min_alg_defs; val incl = let val prem = HOLogic.mk_Trueprop (mk_alg Bs ss); val goal = Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_mor min_algs ss Bs ss active_ids)); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => EVERY' (rtac ctxt mor_incl_thm :: map (etac ctxt) leasts) 1) |> Thm.close_derivation \<^here> end; in (alg_min_alg, map2 mk_card_of_thm min_algs min_alg_defs, leasts, incl) end; val timer = time (timer "Minimal algebra definition & thms"); val II_repT = HOLogic.mk_prodT (HOLogic.mk_tupleT II_BTs, HOLogic.mk_tupleT II_sTs); val IIT_bind = mk_internal_b IITN; val ((IIT_name, (IIT_glob_info, IIT_loc_info)), lthy) = typedef (IIT_bind, params, NoSyn) (HOLogic.mk_UNIV II_repT) NONE (fn ctxt => EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) val IIT = Type (IIT_name, params'); val Abs_IIT = Const (#Abs_name IIT_glob_info, II_repT --> IIT); val Rep_IIT = Const (#Rep_name IIT_glob_info, IIT --> II_repT); val Abs_IIT_inverse_thm = UNIV_I RS #Abs_inverse IIT_loc_info; val initT = IIT --> Asuc_bdT; val active_initTs = replicate n initT; val init_FTs = map2 (fn Ds => mk_T_of_bnf Ds (passiveAs @ active_initTs)) Dss bnfs; val init_fTs = map (fn T => initT --> T) activeAs; val ((((II_Bs, II_ss), (iidx, iidx')), init_xFs), _) = lthy |> mk_Frees "IIB" II_BTs ||>> mk_Frees "IIs" II_sTs ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") IIT ||>> mk_Frees "x" init_FTs; val II = HOLogic.mk_Collect (fst iidx', IIT, list_exists_free (II_Bs @ II_ss) (HOLogic.mk_conj (HOLogic.mk_eq (iidx, Abs_IIT $ (HOLogic.mk_prod (HOLogic.mk_tuple II_Bs, HOLogic.mk_tuple II_ss))), mk_alg II_Bs II_ss))); val select_Bs = map (mk_nthN n (HOLogic.mk_fst (Rep_IIT $ iidx))) ks; val select_ss = map (mk_nthN n (HOLogic.mk_snd (Rep_IIT $ iidx))) ks; val str_init_binds = mk_internal_bs str_initN; fun str_init_bind i = nth str_init_binds (i - 1); val str_init_def_bind = rpair [] o Thm.def_binding o str_init_bind; fun str_init_spec i = let val init_xF = nth init_xFs (i - 1) val select_s = nth select_ss (i - 1); val map = mk_map_of_bnf (nth Dss (i - 1)) (passiveAs @ active_initTs) (passiveAs @ replicate n Asuc_bdT) (nth bnfs (i - 1)); val map_args = passive_ids @ replicate n (mk_rapp iidx Asuc_bdT); val rhs = select_s $ (Term.list_comb (map, map_args) $ init_xF); in fold_rev (Term.absfree o Term.dest_Free) [init_xF, iidx] rhs end; val ((str_init_frees, (_, str_init_def_frees)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> fold_map (fn i => Local_Theory.define ((str_init_bind i, NoSyn), (str_init_def_bind i, str_init_spec i))) ks |>> apsnd split_list o split_list ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val str_inits = map (Term.subst_atomic_types (map (`(Morphism.typ phi)) params') o Morphism.term phi) str_init_frees; val str_init_defs = map (fn def => mk_unabs_def 2 (HOLogic.mk_obj_eq (Morphism.thm phi def))) str_init_def_frees; val car_inits = map (mk_min_alg str_inits) ks; val (((((((((Bs, ss), Asuc_fs), (iidx, iidx')), init_xs), (init_xFs, init_xFs')), init init_fs_copy), init_phis), _) = lthy |> mk_Frees "B" BTs ||>> mk_Frees "s" sTs ||>> mk_Frees "f" (map (fn T => Asuc_bdT --> T) activeAs) ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") IIT ||>> mk_Frees "ix" active_initTs ||>> mk_Frees' "x" init_FTs ||>> mk_Frees "f" init_fTs ||>> mk_Frees "f" init_fTs ||>> mk_Frees "P" (replicate n (mk_pred1T initT)); val alg_init_thm = infer_instantiate' lthy (map (SOME o Thm.cterm_of lthy) str_inits) alg_min_alg_t val alg_select_thm = Goal.prove_sorry lthy [] [] (HOLogic.mk_Trueprop (mk_Ball II (Term.absfree iidx' (mk_alg select_Bs select_ss)))) (fn {context = ctxt, prems = _} => mk_alg_select_tac ctxt Abs_IIT_inverse_thm) |> Thm.close_derivation \<^here>; val mor_select_thm = let val i_prem = mk_Trueprop_mem (iidx, II); val mor_prem = HOLogic.mk_Trueprop (mk_mor select_Bs select_ss active_UNIVs ss Asuc_fs); val prems = [i_prem, mor_prem]; val concl = HOLogic.mk_Trueprop (mk_mor car_inits str_inits active_UNIVs ss (map (fn f => HOLogic.mk_comp (f, mk_rapp iidx Asuc_bdT)) Asuc_fs)); val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; in Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) (fn {context = ctxt, prems = _} => mk_mor_select_tac ctxt mor_def mor_cong_thm mor_comp_thm mor_incl_min_alg_thm alg_def alg_select_thm alg_set_thms set_mapss str_init_defs) |> Thm.close_derivation \<^here> end; val init_unique_mor_thms = let val prems = map2 (HOLogic.mk_Trueprop oo curry HOLogic.mk_mem) init_xs car_inits val mor_prems = map HOLogic.mk_Trueprop [mk_mor car_inits str_inits Bs ss init_fs, mk_mor car_inits str_inits Bs ss init_fs_copy]; fun mk_fun_eq f g x = HOLogic.mk_eq (f $ x, g $ x); val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (@{map 3} mk_fun_eq init_fs init_fs_copy init_xs)); val cts = map (Thm.cterm_of lthy) ss; val all_prems = prems @ mor_prems; val vars = fold (Variable.add_free_names lthy) (unique :: all_prems) []; val unique_mor = Goal.prove_sorry lthy vars [] (Logic.list_implies (all_prems, unique)) (fn {context = ctxt, prems = _} => mk_init_unique_mor_tac ctxt cts m alg_def alg_init_thm least_min_alg_thms in_mono'_thms alg_set_thms morE_thms map_cong0s) |> Thm.close_derivation \<^here>; in split_conj_thm unique_mor end; val init_setss = mk_setss (passiveAs @ active_initTs); val active_init_setss = map (drop m) init_setss; val init_ins = map2 (fn sets => mk_in (passive_UNIVs @ car_inits) sets) init_setss init_FTs; fun mk_closed phis = let fun mk_conjunct phi str_init init_sets init_in x x' = let val prem = Library.foldr1 HOLogic.mk_conj (map2 (fn set => mk_Ball (set $ x)) init_sets phis); val concl = phi $ (str_init $ x); in mk_Ball init_in (Term.absfree x' (HOLogic.mk_imp (prem, concl))) end; in Library.foldr1 HOLogic.mk_conj (@{map 6} mk_conjunct phis str_inits active_init_setss init_ins init_xFs init_xFs') end; val init_induct_thm = let val prem = HOLogic.mk_Trueprop (mk_closed init_phis); val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_Ball car_inits init_phis)); val vars = fold (Variable.add_free_names lthy) [concl, prem] []; in Goal.prove_sorry lthy vars [] (Logic.mk_implies (prem, concl)) (fn {context = ctxt, prems = _} => mk_init_induct_tac ctxt m alg_def alg_init_thm least_min_alg_thms alg_set_thms) |> Thm.close_derivation \<^here> end; val timer = time (timer "Initiality definition & thms"); val ((T_names, (T_glob_infos, T_loc_infos)), lthy) = lthy |> @{fold_map 3} (fn b => fn mx => fn car_init => typedef (b, params, mx) car_init NONE (fn ctxt => EVERY' [rtac ctxt iffD2, rtac ctxt @{thm ex_in_conv}, resolve_tac ctxt alg_not_e rtac ctxt alg_init_thm] 1)) bs mixfixes car_inits |>> apsnd split_list o split_list; val Ts = map (fn name => Type (name, params')) T_names; fun mk_Ts passive = map (Term.typ_subst_atomic (passiveAs ~~ passive)) Ts; val Ts' = mk_Ts passiveBs; val Rep_Ts = map2 (fn info => fn T => Const (#Rep_name info, T --> initT)) T_glob_infos Ts; val Abs_Ts = map2 (fn info => fn T => Const (#Abs_name info, initT --> T)) T_glob_infos Ts; val type_defs = map #type_definition T_loc_infos; val Reps = map #Rep T_loc_infos; val Rep_inverses = map #Rep_inverse T_loc_infos; val Abs_inverses = map #Abs_inverse T_loc_infos; val timer = time (timer "THE TYPEDEFs & Rep/Abs thms"); val UNIVs = map HOLogic.mk_UNIV Ts; val FTs = mk_FTs (passiveAs @ Ts); val FTs' = mk_FTs (passiveBs @ Ts'); fun mk_set_Ts T = passiveAs @ replicate n (HOLogic.mk_setT T); val setFTss = map (mk_FTs o mk_set_Ts) passiveAs; val FTs_setss = mk_setss (passiveAs @ Ts); val FTs'_setss = mk_setss (passiveBs @ Ts'); val map_FT_inits = map2 (fn Ds => mk_map_of_bnf Ds (passiveAs @ Ts) (passiveAs @ active_initTs)) Dss bnfs; val fTs = map2 (curry op -->) Ts activeAs; val foldT = Library.foldr1 HOLogic.mk_prodT (map2 (curry op -->) Ts activeAs); val ((ss, (fold_f, fold_f')), _) = lthy |> mk_Frees "s" sTs ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "f") foldT; fun ctor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctorN ^ "_"); val ctor_def_bind = rpair [] o Binding.concealed o Thm.def_binding o ctor_bind; fun ctor_spec abs str map_FT_init = Library.foldl1 HOLogic.mk_comp [abs, str, Term.list_comb (map_FT_init, map HOLogic.id_const passiveAs @ Rep_Ts)]; val ((ctor_frees, (_, ctor_def_frees)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> @{fold_map 4} (fn i => fn abs => fn str => fn mapx => Local_Theory.define ((ctor_bind i, NoSyn), (ctor_def_bind i, ctor_spec abs str mapx))) ks Abs_Ts str_inits map_FT_inits |>> apsnd split_list o split_list ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; fun mk_ctors passive = map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ (mk_params passive)) Morphism.term phi) ctor_frees; val ctors = mk_ctors passiveAs; val ctor's = mk_ctors passiveBs; val ctor_defs = map (fn def => HOLogic.mk_obj_eq (Morphism.thm phi def)) ctor_def_frees; val (mor_Rep_thm, mor_Abs_thm) = let val defs = mor_def :: ctor_defs; val mor_Rep = Goal.prove_sorry lthy [] [] (HOLogic.mk_Trueprop (mk_mor UNIVs ctors car_inits str_inits Rep_Ts)) (fn {context = ctxt, prems = _} => mk_mor_Rep_tac ctxt m defs Reps Abs_inverses alg_min_alg_thm alg_set_thms set_mapss) |> Thm.close_derivation \<^here>; fun mk_ct initFT str abs = Term.absdummy initFT (abs $ (str $ Bound 0)) val cts = @{map 3} (Thm.cterm_of lthy ooo mk_ct) init_FTs str_inits Abs_Ts; val mor_Abs = Goal.prove_sorry lthy [] [] (HOLogic.mk_Trueprop (mk_mor car_inits str_inits UNIVs ctors Abs_Ts)) (fn {context = ctxt, prems = _} => mk_mor_Abs_tac ctxt cts defs Abs_inverses map_comp_id_thms map_cong0L_thms) |> Thm.close_derivation \<^here>; in (mor_Rep, mor_Abs) end; val timer = time (timer "ctor definitions & thms"); val fold_fun = Term.absfree fold_f' (mk_mor UNIVs ctors active_UNIVs ss (map (mk_nthN n fold_f) ks)); val foldx = HOLogic.choice_const foldT $ fold_fun; fun fold_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctor_foldN ^ "_"); val fold_def_bind = rpair [] o Binding.concealed o Thm.def_binding o fold_bind; fun fold_spec i = fold_rev (Term.absfree o Term.dest_Free) ss (mk_nthN n foldx i); val ((fold_frees, (_, fold_def_frees)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> fold_map (fn i => Local_Theory.define ((fold_bind i, NoSyn), (fold_def_bind i, fold_spec i))) ks |>> apsnd split_list o split_list ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val folds = map (Morphism.term phi) fold_frees; val fold_names = map (fst o dest_Const) folds; fun mk_folds passives actives = @{map 3} (fn name => fn T => fn active => Const (name, Library.foldr (op -->) (map2 (curry op -->) (mk_FTs (passives @ actives)) actives, T --> active))) fold_names (mk_Ts passives) actives; fun mk_fold Ts ss i = Term.list_comb (Const (nth fold_names (i - 1), Library.foldr (op -->) (map fastype_of ss, nth Ts (i - 1) --> range_type (fastype_of (nth ss (i - 1))))), ss); val fold_defs = map (fn def => mk_unabs_def n (HOLogic.mk_obj_eq (Morphism.thm phi def))) fold_def_frees; (* algebra copies *) val ((((((Bs, B's), ss), s's), inv_fs), fs), _) = lthy |> mk_Frees "B" BTs ||>> mk_Frees "B'" B'Ts ||>> mk_Frees "s" sTs ||>> mk_Frees "s'" s'Ts ||>> mk_Frees "f" inv_fTs ||>> mk_Frees "f" fTs; val copy_thm = let val prems = HOLogic.mk_Trueprop (mk_alg Bs ss) :: @{map 3} (HOLogic.mk_Trueprop ooo mk_bij_betw) inv_fs B's Bs; val concl = HOLogic.mk_Trueprop (list_exists_free s's (HOLogic.mk_conj (mk_alg B's s's, mk_mor B's s's Bs ss inv_fs))); val vars = fold (Variable.add_free_names lthy) (concl :: prems) []; in Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, concl)) (fn {context = ctxt, prems = _} => mk_copy_tac ctxt m alg_def mor_def alg_set_thms set_mapss) |> Thm.close_derivation \<^here> end; val init_ex_mor_thm = let val goal = HOLogic.mk_Trueprop (list_exists_free fs (mk_mor UNIVs ctors active_UNIVs ss fs)); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_init_ex_mor_tac ctxt Abs_IIT_inverse_thm (alg_min_alg_thm RS copy_thm) card_of_min_alg_thms mor_Rep_thm mor_comp_thm mor_select_thm mor_incl_thm) |> Thm.close_derivation \<^here> end; val mor_fold_thm = let val mor_cong = mor_cong_thm OF (map (mk_nth_conv n) ks); val cT = Thm.ctyp_of lthy foldT; val ct = Thm.cterm_of lthy fold_fun val goal = HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss (map (mk_fold Ts ss) ks)); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, ...} => mk_mor_fold_tac ctxt cT ct fold_defs init_ex_mor_thm mor_cong) |> Thm.close_derivation \<^here> end; val ctor_fold_thms = map (fn morE => rule_by_tactic lthy ((rtac lthy CollectI THEN' CONJ_WRAP' (K (rtac lthy @{thm subset_UNIV})) (1 upto m + n)) 1) (mor_fold_thm RS morE)) morE_thms; val (fold_unique_mor_thms, fold_unique_mor_thm) = let val prem = HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss fs); fun mk_fun_eq f i = HOLogic.mk_eq (f, mk_fold Ts ss i); val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_fun_eq fs ks)); val vars = fold (Variable.add_free_names lthy) [prem, unique] []; val unique_mor = Goal.prove_sorry lthy vars [] (Logic.mk_implies (prem, unique)) (fn {context = ctxt, prems = _} => mk_fold_unique_mor_tac ctxt type_defs init_unique_mor_thms Reps mor_comp_thm mor_Abs_thm mor_fold_thm) |> Thm.close_derivation \<^here>; in `split_conj_thm unique_mor end; val (ctor_fold_unique_thms, ctor_fold_unique_thm) = `split_conj_thm (mk_conjIN n RS (mor_UNIV_thm RS iffD2 RS fold_unique_mor_thm)) val fold_ctor_thms = map (fn thm => (mor_incl_thm OF replicate n @{thm subset_UNIV}) RS thm RS sym) fold_unique_mor_thms; val ctor_o_fold_thms = let val mor = mor_comp_thm OF [mor_fold_thm, mor_str_thm]; in map2 (fn unique => fn fold_ctor => trans OF [mor RS unique, fold_ctor]) fold_unique_mor_thms fold_ctor_thms end; val timer = time (timer "fold definitions & thms"); val map_ctors = map2 (fn Ds => fn bnf => Term.list_comb (mk_map_of_bnf Ds (passiveAs @ FTs) (passiveAs @ Ts) bnf, map HOLogic.id_const passiveAs @ ctors)) Dss bnfs; fun dtor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (dtorN ^ "_"); val dtor_def_bind = rpair [] o Binding.concealed o Thm.def_binding o dtor_bind; fun dtor_spec i = mk_fold Ts map_ctors i; val ((dtor_frees, (_, dtor_def_frees)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> fold_map (fn i => Local_Theory.define ((dtor_bind i, NoSyn), (dtor_def_bind i, dtor_spec i))) ks |>> apsnd split_list o split_list ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; fun mk_dtors params = map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ params) o Morphism.te dtor_frees; val dtors = mk_dtors params'; val dtor_defs = map (fn def => HOLogic.mk_obj_eq (Morphism.thm phi def)) dtor_def_frees; val ctor_o_dtor_thms = map2 (Local_Defs.fold lthy o single) dtor_defs ctor_o_fold_thms; val dtor_o_ctor_thms = let fun mk_goal dtor ctor FT = mk_Trueprop_eq (HOLogic.mk_comp (dtor, ctor), HOLogic.id_const FT); val goals = @{map 3} mk_goal dtors ctors FTs; in @{map 5} (fn goal => fn dtor_def => fn foldx => fn map_comp_id => fn map_cong0L => Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => mk_dtor_o_ctor_tac ctxt dtor_def foldx map_comp_id map_cong0L ctor_o_fold_thms) |> Thm.close_derivation \<^here>) goals dtor_defs ctor_fold_thms map_comp_id_thms map_cong0L_thms end; val dtor_ctor_thms = map (fn thm => thm RS @{thm pointfree_idE}) dtor_o_ctor_thms; val ctor_dtor_thms = map (fn thm => thm RS @{thm pointfree_idE}) ctor_o_dtor_thms; val bij_dtor_thms = map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) ctor_o_dtor_thms dtor_o_ctor_thms; val inj_dtor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_dtor_thms; val surj_dtor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_dtor_thms; val dtor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_dtor_thms; val dtor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_dtor_thms; val dtor_exhaust_thms = map (fn thm => thm RS exE) dtor_nchotomy_thms; val bij_ctor_thms = map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) dtor_o_ctor_thms ctor_o_dtor_thms; val inj_ctor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_ctor_thms; val surj_ctor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_ctor_thms; val ctor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_ctor_thms; val ctor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_ctor_thms; val ctor_exhaust_thms = map (fn thm => thm RS exE) ctor_nchotomy_thms; val timer = time (timer "dtor definitions & thms"); val (((((((Izs, (Izs1, Izs1'))), (Izs2, Izs2')), xFs), yFs), init_phis), _) = lthy |> mk_Frees "z" Ts ||>> mk_Frees' "z1" Ts ||>> mk_Frees' "z2" Ts' ||>> mk_Frees "x" FTs ||>> mk_Frees "y" FTs' ||>> mk_Frees "P" (replicate n (mk_pred1T initT)); val phis = map2 retype_const_or_free (map mk_pred1T Ts) init_phis; val phi2s = map2 retype_const_or_free (map2 mk_pred2T Ts Ts') init_phis; val (ctor_induct_thm, induct_params) = let fun mk_prem phi ctor sets x = let fun mk_IH phi set z = let val prem = mk_Trueprop_mem (z, set $ x); val concl = HOLogic.mk_Trueprop (phi $ z); in Logic.all z (Logic.mk_implies (prem, concl)) end; val IHs = @{map 3} mk_IH phis (drop m sets) Izs; val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x)); in Logic.all x (Logic.list_implies (IHs, concl)) end; val prems = @{map 4} mk_prem phis ctors FTs_setss xFs; fun mk_concl phi z = phi $ z; val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_concl phis Izs)) val goal = Logic.list_implies (prems, concl); val vars = Variable.add_free_names lthy goal []; in (Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_ctor_induct_tac ctxt m set_mapss init_induct_thm morE_thms mor_Abs_thm Rep_inverses Abs_inverses Reps) |> Thm.close_derivation \<^here>, rev (Term.add_tfrees goal [])) end; val cTs = map (SOME o Thm.ctyp_of lthy o TFree) induct_params; val weak_ctor_induct_thms = let fun insts i = (replicate (i - 1) TrueI) @ (asm_rl :: replicate (n - i) TrueI); in map (fn i => (ctor_induct_thm OF insts i) RS mk_conjunctN n i) ks end; val (ctor_induct2_thm, induct2_params) = let fun mk_prem phi ctor ctor' sets sets' x y = let fun mk_IH phi set set' z1 z2 = let val prem1 = mk_Trueprop_mem (z1, (set $ x)); val prem2 = mk_Trueprop_mem (z2, (set' $ y)); val concl = HOLogic.mk_Trueprop (phi $ z1 $ z2); in fold_rev Logic.all [z1, z2] (Logic.list_implies ([prem1, prem2], concl)) end; val IHs = @{map 5} mk_IH phi2s (drop m sets) (drop m sets') Izs1 Izs2; val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x) $ (ctor' $ y)); in fold_rev Logic.all [x, y] (Logic.list_implies (IHs, concl)) end; val prems = @{map 7} mk_prem phi2s ctors ctor's FTs_setss FTs'_setss xFs yFs; fun mk_concl phi z1 z2 = phi $ z1 $ z2; val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (@{map 3} mk_concl phi2s Izs1 Izs2)); fun mk_t phi (z1, z1') (z2, z2') = Term.absfree z1' (HOLogic.mk_all (fst z2', snd z2', phi $ z1 $ z2)); val cts = @{map 3} (SOME o Thm.cterm_of lthy ooo mk_t) phi2s (Izs1 ~~ Izs1') (Izs2 ~~ Izs2'); val goal = Logic.list_implies (prems, concl); val vars = Variable.add_free_names lthy goal []; in (Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_ctor_induct2_tac ctxt cTs cts ctor_induct_thm weak_ctor_induct_thms) |> Thm.close_derivation \<^here>, rev (Term.add_tfrees goal [])) end; val timer = time (timer "induction"); fun mk_ctor_map_DEADID_thm ctor_inject map_id0 = trans OF [id_apply, iffD2 OF [ctor_inject, map_id0 RS sym]]; fun mk_ctor_map_unique_DEADID_thm () = let val (funs, algs) = HOLogic.conjuncts (HOLogic.dest_Trueprop (Thm.concl_of ctor_fold_unique_thm)) |> map_split HOLogic.dest_eq ||> snd o strip_comb o hd |> @{apply 2} (map (fst o dest_Var)); fun mk_fun_insts T ix = Thm.cterm_of lthy (Var (ix, T --> T)); val theta = (funs ~~ @{map 2} mk_fun_insts Ts funs) @ (algs ~~ map (Thm.cterm_of lthy) ctors); val ctor_fold_ctors = (ctor_fold_unique_thm OF map (fn thm => mk_trans @{thm id_o} (mk_sym (thm RS @{thm trans[OF arg_cong2[of _ _ _ _ "(\ |> split_conj_thm |> map mk_sym; in infer_instantiate lthy theta ctor_fold_unique_thm |> unfold_thms lthy ctor_fold_ctors |> Morphism.thm (Local_Theory.target_morphism lthy) end; fun mk_ctor_Irel_DEADID_thm ctor_inject bnf = trans OF [ctor_inject, rel_eq_of_bnf bnf RS @{thm predicate2_eqD} RS sym]; val IphiTs = map2 mk_pred2T passiveAs passiveBs; val Ipsi1Ts = map2 mk_pred2T passiveAs passiveCs; val Ipsi2Ts = map2 mk_pred2T passiveCs passiveBs; val activephiTs = map2 mk_pred2T activeAs activeBs; val activeIphiTs = map2 mk_pred2T Ts Ts'; val rels = map2 (fn Ds => mk_rel_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs; (*register new datatypes as BNFs*) val (timer, Ibnfs, (ctor_Imap_o_thms, ctor_Imap_thms), ctor_Imap_unique_thm, ctor_Iset ctor_Irel_thms, Ibnf_notes, lthy) = if m = 0 then (timer, replicate n DEADID_bnf, map_split (`(mk_pointfree2 lthy)) (map2 mk_ctor_map_DEADID_thm ctor_inject_thms map_id mk_ctor_map_unique_DEADID_thm (), replicate n [], map2 mk_ctor_Irel_DEADID_thm ctor_inject_thms bnfs, [], lthy) else let val fTs = map2 (curry op -->) passiveAs passiveBs; val uTs = map2 (curry op -->) Ts Ts'; val ((((fs, fs'), (AFss, AFss')), (ys, ys')), _) = lthy |> mk_Frees' "f" fTs ||>> mk_Freess' "z" setFTss ||>> mk_Frees' "y" passiveAs; val map_FTFT's = map2 (fn Ds => mk_map_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs; fun mk_passive_maps ATs BTs Ts = map2 (fn Ds => mk_map_of_bnf Ds (ATs @ Ts) (BTs @ Ts)) Dss bnfs; fun mk_map_fold_arg fs Ts ctor fmap = HOLogic.mk_comp (ctor, Term.list_comb (fmap, fs @ map HOLogic.id_const Ts)); fun mk_map Ts fs Ts' ctors mk_maps = mk_fold Ts (map2 (mk_map_fold_arg fs Ts') ctors (mk_maps Ts')); val pmapsABT' = mk_passive_maps passiveAs passiveBs; val fs_maps = map (mk_map Ts fs Ts' ctor's pmapsABT') ks; val ls = 1 upto m; val setsss = map (mk_setss o mk_set_Ts) passiveAs; fun mk_col l T z z' sets = let fun mk_UN set = mk_Union T $ (set $ z); in Term.absfree z' (mk_union (nth sets (l - 1) $ z, Library.foldl1 mk_union (map mk_UN (drop m sets)))) end; val colss = @{map 5} (fn l => fn T => @{map 3} (mk_col l T)) ls passiveAs AFss AFss' setsss; val setss_by_range = map (fn cols => map (mk_fold Ts cols) ks) colss; val setss_by_bnf = transpose setss_by_range; val set_bss = map (flat o map2 (fn B => fn b => if member (op =) deads (TFree B) then [] else [b]) resBs) set_bss0; val ctor_witss = let val witss = map2 (fn Ds => fn bnf => mk_wits_of_bnf (replicate (nwits_of_bnf bnf) Ds) (replicate (nwits_of_bnf bnf) (passiveAs @ Ts)) bnf) Dss bnfs; fun close_wit (I, wit) = fold_rev Term.absfree (map (nth ys') I) wit; fun wit_apply (arg_I, arg_wit) (fun_I, fun_wit) = (union (op =) arg_I fun_I, fun_wit $ arg_wit); fun gen_arg support i = if i < m then [([i], nth ys i)] else maps (mk_wit support (nth ctors (i - m)) (i - m)) (nth support (i - m)) and mk_wit support ctor i (I, wit) = let val args = map (gen_arg (nth_map i (remove (op =) (I, wit)) support)) I; in (args, [([], wit)]) |-> fold (map_product wit_apply) |> map (apsnd (fn t => ctor $ t)) |> minimize_wits end; in @{map 3} (fn ctor => fn i => map close_wit o minimize_wits o maps (mk_wit witss ctor i)) ctors (0 upto n - 1) witss end; val (lthy, sbd0, sbd0_card_order, sbd0_Cinfinite, set_sbd0ss) = if n = 1 then (lthy, hd bd0s, hd bd0_card_orders, hd bd0_Cinfinites, set_bd0ss) else let val sum_bd0 = Library.foldr1 (uncurry mk_csum) bd0s; val sum_bd0T = fst (dest_relT (fastype_of sum_bd0)); val (sum_bd0T_params, sum_bd0T_params') = `(map TFree) (Term.add_tfreesT sum_bd0T val sbd0T_bind = mk_internal_b (sum_bdTN ^ "0"); val ((sbd0T_name, (sbd0T_glob_info, sbd0T_loc_info)), lthy) = typedef (sbd0T_bind, sum_bd0T_params', NoSyn) (HOLogic.mk_UNIV sum_bd0T) NONE (fn ctxt => EVERY' [rtac ctxt exI, rtac ctxt UNIV_I] 1) lthy; val sbd0T = Type (sbd0T_name, sum_bd0T_params); val Abs_sbd0T = Const (#Abs_name sbd0T_glob_info, sum_bd0T --> sbd0T); val sbd0_bind = mk_internal_b (sum_bdN ^ "0"); val sbd0_def_bind = (Thm.def_binding sbd0_bind, []); val sbd0_spec = mk_dir_image sum_bd0 Abs_sbd0T; val ((sbd0_free, (_, sbd0_def_free)), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> Local_Theory.define ((sbd0_bind, NoSyn), (sbd0_def_bind, sbd0_spec)) ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val sbd0_def = HOLogic.mk_obj_eq (Morphism.thm phi sbd0_def_free); val sbd0 = Const (fst (Term.dest_Const (Morphism.term phi sbd0_free)), mk_relT (`I sbd0T)); val Abs_sbd0T_inj = mk_Abs_inj_thm (#Abs_inject sbd0T_loc_info); val Abs_sbd0T_bij = mk_Abs_bij_thm lthy Abs_sbd0T_inj (#Abs_cases sbd0T_loc_info); val sum_Cinfinite = mk_sum_Cinfinite bd0_Cinfinites; val sum_Card_order = sum_Cinfinite RS conjunct2; val sum_card_order = mk_sum_card_order bd0_card_orders; val sbd0_ordIso = @{thm ssubst_Pair_rhs} OF [@{thm dir_image} OF [Abs_sbd0T_inj, sum_Card_order], sbd0_def]; val sbd0_Cinfinite = @{thm Cinfinite_cong} OF [sbd0_ordIso, sum_Cinfinite]; val sbd0_card_order = @{thm iffD2[OF arg_cong[of _ _ card_order]]} OF [sbd0_def, @{thm card_order_dir_image} OF [Abs_sbd0T_bij, sum_card_order]]; fun mk_set_sbd0 i bd0_Card_order bd0s = map (fn thm => @{thm ordLeq_ordIso_trans} OF [bd0_Card_order RS mk_ordLeq_csum n i thm, sbd0_ordIso]) bd0s; val set_sbd0ss = @{map 3} mk_set_sbd0 ks bd0_Card_orders set_bd0ss; in (lthy, sbd0, sbd0_card_order, sbd0_Cinfinite, set_sbd0ss) end; val (Ibnf_consts, lthy) = @{fold_map 9} (fn b => fn map_b => fn rel_b => fn pred_b => fn set_bs => fn mapx => fn sets => fn wits => fn T => fn lthy => define_bnf_consts Hardly_Inline (user_policy Note_Some lthy) false (SOME deads) map_b rel_b pred_b set_bs (((((((b, T), fold_rev Term.absfree fs' mapx), sets), sbd0), wits), NONE), NONE) lth bs map_bs rel_bs pred_bs set_bss fs_maps setss_by_bnf ctor_witss Ts lthy; val ((((((((((((((Izs, (Izs1, Izs1')), (Izs2, Izs2')), xFs), yFs))), Iphis), Ipsi1s), Ipsi2s), fs), fs_copy), us), (ys, ys')), _) = lthy |> mk_Frees "z" Ts ||>> mk_Frees' "z1" Ts ||>> mk_Frees' "z2" Ts' ||>> mk_Frees "x" FTs ||>> mk_Frees "y" FTs' ||>> mk_Frees "R" IphiTs ||>> mk_Frees "R" Ipsi1Ts ||>> mk_Frees "Q" Ipsi2Ts ||>> mk_Frees "f" fTs ||>> mk_Frees "f" fTs ||>> mk_Frees "u" uTs ||>> mk_Frees' "y" passiveAs; val (_, Iconsts, Iconst_defs, mk_Iconsts) = @{split_list 4} Ibnf_consts; val (_, Isetss, Ibds_Ds, Iwitss_Ds, _, _) = @{split_list 6} Iconsts; val (Imap_defs, Iset_defss, Ibd_defs, Iwit_defss, Irel_defs, Ipred_defs) = @{split_list 6} Iconst_defs; val (mk_Imaps_Ds, mk_It_Ds, _, mk_Irels_Ds, mk_Ipreds_Ds, _, _) = @{split_list 7} mk_Iconsts; val Irel_unabs_defs = map (fn def => mk_unabs_def m (HOLogic.mk_obj_eq def)) Irel_defs; val Ipred_unabs_defs = map (fn def => mk_unabs_def m (HOLogic.mk_obj_eq def)) Ipred_defs; val Iset_defs = flat Iset_defss; fun mk_Imaps As Bs = map (fn mk => mk deads As Bs) mk_Imaps_Ds; fun mk_Isetss As = map2 (fn mk => fn Isets => map (mk deads As) Isets) mk_It_Ds Isetss; val Ibds = map2 (fn mk => mk deads passiveAs) mk_It_Ds Ibds_Ds; val Iwitss = map2 (fn mk => fn Iwits => map (mk deads passiveAs o snd) Iwits) mk_It_Ds Iwitss_Ds; fun mk_Irels As Bs = map (fn mk => mk deads As Bs) mk_Irels_Ds; fun mk_Ipreds As = map (fn mk => mk deads As) mk_Ipreds_Ds; val Imaps = mk_Imaps passiveAs passiveBs; val fs_Imaps = map (fn m => Term.list_comb (m, fs)) Imaps; val fs_copy_Imaps = map (fn m => Term.list_comb (m, fs_copy)) Imaps; val (Isetss_by_range, Isetss_by_bnf) = `transpose (mk_Isetss passiveAs); val map_setss = map (fn T => map2 (fn Ds => mk_map_of_bnf Ds (passiveAs @ Ts) (mk_set_Ts T)) Dss bnfs) passiveAs; val timer = time (timer "bnf constants for the new datatypes"); val (ctor_Imap_thms, ctor_Imap_o_thms) = let fun mk_goal fs_map map ctor ctor' = mk_Trueprop_eq (HOLogic.mk_comp (fs_map, ctor), HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ fs_Imaps))); val goals = @{map 4} mk_goal fs_Imaps map_FTFT's ctors ctor's; val maps = @{map 4} (fn goal => fn foldx => fn map_comp_id => fn map_cong0 => Variable.add_free_names lthy goal [] |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN mk_map_tac ctxt m n foldx map_comp_id map_cong0)) |> Thm.close_derivation \<^here>) goals ctor_fold_thms map_comp_id_thms map_cong0s; in `(map (fn thm => thm RS @{thm comp_eq_dest})) maps end; val (ctor_Imap_unique_thms, ctor_Imap_unique_thm) = let fun mk_prem u map ctor ctor' = mk_Trueprop_eq (HOLogic.mk_comp (u, ctor), HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ us))); val prems = @{map 4} mk_prem us map_FTFT's ctors ctor's; val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) us fs_Imaps)); val vars = fold (Variable.add_free_names lthy) (goal :: prems) []; val unique = Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, goal)) (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN mk_ctor_map_unique_tac ctxt ctor_fold_unique_thm sym_map_comps) |> Thm.close_derivation \<^here>; in `split_conj_thm unique end; val timer = time (timer "map functions for the new datatypes"); val ctor_Iset_thmss = let fun mk_goal sets ctor set col map = mk_Trueprop_eq (HOLogic.mk_comp (set, ctor), HOLogic.mk_comp (col, Term.list_comb (map, passive_ids @ sets))); val goalss = @{map 3} (fn sets => @{map 4} (mk_goal sets) ctors sets) Isetss_by_range colss map_setss; val setss = map (map2 (fn foldx => fn goal => Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => --> -------------------- --> maximum size reached --> -------------------- ¤ Dauer der Verarbeitung: 0.33 Sekunden (vorverarbeitet) ¤ |
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