--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/BNF/bnf_gfp_grec.ML Tue Mar 22 12:39:37 2016 +0100
@@ -0,0 +1,3234 @@
+(* 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 enforce_type: Proof.context -> (typ -> typ) -> typ -> 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 enforce_type ctxt get_T T t =
+ Term.subst_TVars (tvar_subst (Proof_Context.theory_of ctxt) [get_T (fastype_of t)] [T]) t;
+
+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 [(b, NONE, NoSyn)] (map (pair Attrib.empty_binding) 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_Def.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 inline_pre_bnfs f lthy =
+ lthy
+ |> Config.put typedef_threshold ~1
+ |> f
+ |> Config.put typedef_threshold (Config.get lthy typedef_threshold);
+
+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 => pair (if alive then SOME Binding.empty else NONE)
+ o rpair @{sort type}) (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*)
+ |> inline_pre_bnfs (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 => pair (if alive then SOME Binding.empty else NONE)
+ o rpair @{sort type}) (fp_alives @ [true]) As;
+ 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*)
+ |> inline_pre_bnfs (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
+ 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_sorry (*FIXME*) (*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
+ 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_sorry (*FIXME*) (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} =>
+ mk_dtor_transfer_tac ctxt dtor_rel_thm))
+ |> Thm.close_derivation
+ 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_sorry (*FIXME*) (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} =>
+ mk_transfer_by_transfer_prover_tac ctxt [const_def] rel_eqs transfers))
+ |> Thm.close_derivation
+ 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_sorry (*FIXME*) (*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
+ 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_sorry (*FIXME*) (*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
+ 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_sorry (*FIXME*) (*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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ end;
+
+fun derive_eval_thm ctxt dtor_inject dtor_unfold_thm eval_def =
+ (trans OF [iffD2 OF [dtor_inject, eval_def RS meta_eq_to_obj_eq RS fun_cong], dtor_unfold_thm])
+ |> unfold_thms ctxt [o_apply, eval_def RS Drule.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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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 [Drule.asm_rl, corecU_pointfree])
+ OF [Drule.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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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
+ 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_fp_sugar = fp_sugar_of ctxt @{type_name prod};
+ val prod_bnf = #fp_bnf prod_fp_sugar;
+
+ 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 (cutSsig_def RS meta_eq_to_obj_eq) 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
+ 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
+ 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
+ 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 = fold_thms 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 = fold_thms ctxt [cong_def] (thm OF [cong_locale]);
+ fun instance_of_old_gen thm = fold_thms 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 (algrho_def RS meta_eq_to_obj_eq);
+
+ val gen_cong_emb =
+ (@{thm gen_cong_emb} OF [old_cong_locale, cong_locale, eval_embL, embL_transfer])
+ |> fold_thms 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])
+ |> fold_thms lthy [old1_cong_def, cong_def];
+ val emb2 = (@{thm gen_cong_emb} OF [old2_cong_locale, cong_locale, eval_embLR, embLR_transfer])
+ |> fold_thms 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 num_fp_tyargs = length fpT_args0;
+ val fp_alives = liveness_of_fp_bnf num_fp_tyargs fp_bnf;
+
+ val (((Es, Fs0), [Y, Z]), names_lthy) = lthy
+ |> mk_TFrees num_fp_tyargs
+ ||>> mk_TFrees num_fp_tyargs
+ ||>> 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 = #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 dead_ssig_rel = mk_rel 1 As Bs (rel_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_uniques 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 = #fp_co_induct_sugar old_ssig_fp_sugar;
+ val ssig_fp_induct_sugar = #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 dead_ssig_rel = mk_rel 1 res_As res_Bs (rel_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 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_uniques 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 {pre_bnf = live_pre_bnf, fp_bnf = live_fp_bnf, fp_res, ...} =
+ checked_fp_sugar_of lthy fpT_name;
+ val num_fp_tyargs = length res_Ds;
+ val live_fp_alives = liveness_of_fp_bnf num_fp_tyargs live_fp_bnf;
+
+ val ((Ds, [Y, Z]), names_lthy) = lthy
+ |> mk_TFrees num_fp_tyargs
+ ||>> 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 = #fp_co_induct_sugar old1_ssig_fp_sugar;
+ val old2_ssig_fp_induct_sugar = #fp_co_induct_sugar old2_ssig_fp_sugar;
+ val ssig_fp_induct_sugar = #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_uniques 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 SOME expr =
+ find_first ((fn {fpT, ...} => Sign.typ_instance thy (res_T, fpT)) o corec_ad_of_expr) exprs;
+ 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 {pre_bnf, fp_bnf = live_fp_bnf, fp_res, ...} = checked_fp_sugar_of lthy fpT_name;
+ val num_fp_tyargs = length res_Ds;
+ val live_fp_alives = liveness_of_fp_bnf num_fp_tyargs live_fp_bnf;
+
+ val fpT_name = fst (dest_Type res_T);
+
+ 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 num_fp_tyargs
+ ||>> 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)) ^ " used like that in friend"));
+
+ 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;