| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/Isabelle/HOL/Tools/BNF/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 122 kB |
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Quelle bnf_fp_def_sugar.MLSprache: SML |
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(* Title: HOL/Tools/BNF/bnf_fp_def_sugar.ML Author: Jasmin Blanchette, TU Muenchen Author: Martin Desharnais, TU Muenchen Copyright 2012, 2013, 2014 Sugared datatype and codatatype constructions. *) signature BNF_FP_DEF_SUGAR = sig type fp_ctr_sugar = {ctrXs_Tss: typ list list, ctor_iff_dtor: thm, ctr_defs: thm list, ctr_sugar: Ctr_Sugar.ctr_sugar, ctr_transfers: thm list, case_transfers: thm list, disc_transfers: thm list, sel_transfers: thm list} type fp_bnf_sugar = {map_thms: thm list, map_disc_iffs: thm list, map_selss: thm list list, rel_injects: thm list, rel_distincts: thm list, rel_sels: thm list, rel_intros: thm list, rel_cases: thm list, pred_injects: thm list, set_thms: thm list, set_selssss: thm list list list list, set_introssss: thm list list list list, set_cases: thm list} type fp_co_induct_sugar = {co_rec: term, common_co_inducts: thm list, co_inducts: thm list, co_rec_def: thm, co_rec_thms: thm list, co_rec_discs: thm list, co_rec_disc_iffs: thm list, co_rec_selss: thm list list, co_rec_codes: thm list, co_rec_transfers: thm list, co_rec_o_maps: thm list, common_rel_co_inducts: thm list, rel_co_inducts: thm list, common_set_inducts: thm list, set_inducts: thm list} type fp_sugar = {T: typ, BT: typ, X: typ, fp: BNF_Util.fp_kind, fp_res_index: int, fp_res: BNF_FP_Util.fp_result, pre_bnf: BNF_Def.bnf, fp_bnf: BNF_Def.bnf, absT_info: BNF_Comp.absT_info, fp_nesting_bnfs: BNF_Def.bnf list, live_nesting_bnfs: BNF_Def.bnf list, fp_ctr_sugar: fp_ctr_sugar, fp_bnf_sugar: fp_bnf_sugar, fp_co_induct_sugar: fp_co_induct_sugar option} val co_induct_of: 'a list -> 'a val strong_co_induct_of: 'a list -> 'a val morph_fp_bnf_sugar: morphism -> fp_bnf_sugar -> fp_bnf_sugar val morph_fp_co_induct_sugar: morphism -> fp_co_induct_sugar -> fp_co_induct_sugar val morph_fp_ctr_sugar: morphism -> fp_ctr_sugar -> fp_ctr_sugar val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar val transfer_fp_sugar: theory -> fp_sugar -> fp_sugar val fp_sugar_of: Proof.context -> string -> fp_sugar option val fp_sugar_of_global: theory -> string -> fp_sugar option val fp_sugars_of: Proof.context -> fp_sugar list val fp_sugars_of_global: theory -> fp_sugar list val fp_sugars_interpretation: string -> (fp_sugar list -> local_theory -> local_theory) -> theory -> theory val interpret_fp_sugars: (string -> bool) -> fp_sugar list -> local_theory -> local_theory val register_fp_sugars_raw: fp_sugar list -> local_theory -> local_theory val register_fp_sugars: (string -> bool) -> fp_sugar list -> local_theory -> local_theory val merge_type_args: BNF_Util.fp_kind -> ''a list * ''a list -> ''a list val type_args_named_constrained_of_spec: (((('a * 'b) * 'c) * 'd) * 'e) * 'f -> 'a val type_binding_of_spec: (((('a * 'b) * 'c) * 'd) * 'e) * 'f -> 'b val mixfix_of_spec: ((('a * 'b) * 'c) * 'd) * 'e -> 'b val mixfixed_ctr_specs_of_spec: (('a * 'b) * 'c) * 'd -> 'b val map_binding_of_spec: ('a * ('b * 'c * 'd)) * 'e -> 'b val rel_binding_of_spec: ('a * ('b * 'c * 'd)) * 'e -> 'c val pred_binding_of_spec: ('a * ('b * 'c * 'd)) * 'e -> 'd val sel_default_eqs_of_spec: 'a * 'b -> 'b val mk_parametricity_goal: Proof.context -> term list -> term -> term -> term val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list -> 'a list val mk_ctor: typ list -> term -> term val mk_dtor: typ list -> term -> term val mk_bnf_sets: BNF_Def.bnf -> string * term list val liveness_of_fp_bnf: int -> BNF_Def.bnf -> bool list val nesting_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list val massage_simple_notes: string -> (bstring * 'a list * (int -> 'b)) list -> ((binding * 'c list) * ('a list * 'b) list) list val massage_multi_notes: string list -> typ list -> (string * 'a list list * (string -> 'b)) list -> ((binding * 'b) * ('a list * 'c list) list) list val define_ctrs_dtrs_for_type: string -> typ -> term -> term -> thm -> thm -> int -> int list -> term -> binding list -> mixfix list -> typ list list -> local_theory -> (term list list * term list * thm * thm list) * local_theory val wrap_ctrs: (string -> bool) -> BNF_Util.fp_kind -> bool -> string -> thm -> int -> int list -> thm -> thm -> binding list -> binding list list -> term list -> term list -> thm -> thm list -> local_theory -> Ctr_Sugar.ctr_sugar * local_theory val derive_map_set_rel_pred_thms: (string -> bool) -> BNF_Util.fp_kind -> int -> typ list -> typ list -> typ -> typ -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> string -> BNF_Def.bnf -> BNF_Def.bnf list -> typ -> term -> thm -> thm -> thm -> thm list -> thm -> thm -> thm list -> thm -> thm list -> thm list -> thm list -> typ list list -> Ctr_Sugar.ctr_sugar -> local_theory -> (thm list * thm list * thm list list * thm list * thm list * thm list * thm list * thm list * thm list * thm list * thm list list list list * thm list list list list * thm list * thm list * thm list * thm list * thm list) * local_theory type lfp_sugar_thms = (thm list * thm * Token.src list) * (thm list list * Token.src list) val morph_lfp_sugar_thms: morphism -> lfp_sugar_thms -> lfp_sugar_thms val transfer_lfp_sugar_thms: theory -> lfp_sugar_thms -> lfp_sugar_thms type gfp_sugar_thms = ((thm list * thm) list * (Token.src list * Token.src list)) * thm list list * thm list list * (thm list list * Token.src list) * (thm list list list * Token.src list) val morph_gfp_sugar_thms: morphism -> gfp_sugar_thms -> gfp_sugar_thms val transfer_gfp_sugar_thms: theory -> gfp_sugar_thms -> gfp_sugar_thms val mk_co_recs_prelims: Proof.context -> BNF_Util.fp_kind -> typ list list list -> typ list -> typ list -> typ list -> typ list -> int list -> int list list -> term list -> term list * (typ list list * typ list list list list * term list list * term list list list list) option * (string * term list * term list list * (((term list list * term list list * term list list list list * term list list list list) * term list list list) * typ list)) option val repair_nullary_single_ctr: typ list list -> typ list list val mk_corec_p_pred_types: typ list -> int list -> typ list list val mk_corec_fun_arg_types: typ list list list -> typ list -> typ list -> typ list -> int list -> int list list -> term -> typ list list * (typ list list list list * typ list list list * typ list list list list * typ list) val define_co_rec_as: BNF_Util.fp_kind -> typ list -> typ -> binding -> term -> local_theory -> (term * thm) * local_theory val define_rec: typ list list * typ list list list list * term list list * term list list list list -> (string -> binding) -> typ list -> typ list -> term list -> term -> Proof.context -> (term * thm) * Proof.context val define_corec: 'a * term list * term list list * (((term list list * term list list * term list list list list * term list list list list) * term list list list) * typ list) -> (string -> binding) -> 'b list -> typ list -> term list -> term -> local_theory -> (term * thm) * local_theory val mk_induct_raw_prem: (term -> term) -> Proof.context -> typ list list -> (string * term list) list -> term -> term -> typ list -> typ list -> term list * ((term * (term * term)) list * (int * term)) list * term val finish_induct_prem: Proof.context -> int -> term list -> term list * ((term * (term * term)) list * (int * term)) list * term -> term val mk_coinduct_prem: Proof.context -> typ list list -> typ list list -> term list -> term -> term -> term -> int -> term list -> term list list -> term list -> term list list -> typ list list -> term val mk_induct_attrs: term list list -> Token.src list val mk_coinduct_attrs: typ list -> term list list -> term list list -> int list list -> Token.src list * Token.src list val derive_induct_recs_thms_for_types: (string -> bool) -> BNF_Def.bnf list -> ('a * typ list list list list * term list list * 'b) option -> thm -> thm list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list -> typ list -> typ list list list -> thm list -> thm list -> thm list -> term list list -> thm list list -> term list -> thm list -> Proof.context -> lfp_sugar_thms val derive_coinduct_thms_for_types: Proof.context -> bool -> (term -> term) -> BNF_Def.bnf list thm -> thm list -> BNF_Def.bnf list -> typ list -> typ list -> typ list list list -> int list -> thm list -> thm list -> (thm -> thm) -> thm list list -> Ctr_Sugar.ctr_sugar list -> (thm list * thm) list val derive_coinduct_corecs_thms_for_types: Proof.context -> BNF_Def.bnf list -> string * term list * term list list * (((term list list * term list list * term list list list list * term list list list list) * term list list list) * typ list) -> thm -> thm list -> thm list -> thm list -> BNF_Def.bnf list -> typ list -> typ list -> typ list -> typ list list list -> int list list -> int list list -> int list -> thm list -> thm list -> (thm -> thm) -> thm list list -> Ctr_Sugar.ctr_sugar list -> term list -> thm list -> gfp_sugar_thms val co_datatypes: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list -> binding list -> binding list list -> binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory -> BNF_FP_Util.fp_result * local_theory) -> Ctr_Sugar.ctr_options * ((((((binding option * (typ * sort)) list * binding) * mixfix) * ((binding, binding * typ) Ctr_Sugar.ctr_spec * mixfix) list) * (binding * binding * binding)) * term list) list -> local_theory -> local_theory val co_datatype_cmd: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list -> binding list -> binding list list -> binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory -> BNF_FP_Util.fp_result * Proof.context) -> ((Proof.context -> Plugin_Name.filter) * bool) * ((((((binding option * (string * string option)) list * binding) * mixfix) * ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list) * (binding * binding * binding)) * string list) list -> Proof.context -> local_theory val parse_ctr_arg: (binding * string) parser val parse_ctr_specs: ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list parser val parse_spec: ((((((binding option * (string * string option)) list * binding) * mixfix) * ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list) * (binding * binding * binding)) * string list) parser val parse_co_datatype: (Ctr_Sugar.ctr_options_cmd * ((((((binding option * (string * string option)) list * binding) * mixfix) * ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list) * (binding * binding * binding)) * string list) list) parser val parse_co_datatype_cmd: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list -> binding list -> binding list list -> binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory -> BNF_FP_Util.fp_result * local_theory) -> (local_theory -> local_theory) parser end; structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR = struct open Ctr_Sugar open BNF_FP_Rec_Sugar_Util open BNF_Util open BNF_Comp open BNF_Def open BNF_FP_Util open BNF_FP_Def_Sugar_Tactics val Eq_prefix = "Eq_"; val case_transferN = "case_transfer"; val ctor_iff_dtorN = "ctor_iff_dtor"; val ctr_transferN = "ctr_transfer"; val disc_transferN = "disc_transfer"; val sel_transferN = "sel_transfer"; val corec_codeN = "corec_code"; val corec_transferN = "corec_transfer"; val map_disc_iffN = "map_disc_iff"; val map_o_corecN = "map_o_corec"; val map_selN = "map_sel"; val pred_injectN = "pred_inject"; val rec_o_mapN = "rec_o_map"; val rec_transferN = "rec_transfer"; val set0N = "set0"; val set_casesN = "set_cases"; val set_introsN = "set_intros"; val set_inductN = "set_induct"; val set_selN = "set_sel"; type fp_ctr_sugar = {ctrXs_Tss: typ list list, ctor_iff_dtor: thm, ctr_defs: thm list, ctr_sugar: Ctr_Sugar.ctr_sugar, ctr_transfers: thm list, case_transfers: thm list, disc_transfers: thm list, sel_transfers: thm list}; type fp_bnf_sugar = {map_thms: thm list, map_disc_iffs: thm list, map_selss: thm list list, rel_injects: thm list, rel_distincts: thm list, rel_sels: thm list, rel_intros: thm list, rel_cases: thm list, pred_injects: thm list, set_thms: thm list, set_selssss: thm list list list list, set_introssss: thm list list list list, set_cases: thm list}; type fp_co_induct_sugar = {co_rec: term, common_co_inducts: thm list, co_inducts: thm list, co_rec_def: thm, co_rec_thms: thm list, co_rec_discs: thm list, co_rec_disc_iffs: thm list, co_rec_selss: thm list list, co_rec_codes: thm list, co_rec_transfers: thm list, co_rec_o_maps: thm list, common_rel_co_inducts: thm list, rel_co_inducts: thm list, common_set_inducts: thm list, set_inducts: thm list}; type fp_sugar = {T: typ, BT: typ, X: typ, fp: fp_kind, fp_res_index: int, fp_res: fp_result, pre_bnf: bnf, fp_bnf: bnf, absT_info: absT_info, fp_nesting_bnfs: bnf list, live_nesting_bnfs: bnf list, fp_ctr_sugar: fp_ctr_sugar, fp_bnf_sugar: fp_bnf_sugar, fp_co_induct_sugar: fp_co_induct_sugar option}; fun co_induct_of (i :: _) = i; fun strong_co_induct_of [_, s] = s; fun morph_fp_bnf_sugar phi ({map_thms, map_disc_iffs, map_selss, rel_injects, rel_disti rel_sels, rel_intros, rel_cases, pred_injects, set_thms, set_selssss, set_introssss, set_cases} : fp_bnf_sugar) = {map_thms = map (Morphism.thm phi) map_thms, map_disc_iffs = map (Morphism.thm phi) map_disc_iffs, map_selss = map (map (Morphism.thm phi)) map_selss, rel_injects = map (Morphism.thm phi) rel_injects, rel_distincts = map (Morphism.thm phi) rel_distincts, rel_sels = map (Morphism.thm phi) rel_sels, rel_intros = map (Morphism.thm phi) rel_intros, rel_cases = map (Morphism.thm phi) rel_cases, pred_injects = map (Morphism.thm phi) pred_injects, set_thms = map (Morphism.thm phi) set_thms, set_selssss = map (map (map (map (Morphism.thm phi)))) set_selssss, set_introssss = map (map (map (map (Morphism.thm phi)))) set_introssss, set_cases = map (Morphism.thm phi) set_cases}; fun morph_fp_co_induct_sugar phi ({co_rec, common_co_inducts, co_inducts, co_rec_def, c co_rec_discs, co_rec_disc_iffs, co_rec_selss, co_rec_codes, co_rec_transfers, co_rec_ common_rel_co_inducts, rel_co_inducts, common_set_inducts, set_inducts} : fp_co_induc {co_rec = Morphism.term phi co_rec, common_co_inducts = map (Morphism.thm phi) common_co_inducts, co_inducts = map (Morphism.thm phi) co_inducts, co_rec_def = Morphism.thm phi co_rec_def, co_rec_thms = map (Morphism.thm phi) co_rec_thms, co_rec_discs = map (Morphism.thm phi) co_rec_discs, co_rec_disc_iffs = map (Morphism.thm phi) co_rec_disc_iffs, co_rec_selss = map (map (Morphism.thm phi)) co_rec_selss, co_rec_codes = map (Morphism.thm phi) co_rec_codes, co_rec_transfers = map (Morphism.thm phi) co_rec_transfers, co_rec_o_maps = map (Morphism.thm phi) co_rec_o_maps, common_rel_co_inducts = map (Morphism.thm phi) common_rel_co_inducts, rel_co_inducts = map (Morphism.thm phi) rel_co_inducts, common_set_inducts = map (Morphism.thm phi) common_set_inducts, set_inducts = map (Morphism.thm phi) set_inducts}; fun morph_fp_ctr_sugar phi ({ctrXs_Tss, ctor_iff_dtor, ctr_defs, ctr_sugar, ctr_transfe case_transfers, disc_transfers, sel_transfers} : fp_ctr_sugar) = {ctrXs_Tss = map (map (Morphism.typ phi)) ctrXs_Tss, ctor_iff_dtor = Morphism.thm phi ctor_iff_dtor, ctr_defs = map (Morphism.thm phi) ctr_defs, ctr_sugar = morph_ctr_sugar phi ctr_sugar, ctr_transfers = map (Morphism.thm phi) ctr_transfers, case_transfers = map (Morphism.thm phi) case_transfers, disc_transfers = map (Morphism.thm phi) disc_transfers, sel_transfers = map (Morphism.thm phi) sel_transfers}; fun morph_fp_sugar phi ({T, BT, X, fp, fp_res, fp_res_index, pre_bnf, fp_bnf, absT_info, fp_nesting_bnfs, live_nesting_bnfs, fp_ctr_sugar, fp_bnf_sugar, fp_co_induct_sugar} : fp_sugar) = {T = Morphism.typ phi T, BT = Morphism.typ phi BT, X = Morphism.typ phi X, fp = fp, fp_res = morph_fp_result phi fp_res, fp_res_index = fp_res_index, pre_bnf = morph_bnf phi pre_bnf, fp_bnf = morph_bnf phi fp_bnf, absT_info = morph_absT_info phi absT_info, fp_nesting_bnfs = map (morph_bnf phi) fp_nesting_bnfs, live_nesting_bnfs = map (morph_bnf phi) live_nesting_bnfs, fp_ctr_sugar = morph_fp_ctr_sugar phi fp_ctr_sugar, fp_bnf_sugar = morph_fp_bnf_sugar phi fp_bnf_sugar, fp_co_induct_sugar = Option.map (morph_fp_co_induct_sugar phi) fp_co_induct_sugar}; val transfer_fp_sugar = morph_fp_sugar o Morphism.transfer_morphism; structure Data = Generic_Data ( type T = fp_sugar Symtab.table; val empty = Symtab.empty; fun merge data : T = Symtab.merge (K true) data; ); fun fp_sugar_of_generic context = Option.map (transfer_fp_sugar (Context.theory_of context)) o Symtab.lookup (Data.get co fun fp_sugars_of_generic context = Symtab.fold (cons o transfer_fp_sugar (Context.theory_of context) o snd) (Data.get contex val fp_sugar_of = fp_sugar_of_generic o Context.Proof; val fp_sugar_of_global = fp_sugar_of_generic o Context.Theory; val fp_sugars_of = fp_sugars_of_generic o Context.Proof; val fp_sugars_of_global = fp_sugars_of_generic o Context.Theory; structure FP_Sugar_Plugin = Plugin(type T = fp_sugar list); fun fp_sugars_interpretation name f = FP_Sugar_Plugin.interpretation name (fn fp_sugars => fn lthy => f (map (transfer_fp_sugar (Proof_Context.theory_of lthy)) fp_sugars) lthy); val interpret_fp_sugars = FP_Sugar_Plugin.data; val register_fp_sugars_raw = fold (fn fp_sugar as {T = Type (s, _), ...} => Local_Theory.declaration {syntax = false, pervasive = true, pos = \<^here>} (fn phi => Data.map (Symtab.update (s, morph_fp_sugar phi fp_sugar)))); fun register_fp_sugars plugins fp_sugars = register_fp_sugars_raw fp_sugars #> interpret_fp_sugars plugins fp_sugars; fun interpret_bnfs_register_fp_sugars plugins Ts BTs Xs fp pre_bnfs absT_infos fp_nesting live_nesting_bnfs fp_res ctrXs_Tsss ctor_iff_dtors ctr_defss ctr_sugars co_recs co_rec_ map_thmss common_co_inducts co_inductss co_rec_thmss co_rec_discss co_rec_selsss rel_i rel_distinctss map_disc_iffss map_selsss rel_selss rel_intross rel_casess pred_injects set_thmss set_selsssss set_introsssss set_casess ctr_transferss case_transferss disc_t sel_transferss co_rec_disc_iffss co_rec_codess co_rec_transferss common_rel_co_induc rel_co_inductss common_set_inducts set_inductss co_rec_o_mapss noted = let val fp_sugars = map_index (fn (kk, T) => {T = T, BT = nth BTs kk, X = nth Xs kk, fp = fp, fp_res = fp_res, fp_res_index = kk, pre_bnf = nth pre_bnfs kk, absT_info = nth absT_infos kk, fp_bnf = nth (#bnfs fp_res) kk, fp_nesting_bnfs = fp_nesting_bnfs, live_nesting_bnfs = live_nesting_bnfs, fp_ctr_sugar = {ctrXs_Tss = nth ctrXs_Tsss kk, ctor_iff_dtor = nth ctor_iff_dtors kk, ctr_defs = nth ctr_defss kk, ctr_sugar = nth ctr_sugars kk, ctr_transfers = nth ctr_transferss kk, case_transfers = nth case_transferss kk, disc_transfers = nth disc_transferss kk, sel_transfers = nth sel_transferss kk}, fp_bnf_sugar = {map_thms = nth map_thmss kk, map_disc_iffs = nth map_disc_iffss kk, map_selss = nth map_selsss kk, rel_injects = nth rel_injectss kk, rel_distincts = nth rel_distinctss kk, rel_sels = nth rel_selss kk, rel_intros = nth rel_intross kk, rel_cases = nth rel_casess kk, pred_injects = nth pred_injectss kk, set_thms = nth set_thmss kk, set_selssss = nth set_selsssss kk, set_introssss = nth set_introsssss kk, set_cases = nth set_casess kk}, fp_co_induct_sugar = SOME {co_rec = nth co_recs kk, common_co_inducts = common_co_inducts, co_inducts = nth co_inductss kk, co_rec_def = nth co_rec_defs kk, co_rec_thms = nth co_rec_thmss kk, co_rec_discs = nth co_rec_discss kk, co_rec_disc_iffs = nth co_rec_disc_iffss kk, co_rec_selss = nth co_rec_selsss kk, co_rec_codes = nth co_rec_codess kk, co_rec_transfers = nth co_rec_transferss kk, co_rec_o_maps = nth co_rec_o_mapss kk, common_rel_co_inducts = common_rel_co_inducts, rel_co_inducts = nth rel_co_inductss kk, common_set_inducts = common_set_inducts, set_inducts = nth set_inductss kk}} |> morph_fp_sugar (substitute_noted_thm noted)) Ts; in register_fp_sugars_raw fp_sugars #> fold (interpret_bnf plugins) (#bnfs fp_res) #> interpret_fp_sugars plugins fp_sugars end; fun quasi_unambiguous_case_names names = let val ps = map (`Long_Name.base_name) names; val dups = Library.duplicates (op =) (map fst ps); fun underscore s = let val ss = Long_Name.explode s in space_implode "_" (drop (length ss - 2) ss) end; in map (fn (base, full) => if member (op =) dups base then underscore full else base) ps |> Name.variant_list [] end; fun zipper_map f = let fun zed _ [] = [] | zed xs (y :: ys) = f (xs, y, ys) :: zed (xs @ [y]) ys; in zed [] end; fun cannot_merge_types fp = error ("Mutually " ^ co_prefix fp ^ "recursive types must have the same type parameters"); fun merge_type_arg fp T T' = if T = T' then T else cannot_merge_types fp; fun merge_type_args fp (As, As') = if length As = length As' then map2 (merge_type_arg fp) As As' else cannot_merge_types fp; fun type_args_named_constrained_of_spec (((((ncAs, _), _), _), _), _) = ncAs; fun type_binding_of_spec (((((_, b), _), _), _), _) = b; fun mixfix_of_spec ((((_, mx), _), _), _) = mx; fun mixfixed_ctr_specs_of_spec (((_, mx_ctr_specs), _), _) = mx_ctr_specs; fun map_binding_of_spec ((_, (b, _, _)), _) = b; fun rel_binding_of_spec ((_, (_, b, _)), _) = b; fun pred_binding_of_spec ((_, (_, _, b)), _) = b; fun sel_default_eqs_of_spec (_, ts) = ts; fun ctr_sugar_kind_of_fp_kind Least_FP = Datatype | ctr_sugar_kind_of_fp_kind Greatest_FP = Codatatype; fun uncurry_thm 0 thm = thm | uncurry_thm 1 thm = thm | uncurry_thm n thm = rotate_prems ~1 (uncurry_thm (n - 1) (rotate_prems 1 (conjI RS thm))); fun choose_binary_fun fs AB = find_first (fastype_of #> binder_types #> (fn [A, B] => AB = (A, B))) fs; fun build_binary_fun_app fs t u = Option.map (rapp u o rapp t) (choose_binary_fun fs (fastype_of t, fastype_of u)); fun build_the_rel ctxt Rs Ts A B = build_rel [] ctxt Ts [] (the o choose_binary_fun Rs) (A, B); fun build_rel_app ctxt Rs Ts t u = build_the_rel ctxt Rs Ts (fastype_of t) (fastype_of u) $ t $ u; fun build_set_app ctxt A t = Term.betapply (build_set ctxt A (fastype_of t), t); fun mk_parametricity_goal ctxt Rs t u = let val prem = build_the_rel ctxt Rs [] (fastype_of t) (fastype_of u) in HOLogic.mk_Trueprop (prem $ t $ u) end; val name_of_set = name_of_const "set function" domain_type; val fundefcong_attrs = @{attributes [fundef_cong]}; val nitpicksimp_attrs = @{attributes [nitpick_simp]}; val simp_attrs = @{attributes [simp]}; val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)); fun flat_corec_predss_getterss qss gss = maps (op @) (qss ~~ gss); fun flat_corec_preds_predsss_gettersss [] [qss] [gss] = flat_corec_predss_getterss qss g | flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (gss :: gsss) = p :: flat_corec_predss_getterss qss gss @ flat_corec_preds_predsss_gettersss ps qsss gsss fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) = Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1)); fun flip_rels ctxt n thm = let val Rs = Term.add_vars (Thm.prop_of thm) []; val Rs' = rev (drop (length Rs - n) Rs); in infer_instantiate ctxt (map (fn f => (fst f, Thm.cterm_of ctxt (mk_flip f))) Rs') thm end; fun mk_ctor_or_dtor get_T Ts t = let val Type (_, Ts0) = get_T (fastype_of t) in Term.subst_atomic_types (Ts0 ~~ Ts) t end; val mk_ctor = mk_ctor_or_dtor range_type; val mk_dtor = mk_ctor_or_dtor domain_type; fun mk_bnf_sets bnf = let val Type (T_name, Us) = T_of_bnf bnf; val lives = lives_of_bnf bnf; val sets = sets_of_bnf bnf; fun mk_set U = (case find_index (curry (op =) U) lives of ~1 => Term.dummy | i => nth sets i); in (T_name, map mk_set Us) end; fun mk_xtor_co_recs thy fp fpTs Cs ts0 = let val nn = length fpTs; val (fpTs0, Cs0) = map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0 |> split_list; val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs); in map (Term.subst_TVars rho) ts0 end; fun liveness_of_fp_bnf n bnf = (case T_of_bnf bnf of Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts | _ => replicate n false); fun add_nesting_bnf_names Us = let fun add (Type (s, Ts)) ss = let val (needs, ss') = fold_map add Ts ss in if exists I needs then (true, insert (op =) s ss') else (false, ss') end | add T ss = (member (op =) Us T, ss); in snd oo add end; fun nesting_bnfs ctxt ctr_Tsss Us = map_filter (bnf_of ctxt) (fold (fold (fold (add_nesting_bnf_names Us))) ctr_Tsss []); fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p; fun massage_simple_notes base = filter_out (null o #2) #> map (fn (thmN, thms, f_attrs) => ((Binding.qualify true base (Binding.name thmN), []), map_index (fn (i, thm) => ([thm], f_attrs i)) thms)); fun massage_multi_notes b_names Ts = maps (fn (thmN, thmss, attrs) => @{map 3} (fn b_name => fn Type (T_name, _) => fn thms => ((Binding.qualify true b_name (Binding.name thmN), attrs T_name), [(thms, [])])) b_names Ts thmss) #> filter_out (null o fst o hd o snd); fun define_ctrs_dtrs_for_type fp_b_name fpT ctor dtor ctor_dtor dtor_ctor n ks abs ctr_bind ctr_mixfixes ctr_Tss lthy = let val ctor_absT = domain_type (fastype_of ctor); val (((w, xss), u'), _) = lthy |> yield_singleton (mk_Frees "w") ctor_absT ||>> mk_Freess "x" ctr_Tss ||>> yield_singleton Variable.variant_fixes fp_b_name; val u = Free (u', fpT); val ctor_iff_dtor_thm = let val goal = fold_rev Logic.all [w, u] (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w))); val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, ...} => mk_ctor_iff_dtor_tac ctxt (map (SOME o Thm.ctyp_of lthy) [ctor_absT, fpT]) (Thm.cterm_of lthy ctor) (Thm.cterm_of lthy dtor) ctor_dtor dtor_ctor) |> Thm.close_derivation \<^here> end; val ctr_rhss = map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $ mk_absumprod ctor_absT abs n k xs)) ks xss; val ((raw_ctrs, raw_ctr_defs), (lthy, lthy_old)) = lthy |> (snd o Local_Theory.begin_nested) |> apfst split_list o @{fold_map 3} (fn b => fn mx => fn rhs => Local_Theory.define ((b, mx), ((Thm.make_def_binding (Config.get lthy bnf_internals) b, []), rhs)) #>> apsnd snd) ctr_bindings ctr_mixfixes ctr_rhss ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy_old lthy; val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; val ctrs0 = map (Morphism.term phi) raw_ctrs; in ((xss, ctrs0, ctor_iff_dtor_thm, ctr_defs), lthy) end; fun wrap_ctrs plugins fp discs_sels fp_b_name ctor_inject n ms abs_inject type_definition disc_bindings sel_bindingss sel_default_eqs ctrs0 ctor_iff_dtor_thm ctr_defs lthy = let val sumEN_thm' = unfold_thms lthy @{thms unit_all_eq1} (mk_absumprodE type_definition ms) fun exhaust_tac {context = ctxt, prems = _} = mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'; val inject_tacss = map2 (fn ctr_def => fn 0 => [] | _ => [fn {context = ctxt, ...} => mk_inject_tac ctxt ctr_def ctor_inject abs_inject]) ctr_defs ms; val half_distinct_tacss = map (map (fn (def, def') => fn {context = ctxt, ...} => mk_half_distinct_tac ctxt ctor_inject abs_inject [def, def'])) (mk_half_pairss (`I ctr_defs)); val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss; fun ctr_spec_of disc_b ctr0 sel_bs = ((disc_b, ctr0), sel_bs); val ctr_specs = @{map 3} ctr_spec_of disc_bindings ctrs0 sel_bindingss; val (ctr_sugar as {case_cong, ...}, lthy) = free_constructors (ctr_sugar_kind_of_fp_kind fp) tacss ((((plugins, discs_sels), standard_binding), ctr_specs), sel_default_eqs) lthy; val anonymous_notes = [([case_cong], fundefcong_attrs)] |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])])); val notes = if Config.get lthy bnf_internals then [(ctor_iff_dtorN, [ctor_iff_dtor_thm], K [])] |> massage_simple_notes fp_b_name else []; in (ctr_sugar, lthy |> Local_Theory.notes (anonymous_notes @ notes) |> snd) end; fun derive_map_set_rel_pred_thms plugins fp live As Bs C E abs_inverses ctr_defs fp_nesting fp_nesting_rel_eq_onps live_nesting_map_id0s live_nesting_set_maps live_nesting_rel live_nesting_rel_eq_onps fp_nested_rel_eq_onps fp_b_name fp_bnf fp_bnfs fpT ctor ctor_d dtor_ctor pre_map_def pre_set_defs pre_rel_def fp_map_thm fp_set_thms fp_rel_thm extra_unfolds_map extra_unfolds_set extra_unfolds_rel ctr_Tss ({casex, case_thms, discs, selss, sel_defs, ctrs, exhaust, exhaust_discs, disc_thmss, sel injects, distincts, distinct_discsss, ...} : ctr_sugar) lthy = let val n = length ctr_Tss; val ms = map length ctr_Tss; val B_ify_T = Term.typ_subst_atomic (As ~~ Bs); val fpBT = B_ify_T fpT; val live_AsBs = filter (op <>) (As ~~ Bs); val live_As = map fst live_AsBs; val fTs = map (op -->) live_AsBs; val ((((((((xss, yss), fs), Ps), Rs), ta), tb), thesis), names_lthy) = lthy |> fold (fold Variable.declare_typ) [As, Bs] |> mk_Freess "x" ctr_Tss ||>> mk_Freess "y" (map (map B_ify_T) ctr_Tss) ||>> mk_Frees "f" fTs ||>> mk_Frees "P" (map mk_pred1T live_As) ||>> mk_Frees "R" (map (uncurry mk_pred2T) live_AsBs) ||>> yield_singleton (mk_Frees "a") fpT ||>> yield_singleton (mk_Frees "b") fpBT ||>> apfst HOLogic.mk_Trueprop o yield_singleton (mk_Frees "thesis") HOLogic.boolT; val ctrAs = map (mk_ctr As) ctrs; val ctrBs = map (mk_ctr Bs) ctrs; val ctr_defs' = map2 (fn m => fn def => mk_unabs_def m (HOLogic.mk_obj_eq def)) ms ctr_defs; val ABfs = live_AsBs ~~ fs; fun derive_rel_case relAsBs rel_inject_thms rel_distinct_thms = let val rel_Rs_a_b = list_comb (relAsBs, Rs) $ ta $ tb; fun mk_assms ctrA ctrB ctxt = let val argA_Ts = binder_types (fastype_of ctrA); val argB_Ts = binder_types (fastype_of ctrB); val ((argAs, argBs), names_ctxt) = ctxt |> mk_Frees "x" argA_Ts ||>> mk_Frees "y" argB_Ts; val ctrA_args = list_comb (ctrA, argAs); val ctrB_args = list_comb (ctrB, argBs); in (fold_rev Logic.all (argAs @ argBs) (Logic.list_implies (mk_Trueprop_eq (ta, ctrA_args) :: mk_Trueprop_eq (tb, ctrB_args) :: map2 (HOLogic.mk_Trueprop oo build_rel_app lthy Rs []) argAs argBs, thesis)), names_ctxt) end; val (assms, names_lthy) = @{fold_map 2} mk_assms ctrAs ctrBs names_lthy; val goal = Logic.list_implies (HOLogic.mk_Trueprop rel_Rs_a_b :: assms, thesis); in Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => mk_rel_case_tac ctxt (Thm.cterm_of ctxt ta) (Thm.cterm_of ctxt tb) exhaust injects rel_inject_thms distincts rel_distinct_thms live_nesting_rel_eqs) |> singleton (Proof_Context.export names_lthy lthy) |> Thm.close_derivation \<^here> end; fun derive_case_transfer rel_case_thm = let val (S, names_lthy) = yield_singleton (mk_Frees "S") (mk_pred2T C E) names_lthy; val caseA = mk_case As C casex; val caseB = mk_case Bs E casex; val goal = mk_parametricity_goal names_lthy (S :: Rs) caseA caseB; in Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => mk_case_transfer_tac ctxt rel_case_thm case_thms) |> singleton (Proof_Context.export names_lthy lthy) |> Thm.close_derivation \<^here> end; in if live = 0 then if plugins transfer_plugin then let val relAsBs = HOLogic.eq_const fpT; val rel_case_thm = derive_rel_case relAsBs [] []; val case_transfer_thm = derive_case_transfer rel_case_thm; val notes = [(case_transferN, [case_transfer_thm], K [])] |> massage_simple_notes fp_b_name; val (noted, lthy') = lthy |> Local_Theory.notes notes; val subst = Morphism.thm (substitute_noted_thm noted); in (([], [], [], [], [], [], [], [], [], [], [], [], [], [], [subst case_transfer_thm], [], []), lthy') end else (([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []), lthy) else let val mapx = mk_map live As Bs (map_of_bnf fp_bnf); val relAsBs = mk_rel live As Bs (rel_of_bnf fp_bnf); val setAs = map (mk_set As) (sets_of_bnf fp_bnf); val discAs = map (mk_disc_or_sel As) discs; val discBs = map (mk_disc_or_sel Bs) discs; val selAss = map (map (mk_disc_or_sel As)) selss; val selBss = map (map (mk_disc_or_sel Bs)) selss; val map_ctor_thm = if fp = Least_FP then fp_map_thm else let val ctorA = mk_ctor As ctor; val ctorB = mk_ctor Bs ctor; val y_T = domain_type (fastype_of ctorA); val (y as Free (y_s, _), _) = lthy |> yield_singleton (mk_Frees "y") y_T; val ctor_cong = infer_instantiate' lthy [NONE, NONE, SOME (Thm.cterm_of lthy ctorB)] arg_cong; val fp_map_thm' = fp_map_thm |> infer_instantiate' lthy (replicate live NONE @ [SOME (Thm.cterm_of lthy (ctorA $ y))]) |> unfold_thms lthy [dtor_ctor]; in (fp_map_thm' RS ctor_cong RS (ctor_dtor RS sym RS trans)) |> Drule.generalize (Names.empty, Names.make1_set y_s) end; val map_thms = let fun mk_goal ctrA ctrB xs ys = let val fmap = list_comb (mapx, fs); fun mk_arg (x as Free (_, T)) (Free (_, U)) = if T = U then x else build_map lthy [] [] (the o AList.lookup (op =) ABfs) (T, U) $ x; val xs' = map2 mk_arg xs ys; in mk_Trueprop_eq (fmap $ list_comb (ctrA, xs), list_comb (ctrB, xs')) end; val goals = @{map 4} mk_goal ctrAs ctrBs xss yss; val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_map_tac ctxt abs_inverses pre_map_def map_ctor_thm live_nesting_map_id0s ctr_defs' extra_unfolds_map) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end; val set0_thms = let fun mk_goal A setA ctrA xs = let val sets = map (build_set_app lthy A) (filter (exists_subtype_in [A] o fastype_of) xs); in mk_Trueprop_eq (setA $ list_comb (ctrA, xs), (if null sets then HOLogic.mk_set A [] else Library.foldl1 mk_union sets)) end; val goals = @{map 2} (fn live_A => fn setA => map2 (mk_goal live_A setA) ctrAs xss) live_As setAs |> flat; in if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_set0_tac ctxt abs_inverses pre_set_defs dtor_ctor fp_set_thms fp_nesting_set_maps live_nesting_set_maps ctr_defs' extra_unfolds_set) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end end; val set_thms = set0_thms |> map (unfold_thms lthy @{thms insert_is_Un[THEN sym] Un_empty_left Un_insert_left}); val rel_ctor_thm = if fp = Least_FP then fp_rel_thm else let val ctorA = mk_ctor As ctor; val ctorB = mk_ctor Bs ctor; val y_T = domain_type (fastype_of ctorA); val z_T = domain_type (fastype_of ctorB); val ((y as Free (y_s, _), z as Free (z_s, _)), _) = lthy |> yield_singleton (mk_Frees "y") y_T ||>> yield_singleton (mk_Frees "z") z_T; in fp_rel_thm |> infer_instantiate' lthy (replicate live NONE @ [SOME (Thm.cterm_of lthy (ctorA $ y)), SOME (Thm.cterm_of lthy (ctorB $ z))]) |> unfold_thms lthy [dtor_ctor] |> Drule.generalize (Names.empty, Names.make2_set y_s z_s) end; val rel_inject_thms = let fun mk_goal ctrA ctrB xs ys = let val lhs = list_comb (relAsBs, Rs) $ list_comb (ctrA, xs) $ list_comb (ctrB, ys); val conjuncts = map2 (build_rel_app lthy Rs []) xs ys; in HOLogic.mk_Trueprop (if null conjuncts then lhs else HOLogic.mk_eq (lhs, Library.foldr1 HOLogic.mk_conj conjuncts)) end; val goals = @{map 4} mk_goal ctrAs ctrBs xss yss; val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_rel_tac ctxt abs_inverses pre_rel_def rel_ctor_thm live_nesting_rel_eqs ctr_defs' extra_unfolds_rel) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end; val half_rel_distinct_thmss = let fun mk_goal ((ctrA, xs), (ctrB, ys)) = HOLogic.mk_Trueprop (HOLogic.mk_not (list_comb (relAsBs, Rs) $ list_comb (ctrA, xs) $ list_comb (ctrB, ys))); val rel_infos = (ctrAs ~~ xss, ctrBs ~~ yss); val goalss = map (map mk_goal) (mk_half_pairss rel_infos); val goals = flat goalss; in unflat goalss (if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_rel_tac ctxt abs_inverses pre_rel_def rel_ctor_thm live_nesting_rel_eqs ctr_defs' extra_unfolds_rel) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end) end; val rel_flip = rel_flip_of_bnf fp_bnf; fun mk_other_half_rel_distinct_thm thm = flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2); val other_half_rel_distinct_thmss = map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss; val (rel_distinct_thms, _) = join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss; fun mk_rel_intro_thm m thm = uncurry_thm m (thm RS iffD2) handle THM _ => thm; val rel_intro_thms = map2 mk_rel_intro_thm ms rel_inject_thms; val rel_code_thms = map (fn thm => thm RS @{thm eq_False[THEN iffD2]}) rel_distinct_thms @ map2 (fn thm => fn 0 => thm RS @{thm eq_True[THEN iffD2]} | _ => thm) rel_inject_thms ms; val ctr_transfer_thms = let val goals = map2 (mk_parametricity_goal names_lthy Rs) ctrAs ctrBs; val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_ctr_transfer_tac ctxt rel_intro_thms live_nesting_rel_eqs) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end; val (set_cases_thms, set_cases_attrss) = let fun mk_prems assms elem t ctxt = (case fastype_of t of Type (type_name, xs) => (case bnf_of ctxt type_name of NONE => ([], ctxt) | SOME bnf => apfst flat (fold_map (fn set => fn ctxt => let val T = HOLogic.dest_setT (range_type (fastype_of set)); val new_var = not (T = fastype_of elem); val (x, ctxt') = if new_var then yield_singleton (mk_Frees "x") T ctxt else (elem, ctxt); in mk_prems (mk_Trueprop_mem (x, set $ t) :: assms) elem x ctxt' |>> map (new_var ? Logic.all x) end) (map (mk_set xs) (sets_of_bnf bnf)) ctxt)) | T => rpair ctxt (if T = fastype_of elem then [fold (curry Logic.mk_implies) assms thesis] else [])); in split_list (map (fn set => let val A = HOLogic.dest_setT (range_type (fastype_of set)); val (elem, names_lthy) = yield_singleton (mk_Frees "e") A names_lthy; val premss = map (fn ctr => let val (args, names_lthy) = mk_Frees "z" (binder_types (fastype_of ctr)) names_lthy; in flat (zipper_map (fn (prev_args, arg, next_args) => let val (args_with_elem, args_without_elem) = if fastype_of arg = A then (prev_args @ [elem] @ next_args, prev_args @ next_args) else `I (prev_args @ [arg] @ next_args); in mk_prems [mk_Trueprop_eq (ta, Term.list_comb (ctr, args_with_elem))] elem arg names_lthy |> fst |> map (fold_rev Logic.all args_without_elem) end) args) end) ctrAs; val goal = Logic.mk_implies (mk_Trueprop_mem (elem, set $ ta), thesis); val vars = Variable.add_free_names lthy goal []; val thm = Goal.prove_sorry lthy vars (flat premss) goal (fn {context = ctxt, prems} => mk_set_cases_tac ctxt (Thm.cterm_of ctxt ta) prems exhaust set_thms) |> Thm.close_derivation \<^here> |> rotate_prems ~1; val cases_set_attr = Attrib.internal \<^here> (K (Induct.cases_pred (name_of_set set))); val ctr_names = quasi_unambiguous_case_names (flat (map (uncurry mk_names o map_prod length name_of_ctr) (premss ~~ ctrAs))); in (* TODO: @{attributes [elim?]} *) (thm, [Attrib.consumes 1, cases_set_attr, Attrib.case_names ctr_names]) end) setAs) end; val (set_intros_thmssss, set_intros_thms) = let fun mk_goals A setA ctr_args t ctxt = (case fastype_of t of Type (type_name, innerTs) => (case bnf_of ctxt type_name of NONE => ([], ctxt) | SOME bnf => apfst flat (fold_map (fn set => fn ctxt => let val T = HOLogic.dest_setT (range_type (fastype_of set)); val (y, ctxt') = yield_singleton (mk_Frees "y") T ctxt; val assm = mk_Trueprop_mem (y, set $ t); in apfst (map (Logic.mk_implies o pair assm)) (mk_goals A setA ctr_args y ctxt') end) (map (mk_set innerTs) (sets_of_bnf bnf)) ctxt)) | T => (if T = A then [mk_Trueprop_mem (t, setA $ ctr_args)] else [], ctxt)); val (goalssss, _) = fold_map (fn set => let val A = HOLogic.dest_setT (range_type (fastype_of set)) in @{fold_map 2} (fn ctr => fn xs => fold_map (mk_goals A set (Term.list_comb (ctr, xs))) xs) ctrAs xss end) setAs lthy; val goals = flat (flat (flat goalssss)); in `(unflattt goalssss) (if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_set_intros_tac ctxt set0_thms) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end) end; val rel_sel_thms = let val n = length discAs; fun mk_conjunct n k discA selAs discB selBs = (if k = n then [] else [HOLogic.mk_eq (discA $ ta, discB $ tb)]) @ (if null selAs then [] else [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [discA $ ta, discB $ tb], Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app names_lthy Rs []) (map (rapp ta) selAs) (map (rapp tb) selBs)))]); val goals = if n = 0 then [] else [mk_Trueprop_eq (build_rel_app names_lthy Rs [] ta tb, (case flat (@{map 5} (mk_conjunct n) (1 upto n) discAs selAss discBs selBss) of [] => \<^term>\<open>True\<close> | conjuncts => Library.foldr1 HOLogic.mk_conj conjuncts))]; fun prove goal = Variable.add_free_names lthy goal [] |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_rel_sel_tac ctxt (Thm.cterm_of ctxt ta) (Thm.cterm_of ctxt tb) exhaust (flat disc_thmss) (flat sel_thmss) rel_inject_thms distincts rel_distinct_thms live_nesting_rel_eqs)) |> Thm.close_derivation \<^here>; in map prove goals end; val (rel_case_thm, rel_case_attrs) = let val thm = derive_rel_case relAsBs rel_inject_thms rel_distinct_thms; val ctr_names = quasi_unambiguous_case_names (map name_of_ctr ctrAs); in (thm, [Attrib.case_names ctr_names, Attrib.consumes 1] @ @{attributes [cases pred]}) end; val case_transfer_thm = derive_case_transfer rel_case_thm; val sel_transfer_thms = if null selAss then [] else let val shared_sels = foldl1 (uncurry (inter (op =))) (map (op ~~) (selAss ~~ selBss)); val goals = map (uncurry (mk_parametricity_goal names_lthy Rs)) shared_sels; in if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_sel_transfer_tac ctxt n sel_defs case_transfer_thm) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end end; val disc_transfer_thms = let val goals = map2 (mk_parametricity_goal names_lthy Rs) discAs discBs in if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_disc_transfer_tac ctxt (the_single rel_sel_thms) (the_single exhaust_discs) (flat (flat distinct_discsss))) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end end; val map_disc_iff_thms = let val discsB = map (mk_disc_or_sel Bs) discs; val discsA_t = map (fn disc1 => Term.betapply (disc1, ta)) discAs; fun mk_goal (discA_t, discB) = if head_of discA_t aconv HOLogic.Not orelse is_refl_bool discA_t then NONE else SOME (mk_Trueprop_eq (betapply (discB, (Term.list_comb (mapx, fs) $ ta)), discA_t)); val goals = map_filter mk_goal (discsA_t ~~ discsB); in if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_map_disc_iff_tac ctxt (Thm.cterm_of ctxt ta) exhaust (flat disc_thmss) map_thms) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end end; val (map_sel_thmss, map_sel_thms) = let fun mk_goal discA selA selB = let val prem = Term.betapply (discA, ta); val lhs = selB $ (Term.list_comb (mapx, fs) $ ta); val lhsT = fastype_of lhs; val map_rhsT = map_atyps (perhaps (AList.lookup (op =) (map swap live_AsBs))) lhsT; val map_rhs = build_map lthy [] [] (the o (AList.lookup (op =) (live_AsBs ~~ fs))) (map_rhsT, lhsT); val rhs = (case map_rhs of Const (\<^const_name>\<open>id\<close>, _) => selA $ ta | _ => map_rhs $ (selA $ ta)); val concl = mk_Trueprop_eq (lhs, rhs); in if is_refl_bool prem then concl else Logic.mk_implies (HOLogic.mk_Trueprop prem, concl) end; val goalss = @{map 3} (map2 o mk_goal) discAs selAss selBss; val goals = flat goalss; in `(unflat goalss) (if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_map_sel_tac ctxt (Thm.cterm_of ctxt ta) exhaust (flat disc_thmss) map_thms (flat sel_thmss) live_nesting_map_id0s) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end) end; val (set_sel_thmssss, set_sel_thms) = let fun mk_goal setA discA selA ctxt = let val prem = Term.betapply (discA, ta); val sel_rangeT = range_type (fastype_of selA); val A = HOLogic.dest_setT (range_type (fastype_of setA)); fun travese_nested_types t ctxt = (case fastype_of t of Type (type_name, innerTs) => (case bnf_of ctxt type_name of NONE => ([], ctxt) | SOME bnf => let fun seq_assm a set ctxt = let val T = HOLogic.dest_setT (range_type (fastype_of set)); val (x, ctxt') = yield_singleton (mk_Frees "x") T ctxt; val assm = mk_Trueprop_mem (x, set $ a); in travese_nested_types x ctxt' |>> map (Logic.mk_implies o pair assm) end; in fold_map (seq_assm t o mk_set innerTs) (sets_of_bnf bnf) ctxt |>> flat end) | T => if T = A then ([mk_Trueprop_mem (t, setA $ ta)], ctxt) else ([], ctxt)); val (concls, ctxt') = if sel_rangeT = A then ([mk_Trueprop_mem (selA $ ta, setA $ ta)], ctxt) else travese_nested_types (selA $ ta) ctxt; in if exists_subtype_in [A] sel_rangeT then if is_refl_bool prem then (concls, ctxt') else (map (Logic.mk_implies o pair (HOLogic.mk_Trueprop prem)) concls, ctxt') else ([], ctxt) end; val (goalssss, _) = fold_map (fn set => @{fold_map 2} (fold_map o mk_goal set) discAs selAss) setAs names_lthy; val goals = flat (flat (flat goalssss)); in `(unflattt goalssss) (if null goals then [] else let val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_set_sel_tac ctxt (Thm.cterm_of ctxt ta) exhaust (flat disc_thmss) (flat sel_thmss) set0_thms) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end) end; val pred_injects = let val rel_eq_onp_with_tops_of = Conv.fconv_rule (HOLogic.Trueprop_conv (Conv.arg1_conv (Conv.top_sweep_rewrs_conv @{thms eq_onp_top_eq_eq[symmetric, THEN eq_reflection]} lt val eq_onps = map rel_eq_onp_with_tops_of (map rel_eq_onp_of_bnf fp_bnfs @ fp_nesting_rel_eq_onps @ live_nesting_rel_eq_onps @ fp_nested_rel_eq_onps); val cTs = map (SOME o Thm.ctyp_of lthy) (maps (replicate 2) live_As); val cts = map (SOME o Thm.cterm_of lthy) (map mk_eq_onp Ps); val get_rhs = Thm.concl_of #> HOLogic.dest_Trueprop #> HOLogic.dest_eq #> snd; val pred_eq_onp_conj = List.foldr (fn (_, thm) => thm RS @{thm eq_onp_live_step}) @{thm refl[of True]}; fun predify_rel_inject rel_inject = let val conjuncts = try (get_rhs #> HOLogic.dest_conj) rel_inject |> the_default []; fun postproc thm = if null conjuncts then thm RS (@{thm eq_onp_same_args} RS iffD1) else @{thm box_equals} OF [thm, @{thm eq_onp_same_args}, pred_eq_onp_conj conjuncts |> unfold_thms lthy @{thms simp_thms(21)}]; in rel_inject |> Thm.instantiate' cTs cts |> Conv.fconv_rule (HOLogic.Trueprop_conv (Conv.arg_conv (Simplifier.rewrite_wrt lthy false @{thms eq_onp_top_eq_eq[symmetric, THEN eq_reflection]}))) |> unfold_thms lthy eq_onps |> postproc |> unfold_thms lthy @{thms top_conj} end; in rel_inject_thms |> map (unfold_thms lthy [@{thm conj_assoc}]) |> map predify_rel_inject |> Proof_Context.export names_lthy lthy end; val anonymous_notes = [(rel_code_thms, nitpicksimp_attrs)] |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])])); val notes = (if Config.get lthy bnf_internals then [(set0N, set0_thms, K [])] else []) @ [(case_transferN, [case_transfer_thm], K []), (ctr_transferN, ctr_transfer_thms, K []), (disc_transferN, disc_transfer_thms, K []), (sel_transferN, sel_transfer_thms, K []), (mapN, map_thms, K (nitpicksimp_attrs @ simp_attrs)), (map_disc_iffN, map_disc_iff_thms, K simp_attrs), (map_selN, map_sel_thms, K []), (pred_injectN, pred_injects, K simp_attrs), (rel_casesN, [rel_case_thm], K rel_case_attrs), (rel_distinctN, rel_distinct_thms, K simp_attrs), (rel_injectN, rel_inject_thms, K simp_attrs), (rel_introsN, rel_intro_thms, K []), (rel_selN, rel_sel_thms, K []), (setN, set_thms, K (case_fp fp nitpicksimp_attrs [] @ simp_attrs)), (set_casesN, set_cases_thms, nth set_cases_attrss), (set_introsN, set_intros_thms, K []), (set_selN, set_sel_thms, K [])] |> massage_simple_notes fp_b_name; val (noted, lthy') = lthy |> uncurry (Spec_Rules.add Binding.empty Spec_Rules.equational) (`(single o lhs_head_of o hd) map_thms) |> fp = Least_FP ? uncurry (Spec_Rules.add Binding.empty Spec_Rules.equational) (`(single o lhs_head_of o hd) rel_code_thms) |> uncurry (Spec_Rules.add Binding.empty Spec_Rules.equational) (`(single o lhs_head_of o hd) set0_thms) |> plugins code_plugin ? Code.declare_default_eqns (map (rpair true) (rel_code_thms @ map_t |> Local_Theory.notes (anonymous_notes @ notes); val subst = Morphism.thm (substitute_noted_thm noted); in ((map subst map_thms, map subst map_disc_iff_thms, map (map subst) map_sel_thmss, map subst rel_inject_thms, map subst rel_distinct_thms, map subst rel_sel_thms, map subst rel_intro_thms, [subst rel_case_thm], map subst pred_injects, map subst set_thms, map (map (map (map subst))) set_sel_thmssss, map (map (map (map subst))) set_intros_thmssss, map subst set_cases_thms, map subst ctr_transfer_thms, [subst case_transfer_thm], map subst disc_transfer_thms, map subst sel_transfer_thms), lthy') end end; type lfp_sugar_thms = (thm list * thm * Token.src list) * (thm list list * Token.src list); fun morph_lfp_sugar_thms phi ((inducts, induct, induct_attrs), (recss, rec_attrs)) = ((map (Morphism.thm phi) inducts, Morphism.thm phi induct, induct_attrs), (map (map (Morphism.thm phi)) recss, rec_attrs)) : lfp_sugar_thms; val transfer_lfp_sugar_thms = morph_lfp_sugar_thms o Morphism.transfer_morphism; type gfp_sugar_thms = ((thm list * thm) list * (Token.src list * Token.src list)) * thm list list * thm list list * (thm list list * Token.src list) * (thm list list list * Token.src list); fun morph_gfp_sugar_thms phi ((coinducts_pairs, coinduct_attrs_pair), corecss, corec_discss, (corec_disc_iffss, corec_disc_iff_attrs), (corec_selsss, corec_sel_attrs)) = ((map (apfst (map (Morphism.thm phi)) o apsnd (Morphism.thm phi)) coinducts_pairs, coinduct_attrs_pair), map (map (Morphism.thm phi)) corecss, map (map (Morphism.thm phi)) corec_discss, (map (map (Morphism.thm phi)) corec_disc_iffss, corec_disc_iff_attrs), (map (map (map (Morphism.thm phi))) corec_selsss, corec_sel_attrs)) : gfp_sugar_thms; val transfer_gfp_sugar_thms = morph_gfp_sugar_thms o Morphism.transfer_morphism; fun unzip_recT (Type (\<^type_name>\<open>prod\<close>, [_, TFree x])) (T as Type (\<^type_name>\<open>prod\<close>, Ts as [_, TFree y])) = if x = y then [T] else Ts | unzip_recT _ (Type (\<^type_name>\<open>prod\<close>, Ts as [_, TFree _])) = Ts | unzip_recT _ T = [T]; fun mk_recs_args_types ctxt ctr_Tsss Cs absTs repTs ns mss ctor_rec_fun_Ts = let val Css = map2 replicate ns Cs; val x_Tssss = @{map 6} (fn absT => fn repT => fn n => fn ms => fn ctr_Tss => fn ctor_rec_fun_T => map2 (map2 unzip_recT) ctr_Tss (dest_absumprodT absT repT n ms (domain_type ctor_rec_fun_T))) absTs repTs ns mss ctr_Tsss ctor_rec_fun_Ts; val x_Tsss' = map (map flat_rec_arg_args) x_Tssss; val f_Tss = map2 (map2 (curry (op --->))) x_Tsss' Css; val ((fss, xssss), _) = ctxt |> mk_Freess "f" f_Tss ||>> mk_Freessss "x" x_Tssss; in (f_Tss, x_Tssss, fss, xssss) end; fun unzip_corecT (Type (\<^type_name>\<open>sum\<close>, _)) T = [T] | unzip_corecT _ (Type (\<^type_name>\<open>sum\<close>, Ts)) = Ts | unzip_corecT _ T = [T]; (*avoid "'a itself" arguments in corecursors*) fun repair_nullary_single_ctr [[]] = [[HOLogic.unitT]] | repair_nullary_single_ctr Tss = Tss; fun mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts = let val ctr_Tsss' = map repair_nullary_single_ctr ctr_Tsss; val g_absTs = map range_type fun_Ts; val g_Tsss = map repair_nullary_single_ctr (@{map 5} dest_absumprodT absTs repTs ns mss g_absTs); val g_Tssss = @{map 3} (fn C => map2 (map2 (map (curry (op -->) C) oo unzip_corecT))) Cs ctr_Tsss' g_Tsss; val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) g_Tssss; in (q_Tssss, g_Tsss, g_Tssss, g_absTs) end; fun mk_corec_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs; fun mk_corec_fun_arg_types ctr_Tsss Cs absTs repTs ns mss dtor_corec = (mk_corec_p_pred_types Cs ns, mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss (binder_fun_types (fastype_of dtor_corec))); fun mk_corecs_args_types ctxt ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts = let val p_Tss = mk_corec_p_pred_types Cs ns; val (q_Tssss, g_Tsss, g_Tssss, corec_types) = mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts; val (((((Free (x, _), cs), pss), qssss), gssss), _) = ctxt |> yield_singleton (mk_Frees "x") dummyT ||>> mk_Frees "a" Cs ||>> mk_Freess "p" p_Tss ||>> mk_Freessss "q" q_Tssss ||>> mk_Freessss "g" g_Tssss; val cpss = map2 (map o rapp) cs pss; fun build_sum_inj mk_inj = build_map ctxt [] [] (uncurry mk_inj o dest_sumT o snd); fun build_dtor_corec_arg _ [] [cg] = cg | build_dtor_corec_arg T [cq] [cg, cg'] = mk_If cq (build_sum_inj Inl_const (fastype_of cg, T) $ cg) (build_sum_inj Inr_const (fastype_of cg', T) $ cg'); val pgss = @{map 3} flat_corec_preds_predsss_gettersss pss qssss gssss; val cqssss = map2 (map o map o map o rapp) cs qssss; val cgssss = map2 (map o map o map o rapp) cs gssss; val cqgsss = @{map 3} (@{map 3} (@{map 3} build_dtor_corec_arg)) g_Tsss cqssss cgssss; in (x, cs, cpss, (((pgss, pss, qssss, gssss), cqgsss), corec_types)) end; fun mk_co_recs_prelims ctxt fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_recs0 = let val thy = Proof_Context.theory_of ctxt; val (xtor_co_rec_fun_Ts, xtor_co_recs) = mk_xtor_co_recs thy fp fpTs Cs xtor_co_recs0 |> `(binder_fun_types o fastype_of o hd); val (recs_args_types, corecs_args_types) = if fp = Least_FP then mk_recs_args_types ctxt ctr_Tsss Cs absTs repTs ns mss xtor_co_rec_fun_Ts |> (rpair NONE o SOME) else mk_corecs_args_types ctxt ctr_Tsss Cs absTs repTs ns mss xtor_co_rec_fun_Ts |> (pair NONE o SOME); in (xtor_co_recs, recs_args_types, corecs_args_types) end; fun mk_preds_getterss_join c cps absT abs cqgss = let val n = length cqgss; val ts = map2 (mk_absumprod absT abs n) (1 upto n) cqgss; in Term.lambda c (mk_IfN absT cps ts) end; fun define_co_rec_as fp Cs fpT b rhs lthy0 = let val thy = Proof_Context.theory_of lthy0; val ((cst, (_, def)), (lthy', lthy)) = lthy0 |> (snd o Local_Theory.begin_nested) |> Local_Theory.define ((b, NoSyn), ((Thm.make_def_binding (Config.get lthy0 bnf_internals) b, []), rhs)) ||> `Local_Theory.end_nested; val phi = Proof_Context.export_morphism lthy lthy'; val cst' = mk_co_rec thy fp Cs fpT (Morphism.term phi cst); val def' = Morphism.thm phi def; in ((cst', def'), lthy') end; fun define_rec (_, _, fss, xssss) mk_binding fpTs Cs reps ctor_rec = let val nn = length fpTs; val (ctor_rec_absTs, fpT) = strip_typeN nn (fastype_of ctor_rec) |>> map domain_type ||> domain_type; in define_co_rec_as Least_FP Cs fpT (mk_binding recN) (fold_rev (fold_rev Term.lambda) fss (Term.list_comb (ctor_rec, @{map 4} (fn ctor_rec_absT => fn rep => fn fs => fn xsss => mk_case_absumprod ctor_rec_absT rep fs (map (map HOLogic.mk_tuple) xsss) (map flat_rec_arg_args xsss)) ctor_rec_absTs reps fss xssss))) end; fun define_corec (_, cs, cpss, (((pgss, _, _, _), cqgsss), f_absTs)) mk_binding fpTs Cs abss dtor_corec = let val nn = length fpTs; val fpT = range_type (snd (strip_typeN nn (fastype_of dtor_corec))); in define_co_rec_as Greatest_FP Cs fpT (mk_binding corecN) (fold_rev (fold_rev Term.lambda) pgss (Term.list_comb (dtor_corec, @{map 5} mk_preds_getterss_join cs cpss f_absTs abss cqgsss))) end; fun mk_induct_raw_prem_prems names_ctxt Xss setss_fp_nesting (x as Free (s, Type (T_name, T (Type (_, Xs_Ts0)) = (case AList.lookup (op =) setss_fp_nesting T_name of NONE => [] | SOME raw_sets0 => let val (Xs_Ts, (Ts, raw_sets)) = filter (exists_subtype_in (flat Xss) o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0)) |> split_list ||> split_list; val sets = map (mk_set Ts0) raw_sets; val (ys, names_ctxt') = names_ctxt |> mk_Frees s Ts; val xysets = map (pair x) (ys ~~ sets); val ppremss = map2 (mk_induct_raw_prem_prems names_ctxt' Xss setss_fp_nesting) ys Xs_Ts; in flat (map2 (map o apfst o cons) xysets ppremss) end) | mk_induct_raw_prem_prems _ Xss _ (x as Free (_, Type _)) X = [([], (find_index (fn Xs => member (op =) Xs X) Xss + 1, x))] | mk_induct_raw_prem_prems _ _ _ _ _ = []; fun mk_induct_raw_prem alter_x names_ctxt Xss setss_fp_nesting p ctr ctr_Ts ctrXs_Ts = let val (xs, names_ctxt') = names_ctxt |> mk_Frees "x" ctr_Ts; val pprems = flat (map2 (mk_induct_raw_prem_prems names_ctxt' Xss setss_fp_nesting) xs ctrXs_Ts); val y = Term.list_comb (ctr, map alter_x xs); val p' = enforce_type names_ctxt domain_type (fastype_of y) p; in (xs, pprems, HOLogic.mk_Trueprop (p' $ y)) end; fun close_induct_prem_prem nn ps xs t = fold_rev Logic.all (map Free (drop (nn + length xs) (rev (Term.add_frees t (map dest_Free xs @ map_filter (try dest_Free) ps))))) t; fun finish_induct_prem_prem ctxt nn ps xs (xysets, (j, x)) = let val p' = enforce_type ctxt domain_type (fastype_of x) (nth ps (j - 1)) in close_induct_prem_prem nn ps xs (Logic.list_implies (map (fn (x', (y, set)) => mk_Trueprop_mem (y, set $ x')) xysets, HOLogic.mk_Trueprop (p' $ x))) end; fun finish_induct_prem ctxt nn ps (xs, raw_pprems, concl) = fold_rev Logic.all xs (Logic.list_implies (map (finish_induct_prem_prem ctxt nn ps xs) raw_pprems, concl)); fun mk_coinduct_prem_ctr_concls ctxt Xss fpTss rs' n k udisc usels vdisc vsels ctrXs_Ts = let fun build_the_rel T Xs_T = build_rel [] ctxt [] [] (fn (T, X) => nth rs' (find_index (fn Xs => member (op =) Xs X) Xss) |> enforce_type ctxt domain_type T) (T, Xs_T) |> Term.subst_atomic_types (flat Xss ~~ flat fpTss); fun build_rel_app usel vsel Xs_T = fold rapp [usel, vsel] (build_the_rel (fastype_of usel) Xs_T); in (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @ (if null usels then [] else [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc], Library.foldr1 HOLogic.mk_conj (@{map 3} build_rel_app usels vsels ctrXs_Ts))]) end; fun mk_coinduct_prem_concl ctxt Xss fpTss rs' n udiscs uselss vdiscs vselss ctrXs_Tss = @{map 6} (mk_coinduct_prem_ctr_concls ctxt Xss fpTss rs' n) (1 upto n) udiscs uselss vdiscs vselss ctrXs_Tss |> flat |> Library.foldr1 HOLogic.mk_conj handle List.Empty => \<^term>\<open>True\<close>; fun mk_coinduct_prem ctxt Xss fpTss rs' uvr u v n udiscs uselss vdiscs vselss ctrXs_Tss = fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr, HOLogic.mk_Trueprop (mk_coinduct_prem_concl ctxt Xss fpTss rs' n udiscs uselss vdiscs vsel ctrXs_Tss))); fun postproc_co_induct ctxt nn prop prop_conj = Drule.zero_var_indexes #> `(conj_dests nn) #>> map (fn thm => Thm.permute_prems 0 ~1 (thm RS prop)) ##> (fn thm => Thm.permute_prems 0 (~ nn) (if nn = 1 then thm RS prop else funpow nn (fn thm => unfold_thms ctxt @{thms conj_assoc} (thm RS prop_conj)) thm)); fun mk_induct_attrs ctrss = let val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss); in [Attrib.case_names induct_cases] end; fun derive_rel_induct_thms_for_types ctxt nn fpA_Ts As Bs ctrAss ctrAs_Tsss exhausts ctor_ ctor_defss ctor_injects pre_rel_defs abs_inverses live_nesting_rel_eqs = let val B_ify_T = Term.typ_subst_atomic (As ~~ Bs); val B_ify = Term.map_types B_ify_T; val fpB_Ts = map B_ify_T fpA_Ts; val ctrBs_Tsss = map (map (map B_ify_T)) ctrAs_Tsss; val ctrBss = map (map B_ify) ctrAss; val ((((Rs, IRs), ctrAsss), ctrBsss), names_ctxt) = ctxt |> mk_Frees "R" (map2 mk_pred2T As Bs) ||>> mk_Frees "IR" (map2 mk_pred2T fpA_Ts fpB_Ts) ||>> mk_Freesss "a" ctrAs_Tsss ||>> mk_Freesss "b" ctrBs_Tsss; val prems = let fun mk_prem ctrA ctrB argAs argBs = fold_rev Logic.all (argAs @ argBs) (fold_rev (curry Logic.mk_implies) (map2 (HOLogic.mk_Trueprop oo build_rel_app names_ctxt (Rs @ IRs) fpA_Ts) argAs argBs) (HOLogic.mk_Trueprop (build_rel_app names_ctxt (Rs @ IRs) fpA_Ts (Term.list_comb (ctrA, argAs)) (Term.list_comb (ctrB, argBs))))); in flat (@{map 4} (@{map 4} mk_prem) ctrAss ctrBss ctrAsss ctrBsss) end; val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_leq (map2 (build_the_rel ctxt (Rs @ IRs) []) fpA_Ts fpB_Ts) IRs)); val vars = Variable.add_free_names ctxt goal []; val rel_induct0_thm = Goal.prove_sorry ctxt vars prems goal (fn {context = ctxt, prems} => mk_rel_induct0_tac ctxt ctor_rel_induct prems (map (Thm.cterm_of ctxt) IRs) exhausts ctor_defss ctor_injects pre_rel_defs abs_inverses live_nesting_rel_eqs) |> Thm.close_derivation \<^here>; in (postproc_co_induct ctxt nn @{thm predicate2D} @{thm predicate2D_conj} rel_induct0_thm, mk_induct_attrs ctrAss) end; fun derive_induct_recs_thms_for_types plugins pre_bnfs rec_args_typess ctor_induct cto live_nesting_bnfs fp_nesting_bnfs fpTs Cs Xs ctrXs_Tsss pre_abs_inverses pre_type_defin abs_inverses ctrss ctr_defss recs rec_defs ctxt = let val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss; val nn = length pre_bnfs; val ns = map length ctr_Tsss; val mss = map (map length) ctr_Tsss; val pre_map_defs = map map_def_of_bnf pre_bnfs; val pre_set_defss = map set_defs_of_bnf pre_bnfs; val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs; val fp_nesting_map_ident0s = map map_ident0_of_bnf fp_nesting_bnfs; val fp_nesting_set_maps = maps set_map_of_bnf fp_nesting_bnfs; val fp_b_names = map base_name_of_typ fpTs; val (((ps, xsss), us'), names_ctxt) = ctxt |> mk_Frees "P" (map mk_pred1T fpTs) ||>> mk_Freesss "x" ctr_Tsss ||>> Variable.variant_fixes fp_b_names; val us = map2 (curry Free) us' fpTs; val setss_fp_nesting = map mk_bnf_sets fp_nesting_bnfs; val (induct_thms, induct_thm) = let val raw_premss = @{map 4} (@{map 3} o mk_induct_raw_prem I names_ctxt (map single Xs) setss_fp_nesting) ps ctrss ctr_Tsss ctrXs_Tsss; val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)); val goal = Library.foldr (Logic.list_implies o apfst (map (finish_induct_prem ctxt nn ps))) (raw_premss, concl); val vars = Variable.add_free_names ctxt goal []; val kksss = map (map (map (fst o snd) o #2)) raw_premss; val ctor_induct' = ctor_induct OF (map2 mk_absumprodE pre_type_definitions mss); val thm = Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, ...} => mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' pre_abs_inverses abs_inverses fp_nesting_set_maps pre_set_defss) |> Thm.close_derivation \<^here>; in `(conj_dests nn) thm end; val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; fun mk_rec_thmss (_, x_Tssss, fss, _) recs rec_defs ctor_rec_thms = let val frecs = map (lists_bmoc fss) recs; fun mk_goal frec xctr f xs fxs = fold_rev (fold_rev Logic.all) (xs :: fss) (mk_Trueprop_eq (frec $ xctr, Term.list_comb (f, fxs))); fun maybe_tick (T, U) u f = if try (fst o HOLogic.dest_prodT) U = SOME T then Term.lambda u (HOLogic.mk_prod (u, f $ u)) else f; fun build_rec (x as Free (_, T)) U = if T = U then x else let val build_simple = indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs (fn kk => fn TU => maybe_tick TU (nth us kk) (nth frecs kk)); in build_map ctxt [] [] build_simple (T, U) $ x end; val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_rec))) xsss x_Tssss; val goalss = @{map 5} (@{map 4} o mk_goal) frecs xctrss fss xsss fxsss; val tacss = @{map 4} (map ooo mk_rec_tac pre_map_defs (fp_nesting_map_ident0s @ live_nesting_map_ident0s) rec_defs) ctor_rec_thms pre_abs_inverses abs_inverses ctr_defss; fun prove goal tac = Goal.prove_sorry ctxt [] [] goal (tac o #context) |> Thm.close_derivation \<^here>; in map2 (map2 prove) goalss tacss end; val rec_thmss = mk_rec_thmss (the rec_args_typess) recs rec_defs ctor_rec_thms; in ((induct_thms, induct_thm, mk_induct_attrs ctrss), (rec_thmss, nitpicksimp_attrs @ simp_attrs)) end; fun mk_coinduct_attrs fpTs ctrss discss mss = let val fp_b_names = map base_name_of_typ fpTs; fun mk_coinduct_concls ms discs ctrs = let fun mk_disc_concl disc = [name_of_disc disc]; fun mk_ctr_concl 0 _ = [] | mk_ctr_concl _ ctr = [name_of_ctr ctr]; val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]]; val ctr_concls = map2 mk_ctr_concl ms ctrs; in flat (map2 append disc_concls ctr_concls) end; val coinduct_cases = quasi_unambiguous_case_names (map (prefix Eq_prefix) fp_b_names); val coinduct_conclss = @{map 3} (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss; val coinduct_case_names_attr = Attrib.case_names coinduct_cases; val coinduct_case_concl_attrs = map2 (fn casex => fn concls => Attrib.case_conclusion (casex, concls)) coinduct_cases coinduct_conclss; val common_coinduct_attrs = coinduct_case_names_attr :: coinduct_case_concl_attrs; val coinduct_attrs = Attrib.consumes 1 :: coinduct_case_names_attr :: coinduct_case_conc in (coinduct_attrs, common_coinduct_attrs) end; fun derive_rel_coinduct_thms_for_types ctxt nn fpA_Ts ns As Bs mss (ctr_sugars : ctr_sugar l abs_inverses abs_injects ctor_injects dtor_ctors rel_pre_defs ctor_defss dtor_rel_coin live_nesting_rel_eqs = let val B_ify_T = Term.typ_subst_atomic (As ~~ Bs); val fpB_Ts = map B_ify_T fpA_Ts; val (Rs, IRs, fpAs, fpBs, _) = let val fp_names = map base_name_of_typ fpA_Ts; val ((((Rs, IRs), fpAs_names), fpBs_names), names_ctxt) = ctxt |> mk_Frees "R" (map2 mk_pred2T As Bs) ||>> mk_Frees "IR" (map2 mk_pred2T fpA_Ts fpB_Ts) ||>> Variable.variant_fixes fp_names ||>> Variable.variant_fixes (map (suffix "'") fp_names); in (Rs, IRs, map2 (curry Free) fpAs_names fpA_Ts, map2 (curry Free) fpBs_names fpB_Ts, names_ctxt) end; val ((discA_tss, selA_tsss), (discB_tss, selB_tsss)) = let val discss = map #discs ctr_sugars; val selsss = map #selss ctr_sugars; fun mk_discss ts Ts = map2 (map o rapp) ts (map (map (mk_disc_or_sel Ts)) discss); fun mk_selsss ts Ts = map2 (map o map o rapp) ts (map (map (map (mk_disc_or_sel Ts))) selsss); in ((mk_discss fpAs As, mk_selsss fpAs As), (mk_discss fpBs Bs, mk_selsss fpBs Bs)) end; val prems = let fun mk_prem_ctr_concls n k discA_t selA_ts discB_t selB_ts = (if k = n then [] else [HOLogic.mk_eq (discA_t, discB_t)]) @ (case (selA_ts, selB_ts) of ([], []) => [] | (_ :: _, _ :: _) => [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [discA_t, discB_t], Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app ctxt (Rs @ IRs) fpA_Ts) selA_ts selB_ts))]); fun mk_prem_concl n discA_ts selA_tss discB_ts selB_tss = Library.foldr1 HOLogic.mk_conj (flat (@{map 5} (mk_prem_ctr_concls n) (1 upto n) discA_ts selA_tss discB_ts selB_tss)) handle List.Empty => \<^term>\<open>True\<close>; fun mk_prem IR tA tB n discA_ts selA_tss discB_ts selB_tss = fold_rev Logic.all [tA, tB] (Logic.mk_implies (HOLogic.mk_Trueprop (IR $ tA $ tB), HOLogic.mk_Trueprop (mk_prem_concl n discA_ts selA_tss discB_ts selB_tss))); in @{map 8} mk_prem IRs fpAs fpBs ns discA_tss selA_tsss discB_tss selB_tsss end; val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_leq IRs (map2 (build_the_rel ctxt (Rs @ IRs) []) fpA_Ts fpB_Ts))); val vars = Variable.add_free_names ctxt goal []; val rel_coinduct0_thm = Goal.prove_sorry ctxt vars prems goal (fn {context = ctxt, prems} => mk_rel_coinduct0_tac ctxt dtor_rel_coinduct (map (Thm.cterm_of ctxt) IRs) prems (map #exhaust ctr_sugars) (map (flat o #disc_thmss) ctr_sugars) (map (flat o #sel_thmss) ctr_sugars) ctor_defss dtor_ctors ctor_injects abs_injects rel_pre_defs abs_inverses live_nesting_rel_eqs) |> Thm.close_derivation \<^here>; in (postproc_co_induct ctxt nn @{thm predicate2D} @{thm predicate2D_conj} rel_coinduct0_th mk_coinduct_attrs fpA_Ts (map #ctrs ctr_sugars) (map #discs ctr_sugars) mss) end; fun derive_set_induct_thms_for_types ctxt nn fpTs ctrss setss dtor_set_inducts exhausts s ctor_defs dtor_ctors Abs_pre_inverses = let fun mk_prems A Ps ctr_args t ctxt = (case fastype_of t of Type (type_name, innerTs) => (case bnf_of ctxt type_name of NONE => ([], ctxt) | SOME bnf => let fun seq_assm a set ctxt = let val X = HOLogic.dest_setT (range_type (fastype_of set)); val (x, ctxt') = yield_singleton (mk_Frees "x") X ctxt; val assm = mk_Trueprop_mem (x, set $ a); in (case build_binary_fun_app Ps x a of NONE => mk_prems A Ps ctr_args x ctxt' |>> map (Logic.all x o Logic.mk_implies o pair assm) | SOME f => ([Logic.all x (Logic.mk_implies (assm, Logic.mk_implies (HOLogic.mk_Trueprop f, HOLogic.mk_Trueprop (the (build_binary_fun_app Ps x ctr_args)))))], ctxt')) end; in fold_map (seq_assm t o mk_set innerTs) (sets_of_bnf bnf) ctxt |>> flat end) | T => if T = A then ([HOLogic.mk_Trueprop (the (build_binary_fun_app Ps t ctr_args))], ctxt) else ([], ctxt)); fun mk_prems_for_ctr A Ps ctr ctxt = let val (args, ctxt') = mk_Frees "z" (binder_types (fastype_of ctr)) ctxt; in fold_map (mk_prems A Ps (list_comb (ctr, args))) args ctxt' |>> map (fold_rev Logic.all args) o flat |>> (fn prems => (prems, mk_names (length prems) (name_of_ctr ctr))) end; fun mk_prems_and_concl_for_type A Ps ((fpT, ctrs), set) ctxt = let val ((x, fp), ctxt') = ctxt |> yield_singleton (mk_Frees "x") A ||>> yield_singleton (mk_Frees "a") fpT; val concl = mk_Ball (set $ fp) (Term.absfree (dest_Free x) (the (build_binary_fun_app Ps x fp))); in fold_map (mk_prems_for_ctr A Ps) ctrs ctxt' |>> split_list |>> map_prod flat flat |>> apfst (rpair concl) end; fun mk_thm ctxt fpTs ctrss sets = let val A = HOLogic.dest_setT (range_type (fastype_of (hd sets))); val (Ps, ctxt') = mk_Frees "P" (map (fn fpT => A --> fpT --> HOLogic.boolT) fpTs) ctxt; val (((prems, concl), case_names), ctxt'') = fold_map (mk_prems_and_concl_for_type A Ps) (fpTs ~~ ctrss ~~ sets) ctxt' |>> apfst split_list o split_list |>> apfst (apfst flat) |>> apfst (apsnd (Library.foldr1 HOLogic.mk_conj)) |>> apsnd flat; val vars = fold (Variable.add_free_names ctxt) (concl :: prems) []; val thm = Goal.prove_sorry ctxt vars prems (HOLogic.mk_Trueprop concl) (fn {context = ctxt, prems} => mk_set_induct0_tac ctxt (map (Thm.cterm_of ctxt'') Ps) prems dtor_set_inducts exhausts set_pre_defs ctor_defs dtor_ctors Abs_pre_inverses) |> Thm.close_derivation \<^here>; val case_names_attr = Attrib.case_names (quasi_unambiguous_case_names case_names); val induct_set_attrs = map (Attrib.internal \<^here> o K o Induct.induct_pred o name_of_set) s in (thm, case_names_attr :: induct_set_attrs) end val consumes_attr = Attrib.consumes 1; in map (mk_thm ctxt fpTs ctrss #> nn = 1 ? map_prod (fn thm => rotate_prems ~1 (thm RS @{thm bspec})) (cons consumes_attr)) (transpose setss) end; fun mk_coinduct_strong_thm coind rel_eqs rel_monos mk_vimage2p ctxt = let val n = Thm.nprems_of coind; val m = Thm.nprems_of (hd rel_monos) - n; fun mk_inst phi = (phi, Thm.cterm_of ctxt (mk_union (Var phi, HOLogic.eq_const (fst (dest_pred2T (#2 phi)))) val insts = Term.add_vars (Thm.prop_of coind) [] |> rev |> take n |> map mk_inst; fun mk_unfold rel_eq rel_mono = let val eq = iffD2 OF [rel_eq RS @{thm predicate2_eqD}, refl]; val mono = rel_mono OF (replicate m @{thm order_refl} @ replicate n @{thm eq_subset}); in mk_vimage2p (eq RS (mono RS @{thm predicate2D})) RS eqTrueI end; val unfolds = map2 mk_unfold rel_eqs rel_monos @ @{thms sup_fun_def sup_bool_def imp_disjL all_conj_distrib subst_eq_imp simp_thms(18,21,35)}; in Thm.instantiate (TVars.empty, Vars.make insts) coind |> unfold_thms ctxt unfolds end; fun derive_coinduct_thms_for_types ctxt strong alter_r pre_bnfs dtor_coinduct dtor_ctor live_nesting_bnfs fpTs Xs ctrXs_Tsss ns pre_abs_inverses abs_inverses mk_vimage2p ctr_de (ctr_sugars : ctr_sugar list) = let val nn = length pre_bnfs; val pre_rel_defs = map rel_def_of_bnf pre_bnfs; val live_nesting_rel_eqs = map rel_eq_of_bnf live_nesting_bnfs; val fp_b_names = map base_name_of_typ fpTs; val discss = map #discs ctr_sugars; val selsss = map #selss ctr_sugars; val exhausts = map #exhaust ctr_sugars; val disc_thmsss = map #disc_thmss ctr_sugars; val sel_thmsss = map #sel_thmss ctr_sugars; val (((rs, us'), vs'), _) = ctxt |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs) ||>> Variable.variant_fixes fp_b_names ||>> Variable.variant_fixes (map (suffix "'") fp_b_names); val us = map2 (curry Free) us' fpTs; val udiscss = map2 (map o rapp) us discss; val uselsss = map2 (map o map o rapp) us selsss; val vs = map2 (curry Free) vs' fpTs; val vdiscss = map2 (map o rapp) vs discss; val vselsss = map2 (map o map o rapp) vs selsss; val uvrs = @{map 3} (fn r => fn u => fn v => r $ u $ v) rs us vs; val uv_eqs = map2 (curry HOLogic.mk_eq) us vs; val strong_rs = @{map 4} (fn u => fn v => fn uvr => fn uv_eq => fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs; val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (@{map 3} (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v))) uvrs us vs)) fun mk_goal rs0' = Logic.list_implies (@{map 9} (mk_coinduct_prem ctxt (map single Xs) (map single fpTs) (map alter_r rs0')) uvrs us vs ns udiscss uselsss vdiscss vselsss ctrXs_Tsss, concl); val goals = map mk_goal ([rs] @ (if strong then [strong_rs] else [])); fun prove dtor_coinduct' goal = Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (fn {context = ctxt, ...} => mk_coinduct_tac ctxt live_nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs pre_abs_inv abs_inverses dtor_ctors exhausts ctr_defss disc_thmsss sel_thmsss)) |> Thm.close_derivation \<^here>; val rel_eqs = map rel_eq_of_bnf pre_bnfs; val rel_monos = map rel_mono_of_bnf pre_bnfs; val dtor_coinducts = [dtor_coinduct] @ (if strong then [mk_coinduct_strong_thm dtor_coinduct rel_eqs rel_monos mk_vimage2p ctxt else []); in map2 (postproc_co_induct ctxt nn mp @{thm conj_commute[THEN iffD1]} oo prove) dtor_coinducts goals end; fun derive_coinduct_corecs_thms_for_types ctxt pre_bnfs (x, cs, cpss, (((pgss, _, _, _), cqgsss), _)) dtor_coinduct dtor_injects dtor_ctors dtor_corec_thms live_nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss mss ns pre_abs_inverses abs_in mk_vimage2p ctr_defss (ctr_sugars : ctr_sugar list) corecs corec_defs = let fun mk_ctor_dtor_corec_thm dtor_inject dtor_ctor corec = iffD1 OF [dtor_inject, trans OF [corec, dtor_ctor RS sym]]; val ctor_dtor_corec_thms = @{map 3} mk_ctor_dtor_corec_thm dtor_injects dtor_ctors dtor_corec_thms; val pre_map_defs = map map_def_of_bnf pre_bnfs; val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs; val fp_b_names = map base_name_of_typ fpTs; val ctrss = map #ctrs ctr_sugars; val discss = map #discs ctr_sugars; val selsss = map #selss ctr_sugars; val disc_thmsss = map #disc_thmss ctr_sugars; val discIss = map #discIs ctr_sugars; val sel_thmsss = map #sel_thmss ctr_sugars; val coinduct_thms_pairs = derive_coinduct_thms_for_types ctxt true I pre_bnfs dtor_coind dtor_ctors live_nesting_bnfs fpTs Xs ctrXs_Tsss ns pre_abs_inverses abs_inverses mk_vima ctr_defss ctr_sugars; fun mk_maybe_not pos = not pos ? HOLogic.mk_not; val gcorecs = map (lists_bmoc pgss) corecs; val corec_thmss = let val (us', _) = ctxt |> Variable.variant_fixes fp_b_names; val us = map2 (curry Free) us' fpTs; fun mk_goal c cps gcorec n k ctr m cfs' = fold_rev (fold_rev Logic.all) ([c] :: pgss) (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps, mk_Trueprop_eq (gcorec $ c, Term.list_comb (ctr, take m cfs')))); val mk_U = typ_subst_nonatomic (map2 (fn C => fn fpT => (mk_sumT (fpT, C), fpT)) Cs fpTs); fun tack (c, u) f = let val x' = Free (x, mk_sumT (fastype_of u, fastype_of c)) in Term.lambda x' (mk_case_sum (Term.lambda u u, Term.lambda c (f $ c)) $ x') end; fun build_corec cqg = let val T = fastype_of cqg in if exists_subtype_in Cs T then let val U = mk_U T; val build_simple = indexify fst (map2 (curry mk_sumT) fpTs Cs) (fn kk => fn _ => tack (nth cs kk, nth us kk) (nth gcorecs kk)); in build_map ctxt [] [] build_simple (T, U) $ cqg end else cqg end; val cqgsss' = map (map (map build_corec)) cqgsss; val goalss = @{map 8} (@{map 4} oooo mk_goal) cs cpss gcorecs ns kss ctrss mss cqgsss'; val tacss = @{map 4} (map ooo mk_corec_tac corec_defs live_nesting_map_ident0s) ctor_dtor_corec_thms pre_map_defs abs_inverses ctr_defss; fun prove goal tac = Goal.prove_sorry ctxt [] [] goal (tac o #context) |> Thm.close_derivation \<^here>; in map2 (map2 prove) goalss tacss |> map (map (unfold_thms ctxt @{thms case_sum_if})) end; val corec_disc_iff_thmss = let fun mk_goal c cps gcorec n k disc = mk_Trueprop_eq (disc $ (gcorec $ c), if n = 1 then \<^Const>\<open>True\<close> else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps)); val goalss = @{map 6} (map2 oooo mk_goal) cs cpss gcorecs ns kss discss; fun mk_case_split' cp = Thm.instantiate' [] [SOME (Thm.cterm_of ctxt cp)] @{thm case_split} val case_splitss' = map (map mk_case_split') cpss; val tacss = @{map 3} (map oo mk_corec_disc_iff_tac) case_splitss' corec_thmss disc_thmsss; fun prove goal tac = Variable.add_free_names ctxt goal [] |> (fn vars => Goal.prove_sorry ctxt vars [] goal (tac o #context)) |> Thm.close_derivation \<^here>; fun proves [_] [_] = [] | proves goals tacs = map2 prove goals tacs; in map2 proves goalss tacss end; fun mk_corec_disc_thms corecs discIs = map (op RS) (corecs ~~ discIs); val corec_disc_thmss = map2 mk_corec_disc_thms corec_thmss discIss; fun mk_corec_sel_thm corec_thm sel sel_thm = let val (domT, ranT) = dest_funT (fastype_of sel); val arg_cong' = Thm.instantiate' (map (SOME o Thm.ctyp_of ctxt) [domT, ranT]) [NONE, NONE, SOME (Thm.cterm_of ctxt sel)] arg_cong |> Thm.varifyT_global; val sel_thm' = sel_thm RSN (2, trans); in corec_thm RS arg_cong' RS sel_thm' end; fun mk_corec_sel_thms corec_thmss = @{map 3} (@{map 3} (map2 o mk_corec_sel_thm)) corec_thmss selsss sel_thmsss; val corec_sel_thmsss = mk_corec_sel_thms corec_thmss; in ((coinduct_thms_pairs, mk_coinduct_attrs fpTs (map #ctrs ctr_sugars) (map #discs ctr_sugars) mss), corec_thmss, corec_disc_thmss, (corec_disc_iff_thmss, simp_attrs), (corec_sel_thmsss, simp_attrs)) end; fun define_co_datatypes prepare_plugins prepare_constraint prepare_typ prepare_term fp ((raw_plugins, discs_sels0), specs) lthy = let val plugins = prepare_plugins lthy raw_plugins; val discs_sels = discs_sels0 orelse fp = Greatest_FP; val nn = length specs; val fp_bs = map type_binding_of_spec specs; val fp_b_names = map Binding.name_of fp_bs; val fp_common_name = mk_common_name fp_b_names; val map_bs = map map_binding_of_spec specs; val rel_bs = map rel_binding_of_spec specs; val pred_bs = map pred_binding_of_spec specs; fun prepare_type_arg (_, (ty, c)) = let val TFree (s, _) = prepare_typ lthy ty in TFree (s, prepare_constraint lthy c) end; val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of_spec) specs; val unsorted_Ass0 = map (map (resort_tfree_or_tvar \<^sort>\<open>type\<close>)) Ass0; val unsorted_As = Library.foldr1 (merge_type_args fp) unsorted_Ass0; val num_As = length unsorted_As; val set_boss = map (map fst o type_args_named_constrained_of_spec) specs; val set_bss = map (map (the_default Binding.empty)) set_boss; fun add_fake_type spec = Typedecl.basic_typedecl {final = true} (type_binding_of_spec spec, num_As, Mixfix.reset_pos (mixfix_of_spec spec)); val (fake_T_names, fake_lthy) = fold_map add_fake_type specs lthy; val qsoty = quote o Syntax.string_of_typ fake_lthy; val _ = (case Library.duplicates (op =) unsorted_As of [] => () | A :: _ => error ("Duplicate type parameter " ^ qsoty A ^ " in " ^ co_prefix fp ^ "datatype specification")); val bad_args = map (Logic.type_map (singleton (Variable.polymorphic lthy))) unsorted_As |> filter_out Term.is_TVar; val _ = null bad_args orelse error ("Locally fixed type argument " ^ qsoty (hd bad_args) ^ " in " ^ co_prefix fp ^ "datatype specification"); val mixfixes = map mixfix_of_spec specs; val _ = (case Library.duplicates Binding.eq_name fp_bs of [] => () | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); val mx_ctr_specss = map mixfixed_ctr_specs_of_spec specs; val ctr_specss = map (map fst) mx_ctr_specss; val ctr_mixfixess = map (map snd) mx_ctr_specss; val disc_bindingss = map (map disc_of_ctr_spec) ctr_specss; val ctr_bindingss = map2 (fn fp_b_name => map (Binding.qualify false fp_b_name o ctr_of_ctr_spec)) fp_b_names ctr_specss; val ctr_argsss = map (map args_of_ctr_spec) ctr_specss; val sel_bindingsss = map (map (map fst)) ctr_argsss; val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; val raw_sel_default_eqss = map sel_default_eqs_of_spec specs; val (As :: _) :: fake_ctr_Tsss = burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0); val As' = map dest_TFree As; val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; val _ = (case subtract (op =) As' rhs_As' of [] => () | extras => error ("Extra type variables on right-hand side: " ^ commas (map (qsoty o TFree) extras))); val fake_Ts = map (fn s => Type (s, As)) fake_T_names; val ((((Bs0, Cs), Es), Xs), _) = lthy |> fold (Variable.declare_typ o resort_tfree_or_tvar dummyS) unsorted_As |> mk_TFrees num_As ||>> mk_TFrees nn ||>> mk_TFrees nn ||>> variant_tfrees fp_b_names; fun eq_fpT_check (T as Type (s, Ts)) (T' as Type (s', Ts')) = s = s' andalso (Ts = Ts' orelse error ("Wrong type arguments in " ^ co_prefix fp ^ "recursive type " ^ qsoty T ^ " (expected " ^ qsoty T' ^ ")")) | eq_fpT_check _ _ = false; fun freeze_fp (T as Type (s, Ts)) = (case find_index (eq_fpT_check T) fake_Ts of ~1 => Type (s, map freeze_fp Ts) | kk => nth Xs kk) | freeze_fp T = T; val unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fake_Ts); val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss; val ctrXs_repTs = map mk_sumprodT_balanced ctrXs_Tsss; val _ = let fun add_deps i = fold (fn T => fold_index (fn (j, X) => (i <> j andalso exists_subtype_in [X] T) ? insert (op =) (i, j)) Xs); val add_missing_nodes = fold (AList.default (op =) o rpair []) (0 upto nn - 1); val deps = fold_index (uncurry (fold o add_deps)) ctrXs_Tsss [] |> AList.group (op =) |> add_missing_nodes; val G = Int_Graph.make (map (apfst (rpair ())) deps); val sccs = map (sort int_ord) (Int_Graph.strong_conn G); val str_of_scc = prefix (co_prefix fp ^ "datatype ") o space_implode " and " o map (suffix " = \<dots>" o Long_Name.base_name); fun warn [_] = () | warn sccs = warning ("Defined types not fully mutually " ^ co_prefix fp ^ "recursive\n\ \Alternative specification:\n" ^ cat_lines (map (prefix " " o str_of_scc o map (nth fp_b_names)) sccs)); in warn (order_strong_conn (op =) Int_Graph.make Int_Graph.topological_order deps sccs) end; val killed_As = map_filter (fn (A, set_bos) => if exists is_none set_bos then SOME A else NONE) (As ~~ transpose set_boss); val (((pre_bnfs, absT_infos), _), (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0 dtors = dtors0, xtor_co_recs = xtor_co_recs0, xtor_co_induct, dtor_ctors, ctor_dtors, ctor_injects, dtor_injects, xtor_maps, xtor_setss, xtor_rels, xtor_co_rec_thms, xtor_rel_co_induct, dtor_set_inducts, xtor_co_rec_transfers, xtor_co_rec_o_maps, ... lthy)) = fixpoint_bnf false I (construct_fp mixfixes map_bs rel_bs pred_bs set_bss) fp_bs (map dest_TFree As) (map dest_TFree killed_As) (map dest_TFree Xs) ctrXs_repTs empty_comp_cache lthy handle BAD_DEAD (X, X_backdrop) => (case X_backdrop of Type (bad_tc, _) => let val fake_T = qsoty (unfreeze_fp X); val fake_T_backdrop = qsoty (unfreeze_fp X_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 " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^ " in type expression " ^ fake_T_backdrop) else if is_some (Old_Datatype_Data.get_info (Proof_Context.theory_of lthy) bad_tc) then error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^ " via the old-style datatype " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^ register_hint ()) else error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^ " via type constructor " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^ register_hint ()) end); val time = time lthy; val timer = time (Timer.startRealTimer ()); val fp_nesting_bnfs = nesting_bnfs lthy ctrXs_Tsss Xs; val live_nesting_bnfs = nesting_bnfs lthy ctrXs_Tsss As; val pre_map_defs = map map_def_of_bnf pre_bnfs; val pre_set_defss = map set_defs_of_bnf pre_bnfs; val pre_rel_defs = map rel_def_of_bnf pre_bnfs; val fp_nesting_set_maps = maps set_map_of_bnf fp_nesting_bnfs; val fp_nesting_rel_eq_onps = map rel_eq_onp_of_bnf fp_nesting_bnfs; val live_nesting_map_id0s = map map_id0_of_bnf live_nesting_bnfs; val live_nesting_map_ident0s = map map_ident0_of_bnf live_nesting_bnfs; val live_nesting_set_maps = maps set_map_of_bnf live_nesting_bnfs; val live_nesting_rel_eqs = map rel_eq_of_bnf live_nesting_bnfs; val live_nesting_rel_eq_onps = map rel_eq_onp_of_bnf live_nesting_bnfs; val liveness = liveness_of_fp_bnf num_As any_fp_bnf; val live = live_of_bnf any_fp_bnf; val _ = if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs @ pred_bs) then warning "Map function, relator, and predicator names ignored" else (); val Bs = @{map 3} (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree_or_tvar S B else A) liveness As Bs0; val B_ify_T = Term.typ_subst_atomic (As ~~ Bs); val B_ify = Term.map_types B_ify_T; val live_AsBs = filter (op <>) (As ~~ Bs); val abss = map #abs absT_infos; val reps = map #rep absT_infos; val absTs = map #absT absT_infos; val repTs = map #repT absT_infos; val abs_injects = map #abs_inject absT_infos; val abs_inverses = map #abs_inverse absT_infos; val type_definitions = map #type_definition absT_infos; val ctors = map (mk_ctor As) ctors0; val dtors = map (mk_dtor As) dtors0; val fpTs = map (domain_type o fastype_of) dtors; val fpBTs = map B_ify_T fpTs; val real_unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fpTs); val ctr_Tsss = map (map (map real_unfreeze_fp)) ctrXs_Tsss; val ns = map length ctr_Tsss; val kss = map (fn n => 1 upto n) ns; val mss = map (map length) ctr_Tsss; val (xtor_co_recs, recs_args_types, corecs_args_types) = mk_co_recs_prelims lthy fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_recs0; fun define_ctrs_dtrs_for_type_etc fp_bnf fp_b fpT C E ctor dtor xtor_co_rec ctor_dtor dtor_ ctor_inject pre_map_def pre_set_defs pre_rel_def fp_map_thm fp_set_thms fp_rel_thm n ks m abs abs_inject type_definition ctr_bindings ctr_mixfixes ctr_Tss disc_bindings sel_bind raw_sel_default_eqs lthy = let val fp_b_name = Binding.name_of fp_b; val ((xss, ctrs0, ctor_iff_dtor_thm, ctr_defs), lthy) = define_ctrs_dtrs_for_type fp_b_name fpT ctor dtor ctor_dtor dtor_ctor n ks abs ctr_bindings ctr_mixfixes ctr_Tss lthy; val ctrs = map (mk_ctr As) ctrs0; val sel_default_eqs = let val sel_Tss = map (map (curry (op -->) fpT)) ctr_Tss; val sel_bTs = flat sel_bindingss ~~ flat sel_Tss |> filter_out (Binding.is_empty o fst) |> distinct (Binding.eq_name o apply2 fst); val sel_default_lthy = fake_local_theory_for_sel_defaults sel_bTs lthy in map (prepare_term sel_default_lthy) raw_sel_default_eqs end; fun mk_binding pre = Binding.qualify false fp_b_name (Binding.prefix_name (pre ^ "_") fp_b); fun massage_res (ctr_sugar, maps_sets_rels) = (maps_sets_rels, (ctrs, xss, ctor_iff_dtor_thm, ctr_defs, ctr_sugar)); in (wrap_ctrs plugins fp discs_sels fp_b_name ctor_inject n ms abs_inject type_definition disc_bindings sel_bindingss sel_default_eqs ctrs0 ctor_iff_dtor_thm ctr_defs #> (fn (ctr_sugar, lthy) => derive_map_set_rel_pred_thms plugins fp live As Bs C E abs_inverses ctr_defs fp_nesting_set_maps fp_nesting_rel_eq_onps live_nesting_map_id0s live_nesting_set_m live_nesting_rel_eqs live_nesting_rel_eq_onps [] fp_b_name fp_bnf fp_bnfs fpT ctor ctor_dtor dtor_ctor pre_map_def pre_set_defs pre_rel_def fp_map_thm fp_set_thms fp_rel_thm [] [] [] ctr_Tss ctr_sugar lthy |>> pair ctr_sugar) ##>> (if fp = Least_FP then define_rec (the recs_args_types) mk_binding fpTs Cs reps else define_corec (the corecs_args_types) mk_binding fpTs Cs abss) xtor_co_rec #>> apfst massage_res, lthy) end; fun wrap_ctrs_derive_map_set_rel_pred_thms_define_co_rec_for_types (wrap_one_etcs, fold_map I wrap_one_etcs lthy |>> apsnd split_list o apfst (apsnd @{split_list 5} o apfst @{split_list 17} o split_list) o split_list; fun mk_simp_thms ({injects, distincts, case_thms, ...} : ctr_sugar) co_recs map_thms rel_i rel_distincts set_thmss = injects @ distincts @ case_thms @ co_recs @ map_thms @ rel_injects @ rel_distincts @ set_thmss; fun mk_co_rec_transfer_goals lthy co_recs = let val BE_ify = Term.subst_atomic_types (live_AsBs @ (Cs ~~ Es)); val ((Rs, Ss), names_lthy) = lthy |> mk_Frees "R" (map (uncurry mk_pred2T) live_AsBs) ||>> mk_Frees "S" (map2 mk_pred2T Cs Es); val co_recBs = map BE_ify co_recs; in (Rs, Ss, map2 (mk_parametricity_goal lthy (Rs @ Ss)) co_recs co_recBs, names_lthy) end; fun derive_rec_transfer_thms lthy recs rec_defs (SOME (_, _, _, xsssss)) = let val (Rs, Ss, goals, _) = mk_co_rec_transfer_goals lthy recs; val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_rec_transfer_tac ctxt nn ns (map (Thm.cterm_of ctxt) Ss) (map (Thm.cterm_of ctxt) Rs) xsssss rec_defs xtor_co_rec_transfers pre_rel_defs live_nesting_rel_eqs) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced nn end; fun derive_rec_o_map_thmss lthy recs rec_defs = if live = 0 then replicate nn [] else let fun variant_names n pre = fst (Variable.variant_fixes (replicate n pre) lthy); val maps0 = map map_of_bnf fp_bnfs; val f_names = variant_names num_As "f"; val fs = map2 (curry Free) f_names (map (op -->) (As ~~ Bs)); val live_gs = AList.find (op =) (fs ~~ liveness) true; val gmaps = map (fn map0 => Term.list_comb (mk_map live As Bs map0, live_gs)) maps0; val rec_arg_Ts = binder_fun_types (hd (map fastype_of recs)); val num_rec_args = length rec_arg_Ts; val g_Ts = map B_ify_T rec_arg_Ts; val g_names = variant_names num_rec_args "g"; val gs = map2 (curry Free) g_names g_Ts; val grecs = map (fn recx => Term.list_comb (Term.map_types B_ify_T recx, gs)) recs; val rec_o_map_lhss = map2 (curry HOLogic.mk_comp) grecs gmaps; val ABfs = (As ~~ Bs) ~~ fs; fun mk_rec_arg_arg (x as Free (_, T)) = let val U = B_ify_T T in if T = U then x else build_map lthy [] [] (the o AList.lookup (op =) ABfs) (T, U) $ x end; fun mk_rec_o_map_arg rec_arg_T h = let val x_Ts = binder_types rec_arg_T; val m = length x_Ts; val x_names = variant_names m "x"; val xs = map2 (curry Free) x_names x_Ts; val xs' = map mk_rec_arg_arg xs; in fold_rev Term.lambda xs (Term.list_comb (h, xs')) end; fun mk_rec_o_map_rhs recx = let val args = map2 mk_rec_o_map_arg rec_arg_Ts gs in Term.list_comb (recx, args) end; val rec_o_map_rhss = map mk_rec_o_map_rhs recs; val rec_o_map_goals = map2 (fold_rev (fold_rev Logic.all) [fs, gs] o HOLogic.mk_Trueprop oo curry HOLogic.mk_eq) rec_o_map_lhss rec_o_map_rhss; val rec_o_map_thms = @{map 3} (fn goal => fn rec_def => fn ctor_rec_o_map => Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} => mk_co_rec_o_map_tac ctxt rec_def pre_map_defs live_nesting_map_ident0s abs_inverses ctor_rec_o_map) |> Thm.close_derivation \<^here>) rec_o_map_goals rec_defs xtor_co_rec_o_maps; in map single rec_o_map_thms end; fun derive_note_induct_recs_thms_for_types ((((map_thmss, map_disc_iffss, map_selsss, rel_injectss, rel_distinctss, rel_selss, rel_intross, rel_casess, pred_injectss, set_thmss, set_selsssss, set_introsssss, set_casess, ctr_transferss, case_transferss, disc_transferss, sel_transferss), (ctrss, _, ctor_iff_dtors, ctr_defss, ctr_sugars)), (recs, rec_defs)), lthy) = let val ((induct_thms, induct_thm, induct_attrs), (rec_thmss, rec_attrs)) = derive_induct_recs_thms_for_types plugins pre_bnfs recs_args_types xtor_co_induct xtor_co_rec_thms live_nesting_bnfs fp_nesting_bnfs fpTs Cs Xs ctrXs_Tsss abs_inverses type_definitions abs_inverses ctrss ctr_defss recs rec_defs lthy; val rec_transfer_thmss = map single (derive_rec_transfer_thms lthy recs rec_defs recs_args_types); val induct_type_attr = Attrib.internal \<^here> o K o Induct.induct_type; val induct_pred_attr = Attrib.internal \<^here> o K o Induct.induct_pred; val ((rel_induct_thmss, common_rel_induct_thms), (rel_induct_attrs, common_rel_induct_attrs)) = if live = 0 then ((replicate nn [], []), ([], [])) else let val ((rel_induct_thms, common_rel_induct_thm), rel_induct_attrs) = derive_rel_induct_thms_for_types lthy nn fpTs As Bs ctrss ctr_Tsss (map #exhaust ctr_sugars) xtor_rel_co_induct ctr_defss ctor_injects pre_rel_defs abs_inverses live_nesting_rel_eqs; in ((map single rel_induct_thms, single common_rel_induct_thm), (rel_induct_attrs, rel_induct_attrs)) end; val rec_o_map_thmss = derive_rec_o_map_thmss lthy recs rec_defs; val simp_thmss = @{map 6} mk_simp_thms ctr_sugars rec_thmss map_thmss rel_injectss rel_distinctss set_thmss; val common_notes = (if nn > 1 then [(inductN, [induct_thm], K induct_attrs), (rel_inductN, common_rel_induct_thms, K common_rel_induct_attrs)] else []) |> massage_simple_notes fp_common_name; val notes = [(inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]), (recN, rec_thmss, K rec_attrs), (rec_o_mapN, rec_o_map_thmss, K []), (rec_transferN, rec_transfer_thmss, K []), (rel_inductN, rel_induct_thmss, K (rel_induct_attrs @ [induct_pred_attr ""])), (simpsN, simp_thmss, K [])] |> massage_multi_notes fp_b_names fpTs; in lthy |> Spec_Rules.add Binding.empty Spec_Rules.equational recs (flat rec_thmss) |> plugins code_plugin ? Code.declare_default_eqns (map (rpair true) (flat rec_thmss)) |> Local_Theory.notes (common_notes @ notes) (* for "datatype_realizer.ML": *) |>> name_noted_thms (dest_Type_name (hd fpTs) ^ implode (map (prefix "_") (tl fp_b_names))) inductN |-> interpret_bnfs_register_fp_sugars plugins fpTs fpBTs Xs Least_FP pre_bnfs absT_infos fp_nesting_bnfs live_nesting_bnfs fp_res ctrXs_Tsss ctor_iff_dtors ctr_defss ctr_sugar recs rec_defs map_thmss [induct_thm] (map single induct_thms) rec_thmss (replicate nn []) (replicate nn []) rel_injectss rel_distinctss map_disc_iffss map_selsss rel_selss rel_intross rel_casess pred_injectss set_thmss set_selsssss set_introsssss set_casess ctr_transferss case_transferss disc_transferss sel_transferss (replicate nn []) (replicate nn []) rec_transfer_thmss common_rel_induct_thms rel_induct_thmss [] (replicate nn []) rec_o_map_thmss end; fun derive_corec_transfer_thms lthy corecs corec_defs = let val (Rs, Ss, goals, _) = mk_co_rec_transfer_goals lthy corecs; val (_, _, _, (((pgss, pss, qssss, gssss), _), _)) = the corecs_args_types; val goal = Logic.mk_conjunction_balanced goals; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_corec_transfer_tac ctxt (map (Thm.cterm_of ctxt) Ss) (map (Thm.cterm_of ctxt) Rs) type_definitions corec_defs xtor_co_rec_transfers pre_rel_defs live_nesting_rel_eqs (flat pgss) pss qssss gssss) |> Thm.close_derivation \<^here> |> Conjunction.elim_balanced (length goals) end; fun derive_map_o_corec_thmss lthy0 lthy2 corecs corec_defs = if live = 0 then replicate nn [] else let fun variant_names n pre = fst (Variable.variant_fixes (replicate n pre) lthy0); val maps0 = map map_of_bnf fp_bnfs; val f_names = variant_names num_As "f"; val fs = map2 (curry Free) f_names (map (op -->) (As ~~ Bs)); val live_fs = AList.find (op =) (fs ~~ liveness) true; val fmaps = map (fn map0 => Term.list_comb (mk_map live As Bs map0, live_fs)) maps0; val corec_arg_Ts = binder_fun_types (hd (map fastype_of corecs)); val num_rec_args = length corec_arg_Ts; val g_names = variant_names num_rec_args "g"; val gs = map2 (curry Free) g_names corec_arg_Ts; val gcorecs = map (fn corecx => Term.list_comb (corecx, gs)) corecs; val map_o_corec_lhss = map2 (curry HOLogic.mk_comp) fmaps gcorecs; val ABfs = (As ~~ Bs) ~~ fs; fun mk_map_o_corec_arg corec_argB_T g = let val T = range_type (fastype_of g); val U = range_type corec_argB_T; in if T = U then g else HOLogic.mk_comp (build_map lthy2 [] [] (the o AList.lookup (op =) ABfs) (T, U), g) end; fun mk_map_o_corec_rhs corecx = let val args = map2 (mk_map_o_corec_arg o B_ify_T) corec_arg_Ts gs in Term.list_comb (B_ify corecx, args) end; val map_o_corec_rhss = map mk_map_o_corec_rhs corecs; val map_o_corec_goals = map2 (fold_rev (fold_rev Logic.all) [fs, gs] o HOLogic.mk_Trueprop oo curry HOLogic.mk_eq) map_o_corec_lhss map_o_corec_rhss; val map_o_corec_thms = @{map 3} (fn goal => fn corec_def => fn dtor_map_o_corec => Goal.prove_sorry lthy2 [] [] goal (fn {context = ctxt, ...} => mk_co_rec_o_map_tac ctxt corec_def pre_map_defs live_nesting_map_ident0s abs_inverses dtor_map_o_corec) |> Thm.close_derivation \<^here>) map_o_corec_goals corec_defs xtor_co_rec_o_maps; in map single map_o_corec_thms end; fun derive_note_coinduct_corecs_thms_for_types ((((map_thmss, map_disc_iffss, map_selsss, rel_injectss, rel_distinctss, rel_selss, rel_intross, rel_casess, pred_injectss, set_thmss, set_selsssss, set_introsssss, set_casess, ctr_transferss, case_transferss, disc_transferss, sel_transferss), (_, _, ctor_iff_dtors, ctr_defss, ctr_sugars)), (corecs, corec_defs)), lthy) = let val (([(coinduct_thms, coinduct_thm), (coinduct_strong_thms, coinduct_strong_thm)], (coinduct_attrs, common_coinduct_attrs)), corec_thmss, corec_disc_thmss, (corec_disc_iff_thmss, corec_disc_iff_attrs), (corec_sel_thmsss, corec_sel_attrs)) = derive_coinduct_corecs_thms_for_types lthy pre_bnfs (the corecs_args_types) xtor_co_i dtor_injects dtor_ctors xtor_co_rec_thms live_nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss mss ns abs_inverses abs_inverses I ctr_defss ctr_sugars corecs corec_defs; fun distinct_prems ctxt thm = Goal.prove (*no sorry*) ctxt [] [] (thm |> Thm.prop_of |> Logic.strip_horn |>> distinct (op aconv) |> Logic.list_implies) (fn _ => HEADGOAL (cut_tac thm THEN' assume_tac ctxt) THEN ALLGOALS eq_assume_tac); fun eq_ifIN _ [thm] = thm | eq_ifIN ctxt (thm :: thms) = distinct_prems ctxt (@{thm eq_ifI} OF (map (unfold_thms ctxt @{thms atomize_imp[of _ "t = u" for t u]}) [thm, eq_ifIN ctxt thms])); val corec_code_thms = map (eq_ifIN lthy) corec_thmss; val corec_sel_thmss = map flat corec_sel_thmsss; val coinduct_type_attr = Attrib.internal \<^here> o K o Induct.coinduct_type; val coinduct_pred_attr = Attrib.internal \<^here> o K o Induct.coinduct_pred; val flat_corec_thms = append oo append; val corec_transfer_thmss = map single (derive_corec_transfer_thms lthy corecs corec_defs val ((rel_coinduct_thmss, common_rel_coinduct_thms), (rel_coinduct_attrs, common_rel_coinduct_attrs)) = if live = 0 then ((replicate nn [], []), ([], [])) else let val ((rel_coinduct_thms, common_rel_coinduct_thm), (rel_coinduct_attrs, common_rel_coinduct_attrs)) = derive_rel_coinduct_thms_for_types lthy nn fpTs ns As Bs mss ctr_sugars abs_inverses abs_injects ctor_injects dtor_ctors pre_rel_defs ctr_defss xtor_rel_co_induct live_nesting_rel_eqs; in ((map single rel_coinduct_thms, single common_rel_coinduct_thm), (rel_coinduct_attrs, common_rel_coinduct_attrs)) end; val map_o_corec_thmss = derive_map_o_corec_thmss lthy lthy corecs corec_defs; val (set_induct_thms, set_induct_attrss) = derive_set_induct_thms_for_types lthy nn fpTs (map #ctrs ctr_sugars) (map (map (mk_set As)) (map sets_of_bnf fp_bnfs)) dtor_set_inducts (map #exhaust ctr_sugars) (flat pre_set_defss) (flat ctr_defss) dtor_ctors abs_inverses |> split_list; val simp_thmss = @{map 6} mk_simp_thms ctr_sugars (@{map 3} flat_corec_thms corec_disc_thmss corec_disc_iff_thmss corec_sel_thmss) map_thmss rel_injectss rel_distinctss set_thmss; val common_notes = (set_inductN, set_induct_thms, nth set_induct_attrss) :: (if nn > 1 then [(coinductN, [coinduct_thm], K common_coinduct_attrs), (coinduct_strongN, [coinduct_strong_thm], K common_coinduct_attrs), (rel_coinductN, common_rel_coinduct_thms, K common_rel_coinduct_attrs)] else []) |> massage_simple_notes fp_common_name; val notes = [(coinductN, map single coinduct_thms, fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]), (coinduct_strongN, map single coinduct_strong_thms, K coinduct_attrs), (corecN, corec_thmss, K []), (corec_codeN, map single corec_code_thms, K (nitpicksimp_attrs)), (corec_discN, corec_disc_thmss, K []), (corec_disc_iffN, corec_disc_iff_thmss, K corec_disc_iff_attrs), (corec_selN, corec_sel_thmss, K corec_sel_attrs), (corec_transferN, corec_transfer_thmss, K []), (map_o_corecN, map_o_corec_thmss, K []), (rel_coinductN, rel_coinduct_thmss, K (rel_coinduct_attrs @ [coinduct_pred_attr ""])), (simpsN, simp_thmss, K [])] |> massage_multi_notes fp_b_names fpTs; in lthy |> fold (Spec_Rules.add Binding.empty Spec_Rules.equational corecs) [flat corec_sel_thmss, flat corec_thmss] |> plugins code_plugin ? Code.declare_default_eqns (map (rpair true) corec_code_thms) |> Local_Theory.notes (common_notes @ notes) |-> interpret_bnfs_register_fp_sugars plugins fpTs fpBTs Xs Greatest_FP pre_bnfs absT_inf fp_nesting_bnfs live_nesting_bnfs fp_res ctrXs_Tsss ctor_iff_dtors ctr_defss ctr_sugar corecs corec_defs map_thmss [coinduct_thm, coinduct_strong_thm] (transpose [coinduct_thms, coinduct_strong_thms]) corec_thmss corec_disc_thmss corec_sel_thmsss rel_injectss rel_distinctss map_disc_iffss map_selsss rel_selss rel_intross rel_casess pred_injectss set_thmss set_selsssss set_introsssss set_casess ctr_transferss case_transferss disc_transferss sel_transferss corec_disc_iff_thmss (map single corec_code_thms) corec_transfer_thmss common_rel_coinduct_thms rel_coinduct_thmss set_induct_thms (replicate nn (if nn = 1 then set_induct_thms else [])) map_o_corec_thmss end; val lthy = lthy |> live > 0 ? fold2 (fn Type (s, _) => fn bnf => register_bnf_raw s bnf) fpTs fp_bnfs |> @{fold_map 29} define_ctrs_dtrs_for_type_etc fp_bnfs fp_bs fpTs Cs Es ctors dtors xtor_co_recs ctor_dtors dtor_ctors ctor_injects pre_map_defs pre_set_defss pre_rel_def xtor_maps xtor_setss xtor_rels ns kss mss abss abs_injects type_definitions ctr_bindingss ctr_mixfixess ctr_Tsss disc_bindingss sel_bindingsss raw_sel_default_eqss |> wrap_ctrs_derive_map_set_rel_pred_thms_define_co_rec_for_types |> case_fp fp derive_note_induct_recs_thms_for_types derive_note_coinduct_corecs_thms_for_types; val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ co_prefix fp ^ "datatype")); in lthy end; fun co_datatypes fp = define_co_datatypes (K I) (K I) (K I) (K I) fp; fun co_datatype_cmd fp construct_fp options lthy = define_co_datatypes Plugin_Name.make_filter Typedecl.read_constraint Syntax.parse_t Syntax.parse_term fp construct_fp options lthy handle EMPTY_DATATYPE s => error ("Cannot define empty datatype " ^ quote s); val parse_ctr_arg = \<^keyword>\<open>(\<close> |-- parse_binding_colon -- Parse.typ --| \<^keyword>\<open>)\<close> || Parse.typ >> pair Binding.empty; val parse_ctr_specs = Parse.enum1 "|" (parse_ctr_spec Parse.binding parse_ctr_arg -- Parse.opt_mixfix); val parse_spec = parse_type_args_named_constrained -- Parse.binding -- Parse.opt_mixfix -- (\<^keyword>\<open>=\<close> |-- parse_ctr_specs) -- parse_map_rel_pred_bindings -- parse_se val parse_co_datatype = parse_ctr_options -- Parse.and_list1 parse_spec; fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp; end;
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2026-05-26