(* Title: HOL/Tools/BNF/bnf_gfp_grec.ML Author: Jasmin Blanchette, Inria, LORIA, MPII Author: Aymeric Bouzy, Ecole polytechnique Author: Dmitriy Traytel, ETH Zürich Copyright 2015, 2016 Generalized corecursor construction. *) signature BNF_GFP_GREC = sig val Tsubst: typ -> typ -> typ -> typ val substT: typ -> typ -> term -> term val freeze_types: Proof.context -> (indexname * sort) list -> typ list -> typ list val dummify_atomic_types: term -> term val define_const: bool -> binding -> int -> string -> term -> local_theory -> (term * thm) * local_theory type buffer = {Oper: term, VLeaf: term, CLeaf: term, ctr_wrapper: term, friends: (typ * term) Symtab.table} val map_buffer: (term -> term) -> buffer -> buffer val specialize_buffer_types: buffer -> buffer type dtor_coinduct_info = {dtor_coinduct: thm, cong_def: thm, cong_locale: thm, cong_base: thm, cong_refl: thm, cong_sym: thm, cong_trans: thm, cong_alg_intros: thm list} type corec_info = {fp_b: binding, version: int, fpT: typ, Y: typ, Z: typ, friend_names: string list, sig_fp_sugars: BNF_FP_Def_Sugar.fp_sugar list, ssig_fp_sugar: BNF_FP_Def_Sugar.fp_sugar, Lam: term, proto_sctr: term, flat: term, eval_core: term, eval: term, algLam: term, corecUU: term, dtor_transfer: thm, Lam_transfer: thm, Lam_pointful_natural: thm, proto_sctr_transfer: thm, flat_simps: thm list, eval_core_simps: thm list, eval_thm: thm, eval_simps: thm list, all_algLam_algs: thm list, algLam_thm: thm, dtor_algLam: thm, corecUU_thm: thm, corecUU_unique: thm, corecUU_transfer: thm, buffer: buffer, all_dead_k_bnfs: BNF_Def.bnf list, Retr: term, equivp_Retr: thm, Retr_coinduct: thm, dtor_coinduct_info: dtor_coinduct_info} type friend_info = {algrho: term, dtor_algrho: thm, algLam_algrho: thm} val not_codatatype: Proof.context -> typ -> 'a val mk_fp_binding: binding -> string -> binding val bnf_kill_all_but: int -> BNF_Def.bnf -> local_theory -> BNF_Def.bnf * local_theory val print_corec_infos: Proof.context -> unit val has_no_corec_info: Proof.context -> string -> bool val corec_info_of: typ -> local_theory -> corec_info * local_theory val maybe_corec_info_of: Proof.context -> typ -> corec_info option val corec_infos_of: Proof.context -> string -> corec_info list val corec_infos_of_generic: Context.generic -> Symtab.key -> corec_info list val prepare_friend_corec: string -> typ -> local_theory -> (corec_info * binding * int * typ * typ * typ * typ * typ * BNF_Def.bnf * BNF_Def.bnf * BNF_FP_Def_Sugar.fp_sugar * BNF_FP_Def_Sugar.fp_sugar * buffer) * local_theory val register_friend_corec: string -> binding -> int -> typ -> typ -> typ -> BNF_Def.bnf -> BNF_FP_Def_Sugar.fp_sugar -> BNF_FP_Def_Sugar.fp_sugar -> term -> term -> thm -> corec_info -> local_theory -> friend_info * local_theory end; structure BNF_GFP_Grec : BNF_GFP_GREC = struct open Ctr_Sugar open BNF_Util open BNF_Def open BNF_Comp open BNF_FP_Util open BNF_LFP open BNF_FP_Def_Sugar open BNF_LFP_Rec_Sugar open BNF_GFP_Grec_Tactics val algLamN = "algLam"; val algLam_algLamN = "algLam_algLam"; val algLam_algrhoN = "algLam_algrho"; val algrhoN = "algrho"; val CLeafN = "CLeaf"; val congN = "congclp"; val cong_alg_introsN = "cong_alg_intros"; val cong_localeN = "cong_locale"; val corecUUN = "corecUU"; val corecUU_transferN = "corecUU_transfer"; val corecUU_uniqueN = "corecUU_unique"; val cutSsigN = "cutSsig"; val dtor_algLamN = "dtor_algLam"; val dtor_algrhoN = "dtor_algrho"; val dtor_coinductN = "dtor_coinduct"; val dtor_transferN = "dtor_transfer"; val embLN = "embL"; val embLLN = "embLL"; val embLRN = "embLR"; val embL_pointful_naturalN = "embL_pointful_natural"; val embL_transferN = "embL_transfer"; val equivp_RetrN = "equivp_Retr"; val evalN = "eval"; val eval_coreN = "eval_core"; val eval_core_pointful_naturalN = "eval_core_pointful_natural"; val eval_core_transferN = "eval_core_transfer"; val eval_flatN = "eval_flat"; val eval_simpsN = "eval_simps"; val flatN = "flat"; val flat_pointful_naturalN = "flat_pointful_natural"; val flat_transferN = "flat_transfer"; val k_as_ssig_naturalN = "k_as_ssig_natural"; val k_as_ssig_transferN = "k_as_ssig_transfer"; val LamN = "Lam"; val Lam_transferN = "Lam_transfer"; val Lam_pointful_naturalN = "Lam_pointful_natural"; val OperN = "Oper"; val proto_sctrN = "proto_sctr"; val proto_sctr_pointful_naturalN = "proto_sctr_pointful_natural"; val proto_sctr_transferN = "proto_sctr_transfer"; val rho_transferN = "rho_transfer"; val Retr_coinductN = "Retr_coinduct"; val sctrN = "sctr"; val sctr_transferN = "sctr_transfer"; val sctr_pointful_naturalN = "sctr_pointful_natural"; val sigN = "sig"; val SigN = "Sig"; val Sig_pointful_naturalN = "Sig_pointful_natural"; val corecUN = "corecU"; val corecU_ctorN = "corecU_ctor"; val corecU_uniqueN = "corecU_unique"; val unsigN = "unsig"; val VLeafN = "VLeaf"; val s_prefix = "s"; (* transforms "sig" into "ssig" *) fun not_codatatype ctxt T = error ("Not a codatatype: " ^ Syntax.string_of_typ ctxt T); fun mutual_codatatype () = error ("Mutually corecursive codatatypes are not supported (try " ^ quote (#1 \<^command_keyword>\primcorec\) ^ " instead of " ^ quote (#1 \<^command_keyword>\corec\) ^ ")"); fun noncorecursive_codatatype () = error ("Noncorecursive codatatypes are not supported (try " ^ quote (#1 \<^command_keyword>\definition\) ^ " instead of " ^ quote (#1 \<^command_keyword>\corec\) ^ ")"); fun singleton_codatatype ctxt = error ("Singleton corecursive codatatypes are not supported (use " ^ quote (Syntax.string_of_typ ctxt \<^typ>\unit\) ^ " instead)"); fun merge_lists eq old1 old2 = (old1 |> subtract eq old2) @ old2; fun add_type_namesT (Type (s, Ts)) = insert (op =) s #> fold add_type_namesT Ts | add_type_namesT _ = I; fun Tsubst Y T = Term.typ_subst_atomic [(Y, T)]; fun substT Y T = Term.subst_atomic_types [(Y, T)]; fun freeze_types ctxt except_tvars Ts = let val As = fold Term.add_tvarsT Ts [] |> subtract (op =) except_tvars; val (Bs, _) = ctxt |> mk_TFrees' (map snd As); in map (Term.typ_subst_TVars (map fst As ~~ Bs)) Ts end; fun typ_unify_disjointly thy (T, T') = if T = T' then T else let val tvars = Term.add_tvar_namesT T []; val tvars' = Term.add_tvar_namesT T' []; val maxidx' = maxidx_of_typ T'; val T = T |> exists (member (op =) tvars') tvars ? Logic.incr_tvar (maxidx' + 1); val maxidx = Integer.max (maxidx_of_typ T) maxidx'; val (tyenv, _) = Sign.typ_unify thy (T, T') (Vartab.empty, maxidx); in Envir.subst_type tyenv T end; val dummify_atomic_types = Term.map_types (Term.map_atyps (K Term.dummyT)); fun mk_internal internal ctxt f = if internal andalso not (Config.get ctxt bnf_internals) then f else I fun mk_fp_binding fp_b pre = Binding.map_name (K pre) fp_b |> Binding.qualify true (Binding.name_of fp_b); fun mk_version_binding version = Binding.qualify false ("v" ^ string_of_int version); fun mk_version_fp_binding internal ctxt = mk_internal internal ctxt Binding.concealed ooo (mk_fp_binding oo mk_version_binding); (*FIXME: get rid of ugly names when typedef and primrec respect qualification*) fun mk_version_binding_ugly version = Binding.suffix_name ("_v" ^ string_of_int version); fun mk_version_fp_binding_ugly internal ctxt version fp_b pre = Binding.prefix_name (pre ^ "_") fp_b |> mk_version_binding_ugly version |> mk_internal internal ctxt Binding.concealed; fun mk_mapN ctxt live_AsBs TA bnf = let val TB = Term.typ_subst_atomic live_AsBs TA in enforce_type ctxt (snd o strip_typeN (length live_AsBs)) (TA --> TB) (map_of_bnf bnf) end; fun mk_relN ctxt live_AsBs TA bnf = let val TB = Term.typ_subst_atomic live_AsBs TA in enforce_type ctxt (snd o strip_typeN (length live_AsBs)) (mk_pred2T TA TB) (rel_of_bnf bnf) end; fun mk_map1 ctxt Y Z = mk_mapN ctxt [(Y, Z)]; fun mk_rel1 ctxt Y Z = mk_relN ctxt [(Y, Z)]; fun define_const internal fp_b version name rhs lthy = let val b = mk_version_fp_binding internal lthy version fp_b name; val ((free, (_, def_free)), (lthy, lthy_old)) = lthy |> Local_Theory.open_target |> snd |> Local_Theory.define ((b, NoSyn), ((Thm.def_binding b |> Binding.concealed, []), rhs)) ||> `Local_Theory.close_target; val phi = Proof_Context.export_morphism lthy_old lthy; val const = Morphism.term phi free; val const' = enforce_type lthy I (fastype_of free) const; in ((const', Morphism.thm phi def_free), lthy) end; fun define_single_primrec b eqs lthy = let val (([free], [def_free], [simps_free]), (lthy, lthy_old)) = lthy |> Local_Theory.open_target |> snd |> Local_Theory.map_background_naming (mk_internal true lthy Name_Space.concealed) (*TODO check*) |> primrec false [] [(b, NONE, NoSyn)] (map (fn eq => ((Binding.empty_atts, eq), [], [])) eqs) ||> `Local_Theory.close_target; val phi = Proof_Context.export_morphism lthy_old lthy; val const = Morphism.term phi free; val const' = enforce_type lthy I (fastype_of free) const; in ((const', Morphism.thm phi def_free, map (Morphism.thm phi) simps_free), lthy) end; type buffer = {Oper: term, VLeaf: term, CLeaf: term, ctr_wrapper: term, friends: (typ * term) Symtab.table}; fun map_buffer f {Oper, VLeaf, CLeaf, ctr_wrapper, friends} = {Oper = f Oper, VLeaf = f VLeaf, CLeaf = f CLeaf, ctr_wrapper = f ctr_wrapper, friends = Symtab.map (K (apsnd f)) friends}; fun morph_buffer phi = map_buffer (Morphism.term phi); fun specialize_buffer_types {Oper, VLeaf, CLeaf, ctr_wrapper, friends} = let val ssig_T as Type (_, Ts) = body_type (fastype_of VLeaf); val Y = List.last Ts; val ssigifyT = substT Y ssig_T; in {Oper = Oper, VLeaf = VLeaf, CLeaf = CLeaf, ctr_wrapper = ssigifyT ctr_wrapper, friends = Symtab.map (K (apsnd ssigifyT)) friends} end; type dtor_coinduct_info = {dtor_coinduct: thm, cong_def: thm, cong_locale: thm, cong_base: thm, cong_refl: thm, cong_sym: thm, cong_trans: thm, cong_alg_intros: thm list}; fun map_dtor_coinduct_info f {dtor_coinduct, cong_def, cong_locale, cong_base, cong_refl, cong_sym, cong_trans, cong_alg_intros} = {dtor_coinduct = f dtor_coinduct, cong_def = f cong_def, cong_locale = f cong_locale, cong_base = f cong_base, cong_refl = f cong_refl, cong_sym = f cong_sym, cong_trans = f cong_trans, cong_alg_intros = map f cong_alg_intros}; fun morph_dtor_coinduct_info phi = map_dtor_coinduct_info (Morphism.thm phi); type corec_ad = {fpT: typ, friend_names: string list}; fun morph_corec_ad phi {fpT, friend_names} = {fpT = Morphism.typ phi fpT, friend_names = friend_names}; type corec_info = {fp_b: binding, version: int, fpT: typ, Y: typ, Z: typ, friend_names: string list, sig_fp_sugars: fp_sugar list, ssig_fp_sugar: fp_sugar, Lam: term, proto_sctr: term, flat: term, eval_core: term, eval: term, algLam: term, corecUU: term, dtor_transfer: thm, Lam_transfer: thm, Lam_pointful_natural: thm, proto_sctr_transfer: thm, flat_simps: thm list, eval_core_simps: thm list, eval_thm: thm, eval_simps: thm list, all_algLam_algs: thm list, algLam_thm: thm, dtor_algLam: thm, corecUU_thm: thm, corecUU_unique: thm, corecUU_transfer: thm, buffer: buffer, all_dead_k_bnfs: bnf list, Retr: term, equivp_Retr: thm, Retr_coinduct: thm, dtor_coinduct_info: dtor_coinduct_info}; fun morph_corec_info phi ({fp_b, version, fpT, Y, Z, friend_names, sig_fp_sugars, ssig_fp_sugar, Lam, proto_sctr, flat, eval_core, eval, algLam, corecUU, dtor_transfer, Lam_transfer, Lam_pointful_natural, proto_sctr_transfer, flat_simps, eval_core_simps, eval_thm, eval_simps, all_algLam_algs, algLam_thm, dtor_algLam, corecUU_thm, corecUU_unique, corecUU_transfer, buffer, all_dead_k_bnfs, Retr, equivp_Retr, Retr_coinduct, dtor_coinduct_info} : corec_info) = {fp_b = fp_b, version = version, fpT = Morphism.typ phi fpT, Y = Morphism.typ phi Y, Z = Morphism.typ phi Z, friend_names = friend_names, sig_fp_sugars = sig_fp_sugars (*no morph*), ssig_fp_sugar = ssig_fp_sugar (*no morph*), Lam = Morphism.term phi Lam, proto_sctr = Morphism.term phi proto_sctr, flat = Morphism.term phi flat, eval_core = Morphism.term phi eval_core, eval = Morphism.term phi eval, algLam = Morphism.term phi algLam, corecUU = Morphism.term phi corecUU, dtor_transfer = dtor_transfer, Lam_transfer = Morphism.thm phi Lam_transfer, Lam_pointful_natural = Morphism.thm phi Lam_pointful_natural, proto_sctr_transfer = Morphism.thm phi proto_sctr_transfer, flat_simps = map (Morphism.thm phi) flat_simps, eval_core_simps = map (Morphism.thm phi) eval_core_simps, eval_thm = Morphism.thm phi eval_thm, eval_simps = map (Morphism.thm phi) eval_simps, all_algLam_algs = map (Morphism.thm phi) all_algLam_algs, algLam_thm = Morphism.thm phi algLam_thm, dtor_algLam = Morphism.thm phi dtor_algLam, corecUU_thm = Morphism.thm phi corecUU_thm, corecUU_unique = Morphism.thm phi corecUU_unique, corecUU_transfer = Morphism.thm phi corecUU_transfer, buffer = morph_buffer phi buffer, all_dead_k_bnfs = map (morph_bnf phi) all_dead_k_bnfs, Retr = Morphism.term phi Retr, equivp_Retr = Morphism.thm phi equivp_Retr, Retr_coinduct = Morphism.thm phi Retr_coinduct, dtor_coinduct_info = morph_dtor_coinduct_info phi dtor_coinduct_info}; datatype ('a, 'b) expr = Ad of 'a * (local_theory -> 'b * local_theory) | Info of 'b; fun is_Ad (Ad _) = true | is_Ad _ = false; fun is_Info (Info _) = true | is_Info _ = false; type corec_info_expr = (corec_ad, corec_info) expr; fun morph_corec_info_expr phi (Ad (ad, f)) = Ad (morph_corec_ad phi ad, f) | morph_corec_info_expr phi (Info info) = Info (morph_corec_info phi info); val transfer_corec_info_expr = morph_corec_info_expr o Morphism.transfer_morphism; type corec_data = int Symtab.table * corec_info_expr list Symtab.table list; structure Data = Generic_Data ( type T = corec_data; val empty = (Symtab.empty, [Symtab.empty]); val extend = I; fun merge ((version_tab1, info_tabs1), (version_tab2, info_tabs2)) : T = (Symtab.join (K Int.max) (version_tab1, version_tab2), info_tabs1 @ info_tabs2); ); fun corec_ad_of_expr (Ad (ad, _)) = ad | corec_ad_of_expr (Info {fpT, friend_names, ...}) = {fpT = fpT, friend_names = friend_names}; fun corec_info_exprs_of_generic context fpT_name = let val thy = Context.theory_of context; val info_tabs = snd (Data.get context); in maps (fn info_tab => these (Symtab.lookup info_tab fpT_name)) info_tabs |> map (transfer_corec_info_expr thy) end; val corec_info_exprs_of = corec_info_exprs_of_generic o Context.Proof; val keep_corec_infos = map_filter (fn Ad _ => NONE | Info info => SOME info); val corec_infos_of_generic = keep_corec_infos oo corec_info_exprs_of_generic; val corec_infos_of = keep_corec_infos oo corec_info_exprs_of; fun str_of_corec_ad ctxt {fpT, friend_names} = "[" ^ Syntax.string_of_typ ctxt fpT ^ "; " ^ commas friend_names ^ "]"; fun str_of_corec_info ctxt {fpT, version, friend_names, ...} = "{" ^ Syntax.string_of_typ ctxt fpT ^ "; " ^ commas friend_names ^ "; v" ^ string_of_int version ^ "}"; fun str_of_corec_info_expr ctxt (Ad (ad, _)) = str_of_corec_ad ctxt ad | str_of_corec_info_expr ctxt (Info info) = str_of_corec_info ctxt info; fun print_corec_infos ctxt = Symtab.fold (fn (fpT_name, exprs) => fn () => writeln (fpT_name ^ ":\n" ^ cat_lines (map (prefix " " o str_of_corec_info_expr ctxt) exprs))) (the_single (snd (Data.get (Context.Proof ctxt)))) (); val has_no_corec_info = null oo corec_info_exprs_of; fun get_name_next_version_of fpT_name ctxt = let val (version_tab, info_tabs) = Data.get (Context.Theory (Proof_Context.theory_of ctxt)); val fp_base = Long_Name.base_name fpT_name; val fp_b = Binding.name fp_base; val version_tab' = Symtab.map_default (fp_base, ~1) (Integer.add 1) version_tab; val SOME version = Symtab.lookup version_tab' fp_base; val ctxt' = ctxt |> Local_Theory.background_theory (Context.theory_map (Data.put (version_tab', info_tabs))); in ((fp_b, version), ctxt') end; type friend_info = {algrho: term, dtor_algrho: thm, algLam_algrho: thm}; fun morph_friend_info phi ({algrho, dtor_algrho, algLam_algrho} : friend_info) = {algrho = Morphism.term phi algrho, dtor_algrho = Morphism.thm phi dtor_algrho, algLam_algrho = Morphism.thm phi algLam_algrho}; fun checked_fp_sugar_of ctxt fpT_name = let val fp_sugar as {X, fp_res = {Ts = fpTs, ...}, fp_ctr_sugar = {ctrXs_Tss, ...}, ...} = (case fp_sugar_of ctxt fpT_name of SOME (fp_sugar as {fp = Greatest_FP, ...}) => fp_sugar | _ => not_codatatype ctxt (Type (fpT_name, [] (*yuck*)))); val _ = if length fpTs > 1 then mutual_codatatype () else if not (exists (exists (Term.exists_subtype (curry (op =) X))) ctrXs_Tss) then noncorecursive_codatatype () else if ctrXs_Tss = [[X]] then singleton_codatatype ctxt else (); in fp_sugar end; fun bnf_kill_all_but nn bnf lthy = ((empty_comp_cache, empty_unfolds), lthy) |> kill_bnf I (live_of_bnf bnf - nn) bnf ||> snd; fun bnf_with_deads_and_lives dead_Es live_As Y fpT T lthy = let val qsoty = quote o Syntax.string_of_typ lthy; val unfreeze_fp = Tsubst Y fpT; fun flatten_tyargs Ass = map dest_TFree live_As |> filter (fn T => exists (fn Ts => member (op =) Ts T) Ass); val ((bnf, _), (_, lthy)) = bnf_of_typ false Do_Inline I flatten_tyargs [Term.dest_TFree Y] (map Term.dest_TFree dead_Es) T ((empty_comp_cache, empty_unfolds), lthy) handle BAD_DEAD (Y, Y_backdrop) => (case Y_backdrop of Type (bad_tc, _) => let val T = qsoty (unfreeze_fp Y); val T_backdrop = qsoty (unfreeze_fp Y_backdrop); fun register_hint () = "\nUse the " ^ quote (#1 \<^command_keyword>\bnf\) ^ " command to register " ^ quote bad_tc ^ " as a bounded natural functor to allow nested (co)recursion through \ \it"; in if is_some (bnf_of lthy bad_tc) orelse is_some (fp_sugar_of lthy bad_tc) then error ("Inadmissible occurrence of type " ^ T ^ " in type expression " ^ T_backdrop) else error ("Unsupported occurrence of type " ^ T ^ " via type constructor " ^ quote bad_tc ^ " in type expression " ^ T_backdrop ^ register_hint ()) end); val phi = Morphism.term_morphism "BNF" (Raw_Simplifier.rewrite_term (Proof_Context.theory_of lthy) @{thms BNF_Composition.id_bnf_def} []) $> Morphism.thm_morphism "BNF" (unfold_thms lthy @{thms BNF_Composition.id_bnf_def}); in (morph_bnf phi bnf, lthy) end; fun define_sig_type fp_b version fp_alives Es Y rhsT lthy = let val T_b = mk_version_fp_binding_ugly true lthy version fp_b sigN; val ctr_b = mk_version_fp_binding false lthy version fp_b SigN; val sel_b = mk_version_fp_binding true lthy version fp_b unsigN; val lthy = Local_Theory.open_target lthy |> snd; val T_name = Local_Theory.full_name lthy T_b; val tyargs = map2 (fn alive => fn T => (if alive then SOME Binding.empty else NONE, (T, Type.sort_of_atyp T))) (fp_alives @ [true]) (Es @ [Y]); val ctr_specs = [(((Binding.empty, ctr_b), [(sel_b, rhsT)]), NoSyn)]; val spec = (((((tyargs, T_b), NoSyn), ctr_specs), (Binding.empty, Binding.empty, Binding.empty)), []); val plugins = Plugin_Name.make_filter lthy (K (curry (op =) transfer_plugin)); val discs_sels = true; val lthy = lthy |> Local_Theory.map_background_naming (mk_internal true lthy Name_Space.concealed) (*TODO check*) |> with_typedef_threshold ~1 (co_datatypes Least_FP construct_lfp ((plugins, discs_sels), [spec])) |> Local_Theory.close_target; val SOME fp_sugar = fp_sugar_of lthy T_name; in (fp_sugar, lthy) end; fun define_ssig_type fp_b version fp_alives Es Y fpT lthy = let val sig_T_b = mk_version_fp_binding_ugly true lthy version fp_b sigN; val T_b = Binding.prefix_name s_prefix sig_T_b; val Oper_b = mk_version_fp_binding false lthy version fp_b OperN; val VLeaf_b = mk_version_fp_binding false lthy version fp_b VLeafN; val CLeaf_b = mk_version_fp_binding false lthy version fp_b CLeafN; val lthy = Local_Theory.open_target lthy |> snd; val sig_T_name = Local_Theory.full_name lthy sig_T_b; val T_name = Long_Name.map_base_name (prefix s_prefix) sig_T_name; val As = Es @ [Y]; val ssig_sig_T = Type (sig_T_name, Es @ [Type (T_name, As)]); val tyargs = map2 (fn alive => fn T => (if alive then SOME Binding.empty else NONE, (T, Type.sort_of_atyp T))) (fp_alives @ [true]) (Es @ [Y]); val ctr_specs = [(((Binding.empty, Oper_b), [(Binding.empty, ssig_sig_T)]), NoSyn), (((Binding.empty, VLeaf_b), [(Binding.empty, Y)]), NoSyn), (((Binding.empty, CLeaf_b), [(Binding.empty, fpT)]), NoSyn)]; val spec = (((((tyargs, T_b), NoSyn), ctr_specs), (Binding.empty, Binding.empty, Binding.empty)), []); val plugins = Plugin_Name.make_filter lthy (K (curry (op =) transfer_plugin)); val discs_sels = false; val lthy = lthy |> Local_Theory.map_background_naming (mk_internal true lthy Name_Space.concealed) (*TODO check*) |> with_typedef_threshold ~1 (co_datatypes Least_FP construct_lfp ((plugins, discs_sels), [spec])) |> Local_Theory.close_target; val SOME fp_sugar = fp_sugar_of lthy T_name; in (fp_sugar, lthy) end; fun embed_Sig ctxt Sig inl_or_r t = Library.foldl1 HOLogic.mk_comp [Sig, inl_or_r, dummify_atomic_types t] |> Syntax.check_term ctxt; fun mk_ctr_wrapper_friends ctxt friend_name friend_T old_sig_T k_T Sig old_buffer = let val embed_Sig_inl = embed_Sig ctxt Sig (Inl_const old_sig_T k_T); val ctr_wrapper = embed_Sig_inl (#ctr_wrapper old_buffer); val friends = Symtab.map (K (apsnd embed_Sig_inl)) (#friends old_buffer) |> Symtab.update_new (friend_name, (friend_T, HOLogic.mk_comp (Sig, Inr_const old_sig_T k_T))); in (ctr_wrapper, friends) end; fun pre_type_of_ctor Y ctor = let val (fp_preT, fpT) = dest_funT (fastype_of ctor); in typ_subst_nonatomic [(fpT, Y)] fp_preT end; fun mk_k_as_ssig Z old_sig_T k_T ssig_T Sig dead_sig_map Oper VLeaf = let val inr' = Inr_const old_sig_T k_T; val dead_sig_map' = substT Z ssig_T dead_sig_map; in Library.foldl1 HOLogic.mk_comp [Oper, dead_sig_map' $ VLeaf, Sig, inr'] end; fun define_embL name fp_b version Y Z fpT old_sig_T old_ssig_T other_summand_T ssig_T Inl_or_r_const dead_old_sig_map Sig old_Oper old_VLeaf old_CLeaf Oper VLeaf CLeaf lthy = let val embL_b = mk_version_fp_binding true lthy version fp_b name; val old_ssig_old_sig_T = Tsubst Y old_ssig_T old_sig_T; val ssig_old_sig_T = Tsubst Y ssig_T old_sig_T; val ssig_other_summand_T = Tsubst Y ssig_T other_summand_T; val sigx = Var (("s", 0), old_ssig_old_sig_T); val x = Var (("x", 0), Y); val j = Var (("j", 0), fpT); val embL = Free (Binding.name_of embL_b, old_ssig_T --> ssig_T); val dead_old_sig_map' = Term.subst_atomic_types [(Y, old_ssig_T), (Z, ssig_T)] dead_old_sig_map; val Sig' = substT Y ssig_T Sig; val inl' = Inl_or_r_const ssig_old_sig_T ssig_other_summand_T; val Oper_eq = mk_Trueprop_eq (embL $ (old_Oper $ sigx), Oper $ (Sig' $ (inl' $ (dead_old_sig_map' $ embL $ sigx)))) |> Logic.all sigx; val VLeaf_eq = mk_Trueprop_eq (embL $ (old_VLeaf $ x), VLeaf $ x) |> Logic.all x; val CLeaf_eq = mk_Trueprop_eq (embL $ (old_CLeaf $ j), CLeaf $ j) |> Logic.all j; in define_single_primrec embL_b [Oper_eq, VLeaf_eq, CLeaf_eq] lthy end; fun define_Lam_base fp_b version Y Z preT ssig_T dead_pre_map Sig unsig dead_sig_map Oper VLeaf lthy = let val YpreT = HOLogic.mk_prodT (Y, preT); val snd' = snd_const YpreT; val dead_pre_map' = substT Z ssig_T dead_pre_map; val Sig' = substT Y ssig_T Sig; val unsig' = substT Y ssig_T unsig; val dead_sig_map' = Term.subst_atomic_types [(Y, YpreT), (Z, ssig_T)] dead_sig_map; val rhs = HOLogic.mk_comp (unsig', dead_sig_map' $ Library.foldl1 HOLogic.mk_comp [Oper, Sig', dead_pre_map' $ VLeaf, snd']); in define_const true fp_b version LamN rhs lthy end; fun define_Lam_step_or_merge fp_b version Y preT unsig left_case right_case lthy = let val YpreT = HOLogic.mk_prodT (Y, preT); val unsig' = substT Y YpreT unsig; val rhs = HOLogic.mk_comp (mk_case_sum (left_case, right_case), unsig'); in define_const true fp_b version LamN rhs lthy end; fun define_Lam_step fp_b version Y Z preT old_ssig_T ssig_T dead_pre_map unsig rho embL old_Lam lthy = let val dead_pre_map' = Term.subst_atomic_types [(Y, old_ssig_T), (Z, ssig_T)] dead_pre_map; val left_case = HOLogic.mk_comp (dead_pre_map' $ embL, old_Lam); in define_Lam_step_or_merge fp_b version Y preT unsig left_case rho lthy end; fun define_Lam_merge fp_b version Y Z preT old1_ssig_T old2_ssig_T ssig_T dead_pre_map unsig embLL embLR old1_Lam old2_Lam lthy = let val dead_pre_map' = Term.subst_atomic_types [(Y, old1_ssig_T), (Z, ssig_T)] dead_pre_map; val dead_pre_map'' = Term.subst_atomic_types [(Y, old2_ssig_T), (Z, ssig_T)] dead_pre_map; val left_case = HOLogic.mk_comp (dead_pre_map' $ embLL, old1_Lam); val right_case = HOLogic.mk_comp (dead_pre_map'' $ embLR, old2_Lam); in define_Lam_step_or_merge fp_b version Y preT unsig left_case right_case lthy end; fun define_proto_sctr_step_or_merge fp_b version old_sig_T right_T Sig old_proto_sctr = let val rhs = Library.foldl1 HOLogic.mk_comp [Sig, Inl_const old_sig_T right_T, old_proto_sctr]; in define_const true fp_b version proto_sctrN rhs end; fun define_flat fp_b version Y Z fpT sig_T ssig_T Oper VLeaf CLeaf dead_sig_map lthy = let val flat_b = mk_version_fp_binding true lthy version fp_b flatN; val ssig_sig_T = Tsubst Y ssig_T sig_T; val ssig_ssig_sig_T = Tsubst Y ssig_T ssig_sig_T; val ssig_ssig_T = Tsubst Y ssig_T ssig_T; val sigx = Var (("s", 0), ssig_ssig_sig_T); val x = Var (("x", 0), ssig_T); val j = Var (("j", 0), fpT); val flat = Free (Binding.name_of flat_b, ssig_ssig_T --> ssig_T); val Oper' = substT Y ssig_T Oper; val VLeaf' = substT Y ssig_T VLeaf; val CLeaf' = substT Y ssig_T CLeaf; val dead_sig_map' = Term.subst_atomic_types [(Y, ssig_ssig_T), (Z, ssig_T)] dead_sig_map; val Oper_eq = mk_Trueprop_eq (flat $ (Oper' $ sigx), Oper $ (dead_sig_map' $ flat $ sigx)) |> Logic.all sigx; val VLeaf_eq = mk_Trueprop_eq (flat $ (VLeaf' $ x), x) |> Logic.all x; val CLeaf_eq = mk_Trueprop_eq (flat $ (CLeaf' $ j), CLeaf $ j) |> Logic.all j; in define_single_primrec flat_b [Oper_eq, VLeaf_eq, CLeaf_eq] lthy end; fun define_eval_core fp_b version Y Z preT fpT sig_T ssig_T dtor Oper VLeaf CLeaf dead_pre_map dead_sig_map dead_ssig_map flat Lam lthy = let val eval_core_b = mk_version_fp_binding true lthy version fp_b eval_coreN; val YpreT = HOLogic.mk_prodT (Y, preT); val Ypre_ssig_T = Tsubst Y YpreT ssig_T; val Ypre_ssig_sig_T = Tsubst Y Ypre_ssig_T sig_T; val ssig_preT = Tsubst Y ssig_T preT; val ssig_YpreT = Tsubst Y ssig_T YpreT; val ssig_ssig_T = Tsubst Y ssig_T ssig_T; val sigx = Var (("s", 0), Ypre_ssig_sig_T); val x = Var (("x", 0), YpreT); val j = Var (("j", 0), fpT); val eval_core = Free (Binding.name_of eval_core_b, Ypre_ssig_T --> ssig_preT); val Oper' = substT Y YpreT Oper; val VLeaf' = substT Y YpreT VLeaf; val CLeaf' = substT Y YpreT CLeaf; val dead_pre_map' = Term.subst_atomic_types [(Y, ssig_ssig_T), (Z, ssig_T)] dead_pre_map; val dead_pre_map'' = substT Z ssig_T dead_pre_map; val dead_pre_map''' = Term.subst_atomic_types [(Y, fpT), (Z, ssig_T)] dead_pre_map; val dead_sig_map' = Term.subst_atomic_types [(Y, Ypre_ssig_T), (Z, ssig_YpreT)] dead_sig_map; val dead_ssig_map' = Term.subst_atomic_types [(Y, YpreT), (Z, Y)] dead_ssig_map; val Lam' = substT Y ssig_T Lam; val fst' = fst_const YpreT; val snd' = snd_const YpreT; val Oper_eq = mk_Trueprop_eq (eval_core $ (Oper' $ sigx), dead_pre_map' $ flat $ (Lam' $ (dead_sig_map' $ (Abs (Name.uu, Ypre_ssig_T, HOLogic.mk_prod (dead_ssig_map' $ fst' $ Bound 0, eval_core $ Bound 0))) $ sigx))) |> Logic.all sigx; val VLeaf_eq = mk_Trueprop_eq (eval_core $ (VLeaf' $ x), dead_pre_map'' $ VLeaf $ (snd' $ x)) |> Logic.all x; val CLeaf_eq = mk_Trueprop_eq (eval_core $ (CLeaf' $ j), dead_pre_map''' $ CLeaf $ (dtor $ j)) |> Logic.all j; in define_single_primrec eval_core_b [Oper_eq, VLeaf_eq, CLeaf_eq] lthy end; fun define_eval fp_b version Y Z preT fpT ssig_T dtor dtor_unfold dead_ssig_map eval_core lthy = let val fp_preT = Tsubst Y fpT preT; val fppreT = HOLogic.mk_prodT (fpT, fp_preT); val fp_ssig_T = Tsubst Y fpT ssig_T; val dtor_unfold' = substT Z fp_ssig_T dtor_unfold; val dead_ssig_map' = Term.subst_atomic_types [(Y, fpT), (Z, fppreT)] dead_ssig_map; val eval_core' = substT Y fpT eval_core; val id' = HOLogic.id_const fpT; val rhs = dtor_unfold' $ HOLogic.mk_comp (eval_core', dead_ssig_map' $ mk_convol (id', dtor)); in define_const true fp_b version evalN rhs lthy end; fun define_cutSsig fp_b version Y Z preT ssig_T dead_pre_map VLeaf dead_ssig_map flat eval_core lthy = let val ssig_preT = Tsubst Y ssig_T preT; val ssig_ssig_T = Tsubst Y ssig_T ssig_T; val ssig_ssig_preT = HOLogic.mk_prodT (ssig_T, ssig_preT); val h = Var (("h", 0), Y --> ssig_preT); val dead_pre_map' = Term.subst_atomic_types [(Y, ssig_ssig_T), (Z, ssig_T)] dead_pre_map; val dead_ssig_map' = substT Z ssig_ssig_preT dead_ssig_map; val eval_core' = substT Y ssig_T eval_core; val rhs = Library.foldl1 HOLogic.mk_comp [dead_pre_map' $ flat, eval_core', dead_ssig_map' $ mk_convol (VLeaf, h)] |> Term.lambda h; in define_const true fp_b version cutSsigN rhs lthy end; fun define_algLam fp_b version Y Z fpT ssig_T Oper VLeaf dead_sig_map eval lthy = let val fp_ssig_T = Tsubst Y fpT ssig_T; val Oper' = substT Y fpT Oper; val VLeaf' = substT Y fpT VLeaf; val dead_sig_map' = Term.subst_atomic_types [(Y, fpT), (Z, fp_ssig_T)] dead_sig_map; val rhs = Library.foldl1 HOLogic.mk_comp [eval, Oper', dead_sig_map' $ VLeaf']; in define_const true fp_b version algLamN rhs lthy end; fun define_corecU fp_b version Y Z preT ssig_T dtor_unfold VLeaf cutSsig lthy = let val ssig_preT = Tsubst Y ssig_T preT; val h = Var (("h", 0), Y --> ssig_preT); val dtor_unfold' = substT Z ssig_T dtor_unfold; val rhs = HOLogic.mk_comp (dtor_unfold' $ (cutSsig $ h), VLeaf) |> Term.lambda h; in define_const true fp_b version corecUN rhs lthy end; fun define_corecUU fp_b version Y Z preT ssig_T dead_pre_map dead_ssig_map flat eval_core sctr corecU lthy = let val ssig_preT = Tsubst Y ssig_T preT; val ssig_ssig_T = Tsubst Y ssig_T ssig_T val ssig_ssig_preT = HOLogic.mk_prodT (ssig_T, ssig_preT); val ssig_pre_ssig_T = Tsubst Y ssig_preT ssig_T; val h = Var (("h", 0), Y --> ssig_pre_ssig_T); val dead_pre_map' = Term.subst_atomic_types [(Y, ssig_ssig_T), (Z, ssig_T)] dead_pre_map; val eval_core' = substT Y ssig_T eval_core; val dead_ssig_map' = Term.subst_atomic_types [(Y, ssig_preT), (Z, ssig_ssig_preT)] dead_ssig_map; val id' = HOLogic.id_const ssig_preT; val rhs = corecU $ Library.foldl1 HOLogic.mk_comp [dead_pre_map' $ flat, eval_core', dead_ssig_map' $ mk_convol (sctr, id'), h] |> Term.lambda h; in define_const true fp_b version corecUUN rhs lthy end; fun derive_sig_transfer maybe_swap ctxt live_AsBs pre_rel sig_rel Rs R const pre_rel_def preT_rel_eqs transfer_thm = let val RRpre_rel = list_comb (pre_rel, Rs) $ R; val RRsig_rel = list_comb (sig_rel, Rs) $ R; val constB = Term.subst_atomic_types live_AsBs const; val goal = uncurry mk_rel_fun (maybe_swap (RRpre_rel, RRsig_rel)) $ const $ constB |> HOLogic.mk_Trueprop; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_sig_transfer_tac ctxt pre_rel_def preT_rel_eqs transfer_thm)) |> Thm.close_derivation \<^here> end; fun derive_transfer_by_transfer_prover ctxt live_AsBs Rs R const const_defs rel_eqs transfers = let val constB = Term.subst_atomic_types live_AsBs const; val goal = mk_parametricity_goal ctxt (Rs @ [R]) const constB; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_transfer_by_transfer_prover_tac ctxt (const_defs @ map (fn thm => thm RS sym) rel_eqs) rel_eqs transfers)) |> Thm.close_derivation \<^here> end; fun derive_dtor_transfer ctxt live_EsFs Y Z pre_rel fp_rel Rs dtor dtor_rel_thm = let val Type (\<^type_name>\fun\, [fpT, Type (\<^type_name>\fun\, [fpTB, \<^typ>\bool\])]) = snd (strip_typeN (length live_EsFs) (fastype_of fp_rel)); val pre_rel' = Term.subst_atomic_types [(Y, fpT), (Z, fpTB)] pre_rel; val Rpre_rel = list_comb (pre_rel', Rs); val Rfp_rel = list_comb (fp_rel, Rs); val dtorB = Term.subst_atomic_types live_EsFs dtor; val goal = HOLogic.mk_Trueprop (mk_rel_fun Rfp_rel (Rpre_rel $ Rfp_rel) $ dtor $ dtorB); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_dtor_transfer_tac ctxt dtor_rel_thm)) |> Thm.close_derivation \<^here> end; fun derive_Lam_or_eval_core_transfer ctxt live_AsBs Y Z preT ssig_T Rs R pre_rel sig_or_ssig_rel ssig_rel const const_def rel_eqs transfers = let val YpreT = HOLogic.mk_prodT (Y, preT); val ZpreTB = typ_subst_atomic live_AsBs YpreT; val ssig_TB = typ_subst_atomic live_AsBs ssig_T; val pre_rel' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssig_TB)] pre_rel; val sig_or_ssig_rel' = Term.subst_atomic_types [(Y, YpreT), (Z, ZpreTB)] sig_or_ssig_rel; val Rsig_or_ssig_rel' = list_comb (sig_or_ssig_rel', Rs); val RRpre_rel = list_comb (pre_rel, Rs) $ R; val RRssig_rel = list_comb (ssig_rel, Rs) $ R; val Rpre_rel' = list_comb (pre_rel', Rs); val constB = subst_atomic_types live_AsBs const; val goal = mk_rel_fun (Rsig_or_ssig_rel' $ mk_rel_prod R RRpre_rel) (Rpre_rel' $ RRssig_rel) $ const $ constB |> HOLogic.mk_Trueprop; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_transfer_by_transfer_prover_tac ctxt [const_def] rel_eqs transfers)) |> Thm.close_derivation \<^here> end; fun derive_proto_sctr_transfer_step_or_merge ctxt Y Z R dead_pre_rel dead_sig_rel proto_sctr proto_sctr_def fp_k_T_rel_eqs transfers = let val proto_sctrZ = substT Y Z proto_sctr; val goal = mk_rel_fun (dead_pre_rel $ R) (dead_sig_rel $ R) $ proto_sctr $ proto_sctrZ |> HOLogic.mk_Trueprop; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_transfer_by_transfer_prover_tac ctxt [proto_sctr_def] fp_k_T_rel_eqs transfers)) |> Thm.close_derivation \<^here> end; fun derive_sctr_transfer ctxt live_AsBs Y Z ssig_T Rs R pre_rel ssig_rel sctr sctr_def fp_k_T_rel_eqs transfers = let val ssig_TB = typ_subst_atomic live_AsBs ssig_T; val pre_rel' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssig_TB)] pre_rel; val Rpre_rel' = list_comb (pre_rel', Rs); val RRssig_rel = list_comb (ssig_rel, Rs) $ R; val sctrB = subst_atomic_types live_AsBs sctr; val goal = HOLogic.mk_Trueprop (mk_rel_fun (Rpre_rel' $ RRssig_rel) RRssig_rel $ sctr $ sctrB); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_transfer_by_transfer_prover_tac ctxt [sctr_def] fp_k_T_rel_eqs transfers)) |> Thm.close_derivation \<^here> end; fun derive_corecUU_transfer ctxt live_AsBs Y Z Rs R preT ssig_T pre_rel fp_rel ssig_rel corecUU cutSsig_def corecU_def corecUU_def fp_k_T_rel_eqs transfers = let val ssig_preT = Tsubst Y ssig_T preT; val ssig_TB = typ_subst_atomic live_AsBs ssig_T; val ssig_preTB = typ_subst_atomic live_AsBs ssig_preT; val pre_rel' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssig_TB)] pre_rel; val ssig_rel' = Term.subst_atomic_types [(Y, ssig_preT), (Z, ssig_preTB)] ssig_rel; val Rpre_rel' = list_comb (pre_rel', Rs); val Rfp_rel = list_comb (fp_rel, Rs); val RRssig_rel = list_comb (ssig_rel, Rs) $ R; val Rssig_rel' = list_comb (ssig_rel', Rs); val corecUUB = subst_atomic_types live_AsBs corecUU; val goal = mk_rel_fun (mk_rel_fun R (Rssig_rel' $ (Rpre_rel' $ RRssig_rel))) (mk_rel_fun R Rfp_rel) $ corecUU $ corecUUB |> HOLogic.mk_Trueprop; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_transfer_by_transfer_prover_tac ctxt [cutSsig_def, corecU_def, corecUU_def] fp_k_T_rel_eqs transfers)) |> Thm.close_derivation \<^here> end; fun mk_natural_goal ctxt simple_T_mapfs fs t u = let fun build_simple (T, _) = (case AList.lookup (op =) simple_T_mapfs T of SOME mapf => mapf | NONE => the (find_first (fn f => domain_type (fastype_of f) = T) fs)); val simple_Ts = map fst simple_T_mapfs; val t_map = build_map ctxt simple_Ts [] build_simple (apply2 (range_type o fastype_of) (t, u)); val u_map = build_map ctxt simple_Ts [] build_simple (apply2 (domain_type o fastype_of) (t, u)); in mk_Trueprop_eq (HOLogic.mk_comp (u, u_map), HOLogic.mk_comp (t_map, t)) end; fun derive_natural_by_unfolding ctxt live_AsBs preT pre_map fs f const map_thms = let val ffpre_map = list_comb (pre_map, fs) $ f; val constB = subst_atomic_types live_AsBs const; val goal = mk_natural_goal ctxt [(preT, ffpre_map)] (fs @ [f]) const constB; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_natural_by_unfolding_tac ctxt map_thms)) |> Thm.close_derivation \<^here> end; fun derive_natural_from_transfer ctxt live_AsBs simple_T_mapfs fs f const transfer bnfs subst_bnfs = let val m = length live_AsBs; val constB = Term.subst_atomic_types live_AsBs const; val goal = mk_natural_goal ctxt simple_T_mapfs (fs @ [f]) const constB; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_natural_from_transfer_tac ctxt m (replicate m true) transfer [] (map rel_Grp_of_bnf bnfs) (map rel_Grp_of_bnf subst_bnfs))) |> Thm.close_derivation \<^here> end; fun derive_natural_from_transfer_with_pre_type ctxt live_AsBs Y Z preT ssig_T pre_map ssig_map fs f = let val ssig_TB = typ_subst_atomic live_AsBs ssig_T; val preT' = Term.typ_subst_atomic [(Y, ssig_T), (Z, ssig_TB)] preT; val ffpre_map = list_comb (pre_map, fs) $ f; val pre_map' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssig_TB)] pre_map; val fpre_map' = list_comb (pre_map', fs); val ffssig_map = list_comb (ssig_map, fs) $ f; val preT_mapfs = [(preT, ffpre_map), (preT', fpre_map' $ ffssig_map)]; in derive_natural_from_transfer ctxt live_AsBs preT_mapfs fs f end; fun derive_Lam_Inl_Inr ctxt Y Z preT old_sig_T old_ssig_T k_T ssig_T dead_pre_map Sig embL old_Lam Lam rho unsig_thm Lam_def = let val YpreT = HOLogic.mk_prodT (Y, preT); val Ypre_old_sig_T = Tsubst Y YpreT old_sig_T; val Ypre_k_T = Tsubst Y YpreT k_T; val inl' = Inl_const Ypre_old_sig_T Ypre_k_T; val inr' = Inr_const Ypre_old_sig_T Ypre_k_T; val dead_pre_map' = Term.subst_atomic_types [(Y, old_ssig_T), (Z, ssig_T)] dead_pre_map; val Sig' = substT Y YpreT Sig; val Lam_o_Sig = HOLogic.mk_comp (Lam, Sig'); val inl_goal = mk_Trueprop_eq (HOLogic.mk_comp (Lam_o_Sig, inl'), HOLogic.mk_comp (dead_pre_map' $ embL, old_Lam)); val inr_goal = mk_Trueprop_eq (HOLogic.mk_comp (Lam_o_Sig, inr'), rho); val goals = [inl_goal, inr_goal]; val goal = Logic.mk_conjunction_balanced goals; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_Lam_Inl_Inr_tac ctxt unsig_thm Lam_def)) |> Conjunction.elim_balanced (length goals) |> map (Thm.close_derivation \<^here>) end; fun derive_flat_VLeaf ctxt Y Z ssig_T x VLeaf dead_ssig_map flat ssig_induct fp_map_id sig_map_cong sig_map_ident sig_map_comp ssig_map_thms flat_simps = let val x' = substT Y ssig_T x; val dead_ssig_map' = substT Z ssig_T dead_ssig_map; val goal = mk_Trueprop_eq (flat $ (dead_ssig_map' $ VLeaf $ x'), x'); val ssig_induct' = infer_instantiate' ctxt [NONE, SOME (Thm.cterm_of ctxt x')] ssig_induct; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_flat_VLeaf_or_flat_tac ctxt ssig_induct' sig_map_cong (fp_map_id :: sig_map_ident :: sig_map_comp :: ssig_map_thms @ flat_simps @ @{thms o_apply id_apply id_def[symmetric]}))) |> Thm.close_derivation \<^here> end; fun derive_flat_flat ctxt Y Z ssig_T x dead_ssig_map flat ssig_induct fp_map_id sig_map_cong sig_map_comp ssig_map_thms flat_simps = let val ssig_ssig_T = Tsubst Y ssig_T ssig_T; val ssig_ssig_ssig_T = Tsubst Y ssig_T ssig_ssig_T; val x' = substT Y ssig_ssig_ssig_T x; val dead_ssig_map' = Term.subst_atomic_types [(Y, ssig_ssig_T), (Z, ssig_T)] dead_ssig_map; val flat' = substT Y ssig_T flat; val goal = mk_Trueprop_eq (flat $ (dead_ssig_map' $ flat $ x'), flat $ (flat' $ x')); val ssig_induct' = infer_instantiate' ctxt [NONE, SOME (Thm.cterm_of ctxt x')] ssig_induct; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_flat_VLeaf_or_flat_tac ctxt ssig_induct' sig_map_cong (o_apply :: fp_map_id :: sig_map_comp :: ssig_map_thms @ flat_simps))) |> Thm.close_derivation \<^here> end; fun derive_eval_core_flat ctxt Y Z preT ssig_T dead_pre_map dead_ssig_map flat eval_core x ssig_induct dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp fp_map_id sig_map_comp sig_map_cong ssig_map_thms ssig_map_comp flat_simps flat_pointful_natural flat_flat Lam_pointful_natural eval_core_simps = let val YpreT = HOLogic.mk_prodT (Y, preT); val ssig_ssig_T = Tsubst Y ssig_T ssig_T; val Ypre_ssig_T = Tsubst Y YpreT ssig_T; val Ypre_ssig_ssig_T = Tsubst Y YpreT ssig_ssig_T; val ssig_YpreT = Tsubst Y ssig_T YpreT; val dead_pre_map' = Term.subst_atomic_types [(Y, ssig_ssig_T), (Z, ssig_T)] dead_pre_map; val dead_ssig_map' = Term.subst_atomic_types [(Y, Ypre_ssig_T), (Z, ssig_YpreT)] dead_ssig_map; val dead_ssig_map'' = Term.subst_atomic_types [(Y, YpreT), (Z, Y)] dead_ssig_map; val flat' = substT Y YpreT flat; val eval_core' = substT Y ssig_T eval_core; val x' = substT Y Ypre_ssig_ssig_T x; val fst' = fst_const YpreT; val goal = mk_Trueprop_eq (eval_core $ (flat' $ x'), dead_pre_map' $ flat $ (eval_core' $ (dead_ssig_map' $ mk_convol (dead_ssig_map'' $ fst', eval_core) $ x'))); val ssig_induct' = infer_instantiate' ctxt [NONE, SOME (Thm.cterm_of ctxt x')] ssig_induct; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_core_flat_tac ctxt ssig_induct' dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp fp_map_id sig_map_comp sig_map_cong ssig_map_thms ssig_map_comp flat_simps flat_pointful_natural flat_flat Lam_pointful_natural eval_core_simps)) |> Thm.close_derivation \<^here> end; fun derive_eval_thm ctxt dtor_inject dtor_unfold_thm eval_def = (trans OF [iffD2 OF [dtor_inject, HOLogic.mk_obj_eq eval_def RS fun_cong], dtor_unfold_thm]) |> unfold_thms ctxt [o_apply, eval_def RS symmetric_thm]; fun derive_eval_flat ctxt Y Z fpT ssig_T dead_ssig_map flat eval x dead_pre_map_comp0 dtor_unfold_unique ssig_map_id ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_core_flat eval_thm = let val fp_ssig_T = Tsubst Y fpT ssig_T; val fp_ssig_ssig_T = Tsubst Y fp_ssig_T ssig_T; val dead_ssig_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_ssig_map; val flat' = substT Y fpT flat; val x' = substT Y fp_ssig_ssig_T x; val goal = mk_Trueprop_eq (eval $ (flat' $ x'), eval $ (dead_ssig_map' $ eval $ x')); val cond_eval_o_flat = infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt (HOLogic.mk_comp (eval, flat')))] (trans OF [dtor_unfold_unique, dtor_unfold_unique RS sym] RS fun_cong) OF [ext, ext]; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_flat_tac ctxt dead_pre_map_comp0 ssig_map_id ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_core_flat eval_thm cond_eval_o_flat)) |> Thm.close_derivation \<^here> end; fun derive_eval_Oper ctxt live Y Z fpT sig_T ssig_T dead_sig_map Oper eval algLam x sig_map_ident sig_map_comp0 sig_map_comp Oper_natural_pointful VLeaf_natural flat_simps eval_flat algLam_def = let val fp_ssig_T = Tsubst Y fpT ssig_T; val fp_ssig_sig_T = Tsubst Y fp_ssig_T sig_T; val dead_sig_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_sig_map; val Oper' = substT Y fpT Oper; val x' = substT Y fp_ssig_sig_T x; val goal = mk_Trueprop_eq (eval $ (Oper' $ x'), algLam $ (dead_sig_map' $ eval $ x')); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_Oper_tac ctxt live sig_map_ident sig_map_comp0 sig_map_comp Oper_natural_pointful VLeaf_natural flat_simps eval_flat algLam_def)) |> Thm.close_derivation \<^here> end; fun derive_eval_V_or_CLeaf ctxt Y fpT V_or_CLeaf eval x dead_pre_map_id dead_pre_map_comp fp_map_id dtor_unfold_unique V_or_CLeaf_map_thm eval_core_simps eval_thm = let val V_or_CLeaf' = substT Y fpT V_or_CLeaf; val x' = substT Y fpT x; val goal = mk_Trueprop_eq (eval $ (V_or_CLeaf' $ x'), x'); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_V_or_CLeaf_tac ctxt dead_pre_map_id dead_pre_map_comp fp_map_id dtor_unfold_unique V_or_CLeaf_map_thm eval_core_simps eval_thm)) |> Thm.close_derivation \<^here> end; fun derive_extdd_mor ctxt Y Z preT fpT ssig_T dead_pre_map dtor extdd cutSsig f g dead_pre_map_comp0 dead_pre_map_comp VLeaf_map_thm ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_thm eval_flat eval_VLeaf cutSsig_def = let val ssig_preT = Tsubst Y ssig_T preT; val dead_pre_map' = Term.subst_atomic_types [(Y, ssig_T), (Z, fpT)] dead_pre_map; val f' = substT Z fpT f; val g' = substT Z ssig_preT g; val extdd_f = extdd $ f'; val prem = mk_Trueprop_eq (HOLogic.mk_comp (dead_pre_map' $ extdd_f, g'), HOLogic.mk_comp (dtor, f')); val goal = mk_Trueprop_eq (HOLogic.mk_comp (dead_pre_map' $ extdd_f, cutSsig $ g'), HOLogic.mk_comp (dtor, extdd_f)); in fold (Variable.add_free_names ctxt) [prem, goal] [] |> (fn vars => Goal.prove_sorry ctxt vars [prem] goal (fn {context = ctxt, prems = [prem]} => mk_extdd_mor_tac ctxt dead_pre_map_comp0 dead_pre_map_comp VLeaf_map_thm ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_thm eval_flat eval_VLeaf cutSsig_def prem)) |> Thm.close_derivation \<^here> end; fun derive_mor_cutSsig_flat ctxt Y Z preT fpT ssig_T dead_pre_map dead_ssig_map dtor flat eval_core eval cutSsig f g dead_pre_map_comp0 dead_pre_map_comp dead_pre_map_cong dtor_unfold_unique dead_ssig_map_comp0 ssig_map_comp flat_simps flat_pointful_natural eval_core_pointful_natural flat_flat flat_VLeaf eval_core_flat cutSsig_def cutSsig_def_pointful_natural eval_thm = let val ssig_preT = Tsubst Y ssig_T preT; val substYZ = Term.subst_atomic_types [(Y, ssig_T), (Z, fpT)]; val dead_pre_map' = substYZ dead_pre_map; val dead_ssig_map' = substYZ dead_ssig_map; val f' = substYZ f; val g' = substT Z ssig_preT g; val cutSsig_g = cutSsig $ g'; val id' = HOLogic.id_const ssig_T; val convol' = mk_convol (id', cutSsig_g); val dead_ssig_map'' = Term.subst_atomic_types [(Y, ssig_T), (Z, range_type (fastype_of convol'))] dead_ssig_map; val eval_core' = substT Y ssig_T eval_core; val eval_core_o_map = HOLogic.mk_comp (eval_core', dead_ssig_map'' $ convol'); val prem = mk_Trueprop_eq (HOLogic.mk_comp (dead_pre_map' $ f', cutSsig_g), HOLogic.mk_comp (dtor, f')); val goal = mk_Trueprop_eq (HOLogic.mk_comp (eval, dead_ssig_map' $ f'), HOLogic.mk_comp (f', flat)); in fold (Variable.add_free_names ctxt) [prem, goal] [] |> (fn vars => Goal.prove_sorry ctxt vars [prem] goal (fn {context = ctxt, prems = [prem]} => mk_mor_cutSsig_flat_tac ctxt eval_core_o_map dead_pre_map_comp0 dead_pre_map_comp dead_pre_map_cong dtor_unfold_unique dead_ssig_map_comp0 ssig_map_comp flat_simps flat_pointful_natural eval_core_pointful_natural flat_flat flat_VLeaf eval_core_flat cutSsig_def cutSsig_def_pointful_natural eval_thm prem)) |> Thm.close_derivation \<^here> end; fun derive_extdd_o_VLeaf ctxt Y Z preT fpT ssig_T dead_pre_map dtor VLeaf extdd f g dead_pre_map_comp0 dead_pre_map_comp dtor_inject ssig_map_thms eval_core_simps eval_thm eval_VLeaf = let val ssig_preT = Tsubst Y ssig_T preT; val substYZ = Term.subst_atomic_types [(Y, ssig_T), (Z, fpT)]; val dead_pre_map' = substYZ dead_pre_map; val f' = substT Z fpT f; val g' = substT Z ssig_preT g; val extdd_f = extdd $ f'; val prem = mk_Trueprop_eq (HOLogic.mk_comp (dead_pre_map' $ extdd_f, g'), HOLogic.mk_comp (dtor, f')); val goal = mk_Trueprop_eq (HOLogic.mk_comp (extdd_f, VLeaf), f'); in fold (Variable.add_free_names ctxt) [prem, goal] [] |> (fn vars => Goal.prove_sorry ctxt vars [prem] goal (fn {context = ctxt, prems = [prem]} => mk_extdd_o_VLeaf_tac ctxt dead_pre_map_comp0 dead_pre_map_comp dtor_inject ssig_map_thms eval_core_simps eval_thm eval_VLeaf prem)) |> Thm.close_derivation \<^here> end; fun derive_corecU_pointfree ctxt Y Z preT fpT ssig_T dead_pre_map dtor extdd corecU g dead_pre_map_comp dtor_unfold_thm ssig_map_thms dead_ssig_map_comp0 flat_simps flat_VLeaf eval_core_simps cutSsig_def mor_cutSsig_flat corecU_def = let val ssig_preT = Tsubst Y ssig_T preT; val substYZ = Term.subst_atomic_types [(Y, ssig_T), (Z, fpT)]; val dead_pre_map' = substYZ dead_pre_map; val g' = substT Z ssig_preT g; val corecU_g = corecU $ g'; val goal = mk_Trueprop_eq (HOLogic.mk_comp (dead_pre_map' $ (extdd $ corecU_g), g'), HOLogic.mk_comp (dtor, corecU_g)); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_corecU_pointfree_tac ctxt dead_pre_map_comp dtor_unfold_thm ssig_map_thms dead_ssig_map_comp0 flat_simps flat_VLeaf eval_core_simps cutSsig_def mor_cutSsig_flat corecU_def)) |> Thm.close_derivation \<^here> end; fun derive_corecU_ctor_unique ctxt Y Z preT fpT ssig_T dead_pre_map ctor dtor VLeaf extdd corecU f g dead_pre_map_comp ctor_dtor dtor_unfold_thm dtor_unfold_unique ssig_map_thms dead_ssig_map_comp0 flat_simps flat_VLeaf eval_core_simps extdd_mor extdd_o_VLeaf cutSsig_def mor_cutSsig_flat corecU_def = let val corecU_pointfree = derive_corecU_pointfree ctxt Y Z preT fpT ssig_T dead_pre_map dtor extdd corecU g dead_pre_map_comp dtor_unfold_thm ssig_map_thms dead_ssig_map_comp0 flat_simps flat_VLeaf eval_core_simps cutSsig_def mor_cutSsig_flat corecU_def; val corecU_thm = corecU_pointfree RS @{thm comp_eq_dest}; val corecU_ctor = let val arg_cong' = infer_instantiate' ctxt [NONE, NONE, SOME (Thm.cterm_of ctxt ctor)] arg_cong; in unfold_thms ctxt [ctor_dtor] (corecU_thm RS arg_cong') end; val corecU_unique = let val substYZ = Term.subst_atomic_types [(Y, ssig_T), (Z, fpT)]; val f' = substYZ f; val abs_f_o_VLeaf = Term.lambda f' (HOLogic.mk_comp (f', VLeaf)); val inject_refine' = infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt abs_f_o_VLeaf), SOME (Thm.cterm_of ctxt extdd)] @{thm inject_refine}; in unfold_thms ctxt @{thms atomize_imp} (((inject_refine' OF [extdd_o_VLeaf, extdd_o_VLeaf] RS iffD1) OF [asm_rl, corecU_pointfree]) OF [asm_rl, trans OF [dtor_unfold_unique, dtor_unfold_unique RS sym] OF [extdd_mor, corecU_pointfree RS extdd_mor]]) RS @{thm obj_distinct_prems} end; in (corecU_ctor, corecU_unique) end; fun derive_dtor_algLam ctxt Y Z preT fpT sig_T ssig_T dead_pre_map dtor dead_sig_map Lam eval algLam x pre_map_comp dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp sig_map_comp Oper_pointful_natural ssig_map_thms dead_ssig_map_comp0 Lam_pointful_natural eval_core_simps eval_thm eval_flat eval_VLeaf algLam_def = let val fp_preT = Tsubst Y fpT preT; val fppreT = HOLogic.mk_prodT (fpT, fp_preT); val fp_sig_T = Tsubst Y fpT sig_T; val fp_ssig_T = Tsubst Y fpT ssig_T; val id' = HOLogic.id_const fpT; val convol' = mk_convol (id', dtor); val dead_pre_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_pre_map; val dead_sig_map' = Term.subst_atomic_types [(Y, fpT), (Z, fppreT)] dead_sig_map; val Lam' = substT Y fpT Lam; val x' = substT Y fp_sig_T x; val goal = mk_Trueprop_eq (dtor $ (algLam $ x'), dead_pre_map' $ eval $ (Lam' $ (dead_sig_map' $ convol' $ x'))); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_dtor_algLam_tac ctxt pre_map_comp dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp sig_map_comp Oper_pointful_natural ssig_map_thms dead_ssig_map_comp0 Lam_pointful_natural eval_core_simps eval_thm eval_flat eval_VLeaf algLam_def)) |> Thm.close_derivation \<^here> end; fun derive_algLam_base ctxt Y Z preT fpT dead_pre_map ctor dtor algLam proto_sctr dead_pre_map_id dead_pre_map_comp ctor_dtor dtor_ctor dtor_unfold_unique unsig_thm Sig_pointful_natural ssig_map_thms Lam_def flat_simps eval_core_simps eval_thm algLam_def = let val fp_preT = Tsubst Y fpT preT; val proto_sctr' = substT Y fpT proto_sctr; val dead_pre_map' = Term.subst_atomic_types [(Y, fpT), (Z, fp_preT)] dead_pre_map; val dead_pre_map_dtor = dead_pre_map' $ dtor; val goal = mk_Trueprop_eq (HOLogic.mk_comp (algLam, proto_sctr'), ctor); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_algLam_base_tac ctxt dead_pre_map_dtor dead_pre_map_id dead_pre_map_comp ctor_dtor dtor_ctor dtor_unfold_unique unsig_thm Sig_pointful_natural ssig_map_thms Lam_def flat_simps eval_core_simps eval_thm algLam_def)) |> Thm.close_derivation \<^here> end; fun derive_flat_embL ctxt Y Z old_ssig_T ssig_T dead_old_ssig_map embL old_flat flat x old_ssig_induct fp_map_id Sig_pointful_natural old_sig_map_comp old_sig_map_cong old_ssig_map_thms old_flat_simps flat_simps embL_simps = let val old_ssig_old_ssig_T = Tsubst Y old_ssig_T old_ssig_T; val dead_old_ssig_map' = Term.subst_atomic_types [(Y, old_ssig_T), (Z, ssig_T)] dead_old_ssig_map; val embL' = substT Y ssig_T embL; val x' = substT Y old_ssig_old_ssig_T x; val goal = mk_Trueprop_eq (flat $ (embL' $ (dead_old_ssig_map' $ embL $ x')), embL $ (old_flat $ x')); val old_ssig_induct' = infer_instantiate' ctxt [NONE, SOME (Thm.cterm_of ctxt x')] old_ssig_induct; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_flat_embL_tac ctxt old_ssig_induct' fp_map_id Sig_pointful_natural old_sig_map_comp old_sig_map_cong old_ssig_map_thms old_flat_simps flat_simps embL_simps)) |> Thm.close_derivation \<^here> end; fun derive_eval_core_embL ctxt Y Z preT old_ssig_T ssig_T dead_pre_map embL old_eval_core eval_core x old_ssig_induct dead_pre_map_comp0 dead_pre_map_comp Sig_pointful_natural unsig_thm old_sig_map_comp old_sig_map_cong old_Lam_pointful_natural Lam_def flat_embL embL_simps embL_pointful_natural old_eval_core_simps eval_core_simps = let val YpreT = HOLogic.mk_prodT (Y, preT); val Ypre_old_ssig_T = Tsubst Y YpreT old_ssig_T; val dead_pre_map' = Term.subst_atomic_types [(Y, old_ssig_T), (Z, ssig_T)] dead_pre_map; val embL' = substT Y YpreT embL; val x' = substT Y Ypre_old_ssig_T x; val goal = mk_Trueprop_eq (eval_core $ (embL' $ x'), dead_pre_map' $ embL $ (old_eval_core $ x')); val old_ssig_induct' = infer_instantiate' ctxt [NONE, SOME (Thm.cterm_of ctxt x')] old_ssig_induct; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_core_embL_tac ctxt old_ssig_induct' dead_pre_map_comp0 dead_pre_map_comp Sig_pointful_natural unsig_thm old_sig_map_comp old_sig_map_cong old_Lam_pointful_natural Lam_def flat_embL old_eval_core_simps eval_core_simps embL_simps embL_pointful_natural)) |> Thm.close_derivation \<^here> end; fun derive_eval_embL ctxt Y fpT embL old_eval eval dead_pre_map_comp0 dtor_unfold_unique embL_pointful_natural eval_core_embL old_eval_thm eval_thm = let val embL' = substT Y fpT embL; val goal = mk_Trueprop_eq (HOLogic.mk_comp (eval, embL'), old_eval); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_embL_tac ctxt dead_pre_map_comp0 dtor_unfold_unique embL_pointful_natural eval_core_embL old_eval_thm eval_thm)) |> Thm.close_derivation \<^here> end; fun derive_algLam_algLam ctxt Inx_const Y fpT Sig old_algLam algLam dead_pre_map_comp dtor_inject unsig_thm sig_map_thm Lam_def eval_embL old_dtor_algLam dtor_algLam = let val Sig' = substT Y fpT Sig; val (left_T, right_T) = dest_sumT (domain_type (fastype_of Sig')); val inx' = Inx_const left_T right_T; val goal = mk_Trueprop_eq (Library.foldl1 HOLogic.mk_comp [algLam, Sig', inx'], old_algLam); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_algLam_algLam_tac ctxt dead_pre_map_comp dtor_inject unsig_thm sig_map_thm Lam_def eval_embL old_dtor_algLam dtor_algLam)) |> Thm.close_derivation \<^here> end; fun derive_eval_core_k_as_ssig ctxt Y preT k_T rho eval_core k_as_ssig x pre_map_comp dead_pre_map_id sig_map_comp ssig_map_thms Lam_natural_pointful Lam_Inr flat_VLeaf eval_core_simps = let val YpreT = HOLogic.mk_prodT (Y, preT); val Ypre_k_T = Tsubst Y YpreT k_T; val k_as_ssig' = substT Y YpreT k_as_ssig; val x' = substT Y Ypre_k_T x; val goal = mk_Trueprop_eq (eval_core $ (k_as_ssig' $ x'), rho $ x'); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_core_k_as_ssig_tac ctxt pre_map_comp dead_pre_map_id sig_map_comp ssig_map_thms Lam_natural_pointful Lam_Inr flat_VLeaf eval_core_simps)) |> Thm.close_derivation \<^here> end; fun derive_algLam_algrho ctxt Y fpT Sig algLam algrho algLam_def algrho_def = let val Sig' = substT Y fpT Sig; val (left_T, right_T) = dest_sumT (domain_type (fastype_of Sig')); val inr' = Inr_const left_T right_T; val goal = mk_Trueprop_eq (Library.foldl1 HOLogic.mk_comp [algLam, Sig', inr'], algrho); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_algLam_algrho_tac ctxt algLam_def algrho_def)) |> Thm.close_derivation \<^here> end; fun derive_dtor_algrho ctxt Y Z preT fpT k_T ssig_T dead_pre_map dead_k_map dtor rho eval algrho x eval_thm k_as_ssig_natural_pointful eval_core_k_as_ssig algrho_def = let val YpreT = HOLogic.mk_prodT (Y, preT); val fppreT = Tsubst Y fpT YpreT; val fp_k_T = Tsubst Y fpT k_T; val fp_ssig_T = Tsubst Y fpT ssig_T; val id' = HOLogic.id_const fpT; val convol' = mk_convol (id', dtor); val dead_pre_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_pre_map; val dead_k_map' = Term.subst_atomic_types [(Y, fpT), (Z, fppreT)] dead_k_map; val rho' = substT Y fpT rho; val x' = substT Y fp_k_T x; val goal = mk_Trueprop_eq (dtor $ (algrho $ x'), dead_pre_map' $ eval $ (rho' $ (dead_k_map' $ convol' $ x'))); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_dtor_algrho_tac ctxt eval_thm k_as_ssig_natural_pointful eval_core_k_as_ssig algrho_def)) |> Thm.close_derivation \<^here> end; fun derive_algLam_step_or_merge ctxt Y fpT ctor proto_sctr algLam proto_sctr_def old_algLam_pointful algLam_algLam = let val proto_sctr' = substT Y fpT proto_sctr; val goal = mk_Trueprop_eq (HOLogic.mk_comp (algLam, proto_sctr'), ctor); val algLam_algLam_pointful = mk_pointful ctxt algLam_algLam; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_algLam_step_tac ctxt proto_sctr_def old_algLam_pointful algLam_algLam_pointful)) |> Thm.close_derivation \<^here> end; fun derive_eval_sctr ctxt Y Z fpT ssig_T dead_pre_map ctor eval sctr proto_sctr_pointful_natural eval_Oper algLam_thm sctr_def = let val fp_ssig_T = Tsubst Y fpT ssig_T; val dead_pre_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_pre_map; val sctr' = substT Y fpT sctr; val goal = mk_Trueprop_eq (HOLogic.mk_comp (eval, sctr'), HOLogic.mk_comp (ctor, dead_pre_map' $ eval)); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_eval_sctr_tac ctxt proto_sctr_pointful_natural eval_Oper algLam_thm sctr_def)) |> Thm.close_derivation \<^here> end; fun derive_corecUU_pointfree_unique ctxt Y Z preT fpT ssig_T dead_pre_map ctor dead_ssig_map eval corecUU f g dead_pre_map_comp0 dead_pre_map_comp dtor_ctor dtor_inject ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_thm eval_flat corecU_ctor corecU_unique sctr_pointful_natural eval_sctr_pointful corecUU_def = let val ssig_preT = Tsubst Y ssig_T preT; val ssig_pre_ssig_T = Tsubst Y ssig_preT ssig_T; val fp_ssig_T = Tsubst Y fpT ssig_T; val dead_pre_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_pre_map; val dead_pre_map'' = Term.subst_atomic_types [(Y, ssig_T), (Z, fp_ssig_T)] dead_pre_map; val dead_ssig_map' = Term.subst_atomic_types [(Y, ssig_preT), (Z, fpT)] dead_ssig_map; val dead_ssig_map'' = substT Z fpT dead_ssig_map; val f' = substT Z ssig_pre_ssig_T f; val g' = substT Z fpT g; val corecUU_f = corecUU $ f'; fun mk_eq fpf = mk_Trueprop_eq (fpf, Library.foldl1 HOLogic.mk_comp [eval, dead_ssig_map' $ Library.foldl1 HOLogic.mk_comp [ctor, dead_pre_map' $ eval, dead_pre_map'' $ (dead_ssig_map'' $ fpf)], f']); val corecUU_pointfree = let val goal = mk_eq corecUU_f; in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_corecUU_pointfree_tac ctxt dead_pre_map_comp0 dead_pre_map_comp dtor_ctor dtor_inject ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_thm eval_flat corecU_ctor sctr_pointful_natural eval_sctr_pointful corecUU_def)) |> Thm.close_derivation \<^here> end; val corecUU_unique = let val prem = mk_eq g'; val goal = mk_Trueprop_eq (g', corecUU_f); in fold (Variable.add_free_names ctxt) [prem, goal] [] |> (fn vars => Goal.prove_sorry ctxt vars [prem] goal (fn {context = ctxt, prems = [prem]} => mk_corecUU_unique_tac ctxt dead_pre_map_comp0 dead_pre_map_comp dtor_ctor ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_thm eval_flat corecU_unique sctr_pointful_natural eval_sctr_pointful corecUU_def prem)) |> Thm.close_derivation \<^here> end; in (corecUU_pointfree, corecUU_unique) end; fun define_flat_etc fp_b version live_AsBs Y Z preT fpT sig_T ssig_T Oper VLeaf CLeaf pre_rel dead_pre_map dtor dtor_unfold dead_sig_map ssig_rel dead_ssig_map Lam Rs R pre_map_transfer fp_k_T_rel_eqs sig_map_transfer ssig_map_transfer Lam_transfer dtor_transfer lthy = let val (flat_data as (flat, flat_def, _), lthy) = lthy |> define_flat fp_b version Y Z fpT sig_T ssig_T Oper VLeaf CLeaf dead_sig_map; val (eval_core_data as (eval_core, eval_core_def, _), lthy) = lthy |> define_eval_core fp_b version Y Z preT fpT sig_T ssig_T dtor Oper VLeaf CLeaf dead_pre_map dead_sig_map dead_ssig_map flat Lam; val ((eval_data as (eval, _), cutSsig_data as (cutSsig, _)), lthy) = lthy |> define_eval fp_b version Y Z preT fpT ssig_T dtor dtor_unfold dead_ssig_map eval_core ||>> define_cutSsig fp_b version Y Z preT ssig_T dead_pre_map VLeaf dead_ssig_map flat eval_core; val ((algLam_data, unfold_data), lthy) = lthy |> define_algLam fp_b version Y Z fpT ssig_T Oper VLeaf dead_sig_map eval ||>> define_corecU fp_b version Y Z preT ssig_T dtor_unfold VLeaf cutSsig; val flat_transfer = derive_transfer_by_transfer_prover lthy live_AsBs Rs R flat [flat_def] [] [sig_map_transfer]; val eval_core_transfer = derive_Lam_or_eval_core_transfer lthy live_AsBs Y Z preT ssig_T Rs R pre_rel ssig_rel ssig_rel eval_core eval_core_def fp_k_T_rel_eqs [pre_map_transfer, sig_map_transfer, ssig_map_transfer, flat_transfer, Lam_transfer, dtor_transfer]; in (((((((flat_data, flat_transfer), (eval_core_data, eval_core_transfer)), eval_data), cutSsig_data), algLam_data), unfold_data), lthy) end; fun derive_Sig_natural_etc ctxt live live_AsBs Y Z preT fpT k_or_fpT sig_T ssig_T pre_map dead_pre_map ctor dtor Sig dead_sig_map Oper VLeaf CLeaf ssig_map dead_ssig_map Lam flat eval_core eval cutSsig algLam corecU x fs f g ctor_dtor dtor_inject dtor_unfold_thm dtor_unfold_unique sig_map_thm ssig_induct ssig_map_thms Oper_map_thm VLeaf_map_thm CLeaf_map_thm Lam_transfer flat_simps flat_transfer eval_core_simps eval_core_transfer eval_def cutSsig_def algLam_def corecU_def live_pre_bnf pre_bnf dead_pre_bnf fp_bnf sig_bnf ssig_bnf dead_ssig_bnf = let val SOME prod_bnf = bnf_of ctxt \<^type_name>\prod\; val f' = substT Z fpT f; val dead_ssig_map' = substT Z fpT dead_ssig_map; val extdd = Term.lambda f' (HOLogic.mk_comp (eval, dead_ssig_map' $ f')); val live_pre_map_def = map_def_of_bnf live_pre_bnf; val pre_map_comp = map_comp_of_bnf pre_bnf; val dead_pre_map_id = map_id_of_bnf dead_pre_bnf; val dead_pre_map_comp0 = map_comp0_of_bnf dead_pre_bnf; val dead_pre_map_comp = map_comp_of_bnf dead_pre_bnf; val dead_pre_map_cong = map_cong_of_bnf dead_pre_bnf; val fp_map_id = map_id_of_bnf fp_bnf; val sig_map_ident = map_ident_of_bnf sig_bnf; val sig_map_comp0 = map_comp0_of_bnf sig_bnf; val sig_map_comp = map_comp_of_bnf sig_bnf; val sig_map_cong = map_cong_of_bnf sig_bnf; val ssig_map_id = map_id_of_bnf ssig_bnf; val ssig_map_comp = map_comp_of_bnf ssig_bnf; val dead_ssig_map_comp0 = map_comp0_of_bnf dead_ssig_bnf; val k_preT_map_id0s = map map_id0_of_bnf (map_filter (bnf_of ctxt) (fold add_type_namesT [preT, k_or_fpT] [])); val Sig_natural = derive_natural_by_unfolding ctxt live_AsBs preT pre_map fs f Sig ([sig_map_thm, live_pre_map_def, @{thm BNF_Composition.id_bnf_def}] @ k_preT_map_id0s); val Oper_natural = derive_natural_by_unfolding ctxt live_AsBs preT pre_map fs f Oper [Oper_map_thm]; val VLeaf_natural = derive_natural_by_unfolding ctxt live_AsBs preT pre_map fs f VLeaf [VLeaf_map_thm]; val Lam_natural = derive_natural_from_transfer_with_pre_type ctxt live_AsBs Y Z preT ssig_T pre_map ssig_map fs f Lam Lam_transfer [prod_bnf, pre_bnf, sig_bnf, ssig_bnf] []; val flat_natural = derive_natural_from_transfer ctxt live_AsBs [] fs f flat flat_transfer [ssig_bnf] []; val eval_core_natural = derive_natural_from_transfer_with_pre_type ctxt live_AsBs Y Z preT ssig_T pre_map ssig_map fs f eval_core eval_core_transfer [prod_bnf, pre_bnf, ssig_bnf] []; val Sig_pointful_natural = mk_pointful ctxt Sig_natural RS sym; val Oper_natural_pointful = mk_pointful ctxt Oper_natural; val Oper_pointful_natural = Oper_natural_pointful RS sym; val flat_pointful_natural = mk_pointful ctxt flat_natural RS sym; val Lam_natural_pointful = mk_pointful ctxt Lam_natural; val Lam_pointful_natural = Lam_natural_pointful RS sym; val eval_core_pointful_natural = mk_pointful ctxt eval_core_natural RS sym; val cutSsig_def_pointful_natural = mk_pointful ctxt (HOLogic.mk_obj_eq cutSsig_def) RS sym; val flat_VLeaf = derive_flat_VLeaf ctxt Y Z ssig_T x VLeaf dead_ssig_map flat ssig_induct fp_map_id sig_map_cong sig_map_ident sig_map_comp ssig_map_thms flat_simps; val flat_flat = derive_flat_flat ctxt Y Z ssig_T x dead_ssig_map flat ssig_induct fp_map_id sig_map_cong sig_map_comp ssig_map_thms flat_simps; val eval_core_flat = derive_eval_core_flat ctxt Y Z preT ssig_T dead_pre_map dead_ssig_map flat eval_core x ssig_induct dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp fp_map_id sig_map_comp sig_map_cong ssig_map_thms ssig_map_comp flat_simps flat_pointful_natural flat_flat Lam_pointful_natural eval_core_simps; val eval_thm = derive_eval_thm ctxt dtor_inject dtor_unfold_thm eval_def; val eval_flat = derive_eval_flat ctxt Y Z fpT ssig_T dead_ssig_map flat eval x dead_pre_map_comp0 dtor_unfold_unique ssig_map_id ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_core_flat eval_thm; val eval_Oper = derive_eval_Oper ctxt live Y Z fpT sig_T ssig_T dead_sig_map Oper eval algLam x sig_map_ident sig_map_comp0 sig_map_comp Oper_natural_pointful VLeaf_natural flat_simps eval_flat algLam_def; val eval_VLeaf = derive_eval_V_or_CLeaf ctxt Y fpT VLeaf eval x dead_pre_map_id dead_pre_map_comp fp_map_id dtor_unfold_unique VLeaf_map_thm eval_core_simps eval_thm; val eval_CLeaf = derive_eval_V_or_CLeaf ctxt Y fpT CLeaf eval x dead_pre_map_id dead_pre_map_comp fp_map_id dtor_unfold_unique CLeaf_map_thm eval_core_simps eval_thm; val extdd_mor = derive_extdd_mor ctxt Y Z preT fpT ssig_T dead_pre_map dtor extdd cutSsig f g dead_pre_map_comp0 dead_pre_map_comp VLeaf_map_thm ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_thm eval_flat eval_VLeaf cutSsig_def; val mor_cutSsig_flat = derive_mor_cutSsig_flat ctxt Y Z preT fpT ssig_T dead_pre_map dead_ssig_map dtor flat eval_core eval cutSsig f g dead_pre_map_comp0 dead_pre_map_comp dead_pre_map_cong dtor_unfold_unique dead_ssig_map_comp0 ssig_map_comp flat_simps flat_pointful_natural eval_core_pointful_natural flat_flat flat_VLeaf eval_core_flat cutSsig_def cutSsig_def_pointful_natural eval_thm; val extdd_o_VLeaf = derive_extdd_o_VLeaf ctxt Y Z preT fpT ssig_T dead_pre_map dtor VLeaf extdd f g dead_pre_map_comp0 dead_pre_map_comp dtor_inject ssig_map_thms eval_core_simps eval_thm eval_VLeaf; val (corecU_ctor, corecU_unique) = derive_corecU_ctor_unique ctxt Y Z preT fpT ssig_T dead_pre_map ctor dtor VLeaf extdd corecU f g dead_pre_map_comp ctor_dtor dtor_unfold_thm dtor_unfold_unique ssig_map_thms dead_ssig_map_comp0 flat_simps flat_VLeaf eval_core_simps extdd_mor extdd_o_VLeaf cutSsig_def mor_cutSsig_flat corecU_def; val dtor_algLam = derive_dtor_algLam ctxt Y Z preT fpT sig_T ssig_T dead_pre_map dtor dead_sig_map Lam eval algLam x pre_map_comp dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp sig_map_comp Oper_pointful_natural ssig_map_thms dead_ssig_map_comp0 Lam_pointful_natural eval_core_simps eval_thm eval_flat eval_VLeaf algLam_def; in (Sig_pointful_natural, flat_pointful_natural, Lam_natural_pointful, Lam_pointful_natural, flat_VLeaf, eval_core_pointful_natural, eval_thm, eval_flat, [eval_Oper, eval_VLeaf, eval_CLeaf], corecU_ctor, corecU_unique, dtor_algLam) end; fun derive_embL_natural_etc ctxt Inx_const old_ssig_bnf ssig_bnf Y Z preT fpT old_ssig_T ssig_T dead_pre_map Sig dead_old_ssig_map embL old_algLam algLam old_flat flat old_eval_core eval_core old_eval eval x f old_ssig_induct dead_pre_map_comp0 dead_pre_map_comp fp_map_id dtor_inject dtor_unfold_unique Sig_pointful_natural unsig_thm sig_map_thm old_sig_map_comp old_sig_map_cong old_ssig_map_thms old_Lam_pointful_natural Lam_def old_flat_simps flat_simps embL_simps embL_transfer old_eval_core_simps eval_core_simps old_eval_thm eval_thm old_dtor_algLam dtor_algLam old_algLam_thm = let val embL_natural = derive_natural_from_transfer ctxt [(Y, Z)] [] [] f embL embL_transfer [old_ssig_bnf, ssig_bnf] []; val embL_pointful_natural = mk_pointful ctxt embL_natural RS sym; val old_algLam_pointful = mk_pointful ctxt old_algLam_thm; val flat_embL = derive_flat_embL ctxt Y Z old_ssig_T ssig_T dead_old_ssig_map embL old_flat flat x old_ssig_induct fp_map_id Sig_pointful_natural old_sig_map_comp old_sig_map_cong old_ssig_map_thms old_flat_simps flat_simps embL_simps; val eval_core_embL = derive_eval_core_embL ctxt Y Z preT old_ssig_T ssig_T dead_pre_map embL old_eval_core eval_core x old_ssig_induct dead_pre_map_comp0 dead_pre_map_comp Sig_pointful_natural unsig_thm old_sig_map_comp old_sig_map_cong old_Lam_pointful_natural Lam_def flat_embL embL_simps embL_pointful_natural old_eval_core_simps eval_core_simps; val eval_embL = derive_eval_embL ctxt Y fpT embL old_eval eval dead_pre_map_comp0 dtor_unfold_unique embL_pointful_natural eval_core_embL old_eval_thm eval_thm; val algLam_algLam = derive_algLam_algLam ctxt Inx_const Y fpT Sig old_algLam algLam dead_pre_map_comp dtor_inject unsig_thm sig_map_thm Lam_def eval_embL old_dtor_algLam dtor_algLam; in (embL_pointful_natural, old_algLam_pointful, eval_embL, algLam_algLam) end; fun define_corecUU_etc fp_b version live_AsBs Y Z preT fpT ssig_T pre_map dead_pre_map pre_rel fp_rel ctor Oper ssig_map dead_ssig_map ssig_rel proto_sctr flat eval_core eval corecU fs f g Rs R pre_map_transfer fp_k_T_rel_eqs dtor_unfold_transfer dtor_transfer ssig_map_transfer proto_sctr_transfer proto_sctr_pointful_natural flat_transfer flat_pointful_natural eval_core_transfer eval_core_pointful_natural eval_thm eval_flat eval_Oper algLam_thm cutSsig_def corecU_def corecU_ctor corecU_unique pre_bnf dead_pre_bnf fp_res ssig_fp_sugar lthy = let val ssig_bnf = #fp_bnf ssig_fp_sugar; val dead_pre_map_comp0 = map_comp0_of_bnf dead_pre_bnf; val dead_pre_map_comp = map_comp_of_bnf dead_pre_bnf; val [dtor_ctor] = #dtor_ctors fp_res; val [dtor_inject] = #dtor_injects fp_res; val ssig_map_comp = map_comp_of_bnf ssig_bnf; val sctr_rhs = HOLogic.mk_comp (Oper, substT Y ssig_T proto_sctr); val ((sctr, sctr_def), lthy) = lthy |> define_const true fp_b version sctrN sctr_rhs; val (corecUU_data as (corecUU, corecUU_def), lthy) = lthy |> define_corecUU fp_b version Y Z preT ssig_T dead_pre_map dead_ssig_map flat eval_core sctr corecU; val eval_sctr = derive_eval_sctr lthy Y Z fpT ssig_T dead_pre_map ctor eval sctr proto_sctr_pointful_natural eval_Oper algLam_thm sctr_def; val sctr_transfer = derive_sctr_transfer lthy live_AsBs Y Z ssig_T Rs R pre_rel ssig_rel sctr sctr_def fp_k_T_rel_eqs [proto_sctr_transfer]; val sctr_natural = derive_natural_from_transfer_with_pre_type lthy live_AsBs Y Z preT ssig_T pre_map ssig_map fs f sctr sctr_transfer [pre_bnf, ssig_bnf] []; val sctr_pointful_natural = mk_pointful lthy sctr_natural RS sym; val eval_sctr_pointful = mk_pointful lthy eval_sctr RS sym; val (corecUU_pointfree, corecUU_unique) = derive_corecUU_pointfree_unique lthy Y Z preT fpT ssig_T dead_pre_map ctor dead_ssig_map eval corecUU f g dead_pre_map_comp0 dead_pre_map_comp dtor_ctor dtor_inject ssig_map_comp flat_pointful_natural eval_core_pointful_natural eval_thm eval_flat corecU_ctor corecU_unique sctr_pointful_natural eval_sctr_pointful corecUU_def; val corecUU_thm = mk_pointful lthy corecUU_pointfree; val corecUU_transfer = derive_corecUU_transfer lthy live_AsBs Y Z Rs R preT ssig_T pre_rel fp_rel ssig_rel corecUU cutSsig_def corecU_def corecUU_def fp_k_T_rel_eqs [pre_map_transfer, dtor_unfold_transfer, dtor_transfer, ssig_map_transfer, flat_transfer, eval_core_transfer, sctr_transfer, @{thm convol_transfer} (*FIXME: needed?*)]; in ((corecUU_data, corecUU_thm, corecUU_unique, corecUU_transfer, eval_sctr, sctr_transfer, sctr_pointful_natural), lthy) end; fun mk_equivp T = Const (\<^const_name>\equivp\, mk_predT [mk_pred2T T T]); fun derive_equivp_Retr ctxt fpT Retr R dead_pre_rel_refl_thm dead_pre_rel_flip_thm dead_pre_rel_mono_thm dead_pre_rel_compp_thm = let val prem = HOLogic.mk_Trueprop (mk_equivp fpT $ R); val goal = Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_equivp fpT $ (betapply (Retr, R)))); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => mk_equivp_Retr_tac ctxt dead_pre_rel_refl_thm dead_pre_rel_flip_thm dead_pre_rel_mono_thm dead_pre_rel_compp_thm)) |> Thm.close_derivation \<^here> end; fun derive_Retr_coinduct ctxt fpT Retr R dtor_rel_coinduct_thm rel_eq_thm = let val goal = HOLogic.mk_Trueprop (list_all_free [R] (HOLogic.mk_imp (mk_leq R (Retr $ R), mk_leq R (HOLogic.eq_const fpT)))); in Goal.prove_sorry ctxt [] [] goal (fn {context = ctxt, prems = _} => mk_Retr_coinduct_tac ctxt dtor_rel_coinduct_thm rel_eq_thm) |> Thm.close_derivation \<^here> end; fun derive_Retr fp_sugar fpT dead_pre_bnf ctor dtor names_lthy lthy = let val (R, _) = names_lthy |> yield_singleton (mk_Frees "R") (mk_pred2T fpT fpT); val pre_fpT = pre_type_of_ctor fpT ctor; val fp_pre_rel = mk_rel1 lthy fpT fpT pre_fpT dead_pre_bnf; val Retr = Abs ("R", fastype_of R, Abs ("a", fpT, Abs ("b", fpT, list_comb (fp_pre_rel, [Bound 2, dtor $ Bound 1, dtor $ Bound 0])))); val equivp_Retr = derive_equivp_Retr lthy fpT Retr R (rel_refl_of_bnf dead_pre_bnf) (rel_flip_of_bnf dead_pre_bnf) (rel_mono_of_bnf dead_pre_bnf) (rel_OO_of_bnf dead_pre_bnf); val Retr_coinduct = derive_Retr_coinduct lthy fpT Retr R (fp_sugar |> #fp_res |> #xtor_rel_co_induct) (fp_sugar |> #fp_bnf |> rel_eq_of_bnf); in (Retr, equivp_Retr, Retr_coinduct) end; fun mk_gen_cong fpT eval_domT = let val fp_relT = mk_pred2T fpT fpT in Const (\<^const_name>\cong.gen_cong\, [mk_predT [fp_relT, eval_domT, eval_domT], eval_domT --> fpT, fp_relT] ---> fp_relT) end; fun mk_cong_locale rel eval Retr = Const (\<^const_name>\cong\, mk_predT (map fastype_of [rel, eval, Retr])); fun derive_cong_locale ctxt rel eval Retr0 tac = let val Retr = enforce_type ctxt domain_type (domain_type (fastype_of rel)) Retr0; val goal = HOLogic.mk_Trueprop (list_comb (mk_cong_locale rel eval Retr, [rel, eval, Retr])); in Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} => tac ctxt)) |> Thm.close_derivation \<^here> end; fun derive_cong_general fp_b version fpT dead_ssig_bnf dead_pre_bnf eval Retr equivp_Retr Retr_coinduct eval_thm eval_core_transfer lthy = let val eval_domT = domain_type (fastype_of eval); fun cong_locale_tac ctxt = mk_cong_locale_tac ctxt (rel_mono_of_bnf dead_pre_bnf) (rel_map_of_bnf dead_pre_bnf) equivp_Retr (rel_mono_of_bnf dead_ssig_bnf) (rel_map_of_bnf dead_ssig_bnf) eval_thm eval_core_transfer; val rel = mk_rel1 lthy fpT fpT eval_domT dead_ssig_bnf; val cong_rhs = list_comb (mk_gen_cong fpT eval_domT, [rel, eval]); val ((_, cong_def), lthy) = lthy |> define_const false fp_b version congN cong_rhs; val cong_locale = derive_cong_locale lthy rel eval Retr cong_locale_tac; val fold_cong_def = Local_Defs.fold lthy [cong_def]; fun instance_of_gen thm = fold_cong_def (thm OF [cong_locale]); val cong_base = instance_of_gen @{thm cong.imp_gen_cong}; val cong_refl = instance_of_gen @{thm cong.gen_cong_reflp}; val cong_sym = instance_of_gen @{thm cong.gen_cong_symp}; val cong_trans = instance_of_gen @{thm cong.gen_cong_transp}; fun mk_cong_rho thm = thm RS instance_of_gen @{thm cong.gen_cong_rho}; val dtor_coinduct = @{thm predicate2I_obj} RS (Retr_coinduct RS instance_of_gen @{thm cong.coinduction} RS @{thm predicate2D_obj}); in (cong_def, cong_locale, cong_base, cong_refl, cong_sym, cong_trans, dtor_coinduct, mk_cong_rho, lthy) end; fun derive_cong_base fp_b version fpT dead_ssig_bnf ssig_fp_bnf_sugar dead_pre_bnf eval eval_thm eval_core_transfer eval_VLeaf eval_sctr sctr_transfer Retr equivp_Retr Retr_coinduct lthy = let val (cong_def, cong_locale, cong_base, cong_refl, cong_sym, cong_trans, dtor_coinduct, mk_cong_rho, lthy) = derive_cong_general fp_b version fpT dead_ssig_bnf dead_pre_bnf eval Retr equivp_Retr Retr_coinduct eval_thm eval_core_transfer lthy; val dead_pre_map_id0 = map_id0_of_bnf dead_pre_bnf; val dead_pre_map_comp0 = map_comp0_of_bnf dead_pre_bnf; val dead_pre_map_cong0 = map_cong0_of_bnf dead_pre_bnf; val dead_pre_map_cong0' = @{thm box_equals[OF _ o_apply[symmetric] id_apply[symmetric]]} RS dead_pre_map_cong0 RS ext; val dead_pre_rel_map = rel_map_of_bnf dead_pre_bnf; val ctor_alt_thm = eval_VLeaf RS (@{thm eq_comp_compI} OF [eval_sctr, trans OF [dead_pre_map_comp0 RS sym, trans OF [dead_pre_map_cong0', dead_pre_map_id0]]]); val cong_ctor_intro = mk_cong_rho ctor_alt_thm |> unfold_thms lthy [o_apply] |> (fn thm => sctr_transfer RS rel_funD RS thm) |> unfold_thms lthy (id_apply :: dead_pre_rel_map @ #rel_injects ssig_fp_bnf_sugar); in ({cong_def = cong_def, cong_locale = cong_locale, cong_base = cong_base, cong_refl = cong_refl, cong_sym = cong_sym, cong_trans = cong_trans, dtor_coinduct = dtor_coinduct, cong_alg_intros = [cong_ctor_intro]}, lthy) end; fun update_cong_alg_intros ctxt cong_def cong_locale old_cong_def old_cong_locale emb = let fun instance_of_gen thm = Local_Defs.fold ctxt [cong_def] (thm OF [cong_locale]); fun instance_of_old_gen thm = Local_Defs.fold ctxt [old_cong_def] (thm OF [old_cong_locale]); val emb_idem = @{thm ord_le_eq_trans} OF [emb, instance_of_gen @{thm cong.gen_cong_idem}]; fun mk_rel_mono bnf = instance_of_old_gen @{thm cong.leq_gen_cong} RS rel_mono_of_bnf bnf RS @{thm predicate2D}; fun mk_intro bnf thm = mk_rel_mono bnf RS (@{thm predicate2D} OF [emb_idem, thm]); in map2 mk_intro end fun derive_cong_step fp_b version fpT dead_ssig_bnf dead_pre_bnf eval eval_thm eval_core_transfer old_dtor_coinduct_info algrho_def k_as_ssig_transfer Retr equivp_Retr Retr_coinduct eval_embL embL_transfer old_all_dead_k_bnfs lthy = let val old_cong_def = #cong_def old_dtor_coinduct_info; val old_cong_locale = #cong_locale old_dtor_coinduct_info; val old_cong_alg_intros = #cong_alg_intros old_dtor_coinduct_info; val (cong_def, cong_locale, cong_base, cong_refl, cong_sym, cong_trans, dtor_coinduct, mk_cong_rho, lthy) = derive_cong_general fp_b version fpT dead_ssig_bnf dead_pre_bnf eval Retr equivp_Retr Retr_coinduct eval_thm eval_core_transfer lthy; val cong_alg_intro = k_as_ssig_transfer RS rel_funD RS mk_cong_rho (HOLogic.mk_obj_eq algrho_def); val gen_cong_emb = (@{thm gen_cong_emb} OF [old_cong_locale, cong_locale, eval_embL, embL_transfer]) |> Local_Defs.fold lthy [old_cong_def, cong_def]; val cong_alg_intros = update_cong_alg_intros lthy cong_def cong_locale old_cong_def old_cong_locale gen_cong_emb old_all_dead_k_bnfs old_cong_alg_intros; in ({cong_def = cong_def, cong_locale = cong_locale, cong_base = cong_base, cong_refl = cong_refl, cong_sym = cong_sym, cong_trans = cong_trans, dtor_coinduct = dtor_coinduct, cong_alg_intros = cong_alg_intro :: cong_alg_intros}, lthy) end; fun derive_cong_merge fp_b version fpT old1_friend_names old2_friend_names dead_ssig_bnf dead_pre_bnf eval eval_thm eval_core_transfer old1_dtor_coinduct_info old2_dtor_coinduct_info Retr equivp_Retr Retr_coinduct eval_embLL embLL_transfer eval_embLR embLR_transfer old1_all_dead_k_bnfs old2_all_dead_k_bnfs lthy = let val old1_cong_def = #cong_def old1_dtor_coinduct_info; val old1_cong_locale = #cong_locale old1_dtor_coinduct_info; val old1_cong_alg_intros = #cong_alg_intros old1_dtor_coinduct_info; val old2_cong_def = #cong_def old2_dtor_coinduct_info; val old2_cong_locale = #cong_locale old2_dtor_coinduct_info; val old2_cong_alg_intros = #cong_alg_intros old2_dtor_coinduct_info; val (cong_def, cong_locale, cong_base, cong_refl, cong_sym, cong_trans, dtor_coinduct, _, lthy) = derive_cong_general fp_b version fpT dead_ssig_bnf dead_pre_bnf eval Retr equivp_Retr Retr_coinduct eval_thm eval_core_transfer lthy; val emb1 = (@{thm gen_cong_emb} OF [old1_cong_locale, cong_locale, eval_embLL, embLL_transfer]) |> Local_Defs.fold lthy [old1_cong_def, cong_def]; val emb2 = (@{thm gen_cong_emb} OF [old2_cong_locale, cong_locale, eval_embLR, embLR_transfer]) |> Local_Defs.fold lthy [old2_cong_def, cong_def]; val cong_alg_intros1 = update_cong_alg_intros lthy cong_def cong_locale old1_cong_def old1_cong_locale emb1 old1_all_dead_k_bnfs old1_cong_alg_intros; val cong_alg_intros2 = update_cong_alg_intros lthy cong_def cong_locale old2_cong_def old2_cong_locale emb2 old2_all_dead_k_bnfs old2_cong_alg_intros; val (cong_algrho_intros1, cong_ctor_intro1) = split_last cong_alg_intros1; val (cong_algrho_intros2, _) = split_last cong_alg_intros2; val (old1_all_rho_k_bnfs, old1_Sig_bnf) = split_last old1_all_dead_k_bnfs; val (old2_all_rho_k_bnfs, _) = split_last old2_all_dead_k_bnfs; val (friend_names, (cong_algrho_intros, all_rho_k_bnfs)) = merge_lists (op = o apply2 fst) (old1_friend_names ~~ (cong_algrho_intros1 ~~ old1_all_rho_k_bnfs)) (old2_friend_names ~~ (cong_algrho_intros2 ~~ old2_all_rho_k_bnfs)) |> split_list ||> split_list; in (({cong_def = cong_def, cong_locale = cong_locale, cong_base = cong_base, cong_refl = cong_refl, cong_sym = cong_sym, cong_trans = cong_trans, dtor_coinduct = dtor_coinduct, cong_alg_intros = cong_algrho_intros @ [cong_ctor_intro1]}, all_rho_k_bnfs @ [old1_Sig_bnf], friend_names), lthy) end; fun derive_corecUU_base fpT_name lthy = let val fp_sugar as {T = Type (_, fpT_args0), pre_bnf, fp_bnf, fp_res, ...} = checked_fp_sugar_of lthy fpT_name; val fpT_Ss = map Type.sort_of_atyp fpT_args0; val fp_alives = liveness_of_fp_bnf (length fpT_args0) fp_bnf; val (((Es, Fs0), [Y, Z]), names_lthy) = lthy |> mk_TFrees' fpT_Ss ||>> mk_TFrees' fpT_Ss ||>> mk_TFrees 2; val Fs = @{map 3} (fn alive => fn E => fn F => if alive then F else E) fp_alives Es Fs0; val As = Es @ [Y]; val Bs = Es @ [Z]; val live_EsFs = filter (op <>) (Es ~~ Fs); val live_AsBs = live_EsFs @ [(Y, Z)]; val fTs = map (op -->) live_EsFs; val RTs = map (uncurry mk_pred2T) live_EsFs; val live = length live_EsFs; val ((((((x, fs), f), g), Rs), R), names_lthy) = names_lthy |> yield_singleton (mk_Frees "x") Y ||>> mk_Frees "f" fTs ||>> yield_singleton (mk_Frees "f") (Y --> Z) ||>> yield_singleton (mk_Frees "g") (Y --> Z) ||>> mk_Frees "R" RTs ||>> yield_singleton (mk_Frees "R") (mk_pred2T Y Z); val ctor = mk_ctor Es (the_single (#ctors fp_res)); val dtor = mk_dtor Es (the_single (#dtors fp_res)); val fpT = Type (fpT_name, Es); val preT = pre_type_of_ctor Y ctor; val ((fp_b, version), lthy) = lthy |> get_name_next_version_of fpT_name; val ((sig_fp_sugar, ssig_fp_sugar), lthy) = lthy |> define_sig_type fp_b version fp_alives Es Y preT ||>> define_ssig_type fp_b version fp_alives Es Y fpT; val sig_bnf = #fp_bnf sig_fp_sugar; val ssig_bnf = #fp_bnf ssig_fp_sugar; val (((dead_pre_bnf, dead_sig_bnf), dead_ssig_bnf), lthy) = lthy |> bnf_kill_all_but 1 pre_bnf ||>> bnf_kill_all_but 1 sig_bnf ||>> bnf_kill_all_but 1 ssig_bnf; val sig_fp_ctr_sugar = #fp_ctr_sugar sig_fp_sugar; val ssig_fp_ctr_sugar = #fp_ctr_sugar ssig_fp_sugar; val sig_fp_bnf_sugar = #fp_bnf_sugar sig_fp_sugar; val ssig_fp_bnf_sugar = #fp_bnf_sugar ssig_fp_sugar; val ssig_fp_induct_sugar = the (#fp_co_induct_sugar ssig_fp_sugar); val sig_ctr_sugar = #ctr_sugar sig_fp_ctr_sugar; val ssig_ctr_sugar = #ctr_sugar ssig_fp_ctr_sugar; val sig_T_name = fst (dest_Type (#T sig_fp_sugar)); val ssig_T_name = fst (dest_Type (#T ssig_fp_sugar)); val sig_T = Type (sig_T_name, As); val ssig_T = Type (ssig_T_name, As); val pre_map = mk_mapN lthy live_AsBs preT pre_bnf; val pre_rel = mk_relN lthy live_AsBs preT pre_bnf; val dead_pre_map = mk_map1 lthy Y Z preT dead_pre_bnf; val fp_rel = mk_relN lthy live_EsFs fpT fp_bnf; val dtor_unfold = mk_co_rec (Proof_Context.theory_of lthy) Greatest_FP [Z] fpT (the_single (#xtor_un_folds fp_res)); val Sig = mk_ctr As (the_single (#ctrs sig_ctr_sugar)); val unsig = mk_disc_or_sel As (the_single (the_single (#selss sig_ctr_sugar))); val sig_rel = mk_relN lthy live_AsBs sig_T sig_bnf; val dead_sig_map = mk_map 1 As Bs (map_of_bnf dead_sig_bnf); val [Oper, VLeaf, CLeaf] = map (mk_ctr As) (#ctrs ssig_ctr_sugar); val ssig_map = mk_mapN lthy live_AsBs ssig_T ssig_bnf; val ssig_rel = mk_relN lthy live_AsBs ssig_T ssig_bnf; val dead_ssig_map = mk_map 1 As Bs (map_of_bnf dead_ssig_bnf); val ((Lam, Lam_def), lthy) = lthy |> define_Lam_base fp_b version Y Z preT ssig_T dead_pre_map Sig unsig dead_sig_map Oper VLeaf; val proto_sctr = Sig; val pre_map_transfer = map_transfer_of_bnf pre_bnf; val pre_rel_def = rel_def_of_bnf pre_bnf; val dead_pre_map_id = map_id_of_bnf dead_pre_bnf; val dead_pre_map_comp = map_comp_of_bnf dead_pre_bnf; val fp_rel_eq = rel_eq_of_bnf fp_bnf; val [ctor_dtor] = #ctor_dtors fp_res; val [dtor_ctor] = #dtor_ctors fp_res; val [dtor_inject] = #dtor_injects fp_res; val [dtor_unfold_thm] = #xtor_un_fold_thms fp_res; val dtor_unfold_unique = #xtor_un_fold_unique fp_res; val [dtor_unfold_transfer] = #xtor_un_fold_transfers fp_res; val [dtor_rel_thm] = #xtor_rels fp_res; val unsig_thm = the_single (the_single (#sel_thmss sig_ctr_sugar)); val [sig_map_thm] = #map_thms sig_fp_bnf_sugar; val [Oper_map_thm, VLeaf_map_thm, CLeaf_map_thm] = #map_thms ssig_fp_bnf_sugar; val sig_map_transfer = map_transfer_of_bnf sig_bnf; val ssig_map_thms = #map_thms ssig_fp_bnf_sugar; val ssig_map_transfer = map_transfer_of_bnf ssig_bnf; val ssig_induct = the_single (#co_inducts ssig_fp_induct_sugar); val dtor_transfer = derive_dtor_transfer lthy live_EsFs Y Z pre_rel fp_rel Rs dtor dtor_rel_thm; val preT_rel_eqs = map rel_eq_of_bnf (map_filter (bnf_of lthy) (add_type_namesT preT [])); val Sig_transfer = derive_sig_transfer I lthy live_AsBs pre_rel sig_rel Rs R Sig pre_rel_def preT_rel_eqs (the_single (#ctr_transfers sig_fp_ctr_sugar)); val proto_sctr_transfer = Sig_transfer; val unsig_transfer = derive_sig_transfer swap lthy live_AsBs pre_rel sig_rel Rs R unsig pre_rel_def preT_rel_eqs (the_single (#sel_transfers sig_fp_ctr_sugar)); val Lam_transfer = derive_Lam_or_eval_core_transfer lthy live_AsBs Y Z preT ssig_T Rs R pre_rel sig_rel ssig_rel Lam Lam_def [] [pre_map_transfer, sig_map_transfer, Sig_transfer, unsig_transfer]; val ((((((((flat, _, flat_simps), flat_transfer), ((eval_core, _, eval_core_simps), eval_core_transfer)), (eval, eval_def)), (cutSsig, cutSsig_def)), (algLam, algLam_def)), (corecU, corecU_def)), lthy) = lthy |> define_flat_etc fp_b version live_AsBs Y Z preT fpT sig_T ssig_T Oper VLeaf CLeaf pre_rel dead_pre_map dtor dtor_unfold dead_sig_map ssig_rel dead_ssig_map Lam Rs R pre_map_transfer [fp_rel_eq] sig_map_transfer ssig_map_transfer Lam_transfer dtor_transfer; val (Sig_pointful_natural, flat_pointful_natural, _, Lam_pointful_natural, _, eval_core_pointful_natural, eval_thm, eval_flat, eval_simps as [eval_Oper, eval_VLeaf, _], corecU_ctor, corecU_unique, dtor_algLam) = derive_Sig_natural_etc lthy live live_AsBs Y Z preT fpT fpT sig_T ssig_T pre_map dead_pre_map ctor dtor Sig dead_sig_map Oper VLeaf CLeaf ssig_map dead_ssig_map Lam flat eval_core eval cutSsig algLam corecU x fs f g ctor_dtor dtor_inject dtor_unfold_thm dtor_unfold_unique sig_map_thm ssig_induct ssig_map_thms Oper_map_thm VLeaf_map_thm CLeaf_map_thm Lam_transfer flat_simps flat_transfer eval_core_simps eval_core_transfer eval_def cutSsig_def algLam_def corecU_def pre_bnf pre_bnf dead_pre_bnf fp_bnf sig_bnf ssig_bnf dead_ssig_bnf; val proto_sctr_pointful_natural = Sig_pointful_natural; val algLam_thm = derive_algLam_base lthy Y Z preT fpT dead_pre_map ctor dtor algLam proto_sctr dead_pre_map_id dead_pre_map_comp ctor_dtor dtor_ctor dtor_unfold_unique unsig_thm Sig_pointful_natural ssig_map_thms Lam_def flat_simps eval_core_simps eval_thm algLam_def; val (((corecUU, _), corecUU_thm, corecUU_unique, corecUU_transfer, eval_sctr, sctr_transfer, sctr_pointful_natural), lthy) = lthy |> define_corecUU_etc fp_b version live_AsBs Y Z preT fpT ssig_T pre_map dead_pre_map pre_rel fp_rel ctor Oper ssig_map dead_ssig_map ssig_rel proto_sctr flat eval_core eval corecU fs f g Rs R pre_map_transfer [] dtor_unfold_transfer dtor_transfer ssig_map_transfer proto_sctr_transfer proto_sctr_pointful_natural flat_transfer flat_pointful_natural eval_core_transfer eval_core_pointful_natural eval_thm eval_flat eval_Oper algLam_thm cutSsig_def corecU_def corecU_ctor corecU_unique pre_bnf dead_pre_bnf fp_res ssig_fp_sugar; val (Retr, equivp_Retr, Retr_coinduct) = lthy |> derive_Retr fp_sugar fpT dead_pre_bnf ctor dtor names_lthy; val (dtor_coinduct_info, lthy) = lthy |> derive_cong_base fp_b version fpT dead_ssig_bnf ssig_fp_bnf_sugar dead_pre_bnf eval eval_thm eval_core_transfer eval_VLeaf eval_sctr sctr_transfer Retr equivp_Retr Retr_coinduct; val buffer = {Oper = Oper, VLeaf = VLeaf, CLeaf = CLeaf, ctr_wrapper = Sig, friends = Symtab.empty}; val notes = [(corecUU_transferN, [corecUU_transfer])] @ (if Config.get lthy bnf_internals then [(algLamN, [algLam_thm]), (cong_alg_introsN, #cong_alg_intros dtor_coinduct_info), (cong_localeN, [#cong_locale dtor_coinduct_info]), (corecU_ctorN, [corecU_ctor]), (corecU_uniqueN, [corecU_unique]), (corecUUN, [corecUU_thm]), (corecUU_uniqueN, [corecUU_unique]), (dtor_algLamN, [dtor_algLam]), (dtor_coinductN, [#dtor_coinduct dtor_coinduct_info]), (dtor_transferN, [dtor_transfer]), (equivp_RetrN, [equivp_Retr]), (evalN, [eval_thm]), (eval_core_pointful_naturalN, [eval_core_pointful_natural]), (eval_core_transferN, [eval_core_transfer]), (eval_flatN, [eval_flat]), (eval_simpsN, eval_simps), (flat_pointful_naturalN, [flat_pointful_natural]), (flat_transferN, [flat_transfer]), (Lam_pointful_naturalN, [Lam_pointful_natural]), (Lam_transferN, [Lam_transfer]), (proto_sctr_pointful_naturalN, [proto_sctr_pointful_natural]), (proto_sctr_transferN, [proto_sctr_transfer]), (Retr_coinductN, [Retr_coinduct]), (sctr_pointful_naturalN, [sctr_pointful_natural]), (sctr_transferN, [sctr_transfer]), (Sig_pointful_naturalN, [Sig_pointful_natural])] else []) |> map (fn (thmN, thms) => ((mk_version_fp_binding true lthy version fp_b thmN, []), [(thms, [])])); in ({fp_b = fp_b, version = version, fpT = fpT, Y = Y, Z = Z, friend_names = [], sig_fp_sugars = [sig_fp_sugar], ssig_fp_sugar = ssig_fp_sugar, Lam = Lam, proto_sctr = proto_sctr, flat = flat, eval_core = eval_core, eval = eval, algLam = algLam, corecUU = corecUU, dtor_transfer = dtor_transfer, Lam_transfer = Lam_transfer, Lam_pointful_natural = Lam_pointful_natural, proto_sctr_transfer = proto_sctr_transfer, flat_simps = flat_simps, eval_core_simps = eval_core_simps, eval_thm = eval_thm, eval_simps = eval_simps, all_algLam_algs = [algLam_thm], algLam_thm = algLam_thm, dtor_algLam = dtor_algLam, corecUU_thm = corecUU_thm, corecUU_unique = corecUU_unique, corecUU_transfer = corecUU_transfer, buffer = buffer, all_dead_k_bnfs = [dead_pre_bnf], Retr = Retr, equivp_Retr = equivp_Retr, Retr_coinduct = Retr_coinduct, dtor_coinduct_info = dtor_coinduct_info} |> morph_corec_info (Local_Theory.target_morphism lthy), lthy |> Local_Theory.notes notes |> snd) end; fun derive_corecUU_step (fpT as Type (fpT_name, res_Ds)) ({friend_names = old_friend_names, sig_fp_sugars = old_sig_fp_sugars as old_sig_fp_sugar :: _, ssig_fp_sugar = old_ssig_fp_sugar, Lam = old_Lam0, proto_sctr = old_proto_sctr0, flat = old_flat0, eval_core = old_eval_core0, eval = old_eval0, algLam = old_algLam0, dtor_transfer, Lam_transfer = old_Lam_transfer, Lam_pointful_natural = old_Lam_pointful_natural, proto_sctr_transfer = old_proto_sctr_transfer, flat_simps = old_flat_simps, eval_core_simps = old_eval_core_simps, eval_thm = old_eval_thm, all_algLam_algs = old_all_algLam_algs, algLam_thm = old_algLam_thm, dtor_algLam = old_dtor_algLam, buffer = old_buffer, all_dead_k_bnfs = old_all_dead_k_bnfs, Retr = old_Retr0, equivp_Retr, Retr_coinduct, dtor_coinduct_info = old_dtor_coinduct_info, ...} : corec_info) friend_name friend_T fp_b version Y Z k_T dead_k_bnf sig_fp_sugar ssig_fp_sugar rho rho_transfer lthy = let val {pre_bnf = live_pre_bnf, fp_bnf = live_fp_bnf, fp_res, ...} = checked_fp_sugar_of lthy fpT_name; val names_lthy = lthy |> fold Variable.declare_typ [Y, Z]; (* FIXME *) val live_EsFs = []; val live_AsBs = live_EsFs @ [(Y, Z)]; val live = length live_EsFs; val ((((x, f), g), R), _) = names_lthy |> yield_singleton (mk_Frees "x") Y ||>> yield_singleton (mk_Frees "f") (Y --> Z) ||>> yield_singleton (mk_Frees "g") (Y --> Z) ||>> yield_singleton (mk_Frees "R") (mk_pred2T Y Z); (* FIXME *) val fs = []; val Rs = []; val ctor = mk_ctor res_Ds (the_single (#ctors fp_res)); val dtor = mk_dtor res_Ds (the_single (#dtors fp_res)); val friend_names = friend_name :: old_friend_names; val old_sig_bnf = #fp_bnf old_sig_fp_sugar; val old_ssig_bnf = #fp_bnf old_ssig_fp_sugar; val sig_bnf = #fp_bnf sig_fp_sugar; val ssig_bnf = #fp_bnf ssig_fp_sugar; val ((((((dead_pre_bnf, dead_fp_bnf), dead_old_sig_bnf), dead_old_ssig_bnf), dead_sig_bnf), dead_ssig_bnf), lthy) = lthy |> bnf_kill_all_but 1 live_pre_bnf ||>> bnf_kill_all_but 0 live_fp_bnf ||>> bnf_kill_all_but 1 old_sig_bnf ||>> bnf_kill_all_but 1 old_ssig_bnf ||>> bnf_kill_all_but 1 sig_bnf ||>> bnf_kill_all_but 1 ssig_bnf; (* FIXME *) val pre_bnf = dead_pre_bnf; val fp_bnf = dead_fp_bnf; val old_ssig_fp_ctr_sugar = #fp_ctr_sugar old_ssig_fp_sugar; val sig_fp_ctr_sugar = #fp_ctr_sugar sig_fp_sugar; val ssig_fp_ctr_sugar = #fp_ctr_sugar ssig_fp_sugar; val sig_fp_bnf_sugar = #fp_bnf_sugar sig_fp_sugar; val old_ssig_fp_bnf_sugar = #fp_bnf_sugar old_ssig_fp_sugar; val ssig_fp_bnf_sugar = #fp_bnf_sugar ssig_fp_sugar; val old_ssig_fp_induct_sugar = the (#fp_co_induct_sugar old_ssig_fp_sugar); val ssig_fp_induct_sugar = the (#fp_co_induct_sugar ssig_fp_sugar); val old_ssig_ctr_sugar = #ctr_sugar old_ssig_fp_ctr_sugar; val sig_ctr_sugar = #ctr_sugar sig_fp_ctr_sugar; val ssig_ctr_sugar = #ctr_sugar ssig_fp_ctr_sugar; val old_sig_T_name = fst (dest_Type (#T old_sig_fp_sugar)); val old_ssig_T_name = fst (dest_Type (#T old_ssig_fp_sugar)); val sig_T_name = fst (dest_Type (#T sig_fp_sugar)); val ssig_T_name = fst (dest_Type (#T ssig_fp_sugar)); val res_As = res_Ds @ [Y]; val res_Bs = res_Ds @ [Z]; val preT = pre_type_of_ctor Y ctor; val YpreT = HOLogic.mk_prodT (Y, preT); val old_sig_T = Type (old_sig_T_name, res_As); val old_ssig_T = Type (old_ssig_T_name, res_As); val sig_T = Type (sig_T_name, res_As); val ssig_T = Type (ssig_T_name, res_As); val old_Lam_domT = Tsubst Y YpreT old_sig_T; val old_eval_core_domT = Tsubst Y YpreT old_ssig_T; val pre_map = mk_mapN lthy live_AsBs preT pre_bnf; val pre_rel = mk_relN lthy live_AsBs preT pre_bnf; val dead_pre_map = mk_map1 lthy Y Z preT dead_pre_bnf; val dead_pre_rel = mk_rel1 lthy Y Z preT dead_pre_bnf; val fp_rel = mk_relN lthy live_EsFs fpT fp_bnf; val dtor_unfold = mk_co_rec (Proof_Context.theory_of lthy) Greatest_FP [Z] fpT (the_single (#xtor_un_folds fp_res)); val dead_k_map = mk_map1 lthy Y Z k_T dead_k_bnf; val Sig = mk_ctr res_As (the_single (#ctrs sig_ctr_sugar)); val unsig = mk_disc_or_sel res_As (the_single (the_single (#selss sig_ctr_sugar))); val sig_rel = mk_relN lthy live_AsBs sig_T sig_bnf; val dead_old_sig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_old_sig_bnf); val dead_sig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_sig_bnf); val dead_sig_rel = mk_rel 1 res_As res_Bs (rel_of_bnf dead_sig_bnf); val [old_Oper, old_VLeaf, old_CLeaf] = map (mk_ctr res_As) (#ctrs old_ssig_ctr_sugar); val [Oper, VLeaf, CLeaf] = map (mk_ctr res_As) (#ctrs ssig_ctr_sugar); val dead_old_ssig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_old_ssig_bnf); val ssig_map = mk_mapN lthy live_AsBs ssig_T ssig_bnf; val ssig_rel = mk_relN lthy live_AsBs ssig_T ssig_bnf; val dead_ssig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_ssig_bnf); val old_Lam = enforce_type lthy domain_type old_Lam_domT old_Lam0; val old_proto_sctr = enforce_type lthy domain_type preT old_proto_sctr0; val old_flat = enforce_type lthy range_type old_ssig_T old_flat0; val old_eval_core = enforce_type lthy domain_type old_eval_core_domT old_eval_core0; val old_eval = enforce_type lthy range_type fpT old_eval0; val old_algLam = enforce_type lthy range_type fpT old_algLam0; val ((embL, embL_def, embL_simps), lthy) = lthy |> define_embL embLN fp_b version Y Z fpT old_sig_T old_ssig_T k_T ssig_T Inl_const dead_old_sig_map Sig old_Oper old_VLeaf old_CLeaf Oper VLeaf CLeaf; val ((Lam, Lam_def), lthy) = lthy |> define_Lam_step fp_b version Y Z preT old_ssig_T ssig_T dead_pre_map unsig rho embL old_Lam; val ((proto_sctr, proto_sctr_def), lthy) = lthy |> define_proto_sctr_step_or_merge fp_b version old_sig_T k_T Sig old_proto_sctr; val pre_map_comp = map_comp_of_bnf pre_bnf; val pre_map_transfer = map_transfer_of_bnf pre_bnf; val dead_pre_map_id = map_id_of_bnf dead_pre_bnf; val dead_pre_map_comp0 = map_comp0_of_bnf dead_pre_bnf; val dead_pre_map_comp = map_comp_of_bnf dead_pre_bnf; val fp_map_id = map_id_of_bnf fp_bnf; val [ctor_dtor] = #ctor_dtors fp_res; val [dtor_inject] = #dtor_injects fp_res; val [dtor_unfold_thm] = #xtor_un_fold_thms fp_res; val dtor_unfold_unique = #xtor_un_fold_unique fp_res; val [dtor_unfold_transfer] = #xtor_un_fold_transfers fp_res; val fp_k_T_rel_eqs = map rel_eq_of_bnf (map_filter (bnf_of lthy) (fold add_type_namesT [fpT, k_T] [])); val unsig_thm = the_single (the_single (#sel_thmss sig_ctr_sugar)); val [sig_map_thm] = #map_thms sig_fp_bnf_sugar; val old_sig_map_comp = map_comp_of_bnf old_sig_bnf; val old_sig_map_cong = map_cong_of_bnf old_sig_bnf; val old_ssig_map_thms = #map_thms old_ssig_fp_bnf_sugar; val [Oper_map_thm, VLeaf_map_thm, CLeaf_map_thm] = #map_thms ssig_fp_bnf_sugar; val old_sig_map_transfer = map_transfer_of_bnf old_sig_bnf; val sig_map_comp = map_comp_of_bnf sig_bnf; val sig_map_transfer = map_transfer_of_bnf sig_bnf; val ssig_map_thms = #map_thms ssig_fp_bnf_sugar; val ssig_map_transfer = map_transfer_of_bnf ssig_bnf; val old_ssig_induct = the_single (#co_inducts old_ssig_fp_induct_sugar); val ssig_induct = the_single (#co_inducts ssig_fp_induct_sugar); val proto_sctr_transfer = derive_proto_sctr_transfer_step_or_merge lthy Y Z R dead_pre_rel dead_sig_rel proto_sctr proto_sctr_def fp_k_T_rel_eqs [old_proto_sctr_transfer]; val embL_transfer = derive_transfer_by_transfer_prover lthy live_AsBs Rs R embL [embL_def] fp_k_T_rel_eqs [old_sig_map_transfer]; val Lam_transfer = derive_Lam_or_eval_core_transfer lthy live_AsBs Y Z preT ssig_T Rs R pre_rel sig_rel ssig_rel Lam Lam_def fp_k_T_rel_eqs [pre_map_transfer, old_Lam_transfer, embL_transfer, rho_transfer]; val ((((((((flat, _, flat_simps), flat_transfer), ((eval_core, _, eval_core_simps), eval_core_transfer)), (eval, eval_def)), (cutSsig, cutSsig_def)), (algLam, algLam_def)), (corecU, corecU_def)), lthy) = lthy |> define_flat_etc fp_b version live_AsBs Y Z preT fpT sig_T ssig_T Oper VLeaf CLeaf pre_rel dead_pre_map dtor dtor_unfold dead_sig_map ssig_rel dead_ssig_map Lam Rs R pre_map_transfer fp_k_T_rel_eqs sig_map_transfer ssig_map_transfer Lam_transfer dtor_transfer; val (Sig_pointful_natural, flat_pointful_natural, Lam_natural_pointful, Lam_pointful_natural, flat_VLeaf, eval_core_pointful_natural, eval_thm, eval_flat, eval_simps as [eval_Oper, _, _], corecU_ctor, corecU_unique, dtor_algLam) = derive_Sig_natural_etc lthy live live_AsBs Y Z preT fpT k_T sig_T ssig_T pre_map dead_pre_map ctor dtor Sig dead_sig_map Oper VLeaf CLeaf ssig_map dead_ssig_map Lam flat eval_core eval cutSsig algLam corecU x fs f g ctor_dtor dtor_inject dtor_unfold_thm dtor_unfold_unique sig_map_thm ssig_induct ssig_map_thms Oper_map_thm VLeaf_map_thm CLeaf_map_thm Lam_transfer flat_simps flat_transfer eval_core_simps eval_core_transfer eval_def cutSsig_def algLam_def corecU_def live_pre_bnf pre_bnf dead_pre_bnf fp_bnf sig_bnf ssig_bnf dead_ssig_bnf; val proto_sctr_natural = derive_natural_from_transfer_with_pre_type lthy live_AsBs Y Z preT ssig_T pre_map ssig_map fs f proto_sctr proto_sctr_transfer [pre_bnf, sig_bnf] []; val proto_sctr_pointful_natural = mk_pointful lthy proto_sctr_natural RS sym; val (embL_pointful_natural, old_algLam_pointful, eval_embL, algLam_algLam) = derive_embL_natural_etc lthy Inl_const old_ssig_bnf ssig_bnf Y Z preT fpT old_ssig_T ssig_T dead_pre_map Sig dead_old_ssig_map embL old_algLam algLam old_flat flat old_eval_core eval_core old_eval eval x f old_ssig_induct dead_pre_map_comp0 dead_pre_map_comp fp_map_id dtor_inject dtor_unfold_unique Sig_pointful_natural unsig_thm sig_map_thm old_sig_map_comp old_sig_map_cong old_ssig_map_thms old_Lam_pointful_natural Lam_def old_flat_simps flat_simps embL_simps embL_transfer old_eval_core_simps eval_core_simps old_eval_thm eval_thm old_dtor_algLam dtor_algLam old_algLam_thm; val algLam_thm = derive_algLam_step_or_merge lthy Y fpT ctor proto_sctr algLam proto_sctr_def old_algLam_pointful algLam_algLam; val k_as_ssig = mk_k_as_ssig Z old_sig_T k_T ssig_T Sig dead_sig_map Oper VLeaf; val k_as_ssig' = substT Y fpT k_as_ssig; val algrho_rhs = HOLogic.mk_comp (eval, k_as_ssig'); val ((algrho, algrho_def), lthy) = lthy |> define_const true fp_b version algrhoN algrho_rhs; val k_as_ssig_transfer = derive_transfer_by_transfer_prover lthy live_AsBs Rs R k_as_ssig [] fp_k_T_rel_eqs [sig_map_transfer]; val k_as_ssig_natural = derive_natural_from_transfer lthy [(Y, Z)] [] [] f k_as_ssig k_as_ssig_transfer [ssig_bnf] [dead_k_bnf]; val k_as_ssig_natural_pointful = mk_pointful lthy k_as_ssig_natural; val [_, Lam_Inr] = derive_Lam_Inl_Inr lthy Y Z preT old_sig_T old_ssig_T k_T ssig_T dead_pre_map Sig embL old_Lam Lam rho unsig_thm Lam_def; val eval_core_k_as_ssig = derive_eval_core_k_as_ssig lthy Y preT k_T rho eval_core k_as_ssig x pre_map_comp dead_pre_map_id sig_map_comp ssig_map_thms Lam_natural_pointful Lam_Inr flat_VLeaf eval_core_simps; val algLam_algrho = derive_algLam_algrho lthy Y fpT Sig algLam algrho algLam_def algrho_def; val dtor_algrho = derive_dtor_algrho lthy Y Z preT fpT k_T ssig_T dead_pre_map dead_k_map dtor rho eval algrho x eval_thm k_as_ssig_natural_pointful eval_core_k_as_ssig algrho_def; val all_algLam_algs = algLam_algLam :: algLam_algrho :: old_all_algLam_algs; val (((corecUU, _), corecUU_thm, corecUU_unique, corecUU_transfer, _, sctr_transfer, sctr_pointful_natural), lthy) = lthy |> define_corecUU_etc fp_b version live_AsBs Y Z preT fpT ssig_T pre_map dead_pre_map pre_rel fp_rel ctor Oper ssig_map dead_ssig_map ssig_rel proto_sctr flat eval_core eval corecU fs f g Rs R pre_map_transfer fp_k_T_rel_eqs dtor_unfold_transfer dtor_transfer ssig_map_transfer proto_sctr_transfer proto_sctr_pointful_natural flat_transfer flat_pointful_natural eval_core_transfer eval_core_pointful_natural eval_thm eval_flat eval_Oper algLam_thm cutSsig_def corecU_def corecU_ctor corecU_unique pre_bnf dead_pre_bnf fp_res ssig_fp_sugar; val (ctr_wrapper, friends) = mk_ctr_wrapper_friends lthy friend_name friend_T old_sig_T k_T Sig old_buffer; val Retr = enforce_type lthy (domain_type o domain_type) fpT old_Retr0; val (dtor_coinduct_info, lthy) = lthy |> derive_cong_step fp_b version fpT dead_ssig_bnf dead_pre_bnf eval eval_thm eval_core_transfer old_dtor_coinduct_info algrho_def k_as_ssig_transfer Retr equivp_Retr Retr_coinduct eval_embL embL_transfer old_all_dead_k_bnfs; val buffer = {Oper = Oper, VLeaf = VLeaf, CLeaf = CLeaf, ctr_wrapper = ctr_wrapper, friends = friends}; val notes = [(corecUU_transferN, [corecUU_transfer])] @ (if Config.get lthy bnf_internals then [(algLamN, [algLam_thm]), (algLam_algLamN, [algLam_algLam]), (algLam_algrhoN, [algLam_algrho]), (cong_alg_introsN, #cong_alg_intros dtor_coinduct_info), (cong_localeN, [#cong_locale dtor_coinduct_info]), (corecU_ctorN, [corecU_ctor]), (corecU_uniqueN, [corecU_unique]), (corecUUN, [corecUU_thm]), (corecUU_uniqueN, [corecUU_unique]), (dtor_algLamN, [dtor_algLam]), (dtor_algrhoN, [dtor_algrho]), (dtor_coinductN, [#dtor_coinduct dtor_coinduct_info]), (embL_pointful_naturalN, [embL_pointful_natural]), (embL_transferN, [embL_transfer]), (evalN, [eval_thm]), (eval_core_pointful_naturalN, [eval_core_pointful_natural]), (eval_core_transferN, [eval_core_transfer]), (eval_flatN, [eval_flat]), (eval_simpsN, eval_simps), (flat_pointful_naturalN, [flat_pointful_natural]), (flat_transferN, [flat_transfer]), (k_as_ssig_naturalN, [k_as_ssig_natural]), (k_as_ssig_transferN, [k_as_ssig_transfer]), (Lam_pointful_naturalN, [Lam_pointful_natural]), (Lam_transferN, [Lam_transfer]), (proto_sctr_pointful_naturalN, [proto_sctr_pointful_natural]), (proto_sctr_transferN, [proto_sctr_transfer]), (rho_transferN, [rho_transfer]), (sctr_pointful_naturalN, [sctr_pointful_natural]), (sctr_transferN, [sctr_transfer]), (Sig_pointful_naturalN, [Sig_pointful_natural])] else []) |> map (fn (thmN, thms) => ((mk_version_fp_binding true lthy version fp_b thmN, []), [(thms, [])])); val phi = Local_Theory.target_morphism lthy; in (({fp_b = fp_b, version = version, fpT = fpT, Y = Y, Z = Z, friend_names = friend_names, sig_fp_sugars = sig_fp_sugar :: old_sig_fp_sugars, ssig_fp_sugar = ssig_fp_sugar, Lam = Lam, proto_sctr = proto_sctr, flat = flat, eval_core = eval_core, eval = eval, algLam = algLam, corecUU = corecUU, dtor_transfer = dtor_transfer, Lam_transfer = Lam_transfer, Lam_pointful_natural = Lam_pointful_natural, proto_sctr_transfer = proto_sctr_transfer, flat_simps = flat_simps, eval_core_simps = eval_core_simps, eval_thm = eval_thm, eval_simps = eval_simps, all_algLam_algs = all_algLam_algs, algLam_thm = algLam_thm, dtor_algLam = dtor_algLam, corecUU_thm = corecUU_thm, corecUU_unique = corecUU_unique, corecUU_transfer = corecUU_transfer, buffer = buffer, all_dead_k_bnfs = dead_k_bnf :: old_all_dead_k_bnfs, Retr = Retr, equivp_Retr = equivp_Retr, Retr_coinduct = Retr_coinduct, dtor_coinduct_info = dtor_coinduct_info} |> morph_corec_info phi, ({algrho = algrho, dtor_algrho = dtor_algrho, algLam_algrho = algLam_algrho} |> morph_friend_info phi)), lthy |> Local_Theory.notes notes |> snd) end; fun derive_corecUU_merge (fpT as Type (fpT_name, res_Ds)) ({friend_names = old1_friend_names, sig_fp_sugars = old1_sig_fp_sugars as old1_sig_fp_sugar :: _, ssig_fp_sugar = old1_ssig_fp_sugar, Lam = old1_Lam0, proto_sctr = old1_proto_sctr0, flat = old1_flat0, eval_core = old1_eval_core0, eval = old1_eval0, algLam = old1_algLam0, dtor_transfer, Lam_transfer = old1_Lam_transfer, Lam_pointful_natural = old1_Lam_pointful_natural, proto_sctr_transfer = old1_proto_sctr_transfer, flat_simps = old1_flat_simps, eval_core_simps = old1_eval_core_simps, eval_thm = old1_eval_thm, all_algLam_algs = old1_all_algLam_algs, algLam_thm = old1_algLam_thm, dtor_algLam = old1_dtor_algLam, buffer = old1_buffer, all_dead_k_bnfs = old1_all_dead_k_bnfs, Retr = old1_Retr0, equivp_Retr, Retr_coinduct, dtor_coinduct_info = old1_dtor_coinduct_info, ...} : corec_info) ({friend_names = old2_friend_names, sig_fp_sugars = old2_sig_fp_sugars as old2_sig_fp_sugar :: _, ssig_fp_sugar = old2_ssig_fp_sugar, Lam = old2_Lam0, flat = old2_flat0, eval_core = old2_eval_core0, eval = old2_eval0, algLam = old2_algLam0, Lam_transfer = old2_Lam_transfer, Lam_pointful_natural = old2_Lam_pointful_natural, flat_simps = old2_flat_simps, eval_core_simps = old2_eval_core_simps, eval_thm = old2_eval_thm, all_algLam_algs = old2_all_algLam_algs, algLam_thm = old2_algLam_thm, dtor_algLam = old2_dtor_algLam, buffer = old2_buffer, all_dead_k_bnfs = old2_all_dead_k_bnfs, dtor_coinduct_info = old2_dtor_coinduct_info, ...} : corec_info) lthy = let val {T = Type (_, fpT_args0), pre_bnf = live_pre_bnf, fp_bnf = live_fp_bnf, fp_res, ...} = checked_fp_sugar_of lthy fpT_name; val fpT_Ss = map Type.sort_of_atyp fpT_args0; val live_fp_alives = liveness_of_fp_bnf (length fpT_args0) live_fp_bnf; val ((Ds, [Y, Z]), names_lthy) = lthy |> mk_TFrees' fpT_Ss ||>> mk_TFrees 2; (* FIXME *) val live_EsFs = []; val live_AsBs = live_EsFs @ [(Y, Z)]; val live = length live_EsFs; val ((((x, f), g), R), _) = names_lthy |> yield_singleton (mk_Frees "x") Y ||>> yield_singleton (mk_Frees "f") (Y --> Z) ||>> yield_singleton (mk_Frees "g") (Y --> Z) ||>> yield_singleton (mk_Frees "R") (mk_pred2T Y Z); (* FIXME *) val fs = []; val Rs = []; val ctor = mk_ctor res_Ds (the_single (#ctors fp_res)); val dtor = mk_dtor res_Ds (the_single (#dtors fp_res)); val old1_sig_T_name = fst (dest_Type (#T old1_sig_fp_sugar)); val old2_sig_T_name = fst (dest_Type (#T old2_sig_fp_sugar)); val old1_ssig_T_name = fst (dest_Type (#T old1_ssig_fp_sugar)); val old2_ssig_T_name = fst (dest_Type (#T old2_ssig_fp_sugar)); val fp_alives = map (K false) live_fp_alives; val As = Ds @ [Y]; val res_As = res_Ds @ [Y]; val res_Bs = res_Ds @ [Z]; val preT = pre_type_of_ctor Y ctor; val YpreT = HOLogic.mk_prodT (Y, preT); val fpT0 = Type (fpT_name, Ds); val old1_sig_T0 = Type (old1_sig_T_name, As); val old2_sig_T0 = Type (old2_sig_T_name, As); val old1_sig_T = Type (old1_sig_T_name, res_As); val old2_sig_T = Type (old2_sig_T_name, res_As); val old1_ssig_T = Type (old1_ssig_T_name, res_As); val old2_ssig_T = Type (old2_ssig_T_name, res_As); val old1_Lam_domT = Tsubst Y YpreT old1_sig_T; val old2_Lam_domT = Tsubst Y YpreT old2_sig_T; val old1_eval_core_domT = Tsubst Y YpreT old1_ssig_T; val old2_eval_core_domT = Tsubst Y YpreT old2_ssig_T; val ((fp_b, version), lthy) = lthy |> get_name_next_version_of fpT_name; val ((sig_fp_sugar, ssig_fp_sugar), lthy) = lthy |> define_sig_type fp_b version fp_alives Ds Y (mk_sumT (old1_sig_T0, old2_sig_T0)) ||>> define_ssig_type fp_b version fp_alives Ds Y fpT0; val sig_T_name = fst (dest_Type (#T sig_fp_sugar)); val ssig_T_name = fst (dest_Type (#T ssig_fp_sugar)); val old1_sig_bnf = #fp_bnf old1_sig_fp_sugar; val old2_sig_bnf = #fp_bnf old2_sig_fp_sugar; val old1_ssig_bnf = #fp_bnf old1_ssig_fp_sugar; val old2_ssig_bnf = #fp_bnf old2_ssig_fp_sugar; val sig_bnf = #fp_bnf sig_fp_sugar; val ssig_bnf = #fp_bnf ssig_fp_sugar; val ((((((((dead_pre_bnf, dead_fp_bnf), dead_old1_sig_bnf), dead_old2_sig_bnf), dead_old1_ssig_bnf), dead_old2_ssig_bnf), dead_sig_bnf), dead_ssig_bnf), lthy) = lthy |> bnf_kill_all_but 1 live_pre_bnf ||>> bnf_kill_all_but 0 live_fp_bnf ||>> bnf_kill_all_but 1 old1_sig_bnf ||>> bnf_kill_all_but 1 old2_sig_bnf ||>> bnf_kill_all_but 1 old1_ssig_bnf ||>> bnf_kill_all_but 1 old2_ssig_bnf ||>> bnf_kill_all_but 1 sig_bnf ||>> bnf_kill_all_but 1 ssig_bnf; (* FIXME *) val pre_bnf = dead_pre_bnf; val fp_bnf = dead_fp_bnf; val old1_ssig_fp_ctr_sugar = #fp_ctr_sugar old1_ssig_fp_sugar; val old2_ssig_fp_ctr_sugar = #fp_ctr_sugar old2_ssig_fp_sugar; val sig_fp_ctr_sugar = #fp_ctr_sugar sig_fp_sugar; val ssig_fp_ctr_sugar = #fp_ctr_sugar ssig_fp_sugar; val sig_fp_bnf_sugar = #fp_bnf_sugar sig_fp_sugar; val old1_ssig_fp_bnf_sugar = #fp_bnf_sugar old1_ssig_fp_sugar; val old2_ssig_fp_bnf_sugar = #fp_bnf_sugar old2_ssig_fp_sugar; val ssig_fp_bnf_sugar = #fp_bnf_sugar ssig_fp_sugar; val old1_ssig_fp_induct_sugar = the (#fp_co_induct_sugar old1_ssig_fp_sugar); val old2_ssig_fp_induct_sugar = the (#fp_co_induct_sugar old2_ssig_fp_sugar); val ssig_fp_induct_sugar = the (#fp_co_induct_sugar ssig_fp_sugar); val old1_ssig_ctr_sugar = #ctr_sugar old1_ssig_fp_ctr_sugar; val old2_ssig_ctr_sugar = #ctr_sugar old2_ssig_fp_ctr_sugar; val sig_ctr_sugar = #ctr_sugar sig_fp_ctr_sugar; val ssig_ctr_sugar = #ctr_sugar ssig_fp_ctr_sugar; val sig_T = Type (sig_T_name, res_As); val ssig_T = Type (ssig_T_name, res_As); val pre_map = mk_mapN lthy live_AsBs preT pre_bnf; val pre_rel = mk_relN lthy live_AsBs preT pre_bnf; val dead_pre_map = mk_map1 lthy Y Z preT dead_pre_bnf; val dead_pre_rel = mk_rel1 lthy Y Z preT dead_pre_bnf; val fp_rel = mk_relN lthy live_EsFs fpT fp_bnf; val dtor_unfold = mk_co_rec (Proof_Context.theory_of lthy) Greatest_FP [Z] fpT (the_single (#xtor_un_folds fp_res)); val Sig = mk_ctr res_As (the_single (#ctrs sig_ctr_sugar)); val unsig = mk_disc_or_sel res_As (the_single (the_single (#selss sig_ctr_sugar))); val sig_rel = mk_relN lthy live_AsBs sig_T sig_bnf; val dead_old1_sig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_old1_sig_bnf); val dead_old2_sig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_old2_sig_bnf); val dead_sig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_sig_bnf); val dead_sig_rel = mk_rel 1 res_As res_Bs (rel_of_bnf dead_sig_bnf); val [old1_Oper, old1_VLeaf, old1_CLeaf] = map (mk_ctr res_As) (#ctrs old1_ssig_ctr_sugar); val [old2_Oper, old2_VLeaf, old2_CLeaf] = map (mk_ctr res_As) (#ctrs old2_ssig_ctr_sugar); val [Oper, VLeaf, CLeaf] = map (mk_ctr res_As) (#ctrs ssig_ctr_sugar); val old1_ssig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_old1_ssig_bnf); val old2_ssig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_old2_ssig_bnf); val ssig_map = mk_mapN lthy live_AsBs ssig_T ssig_bnf; val ssig_rel = mk_relN lthy live_AsBs ssig_T ssig_bnf; val dead_ssig_map = mk_map 1 res_As res_Bs (map_of_bnf dead_ssig_bnf); val old1_Lam = enforce_type lthy domain_type old1_Lam_domT old1_Lam0; val old2_Lam = enforce_type lthy domain_type old2_Lam_domT old2_Lam0; val old1_proto_sctr = enforce_type lthy domain_type preT old1_proto_sctr0; val old1_flat = enforce_type lthy range_type old1_ssig_T old1_flat0; val old2_flat = enforce_type lthy range_type old2_ssig_T old2_flat0; val old1_eval_core = enforce_type lthy domain_type old1_eval_core_domT old1_eval_core0; val old2_eval_core = enforce_type lthy domain_type old2_eval_core_domT old2_eval_core0; val old1_eval = enforce_type lthy range_type fpT old1_eval0; val old2_eval = enforce_type lthy range_type fpT old2_eval0; val old1_algLam = enforce_type lthy range_type fpT old1_algLam0; val old2_algLam = enforce_type lthy range_type fpT old2_algLam0; val ((embLL, embLL_def, embLL_simps), lthy) = lthy |> define_embL embLLN fp_b version Y Z fpT old1_sig_T old1_ssig_T old2_sig_T ssig_T Inl_const dead_old1_sig_map Sig old1_Oper old1_VLeaf old1_CLeaf Oper VLeaf CLeaf; val ((embLR, embLR_def, embLR_simps), lthy) = lthy |> define_embL embLRN fp_b version Y Z fpT old2_sig_T old2_ssig_T old1_sig_T ssig_T (fn T => fn U => Inr_const U T) dead_old2_sig_map Sig old2_Oper old2_VLeaf old2_CLeaf Oper VLeaf CLeaf; val ((Lam, Lam_def), lthy) = lthy |> define_Lam_merge fp_b version Y Z preT old1_ssig_T old2_ssig_T ssig_T dead_pre_map unsig embLL embLR old1_Lam old2_Lam; val ((proto_sctr, proto_sctr_def), lthy) = lthy |> define_proto_sctr_step_or_merge fp_b version old1_sig_T old2_sig_T Sig old1_proto_sctr; val pre_map_transfer = map_transfer_of_bnf pre_bnf; val dead_pre_map_comp0 = map_comp0_of_bnf dead_pre_bnf; val dead_pre_map_comp = map_comp_of_bnf dead_pre_bnf; val fp_map_id = map_id_of_bnf fp_bnf; val fp_rel_eq = rel_eq_of_bnf fp_bnf; val [ctor_dtor] = #ctor_dtors fp_res; val [dtor_inject] = #dtor_injects fp_res; val [dtor_unfold_thm] = #xtor_un_fold_thms fp_res; val dtor_unfold_unique = #xtor_un_fold_unique fp_res; val [dtor_unfold_transfer] = #xtor_un_fold_transfers fp_res; val unsig_thm = the_single (the_single (#sel_thmss sig_ctr_sugar)); val [sig_map_thm] = #map_thms sig_fp_bnf_sugar; val old1_sig_map_comp = map_comp_of_bnf old1_sig_bnf; val old2_sig_map_comp = map_comp_of_bnf old2_sig_bnf; val old1_sig_map_cong = map_cong_of_bnf old1_sig_bnf; val old2_sig_map_cong = map_cong_of_bnf old2_sig_bnf; val old1_ssig_map_thms = #map_thms old1_ssig_fp_bnf_sugar; val old2_ssig_map_thms = #map_thms old2_ssig_fp_bnf_sugar; val [Oper_map_thm, VLeaf_map_thm, CLeaf_map_thm] = #map_thms ssig_fp_bnf_sugar; val old1_sig_map_transfer = map_transfer_of_bnf old1_sig_bnf; val old2_sig_map_transfer = map_transfer_of_bnf old2_sig_bnf; val sig_map_transfer = map_transfer_of_bnf sig_bnf; val ssig_map_thms = #map_thms ssig_fp_bnf_sugar; val ssig_map_transfer = map_transfer_of_bnf ssig_bnf; val old1_ssig_induct = the_single (#co_inducts old1_ssig_fp_induct_sugar); val old2_ssig_induct = the_single (#co_inducts old2_ssig_fp_induct_sugar); val ssig_induct = the_single (#co_inducts ssig_fp_induct_sugar); val proto_sctr_transfer = derive_proto_sctr_transfer_step_or_merge lthy Y Z R dead_pre_rel dead_sig_rel proto_sctr proto_sctr_def [] [old1_proto_sctr_transfer]; val embLL_transfer = derive_transfer_by_transfer_prover lthy live_AsBs Rs R embLL [embLL_def] [] [old1_sig_map_transfer]; val embLR_transfer = derive_transfer_by_transfer_prover lthy live_AsBs Rs R embLR [embLR_def] [] [old2_sig_map_transfer]; val Lam_transfer = derive_Lam_or_eval_core_transfer lthy live_AsBs Y Z preT ssig_T Rs R pre_rel sig_rel ssig_rel Lam Lam_def [] [pre_map_transfer, old1_Lam_transfer, old2_Lam_transfer, embLL_transfer, embLR_transfer]; val ((((((((flat, _, flat_simps), flat_transfer), ((eval_core, _, eval_core_simps), eval_core_transfer)), (eval, eval_def)), (cutSsig, cutSsig_def)), (algLam, algLam_def)), (corecU, corecU_def)), lthy) = lthy |> define_flat_etc fp_b version live_AsBs Y Z preT fpT sig_T ssig_T Oper VLeaf CLeaf pre_rel dead_pre_map dtor dtor_unfold dead_sig_map ssig_rel dead_ssig_map Lam Rs R pre_map_transfer [fp_rel_eq] sig_map_transfer ssig_map_transfer Lam_transfer dtor_transfer; val (Sig_pointful_natural, flat_pointful_natural, _, Lam_pointful_natural, _, eval_core_pointful_natural, eval_thm, eval_flat, eval_simps as [eval_Oper, _, _], corecU_ctor, corecU_unique, dtor_algLam) = derive_Sig_natural_etc lthy live live_AsBs Y Z preT fpT fpT sig_T ssig_T pre_map dead_pre_map ctor dtor Sig dead_sig_map Oper VLeaf CLeaf ssig_map dead_ssig_map Lam flat eval_core eval cutSsig algLam corecU x fs f g ctor_dtor dtor_inject dtor_unfold_thm dtor_unfold_unique sig_map_thm ssig_induct ssig_map_thms Oper_map_thm VLeaf_map_thm CLeaf_map_thm Lam_transfer flat_simps flat_transfer eval_core_simps eval_core_transfer eval_def cutSsig_def algLam_def corecU_def live_pre_bnf pre_bnf dead_pre_bnf fp_bnf sig_bnf ssig_bnf dead_ssig_bnf; val proto_sctr_natural = derive_natural_from_transfer_with_pre_type lthy live_AsBs Y Z preT ssig_T pre_map ssig_map fs f proto_sctr proto_sctr_transfer [pre_bnf, sig_bnf] []; val proto_sctr_pointful_natural = mk_pointful lthy proto_sctr_natural RS sym; val (embLL_pointful_natural, old1_algLam_pointful, eval_embLL, algLam_algLamL) = derive_embL_natural_etc lthy Inl_const old1_ssig_bnf ssig_bnf Y Z preT fpT old1_ssig_T ssig_T dead_pre_map Sig old1_ssig_map embLL old1_algLam algLam old1_flat flat old1_eval_core eval_core old1_eval eval x f old1_ssig_induct dead_pre_map_comp0 dead_pre_map_comp fp_map_id dtor_inject dtor_unfold_unique Sig_pointful_natural unsig_thm sig_map_thm old1_sig_map_comp old1_sig_map_cong old1_ssig_map_thms old1_Lam_pointful_natural Lam_def old1_flat_simps flat_simps embLL_simps embLL_transfer old1_eval_core_simps eval_core_simps old1_eval_thm eval_thm old1_dtor_algLam dtor_algLam old1_algLam_thm; val (embLR_pointful_natural, _, eval_embLR, algLam_algLamR) = derive_embL_natural_etc lthy Inr_const old2_ssig_bnf ssig_bnf Y Z preT fpT old2_ssig_T ssig_T dead_pre_map Sig old2_ssig_map embLR old2_algLam algLam old2_flat flat old2_eval_core eval_core old2_eval eval x f old2_ssig_induct dead_pre_map_comp0 dead_pre_map_comp fp_map_id dtor_inject dtor_unfold_unique Sig_pointful_natural unsig_thm sig_map_thm old2_sig_map_comp old2_sig_map_cong old2_ssig_map_thms old2_Lam_pointful_natural Lam_def old2_flat_simps flat_simps embLR_simps embLR_transfer old2_eval_core_simps eval_core_simps old2_eval_thm eval_thm old2_dtor_algLam dtor_algLam old2_algLam_thm; val algLam_thm = derive_algLam_step_or_merge lthy Y fpT ctor proto_sctr algLam proto_sctr_def old1_algLam_pointful algLam_algLamL; val all_algLam_algs = algLam_algLamL :: algLam_algLamR :: merge_lists (Thm.eq_thm_prop o apply2 zero_var_indexes) old1_all_algLam_algs old2_all_algLam_algs; val (((corecUU, _), corecUU_thm, corecUU_unique, corecUU_transfer, _, sctr_transfer, sctr_pointful_natural), lthy) = lthy |> define_corecUU_etc fp_b version live_AsBs Y Z preT fpT ssig_T pre_map dead_pre_map pre_rel fp_rel ctor Oper ssig_map dead_ssig_map ssig_rel proto_sctr flat eval_core eval corecU fs f g Rs R pre_map_transfer [] dtor_unfold_transfer dtor_transfer ssig_map_transfer proto_sctr_transfer proto_sctr_pointful_natural flat_transfer flat_pointful_natural eval_core_transfer eval_core_pointful_natural eval_thm eval_flat eval_Oper algLam_thm cutSsig_def corecU_def corecU_ctor corecU_unique pre_bnf dead_pre_bnf fp_res ssig_fp_sugar; val Retr = enforce_type lthy (domain_type o domain_type) fpT old1_Retr0; val embed_Sig_inl = embed_Sig lthy Sig (Inl_const old1_sig_T old2_sig_T); val embed_Sig_inr = embed_Sig lthy Sig (Inr_const old1_sig_T old2_sig_T); val ctr_wrapper = embed_Sig_inl (#ctr_wrapper old1_buffer); val friends = Symtab.merge (K true) (Symtab.map (K (apsnd embed_Sig_inl)) (#friends old1_buffer), Symtab.map (K (apsnd embed_Sig_inr)) (#friends old2_buffer)); val old_fp_sugars = merge_lists (op = o apply2 (fst o dest_Type o #T)) old1_sig_fp_sugars old2_sig_fp_sugars; val ((dtor_coinduct_info, all_dead_k_bnfs, friend_names), lthy) = lthy |> derive_cong_merge fp_b version fpT old1_friend_names old2_friend_names dead_ssig_bnf dead_pre_bnf eval eval_thm eval_core_transfer old1_dtor_coinduct_info old2_dtor_coinduct_info Retr equivp_Retr Retr_coinduct eval_embLL embLL_transfer eval_embLR embLR_transfer old1_all_dead_k_bnfs old2_all_dead_k_bnfs; val buffer = {Oper = Oper, VLeaf = VLeaf, CLeaf = CLeaf, ctr_wrapper = ctr_wrapper, friends = friends}; val notes = [(corecUU_transferN, [corecUU_transfer])] @ (if Config.get lthy bnf_internals then [(algLamN, [algLam_thm]), (algLam_algLamN, [algLam_algLamL, algLam_algLamR]), (cong_alg_introsN, #cong_alg_intros dtor_coinduct_info), (cong_localeN, [#cong_locale dtor_coinduct_info]), (corecU_ctorN, [corecU_ctor]), (corecU_uniqueN, [corecU_unique]), (corecUUN, [corecUU_thm]), (corecUU_uniqueN, [corecUU_unique]), (dtor_algLamN, [dtor_algLam]), (dtor_coinductN, [#dtor_coinduct dtor_coinduct_info]), (eval_core_pointful_naturalN, [eval_core_pointful_natural]), (eval_core_transferN, [eval_core_transfer]), (embL_pointful_naturalN, [embLL_pointful_natural, embLR_pointful_natural]), (embL_transferN, [embLL_transfer, embLR_transfer]), (evalN, [eval_thm]), (eval_flatN, [eval_flat]), (eval_simpsN, eval_simps), (flat_pointful_naturalN, [flat_pointful_natural]), (flat_transferN, [flat_transfer]), (Lam_pointful_naturalN, [Lam_pointful_natural]), (Lam_transferN, [Lam_transfer]), (proto_sctr_pointful_naturalN, [proto_sctr_pointful_natural]), (proto_sctr_transferN, [proto_sctr_transfer]), (sctr_pointful_naturalN, [sctr_pointful_natural]), (sctr_transferN, [sctr_transfer]), (Sig_pointful_naturalN, [Sig_pointful_natural])] else []) |> map (fn (thmN, thms) => ((mk_version_fp_binding true lthy version fp_b thmN, []), [(thms, [])])); in ({fp_b = fp_b, version = version, fpT = fpT, Y = Y, Z = Z, friend_names = friend_names, sig_fp_sugars = sig_fp_sugar :: old_fp_sugars, ssig_fp_sugar = ssig_fp_sugar, Lam = Lam, proto_sctr = proto_sctr, flat = flat, eval_core = eval_core, eval = eval, algLam = algLam, corecUU = corecUU, dtor_transfer = dtor_transfer, Lam_transfer = Lam_transfer, Lam_pointful_natural = Lam_pointful_natural, proto_sctr_transfer = proto_sctr_transfer, flat_simps = flat_simps, eval_core_simps = eval_core_simps, eval_thm = eval_thm, eval_simps = eval_simps, all_algLam_algs = all_algLam_algs, algLam_thm = algLam_thm, dtor_algLam = dtor_algLam, corecUU_thm = corecUU_thm, corecUU_unique = corecUU_unique, corecUU_transfer = corecUU_transfer, buffer = buffer, all_dead_k_bnfs = all_dead_k_bnfs, Retr = Retr, equivp_Retr = equivp_Retr, Retr_coinduct = Retr_coinduct, dtor_coinduct_info = dtor_coinduct_info} |> morph_corec_info (Local_Theory.target_morphism lthy), lthy |> Local_Theory.notes notes |> snd) end; fun set_corec_info_exprs fpT_name f = Local_Theory.declaration {syntax = false, pervasive = true} (fn phi => let val exprs = f phi in Data.map (apsnd (fn [info_tab] => [Symtab.map_default (fpT_name, exprs) (K exprs) info_tab])) end); fun subsume_corec_info_ad ctxt {fpT = fpT1, friend_names = friend_names1} {fpT = fpT2, friend_names = friend_names2} = Sign.typ_instance (Proof_Context.theory_of ctxt) (fpT1, fpT2) andalso subset (op =) (friend_names1, friend_names2); fun subsume_corec_info_expr ctxt expr1 expr2 = subsume_corec_info_ad ctxt (corec_ad_of_expr expr1) (corec_ad_of_expr expr2); fun instantiate_corec_info thy res_T (info as {fpT, ...}) = let val As_rho = tvar_subst thy [fpT] [res_T]; val substAT = Term.typ_subst_TVars As_rho; val substA = Term.subst_TVars As_rho; val phi = Morphism.typ_morphism "BNF" substAT $> Morphism.term_morphism "BNF" substA; in morph_corec_info phi info end; fun instantiate_corec_info_expr thy res_T (Ad ({friend_names, ...}, f)) = Ad ({fpT = res_T, friend_names = friend_names}, f #>> instantiate_corec_info thy res_T) | instantiate_corec_info_expr thy res_T (Info info) = Info (instantiate_corec_info thy res_T info); fun ensure_Info expr = corec_info_of_expr expr #>> Info and ensure_Info_if_Info old_expr (expr, lthy) = if is_Info old_expr then ensure_Info expr lthy else (expr, lthy) and merge_corec_info_exprs old_exprs expr1 expr2 lthy = if subsume_corec_info_expr lthy expr2 expr1 then if subsume_corec_info_expr lthy expr1 expr2 andalso is_Ad expr1 then (expr2, lthy) else ensure_Info_if_Info expr2 (expr1, lthy) else if subsume_corec_info_expr lthy expr1 expr2 then ensure_Info_if_Info expr1 (expr2, lthy) else let val thy = Proof_Context.theory_of lthy; val {fpT = fpT1, friend_names = friend_names1} = corec_ad_of_expr expr1; val {fpT = fpT2, friend_names = friend_names2} = corec_ad_of_expr expr2; val fpT0 = typ_unify_disjointly thy (fpT1, fpT2); val fpT = singleton (freeze_types lthy []) fpT0; val friend_names = merge_lists (op =) friend_names1 friend_names2; val expr = Ad ({fpT = fpT, friend_names = friend_names}, corec_info_of_expr expr1 ##>> corec_info_of_expr expr2 #-> uncurry (derive_corecUU_merge fpT)); val old_same_type_exprs = if old_exprs then [] |> Sign.typ_instance thy (fpT1, fpT0) ? cons expr1 |> Sign.typ_instance thy (fpT2, fpT0) ? cons expr2 else []; in (expr, lthy) |> fold ensure_Info_if_Info old_same_type_exprs end and insert_corec_info_expr expr exprs lthy = let val thy = Proof_Context.theory_of lthy; val {fpT = new_fpT, ...} = corec_ad_of_expr expr; val is_Tinst = curry (Sign.typ_instance thy); fun is_Tequiv T U = is_Tinst T U andalso is_Tinst U T; val (((equiv_exprs, sub_exprs), sup_exprs), incomp_exprs) = exprs |> List.partition ((fn {fpT, ...} => is_Tequiv fpT new_fpT) o corec_ad_of_expr) ||>> List.partition ((fn {fpT, ...} => is_Tinst fpT new_fpT) o corec_ad_of_expr) ||>> List.partition ((fn {fpT, ...} => is_Tinst new_fpT fpT) o corec_ad_of_expr); fun add_instantiated_incomp_expr expr exprs = let val {fpT, ...} = corec_ad_of_expr expr in (case try (typ_unify_disjointly thy) (fpT, new_fpT) of SOME new_T => let val subsumes = (fn {fpT, ...} => is_Tinst new_T fpT) o corec_ad_of_expr in if exists (exists subsumes) [exprs, sub_exprs] then exprs else instantiate_corec_info_expr thy new_T expr :: exprs end | NONE => exprs) end; val unincomp_exprs = fold add_instantiated_incomp_expr incomp_exprs []; val ((merged_sub_exprs, merged_unincomp_exprs), lthy) = lthy |> fold_map (merge_corec_info_exprs true expr) sub_exprs ||>> fold_map (merge_corec_info_exprs false expr) unincomp_exprs; val (merged_equiv_expr, lthy) = (expr, lthy) |> fold (uncurry o merge_corec_info_exprs true) equiv_exprs; in (merged_unincomp_exprs @ merged_sub_exprs @ merged_equiv_expr :: sup_exprs @ incomp_exprs |> sort (rev_order o int_ord o apply2 (length o #friend_names o corec_ad_of_expr)), lthy) end and register_corec_info (info as {fpT = Type (fpT_name, _), ...}) lthy = let val (exprs, lthy) = insert_corec_info_expr (Info info) (corec_info_exprs_of lthy fpT_name) lthy; in lthy |> set_corec_info_exprs fpT_name (fn phi => map (morph_corec_info_expr phi) exprs) end and corec_info_of_expr (Ad (_, f)) lthy = f lthy | corec_info_of_expr (Info info) lthy = (info, lthy); fun nonempty_corec_info_exprs_of fpT_name lthy = (case corec_info_exprs_of lthy fpT_name of [] => derive_corecUU_base fpT_name lthy |> (fn (info, lthy) => ([Info info], lthy |> set_corec_info_exprs fpT_name (fn phi => [Info (morph_corec_info phi info)]))) | exprs => (exprs, lthy)); fun corec_info_of res_T lthy = (case res_T of Type (fpT_name, _) => let val (exprs, lthy) = nonempty_corec_info_exprs_of fpT_name lthy; val thy = Proof_Context.theory_of lthy; val expr = (case find_first ((fn {fpT, ...} => Sign.typ_instance thy (res_T, fpT)) o corec_ad_of_expr) exprs of SOME expr => expr | NONE => error ("Invalid type: " ^ Syntax.string_of_typ lthy res_T)); val (info, lthy) = corec_info_of_expr expr lthy; in (instantiate_corec_info thy res_T info, lthy |> is_Ad expr ? register_corec_info info) end | _ => not_codatatype lthy res_T); fun maybe_corec_info_of ctxt res_T = (case res_T of Type (fpT_name, _) => let val thy = Proof_Context.theory_of ctxt; val infos = corec_infos_of ctxt fpT_name; in find_first (fn {fpT, ...} => Sign.typ_instance thy (res_T, fpT)) infos |> Option.map (instantiate_corec_info thy res_T) end | _ => not_codatatype ctxt res_T); fun prepare_friend_corec friend_name friend_T lthy = let val (arg_Ts, res_T) = strip_type friend_T; val Type (fpT_name, res_Ds) = (case res_T of T as Type _ => T | T => error (not_codatatype lthy T)); val _ = not (null arg_Ts) orelse error "Function with no argument cannot be registered as friend"; val {T = Type (fpT_name, fpT_args0), pre_bnf, fp_bnf = live_fp_bnf, fp_res, ...} = checked_fp_sugar_of lthy fpT_name; val num_fp_tyargs = length fpT_args0; val fpT_Ss = map Type.sort_of_atyp fpT_args0; val live_fp_alives = liveness_of_fp_bnf num_fp_tyargs live_fp_bnf; val (old_info as {friend_names = old_friend_names, sig_fp_sugars = old_sig_fp_sugar :: _, buffer = old_buffer, ...}, lthy) = corec_info_of res_T lthy; val old_sig_T_name = fst (dest_Type (#T old_sig_fp_sugar)); val old_sig_alives = liveness_of_fp_bnf (num_fp_tyargs + 1) (#fp_bnf old_sig_fp_sugar); (* FIXME: later *) val fp_alives = fst (split_last old_sig_alives); val fp_alives = map (K false) live_fp_alives; val _ = not (member (op =) old_friend_names friend_name) orelse error ("Function " ^ quote (Syntax.string_of_term lthy (Const (friend_name, friend_T))) ^ " already registered as friend"); val lthy = lthy |> Variable.declare_typ friend_T; val ((Ds, [Y, Z]), _) = lthy |> mk_TFrees' fpT_Ss ||>> mk_TFrees 2; (* FIXME *) val dead_Ds = Ds; val live_As = [Y]; val ctor = mk_ctor res_Ds (the_single (#ctors fp_res)); val fpT0 = Type (fpT_name, Ds); val k_Ts0 = map (typ_subst_nonatomic (res_Ds ~~ Ds) o typ_subst_nonatomic [(res_T, Y)]) arg_Ts; val k_T0 = mk_tupleT_balanced k_Ts0; val As = Ds @ [Y]; val res_As = res_Ds @ [Y]; val k_As = fold Term.add_tfreesT k_Ts0 []; val _ = (case filter_out (member (op =) As o TFree) k_As of [] => () | k_A :: _ => error ("Cannot have type variable " ^ quote (Syntax.string_of_typ lthy (TFree k_A)) ^ " in the argument types when it does not occur as an immediate argument of the result \ \type constructor")); val substDT = Term.typ_subst_atomic (Ds ~~ res_Ds); val old_sig_T0 = Type (old_sig_T_name, As); val ((fp_b, version), lthy) = lthy |> get_name_next_version_of fpT_name; val (((dead_k_bnf, sig_fp_sugar), ssig_fp_sugar), lthy) = lthy |> bnf_with_deads_and_lives dead_Ds live_As Y fpT0 k_T0 ||>> define_sig_type fp_b version fp_alives Ds Y (mk_sumT (old_sig_T0, k_T0)) ||>> define_ssig_type fp_b version fp_alives Ds Y fpT0; val _ = live_of_bnf dead_k_bnf = 1 orelse error "Impossible type for friend (the result codatatype must occur live in the arguments)"; val (dead_pre_bnf, lthy) = lthy |> bnf_kill_all_but 1 pre_bnf; val sig_fp_ctr_sugar = #fp_ctr_sugar sig_fp_sugar; val ssig_fp_ctr_sugar = #fp_ctr_sugar ssig_fp_sugar; val sig_ctr_sugar = #ctr_sugar sig_fp_ctr_sugar; val ssig_ctr_sugar = #ctr_sugar ssig_fp_ctr_sugar; val ssig_T_name = fst (dest_Type (#T ssig_fp_sugar)); val preT = pre_type_of_ctor Y ctor; val old_sig_T = substDT old_sig_T0; val k_T = substDT k_T0; val ssig_T = Type (ssig_T_name, res_As); val Sig = mk_ctr res_As (the_single (#ctrs sig_ctr_sugar)); val [Oper, VLeaf, CLeaf] = map (mk_ctr res_As) (#ctrs ssig_ctr_sugar); val (ctr_wrapper, friends) = mk_ctr_wrapper_friends lthy friend_name friend_T old_sig_T k_T Sig old_buffer; val buffer = {Oper = Oper, VLeaf = VLeaf, CLeaf = CLeaf, ctr_wrapper = ctr_wrapper, friends = friends}; in ((old_info, fp_b, version, Y, Z, preT, k_T, ssig_T, dead_pre_bnf, dead_k_bnf, sig_fp_sugar, ssig_fp_sugar, buffer), lthy) end; fun register_friend_corec key fp_b version Y Z k_T dead_k_bnf sig_fp_sugar ssig_fp_sugar friend_const rho rho_transfer old_info lthy = let val friend_T = fastype_of friend_const; val res_T = body_type friend_T; in derive_corecUU_step res_T old_info key friend_T fp_b version Y Z k_T dead_k_bnf sig_fp_sugar ssig_fp_sugar rho rho_transfer lthy |> (fn ((info, friend_info), lthy) => (friend_info, register_corec_info info lthy)) end; fun merge_corec_info_exprss exprs1 exprs2 lthy = let fun all_friend_names_of exprs = fold (union (op =)) (map (#friend_names o corec_ad_of_expr) exprs) []; val friend_names1 = all_friend_names_of exprs1; val friend_names2 = all_friend_names_of exprs2; in if subset (op =) (friend_names2, friend_names1) then if subset (op =) (friend_names1, friend_names2) andalso length (filter is_Info exprs2) > length (filter is_Info exprs1) then (exprs2, lthy) else (exprs1, lthy) else if subset (op =) (friend_names1, friend_names2) then (exprs2, lthy) else fold_rev (uncurry o insert_corec_info_expr) exprs2 (exprs1, lthy) end; fun merge_corec_info_tabs info_tab1 info_tab2 lthy = let val fpT_names = union (op =) (Symtab.keys info_tab1) (Symtab.keys info_tab2); fun add_infos_of fpT_name (info_tab, lthy) = (case Symtab.lookup info_tab1 fpT_name of NONE => (Symtab.update_new (fpT_name, the (Symtab.lookup info_tab2 fpT_name)) info_tab, lthy) | SOME exprs1 => (case Symtab.lookup info_tab2 fpT_name of NONE => (Symtab.update_new (fpT_name, exprs1) info_tab, lthy) | SOME exprs2 => let val (exprs, lthy) = merge_corec_info_exprss exprs1 exprs2 lthy in (Symtab.update_new (fpT_name, exprs) info_tab, lthy) end)); in fold add_infos_of fpT_names (Symtab.empty, lthy) end; fun consolidate lthy = (case snd (Data.get (Context.Proof lthy)) of [_] => raise Same.SAME | info_tab :: info_tabs => let val (info_tab', lthy) = fold_rev (uncurry o merge_corec_info_tabs) info_tabs (info_tab, lthy); in Local_Theory.declaration {syntax = false, pervasive = true} (fn phi => Data.map (apsnd (fn _ => [Symtab.map (K (map (morph_corec_info_expr phi))) info_tab']))) lthy end); fun consolidate_global thy = SOME (Named_Target.theory_map consolidate thy) handle Same.SAME => NONE; val _ = Theory.setup (Theory.at_begin consolidate_global); end;