signature BNF_GFP_GREC = sig val Tsubst: typ -> typ -> typ -> typ val substT: typ -> typ -> term -> term val freeze_types: Proof.context -> (indexname * sort) list -> typ list -> typ list val dummify_atomic_types: term -> term val define_const: bool -> binding -> int -> string -> term -> local_theory ->
(term * thm) * local_theory
type 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>\<open>primcorec\<close>) ^ " instead of " ^
quote (#1 \<^command_keyword>\<open>corec\<close>) ^ ")"); fun noncorecursive_codatatype () =
error ("Noncorecursive codatatypes are not supported (try " ^
quote (#1 \<^command_keyword>\<open>definition\<close>) ^ " instead of " ^
quote (#1 \<^command_keyword>\<open>corec\<close>) ^ ")"); fun singleton_codatatype ctxt =
error ("Singleton corecursive codatatypes are not supported (use " ^
quote (Syntax.string_of_typ ctxt \<^typ>\<open>unit\<close>) ^ " instead)");
fun add_type_namesT (Type (s, Ts)) = insert (op =) s #> fold add_type_namesT Ts
| add_type_namesT _ = I;
fun Tsubst Y T = Term.typ_subst_atomic [(Y, T)]; fun substT Y T = Term.subst_atomic_types [(Y, T)];
fun freeze_types ctxt except_tvars Ts = let val As = fold Term.add_tvarsT Ts [] |> subtract (op =) except_tvars; val (Bs, _) = ctxt |> mk_TFrees' (map snd As); in map (Term.typ_subst_TVars (map fst As ~~ Bs)) Ts end;
fun typ_unify_disjointly thy (T, T') = if T = T' then
T else let val tvars = Term.add_tvar_namesT T []; val tvars' = Term.add_tvar_namesT T' []; val maxidx' = maxidx_of_typ T'; val T = T |> exists (member (op =) tvars') tvars ? Logic.incr_tvar (maxidx' + 1); val maxidx = Integer.max (maxidx_of_typ T) maxidx'; val (tyenv, _) = Sign.typ_unify thy (T, T') (Vartab.empty, maxidx); in
Envir.subst_type tyenv T end;
val dummify_atomic_types = Term.map_types (Term.map_atyps (K Term.dummyT));
fun mk_internal internal ctxt f = if internal andalso not (Config.get ctxt bnf_internals) then f else I fun mk_fp_binding fp_b pre = Binding.map_name (K pre) fp_b
|> Binding.qualify true (Binding.name_of fp_b); fun mk_version_binding version = Binding.qualify false ("v" ^ string_of_int version); fun mk_version_fp_binding internal ctxt =
mk_internal internal ctxt Binding.concealed ooo (mk_fp_binding oo mk_version_binding); (*FIXME: get rid of ugly names when typedef and primrec respect qualification*) fun mk_version_binding_ugly version = Binding.suffix_name ("_v" ^ string_of_int version); fun mk_version_fp_binding_ugly internal ctxt version fp_b pre =
Binding.prefix_name (pre ^ "_") fp_b
|> mk_version_binding_ugly version
|> mk_internal internal ctxt Binding.concealed;
fun mk_mapN ctxt live_AsBs TA bnf = letval 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 = letval 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
|> (snd o Local_Theory.begin_nested)
|> Local_Theory.define ((b, NoSyn), ((Thm.def_binding b |> Binding.concealed, []), rhs))
||> `Local_Theory.end_nested;
val phi = Proof_Context.export_morphism lthy_old lthy;
valconst = Morphism.term phi free; valconst' = 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
|> (snd o Local_Theory.begin_nested)
|> Local_Theory.map_background_naming (mk_internal true lthy Name_Space.concealed) (*TODO check*)
|> primrec false [] [(b, NONE, NoSyn)] (map (fn eq => ((Binding.empty_atts, eq), [], [])) eqs)
||> `Local_Theory.end_nested;
val phi = Proof_Context.export_morphism lthy_old lthy;
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: stringlist};
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 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 () elseifnot (exists (exists (Term.exists_subtype (curry (op =) X))) ctrXs_Tss) then
noncorecursive_codatatype () elseif ctrXs_Tss = [[X]] then
singleton_codatatype ctxt else
(); in
fp_sugar end;
fun bnf_kill_all_but nn bnf lthy =
((empty_comp_cache, empty_unfolds), lthy)
|> kill_bnf I (live_of_bnf bnf - nn) bnf
||> snd;
fun bnf_with_deads_and_lives dead_Es live_As Y fpT T lthy = let val qsoty = quote o Syntax.string_of_typ lthy;
val unfreeze_fp = Tsubst Y fpT;
fun flatten_tyargs Ass = map dest_TFree live_As
|> filter (fn T => exists (fn Ts => member (op =) Ts T) Ass);
val ((bnf, _), (_, lthy)) =
bnf_of_typ false Do_Inline I flatten_tyargs [Term.dest_TFree Y] (map Term.dest_TFree dead_Es)
T ((empty_comp_cache, empty_unfolds), lthy) handle BAD_DEAD (Y, Y_backdrop) =>
(case Y_backdrop of Type (bad_tc, _) => let val T = qsoty (unfreeze_fp Y); val T_backdrop = qsoty (unfreeze_fp Y_backdrop); fun register_hint () = "\nUse the " ^ quote (#1 \<^command_keyword>\<open>bnf\<close>) ^ " 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);
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 = (snd o Local_Theory.begin_nested) lthy;
val T_name = Local_Theory.full_name lthy T_b;
val tyargs = map2 (fn alive => fn T =>
(if alive then SOME Binding.empty else NONE, (T, Type.sort_of_atyp T)))
(fp_alives @ [true]) (Es @ [Y]); val ctr_specs = [(((Binding.empty, ctr_b), [(sel_b, rhsT)]), NoSyn)]; val spec = (((((tyargs, T_b), NoSyn), ctr_specs),
(Binding.empty, Binding.empty, Binding.empty)), []);
val plugins = Plugin_Name.make_filter lthy (K (curry (op =) transfer_plugin)); val discs_sels = true;
val 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 = (snd o Local_Theory.begin_nested) lthy;
val sig_T_name = Local_Theory.full_name lthy sig_T_b; val T_name = Long_Name.map_base_name (prefix s_prefix) sig_T_name;
val As = Es @ [Y]; val ssig_sig_T = Type (sig_T_name, Es @ [Type (T_name, As)]);
val tyargs = map2 (fn alive => fn T =>
(if alive then SOME Binding.empty else NONE, (T, Type.sort_of_atyp T)))
(fp_alives @ [true]) (Es @ [Y]); val ctr_specs =
[(((Binding.empty, Oper_b), [(Binding.empty, ssig_sig_T)]), NoSyn),
(((Binding.empty, VLeaf_b), [(Binding.empty, Y)]), NoSyn),
(((Binding.empty, CLeaf_b), [(Binding.empty, fpT)]), NoSyn)]; val spec = (((((tyargs, T_b), NoSyn), ctr_specs),
(Binding.empty, Binding.empty, Binding.empty)), []);
val plugins = Plugin_Name.make_filter lthy (K (curry (op =) transfer_plugin)); val discs_sels = false;
val 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; valSig' = substT Y ssig_T Sig; val inl' = Inl_or_r_const ssig_old_sig_T ssig_other_summand_T;
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; valSig' = 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;
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;
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;
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;
fun derive_proto_sctr_transfer_step_or_merge ctxt Y Z R dead_pre_rel dead_sig_rel proto_sctr
proto_sctr_def fp_k_T_rel_eqs transfers = let val proto_sctrZ = substT Y Z proto_sctr; val goal = mk_rel_fun (dead_pre_rel $ R) (dead_sig_rel $ R) $ proto_sctr $ proto_sctrZ
|> HOLogic.mk_Trueprop; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_transfer_by_transfer_prover_tac ctxt [proto_sctr_def] fp_k_T_rel_eqs transfers))
|> Thm.close_derivation \<^here> end;
fun derive_sctr_transfer ctxt live_AsBs Y Z ssig_T Rs R pre_rel ssig_rel sctr sctr_def
fp_k_T_rel_eqs transfers = let val ssig_TB = typ_subst_atomic live_AsBs ssig_T;
val pre_rel' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssig_TB)] pre_rel; val Rpre_rel' = list_comb (pre_rel', Rs); val RRssig_rel = list_comb (ssig_rel, Rs) $ R; val sctrB = subst_atomic_types live_AsBs sctr;
fun derive_corecUU_transfer ctxt live_AsBs Y Z Rs R preT ssig_T pre_rel fp_rel ssig_rel corecUU
cutSsig_def corecU_def corecUU_def fp_k_T_rel_eqs transfers = let val ssig_preT = Tsubst Y ssig_T preT; val ssig_TB = typ_subst_atomic live_AsBs ssig_T; val ssig_preTB = typ_subst_atomic live_AsBs ssig_preT;
val pre_rel' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssig_TB)] pre_rel; val ssig_rel' = Term.subst_atomic_types [(Y, ssig_preT), (Z, ssig_preTB)] ssig_rel; val Rpre_rel' = list_comb (pre_rel', Rs); val Rfp_rel = list_comb (fp_rel, Rs); val RRssig_rel = list_comb (ssig_rel, Rs) $ R; val Rssig_rel' = list_comb (ssig_rel', Rs); val corecUUB = subst_atomic_types live_AsBs corecUU;
val goal = mk_rel_fun (mk_rel_fun R (Rssig_rel' $ (Rpre_rel' $ RRssig_rel)))
(mk_rel_fun R Rfp_rel) $ corecUU $ corecUUB
|> HOLogic.mk_Trueprop; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove (*no sorry*) ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_transfer_by_transfer_prover_tac ctxt [cutSsig_def, corecU_def, corecUU_def] fp_k_T_rel_eqs
transfers))
|> Thm.close_derivation \<^here> end;
fun mk_natural_goal ctxt simple_T_mapfs fs t u = let fun build_simple (T, _) =
(case AList.lookup (op =) simple_T_mapfs T of
SOME mapf => mapf
| NONE => the (find_first (fn f => domain_type (fastype_of f) = T) fs));
val simple_Ts = map fst simple_T_mapfs;
val t_map = build_map ctxt simple_Ts [] build_simple (apply2 (range_type o fastype_of) (t, u)); val u_map = build_map ctxt simple_Ts [] build_simple (apply2 (domain_type o fastype_of) (t, u)); in
mk_Trueprop_eq (HOLogic.mk_comp (u, u_map), HOLogic.mk_comp (t_map, t)) end;
fun derive_natural_by_unfolding ctxt live_AsBs preT pre_map fs f const map_thms = let val ffpre_map = list_comb (pre_map, fs) $ f; val constB = subst_atomic_types live_AsBs const;
fun derive_natural_from_transfer ctxt live_AsBs simple_T_mapfs fs f const transfer bnfs subst_bnfs = let val m = length live_AsBs;
val constB = Term.subst_atomic_types live_AsBs const; val goal = mk_natural_goal ctxt simple_T_mapfs (fs @ [f]) const constB; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_natural_from_transfer_tac ctxt m (replicate m true) transfer [] (map rel_Grp_of_bnf bnfs)
(map rel_Grp_of_bnf subst_bnfs)))
|> Thm.close_derivation \<^here> end;
fun derive_natural_from_transfer_with_pre_type ctxt live_AsBs Y Z preT ssig_T pre_map ssig_map fs
f = let val ssig_TB = typ_subst_atomic live_AsBs ssig_T; val preT' = Term.typ_subst_atomic [(Y, ssig_T), (Z, ssig_TB)] preT;
val ffpre_map = list_comb (pre_map, fs) $ f; val pre_map' = Term.subst_atomic_types [(Y, ssig_T), (Z, ssig_TB)] pre_map; val fpre_map' = list_comb (pre_map', fs); val ffssig_map = list_comb (ssig_map, fs) $ f;
val preT_mapfs = [(preT, ffpre_map), (preT', fpre_map' $ ffssig_map)]; in
derive_natural_from_transfer ctxt live_AsBs preT_mapfs fs f end;
fun derive_Lam_Inl_Inr ctxt Y Z preT old_sig_T old_ssig_T k_T ssig_T dead_pre_map Sig embL old_Lam
Lam rho unsig_thm Lam_def = let val YpreT = HOLogic.mk_prodT (Y, preT); val Ypre_old_sig_T = Tsubst Y YpreT old_sig_T; val Ypre_k_T = Tsubst Y YpreT k_T;
val inl' = Inl_const Ypre_old_sig_T Ypre_k_T; val inr' = Inr_const Ypre_old_sig_T Ypre_k_T; val dead_pre_map' = Term.subst_atomic_types [(Y, old_ssig_T), (Z, ssig_T)] dead_pre_map; valSig' = substT Y YpreT Sig; val Lam_o_Sig = HOLogic.mk_comp (Lam, Sig');
val inl_goal = mk_Trueprop_eq (HOLogic.mk_comp (Lam_o_Sig, inl'),
HOLogic.mk_comp (dead_pre_map' $ embL, old_Lam)); val inr_goal = mk_Trueprop_eq (HOLogic.mk_comp (Lam_o_Sig, inr'), rho); val goals = [inl_goal, inr_goal]; val goal = Logic.mk_conjunction_balanced goals; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal
(fn {context = ctxt, prems = _} => mk_Lam_Inl_Inr_tac ctxt unsig_thm Lam_def))
|> Conjunction.elim_balanced (length goals)
|> map (Thm.close_derivation \<^here>) end;
fun derive_flat_VLeaf ctxt Y Z ssig_T x VLeaf dead_ssig_map flat ssig_induct fp_map_id sig_map_cong
sig_map_ident sig_map_comp ssig_map_thms flat_simps = let val x' = substT Y ssig_T x; val dead_ssig_map' = substT Z ssig_T dead_ssig_map;
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 ssig_induct' = infer_instantiate' ctxt [NONE, SOME (Thm.cterm_of ctxt x')] ssig_induct; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_flat_VLeaf_or_flat_tac ctxt ssig_induct' sig_map_cong
(o_apply :: fp_map_id :: sig_map_comp :: ssig_map_thms @ flat_simps)))
|> Thm.close_derivation \<^here> end;
fun derive_eval_core_flat ctxt Y Z preT ssig_T dead_pre_map dead_ssig_map flat eval_core x
ssig_induct dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp fp_map_id sig_map_comp
sig_map_cong ssig_map_thms ssig_map_comp flat_simps flat_pointful_natural flat_flat
Lam_pointful_natural eval_core_simps = let val YpreT = HOLogic.mk_prodT (Y, preT); val ssig_ssig_T = Tsubst Y ssig_T ssig_T; val Ypre_ssig_T = Tsubst Y YpreT ssig_T; val Ypre_ssig_ssig_T = Tsubst Y YpreT ssig_ssig_T; val ssig_YpreT = Tsubst Y ssig_T YpreT;
val dead_pre_map' = Term.subst_atomic_types [(Y, ssig_ssig_T), (Z, ssig_T)] dead_pre_map; val dead_ssig_map' = Term.subst_atomic_types [(Y, Ypre_ssig_T), (Z, ssig_YpreT)] dead_ssig_map; val dead_ssig_map'' = Term.subst_atomic_types [(Y, YpreT), (Z, Y)] dead_ssig_map; val flat' = substT Y YpreT flat; val eval_core' = substT Y ssig_T eval_core; val x' = substT Y Ypre_ssig_ssig_T x; val fst' = fst_const YpreT;
fun derive_eval_thm ctxt dtor_inject dtor_unfold_thm eval_def =
(trans OF [iffD2 OF [dtor_inject, HOLogic.mk_obj_eq eval_def RS fun_cong], dtor_unfold_thm])
|> unfold_thms ctxt [o_apply, eval_def RS symmetric_thm];
fun derive_eval_flat ctxt Y Z fpT ssig_T dead_ssig_map flat eval x dead_pre_map_comp0
dtor_unfold_unique ssig_map_id ssig_map_comp flat_pointful_natural eval_core_pointful_natural
eval_core_flat eval_thm = let val fp_ssig_T = Tsubst Y fpT ssig_T; val fp_ssig_ssig_T = Tsubst Y fp_ssig_T ssig_T;
val dead_ssig_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_ssig_map; val flat' = substT Y fpT flat; val x' = substT Y fp_ssig_ssig_T x;
val cond_eval_o_flat =
infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt (HOLogic.mk_comp (eval, flat')))]
(trans OF [dtor_unfold_unique, dtor_unfold_unique RS sym] RS fun_cong) OF [ext, ext]; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_eval_flat_tac ctxt dead_pre_map_comp0 ssig_map_id ssig_map_comp flat_pointful_natural
eval_core_pointful_natural eval_core_flat eval_thm cond_eval_o_flat))
|> Thm.close_derivation \<^here> end;
fun derive_eval_Oper ctxt live Y Z fpT sig_T ssig_T dead_sig_map Oper eval algLam x sig_map_ident
sig_map_comp0 sig_map_comp Oper_natural_pointful VLeaf_natural flat_simps eval_flat algLam_def = let val fp_ssig_T = Tsubst Y fpT ssig_T; val fp_ssig_sig_T = Tsubst Y fp_ssig_T sig_T;
val dead_sig_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_sig_map; val Oper' = substT Y fpT Oper; val x' = substT Y fp_ssig_sig_T x;
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;
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';
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');
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';
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';
fun derive_corecU_ctor_unique ctxt Y Z preT fpT ssig_T dead_pre_map ctor dtor VLeaf extdd corecU f g
dead_pre_map_comp ctor_dtor dtor_unfold_thm dtor_unfold_unique ssig_map_thms dead_ssig_map_comp0
flat_simps flat_VLeaf eval_core_simps extdd_mor extdd_o_VLeaf cutSsig_def mor_cutSsig_flat
corecU_def = let val corecU_pointfree = derive_corecU_pointfree ctxt Y Z preT fpT ssig_T dead_pre_map dtor extdd
corecU g dead_pre_map_comp dtor_unfold_thm ssig_map_thms dead_ssig_map_comp0 flat_simps
flat_VLeaf eval_core_simps cutSsig_def mor_cutSsig_flat corecU_def;
val corecU_thm = corecU_pointfree RS @{thm comp_eq_dest};
val corecU_ctor = let val arg_cong' =
infer_instantiate' ctxt [NONE, NONE, SOME (Thm.cterm_of ctxt ctor)] arg_cong; in
unfold_thms ctxt [ctor_dtor] (corecU_thm RS arg_cong') end;
val corecU_unique = let val substYZ = Term.subst_atomic_types [(Y, ssig_T), (Z, fpT)];
val f' = substYZ f; val abs_f_o_VLeaf = Term.lambda f' (HOLogic.mk_comp (f', VLeaf));
val inject_refine' = infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt abs_f_o_VLeaf),
SOME (Thm.cterm_of ctxt extdd)] @{thm inject_refine}; in
unfold_thms ctxt @{thms atomize_imp}
(((inject_refine' OF [extdd_o_VLeaf, extdd_o_VLeaf] RS iffD1) OF [asm_rl, corecU_pointfree]) OF [asm_rl, trans OF [dtor_unfold_unique, dtor_unfold_unique RS sym] OF [extdd_mor, corecU_pointfree RS extdd_mor]])
RS @{thm obj_distinct_prems} end; in
(corecU_ctor, corecU_unique) end;
fun derive_dtor_algLam ctxt Y Z preT fpT sig_T ssig_T dead_pre_map dtor dead_sig_map Lam eval algLam
x pre_map_comp dead_pre_map_id dead_pre_map_comp0 dead_pre_map_comp sig_map_comp
Oper_pointful_natural ssig_map_thms dead_ssig_map_comp0 Lam_pointful_natural eval_core_simps
eval_thm eval_flat eval_VLeaf algLam_def = let val fp_preT = Tsubst Y fpT preT; val fppreT = HOLogic.mk_prodT (fpT, fp_preT); val fp_sig_T = Tsubst Y fpT sig_T; val fp_ssig_T = Tsubst Y fpT ssig_T;
val id' = HOLogic.id_const fpT; val convol' = mk_convol (id', dtor); val dead_pre_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_pre_map; val dead_sig_map' = Term.subst_atomic_types [(Y, fpT), (Z, fppreT)] dead_sig_map; val Lam' = substT Y fpT Lam; val x' = substT Y fp_sig_T x;
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;
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 old_ssig_induct' =
infer_instantiate' ctxt [NONE, SOME (Thm.cterm_of ctxt x')] old_ssig_induct; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_flat_embL_tac ctxt old_ssig_induct' fp_map_id Sig_pointful_natural old_sig_map_comp
old_sig_map_cong old_ssig_map_thms old_flat_simps flat_simps embL_simps))
|> Thm.close_derivation \<^here> end;
fun derive_eval_core_embL ctxt Y Z preT old_ssig_T ssig_T dead_pre_map embL old_eval_core eval_core
x old_ssig_induct dead_pre_map_comp0 dead_pre_map_comp Sig_pointful_natural unsig_thm
old_sig_map_comp old_sig_map_cong old_Lam_pointful_natural Lam_def flat_embL embL_simps
embL_pointful_natural old_eval_core_simps eval_core_simps = let val YpreT = HOLogic.mk_prodT (Y, preT); val Ypre_old_ssig_T = Tsubst Y YpreT old_ssig_T;
val dead_pre_map' = Term.subst_atomic_types [(Y, old_ssig_T), (Z, ssig_T)] dead_pre_map; val embL' = substT Y YpreT embL; val x' = substT Y Ypre_old_ssig_T x;
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;
fun derive_algLam_algrho ctxt Y fpT Sig algLam algrho algLam_def algrho_def = let valSig' = substT Y fpT Sig; val (left_T, right_T) = dest_sumT (domain_type (fastype_of Sig')); val inr' = Inr_const left_T right_T;
val goal = mk_Trueprop_eq (Library.foldl1 HOLogic.mk_comp [algLam, Sig', inr'], algrho); in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_algLam_algrho_tac ctxt algLam_def algrho_def))
|> Thm.close_derivation \<^here> end;
fun derive_dtor_algrho ctxt Y Z preT fpT k_T ssig_T dead_pre_map dead_k_map dtor rho eval algrho x
eval_thm k_as_ssig_natural_pointful eval_core_k_as_ssig algrho_def = let val YpreT = HOLogic.mk_prodT (Y, preT); val fppreT = Tsubst Y fpT YpreT; val fp_k_T = Tsubst Y fpT k_T; val fp_ssig_T = Tsubst Y fpT ssig_T;
val id' = HOLogic.id_const fpT; val convol' = mk_convol (id', dtor); val dead_pre_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_pre_map; val dead_k_map' = Term.subst_atomic_types [(Y, fpT), (Z, fppreT)] dead_k_map; val rho' = substT Y fpT rho; val x' = substT Y fp_k_T x;
fun derive_algLam_step_or_merge ctxt Y fpT ctor proto_sctr algLam proto_sctr_def old_algLam_pointful
algLam_algLam = let val proto_sctr' = substT Y fpT proto_sctr; val goal = mk_Trueprop_eq (HOLogic.mk_comp (algLam, proto_sctr'), ctor);
val algLam_algLam_pointful = mk_pointful ctxt algLam_algLam; in
Variable.add_free_names ctxt goal []
|> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, prems = _} =>
mk_algLam_step_tac ctxt proto_sctr_def old_algLam_pointful algLam_algLam_pointful))
|> Thm.close_derivation \<^here> end;
fun derive_eval_sctr ctxt Y Z fpT ssig_T dead_pre_map ctor eval sctr proto_sctr_pointful_natural
eval_Oper algLam_thm sctr_def = let val fp_ssig_T = Tsubst Y fpT ssig_T;
val dead_pre_map' = Term.subst_atomic_types [(Y, fp_ssig_T), (Z, fpT)] dead_pre_map; val sctr' = substT Y fpT sctr;
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';
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