author  blanchet 
Wed, 05 Jun 2013 11:30:24 +0200  
changeset 52300  4a4da43e855a 
parent 52299  085771de5720 
child 52301  7935e82a4ae4 
permissions  rwrr 
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(* Title: HOL/BNF/Tools/bnf_fp_def_sugar.ML 
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Author: Jasmin Blanchette, TU Muenchen 
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Copyright 2012 

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Sugared datatype and codatatype constructions. 
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*) 
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signature BNF_FP_DEF_SUGAR = 
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sig 
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type fp_sugar = 
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{T: typ, 
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fp: BNF_FP_Util.fp_kind, 
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index: int, 
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pre_bnfs: BNF_Def.bnf list, 

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fp_res: BNF_FP_Util.fp_result, 
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ctr_defss: thm list list, 
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ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list, 
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un_folds: term list, 
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co_recs: term list, 
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co_induct: thm, 
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strong_co_induct: thm, 

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un_fold_thmss: thm list list, 
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co_rec_thmss: thm list list}; 
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val of_fp_sugar: (fp_sugar > 'a list) > fp_sugar > 'a 
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val morph_fp_sugar: morphism > fp_sugar > fp_sugar 
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val fp_sugar_of: Proof.context > string > fp_sugar option 

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val tvar_subst: theory > typ list > typ list > ((string * int) * typ) list 
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val exists_subtype_in: typ list > typ > bool 
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val flat_rec: ('a > 'b list) > 'a list > 'b list 
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val mk_co_iter: theory > BNF_FP_Util.fp_kind > typ > typ list > term > term 
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val nesty_bnfs: Proof.context > typ list list list > typ list > BNF_Def.bnf list 
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val indexify_fst: ''a list > (int > ''a * 'b > 'c) > ''a * 'b > 'c 
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val mk_un_fold_co_rec_prelims: BNF_FP_Util.fp_kind > typ list > typ list > int list > 
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int list list > term list > term list > Proof.context > 
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(term list * term list * ((term list list * typ list list * term list list list list) 
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* (term list list * typ list list * term list list list list)) option 
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* (term list * term list list 
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* ((term list list * term list list list list * term list list list list) 

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* (typ list * typ list list list * typ list list)) 

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* ((term list list * term list list list list * term list list list list) 

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* (typ list * typ list list list * typ list list))) option) 

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* Proof.context 

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val mk_map: int > typ list > typ list > term > term 
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val build_map: local_theory > (typ * typ > term) > typ * typ > term 
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val mk_iter_fun_arg_typessss: typ list > int list > int list list > term > 
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typ list list list list 
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val define_fold_rec: (term list list * typ list list * term list list list list) 
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* (term list list * typ list list * term list list list list) > (string > binding) > 
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typ list > typ list > term > term > Proof.context > 
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(term * term * thm * thm) * Proof.context 
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val define_unfold_corec: term list * term list list 
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* ((term list list * term list list list list * term list list list list) 

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* (typ list * typ list list list * typ list list)) 

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* ((term list list * term list list list list * term list list list list) 

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* (typ list * typ list list list * typ list list)) > 

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(string > binding) > typ list > typ list > term > term > Proof.context > 
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(term * term * thm * thm) * Proof.context 
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val derive_induct_fold_rec_thms_for_types: BNF_Def.bnf list > term list > term list > thm > 
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thm list > thm list > BNF_Def.bnf list > BNF_Def.bnf list > typ list > typ list > 
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term list list > thm list list > term list > term list > thm list > thm list > 
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local_theory > 
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(thm * thm list * Args.src list) * (thm list list * Args.src list) 
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* (thm list list * Args.src list) 
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val derive_coinduct_unfold_corec_thms_for_types: BNF_Def.bnf list > term list > term list > 
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thm > thm > thm list > thm list > thm list > BNF_Def.bnf list > BNF_Def.bnf list > 
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typ list > typ list > typ list > int list list > int list list > int list > 
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thm list list > BNF_Ctr_Sugar.ctr_sugar list > term list > term list > thm list > 
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thm list > local_theory > 
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(thm * thm list * thm * thm list * Args.src list) 
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* (thm list list * thm list list * Args.src list) 

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* (thm list list * thm list list) * (thm list list * thm list list * Args.src list) 
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* (thm list list * thm list list * Args.src list) 
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* (thm list list * thm list list * Args.src list) 

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val co_datatypes: BNF_FP_Util.fp_kind > (mixfix list > binding list > binding list > 
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binding list list > binding list > (string * sort) list > typ list * typ list list > 
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BNF_Def.bnf list > local_theory > BNF_FP_Util.fp_result * local_theory) > 
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(bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) * 
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((((binding * binding) * (binding * typ) list) * (binding * term) list) * 
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mixfix) list) list > 

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local_theory > local_theory 
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val parse_co_datatype_cmd: BNF_FP_Util.fp_kind > (mixfix list > binding list > binding list > 
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binding list list > binding list > (string * sort) list > typ list * typ list list > 
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BNF_Def.bnf list > local_theory > BNF_FP_Util.fp_result * local_theory) > 

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(local_theory > local_theory) parser 
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end; 
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structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR = 
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struct 
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open BNF_Util 
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open BNF_Ctr_Sugar 
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open BNF_Def 
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open BNF_FP_Util 
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open BNF_FP_Def_Sugar_Tactics 
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val EqN = "Eq_"; 
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type fp_sugar = 
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{T: typ, 
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fp: fp_kind, 
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index: int, 
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pre_bnfs: bnf list, 

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fp_res: fp_result, 
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ctr_defss: thm list list, 
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ctr_sugars: ctr_sugar list, 
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un_folds: term list, 
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co_recs: term list, 
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co_induct: thm, 
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strong_co_induct: thm, 

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un_fold_thmss: thm list list, 
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co_rec_thmss: thm list list}; 
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fun of_fp_sugar f (fp_sugar as {index, ...}) = nth (f fp_sugar) index; 
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fun eq_fp_sugar ({T = T1, fp = fp1, index = index1, fp_res = fp_res1, ...} : fp_sugar, 
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{T = T2, fp = fp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) = 
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T1 = T2 andalso fp1 = fp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2); 
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fun morph_fp_sugar phi {T, fp, index, pre_bnfs, fp_res, ctr_defss, ctr_sugars, un_folds, 
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co_recs, co_induct, strong_co_induct, un_fold_thmss, co_rec_thmss} = 

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{T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi) 

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pre_bnfs, fp_res = morph_fp_result phi fp_res, 

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ctr_defss = map (map (Morphism.thm phi)) ctr_defss, 
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ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars, un_folds = map (Morphism.term phi) un_folds, 
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co_recs = map (Morphism.term phi) co_recs, co_induct = Morphism.thm phi co_induct, 

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strong_co_induct = Morphism.thm phi strong_co_induct, 

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un_fold_thmss = map (map (Morphism.thm phi)) un_fold_thmss, 
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co_rec_thmss = map (map (Morphism.thm phi)) co_rec_thmss}; 
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structure Data = Generic_Data 
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( 
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type T = fp_sugar Symtab.table; 
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val empty = Symtab.empty; 
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val extend = I; 
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val merge = Symtab.merge eq_fp_sugar; 
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); 
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val fp_sugar_of = Symtab.lookup o Data.get o Context.Proof; 
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fun register_fp_sugar key fp_sugar = 
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Local_Theory.declaration {syntax = false, pervasive = true} 
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(fn phi => Data.map (Symtab.update_new (key, morph_fp_sugar phi fp_sugar))); 
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fun register_fp_sugars fp pre_bnfs (fp_res as {Ts, ...}) ctr_defss ctr_sugars un_folds co_recs 
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co_induct strong_co_induct un_fold_thmss co_rec_thmss lthy = 

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(0, lthy) 
51859  151 
> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1, 
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register_fp_sugar s {T = T, fp = fp, index = kk, pre_bnfs = pre_bnfs, fp_res = fp_res, 
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ctr_defss = ctr_defss, ctr_sugars = ctr_sugars, un_folds = un_folds, co_recs = co_recs, 

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co_induct = co_induct, strong_co_induct = strong_co_induct, un_fold_thmss = un_fold_thmss, 

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co_rec_thmss = co_rec_thmss} lthy)) Ts 
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> snd; 
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(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *) 
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fun quasi_unambiguous_case_names names = 
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let 

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val ps = map (`Long_Name.base_name) names; 

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val dups = Library.duplicates (op =) (map fst ps); 

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fun underscore s = 

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let val ss = space_explode Long_Name.separator s in 

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space_implode "_" (drop (length ss  2) ss) 

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end; 

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in 

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map (fn (base, full) => if member (op =) dups base then underscore full else base) ps 

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end; 

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val mp_conj = @{thm mp_conj}; 
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val simp_attrs = @{attributes [simp]}; 
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val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs; 
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fun tvar_subst thy Ts Us = 
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Vartab.fold (cons o apsnd snd) (fold (Sign.typ_match thy) (Ts ~~ Us) Vartab.empty) []; 
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val exists_subtype_in = Term.exists_subtype o member (op =); 
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fun resort_tfree S (TFree (s, _)) = TFree (s, S); 
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fun typ_subst_nonatomic inst (T as Type (s, Ts)) = 
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(case AList.lookup (op =) inst T of 
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NONE => Type (s, map (typ_subst_nonatomic inst) Ts) 
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 SOME T' => T') 
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 typ_subst_nonatomic inst T = the_default T (AList.lookup (op =) inst T); 
49205  188 

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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)); 
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fun flat_rec unzipf xs = 
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let val ps = map unzipf xs in 

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(* The first line below gives the preferred order. The second line is for compatibility with the 

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old datatype package: *) 

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(* 
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flat ps 
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*) 
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map hd ps @ maps tl ps 
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end; 
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51829  201 
fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss); 
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fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss 

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 flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) = 

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p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss; 

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fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); 
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs; 
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209 
fun mk_uncurried2_fun f xss = 
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210 
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat_rec I xss); 
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211 

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fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) = 
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213 
Abs ("x", T1, Abs ("y", T2, Var (x, T2 > T1 > T3) $ Bound 0 $ Bound 1)); 
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214 

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215 
fun flip_rels lthy n thm = 
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216 
let 
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217 
val Rs = Term.add_vars (prop_of thm) []; 
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val Rs' = rev (drop (length Rs  n) Rs); 
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219 
val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs'; 
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220 
in 
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221 
Drule.cterm_instantiate cRs thm 
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222 
end; 
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223 

49536  224 
fun mk_ctor_or_dtor get_T Ts t = 
225 
let val Type (_, Ts0) = get_T (fastype_of t) in 

226 
Term.subst_atomic_types (Ts0 ~~ Ts) t 

227 
end; 

228 

229 
val mk_ctor = mk_ctor_or_dtor range_type; 

230 
val mk_dtor = mk_ctor_or_dtor domain_type; 

231 

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232 
fun mk_co_iter thy fp fpT Cs t = 
49536  233 
let 
234 
val (bindings, body) = strip_type (fastype_of t); 

52197  235 
val (f_Cs, prebody) = split_last bindings; 
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val fpT0 = if fp = Least_FP then prebody else body; 
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val Cs0 = distinct (op =) (map (if fp = Least_FP then body_type else domain_type) f_Cs); 
52197  238 
val rho = tvar_subst thy (fpT0 :: Cs0) (fpT :: Cs); 
49536  239 
in 
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Term.subst_TVars rho t 
49536  241 
end; 
242 

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fun mk_co_iters thy fp fpTs Cs ts0 = 
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let 
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val nn = length fpTs; 
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val (fpTs0, Cs0) = 
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map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0 
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> split_list; 
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val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs); 
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250 
in 
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map (Term.subst_TVars rho) ts0 
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252 
end; 
51827  253 

52169  254 
val mk_fp_iter_fun_types = fst o split_last o binder_types o fastype_of; 
255 

52297  256 
fun project_co_recT special_Tname Cs proj = 
51827  257 
let 
52297  258 
fun project (Type (s, Ts as [T, U])) = 
259 
if s = special_Tname andalso member (op =) Cs U then proj (T, U) 

52209  260 
else Type (s, map project Ts) 
52297  261 
 project (Type (s, Ts)) = Type (s, map project Ts) 
52209  262 
 project T = T; 
263 
in project end; 

264 

265 
val project_corecT = project_co_recT @{type_name sum}; 

266 

52296  267 
fun unzip_recT Cs (T as Type (@{type_name prod}, Ts as [_, U])) = 
268 
if member (op =) Cs U then Ts else [T] 

52216  269 
 unzip_recT _ T = [T]; 
51827  270 

51846  271 
fun mk_fun_arg_typess n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type; 
272 

52296  273 
fun mk_iter_fun_arg_typessss Cs ns mss = 
51885  274 
mk_fp_iter_fun_types 
275 
#> map3 mk_fun_arg_typess ns mss 

52296  276 
#> map (map (map (unzip_recT Cs))); 
51885  277 

52296  278 
fun mk_fold_rec_args_types Cs ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy = 
51832  279 
let 
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val Css = map2 replicate ns Cs; 
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val y_Tsss = map3 mk_fun_arg_typess ns mss ctor_fold_fun_Ts; 
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val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts > C)) Cs y_Tsss; 
51832  283 

284 
val ((gss, ysss), lthy) = 

285 
lthy 

286 
> mk_Freess "f" g_Tss 

287 
>> mk_Freesss "x" y_Tsss; 

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val yssss = map (map (map single)) ysss; 
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289 

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val z_Tssss = 
52296  291 
map3 (fn n => fn ms => map2 (map (unzip_recT Cs) oo dest_tupleT) ms o 
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292 
dest_sumTN_balanced n o domain_type) ns mss ctor_rec_fun_Ts; 
51832  293 

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294 
val z_Tsss' = map (map (flat_rec I)) z_Tssss; 
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295 
val h_Tss = map2 (map2 (curry (op >))) z_Tsss' Css; 
51832  296 

297 
val hss = map2 (map2 retype_free) h_Tss gss; 

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298 
val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss; 
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299 
val (zssss_tl, lthy) = 
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300 
lthy 
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301 
> mk_Freessss "y" (map (map (map tl)) z_Tssss); 
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302 
val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl; 
51832  303 
in 
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304 
(((gss, g_Tss, yssss), (hss, h_Tss, zssss)), lthy) 
51832  305 
end; 
306 

52297  307 
fun mk_unfold_corec_args_types Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy = 
51829  308 
let 
309 
(*avoid "'a itself" arguments in coiterators and corecursors*) 

310 
fun repair_arity [0] = [1] 

311 
 repair_arity ms = ms; 

312 

313 
fun unzip_corecT T = 

52297  314 
if exists_subtype_in Cs T then [project_corecT Cs fst T, project_corecT Cs snd T] 
52209  315 
else [T]; 
51829  316 

51831  317 
val p_Tss = map2 (fn n => replicate (Int.max (0, n  1)) o mk_pred1T) ns Cs; 
51829  318 

319 
fun mk_types maybe_unzipT fun_Ts = 

320 
let 

321 
val f_sum_prod_Ts = map range_type fun_Ts; 

322 
val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts; 

323 
val f_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss; 

51889  324 
val f_Tssss = map2 (fn C => map (map (map (curry (op >) C) o maybe_unzipT))) Cs f_Tsss; 
51829  325 
val q_Tssss = 
52213  326 
map (map (map (fn [_] => []  [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss; 
51829  327 
val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss; 
51889  328 
in (q_Tssss, f_Tssss, (f_sum_prod_Ts, f_Tsss, pf_Tss)) end; 
51829  329 

51889  330 
val (r_Tssss, g_Tssss, unfold_types) = mk_types single dtor_unfold_fun_Ts; 
331 
val (s_Tssss, h_Tssss, corec_types) = mk_types unzip_corecT dtor_corec_fun_Ts; 

51831  332 

51829  333 
val (((cs, pss), gssss), lthy) = 
334 
lthy 

335 
> mk_Frees "a" Cs 

336 
>> mk_Freess "p" p_Tss 

337 
>> mk_Freessss "g" g_Tssss; 

338 
val rssss = map (map (map (fn [] => []))) r_Tssss; 

339 

340 
val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss; 

341 
val ((sssss, hssss_tl), lthy) = 

342 
lthy 

343 
> mk_Freessss "q" s_Tssss 

344 
>> mk_Freessss "h" (map (map (map tl)) h_Tssss); 

345 
val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl; 

51831  346 

347 
val cpss = map2 (map o rapp) cs pss; 

51829  348 

51889  349 
fun mk_args qssss fssss = 
51831  350 
let 
351 
val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss; 

352 
val cqssss = map2 (map o map o map o rapp) cs qssss; 

353 
val cfssss = map2 (map o map o map o rapp) cs fssss; 

354 
in (pfss, cqssss, cfssss) end; 

355 

51889  356 
val unfold_args = mk_args rssss gssss; 
357 
val corec_args = mk_args sssss hssss; 

51831  358 
in 
51889  359 
((cs, cpss, (unfold_args, unfold_types), (corec_args, corec_types)), lthy) 
51831  360 
end; 
51829  361 

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362 
fun mk_un_fold_co_rec_prelims fp fpTs Cs ns mss fp_folds0 fp_recs0 lthy = 
51903  363 
let 
52169  364 
val thy = Proof_Context.theory_of lthy; 
365 

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366 
val (fp_fold_fun_Ts, fp_folds) = mk_co_iters thy fp fpTs Cs fp_folds0 
52173  367 
> `(mk_fp_iter_fun_types o hd); 
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368 
val (fp_rec_fun_Ts, fp_recs) = mk_co_iters thy fp fpTs Cs fp_recs0 
52173  369 
> `(mk_fp_iter_fun_types o hd); 
51903  370 

371 
val ((fold_rec_args_types, unfold_corec_args_types), lthy') = 

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372 
if fp = Least_FP then 
52296  373 
mk_fold_rec_args_types Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy 
51903  374 
>> (rpair NONE o SOME) 
375 
else 

52297  376 
mk_unfold_corec_args_types Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy 
51903  377 
>> (pair NONE o SOME) 
378 
in 

379 
((fp_folds, fp_recs, fold_rec_args_types, unfold_corec_args_types), lthy') 

380 
end; 

381 

49536  382 
fun mk_map live Ts Us t = 
383 
let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) >> List.last in 

384 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 

385 
end; 

386 

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387 
fun mk_rel live Ts Us t = 
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388 
let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in 
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389 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
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390 
end; 
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391 

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392 
fun liveness_of_fp_bnf n bnf = 
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393 
(case T_of_bnf bnf of 
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394 
Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts 
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395 
 _ => replicate n false); 
49536  396 

49124  397 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  398 

49298
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399 
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types (); 
49119  400 

49298
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401 
fun merge_type_args (As, As') = 
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402 
if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types (); 
49119  403 

49591
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404 
fun reassoc_conjs thm = 
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405 
reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]}) 
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406 
handle THM _ => thm; 
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407 

51767
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408 
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs; 
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409 
fun type_binding_of ((((_, b), _), _), _) = b; 
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410 
fun map_binding_of (((_, (b, _)), _), _) = b; 
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411 
fun rel_binding_of (((_, (_, b)), _), _) = b; 
49181  412 
fun mixfix_of ((_, mx), _) = mx; 
49121  413 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  414 

49286  415 
fun disc_of ((((disc, _), _), _), _) = disc; 
416 
fun ctr_of ((((_, ctr), _), _), _) = ctr; 

417 
fun args_of (((_, args), _), _) = args; 

418 
fun defaults_of ((_, ds), _) = ds; 

49181  419 
fun ctr_mixfix_of (_, mx) = mx; 
49119  420 

51907  421 
fun add_nesty_bnf_names Us = 
422 
let 

423 
fun add (Type (s, Ts)) ss = 

424 
let val (needs, ss') = fold_map add Ts ss in 

425 
if exists I needs then (true, insert (op =) s ss') else (false, ss') 

426 
end 

427 
 add T ss = (member (op =) Us T, ss); 

428 
in snd oo add end; 

429 

430 
fun nesty_bnfs ctxt ctr_Tsss Us = 

431 
map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []); 

432 

51855  433 
fun indexify_fst xs f (x, y) = f (find_index (curry (op =) x) xs) (x, y); 
434 

51854  435 
fun build_map lthy build_simple = 
51853  436 
let 
437 
fun build (TU as (T, U)) = 

438 
if T = U then 

439 
id_const T 

440 
else 

441 
(case TU of 

51854  442 
(Type (s, Ts), Type (s', Us)) => 
443 
if s = s' then 

444 
let 

445 
val bnf = the (bnf_of lthy s); 

446 
val live = live_of_bnf bnf; 

447 
val mapx = mk_map live Ts Us (map_of_bnf bnf); 

448 
val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx))); 

449 
in Term.list_comb (mapx, map build TUs') end 

450 
else 

451 
build_simple TU 

51853  452 
 _ => build_simple TU); 
453 
in build end; 

454 

52298  455 
fun mk_iter_body ctor_iter fss xssss = 
456 
Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss); 

51884  457 

51900  458 
fun mk_preds_getterss_join c cps sum_prod_T cqfss = 
459 
let val n = length cqfss in 

460 
Term.lambda c (mk_IfN sum_prod_T cps 

461 
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n))) 

462 
end; 

51886  463 

51900  464 
fun mk_coiter_body lthy cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter = 
51888  465 
let 
466 
fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd); 

467 

468 
fun build_dtor_coiter_arg _ [] [cf] = cf 

469 
 build_dtor_coiter_arg T [cq] [cf, cf'] = 

470 
mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf) 

471 
(build_sum_inj Inr_const (fastype_of cf', T) $ cf') 

472 

473 
val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss; 

474 
in 

51900  475 
Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss) 
51888  476 
end; 
51886  477 

52172  478 
fun define_fold_rec (fold_only, rec_only) mk_binding fpTs Cs ctor_fold ctor_rec lthy0 = 
51897  479 
let 
52170
564be617ae84
generalized "mk_co_iter" to handle mutualized (co)iterators
blanchet
parents:
52169
diff
changeset

480 
val thy = Proof_Context.theory_of lthy0; 
564be617ae84
generalized "mk_co_iter" to handle mutualized (co)iterators
blanchet
parents:
52169
diff
changeset

481 

51899  482 
val nn = length fpTs; 
483 

52170
564be617ae84
generalized "mk_co_iter" to handle mutualized (co)iterators
blanchet
parents:
52169
diff
changeset

484 
val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of ctor_fold)); 
51897  485 

52214
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

486 
fun generate_iter (suf, ctor_iter, (fss, f_Tss, xssss)) = 
51897  487 
let 
51899  488 
val res_T = fold_rev (curry (op >)) f_Tss fpT_to_C; 
51897  489 
val binding = mk_binding suf; 
490 
val spec = 

491 
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)), 

52298  492 
mk_iter_body ctor_iter fss xssss); 
51897  493 
in (binding, spec) end; 
494 

495 
val binding_specs = 

496 
map generate_iter [(foldN, ctor_fold, fold_only), (recN, ctor_rec, rec_only)]; 

497 

51907  498 
val ((csts, defs), (lthy', lthy)) = lthy0 
51897  499 
> apfst split_list o fold_map (fn (b, spec) => 
500 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

501 
#>> apsnd snd) binding_specs 

502 
> `Local_Theory.restore; 

503 

504 
val phi = Proof_Context.export_morphism lthy lthy'; 

505 

506 
val [fold_def, rec_def] = map (Morphism.thm phi) defs; 

507 

52207
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

508 
val [foldx, recx] = map (mk_co_iter thy Least_FP fpT Cs o Morphism.term phi) csts; 
51897  509 
in 
510 
((foldx, recx, fold_def, rec_def), lthy') 

511 
end; 

512 

52207
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

513 
(* TODO: merge with above function? *) 
52172  514 
fun define_unfold_corec (cs, cpss, unfold_only, corec_only) mk_binding fpTs Cs dtor_unfold 
51907  515 
dtor_corec lthy0 = 
51897  516 
let 
52170
564be617ae84
generalized "mk_co_iter" to handle mutualized (co)iterators
blanchet
parents:
52169
diff
changeset

517 
val thy = Proof_Context.theory_of lthy0; 
564be617ae84
generalized "mk_co_iter" to handle mutualized (co)iterators
blanchet
parents:
52169
diff
changeset

518 

51899  519 
val nn = length fpTs; 
520 

52170
564be617ae84
generalized "mk_co_iter" to handle mutualized (co)iterators
blanchet
parents:
52169
diff
changeset

521 
val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of dtor_unfold)); 
51897  522 

523 
fun generate_coiter (suf, dtor_coiter, ((pfss, cqssss, cfssss), 

524 
(f_sum_prod_Ts, f_Tsss, pf_Tss))) = 

525 
let 

51899  526 
val res_T = fold_rev (curry (op >)) pf_Tss C_to_fpT; 
51897  527 
val binding = mk_binding suf; 
528 
val spec = 

529 
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)), 

51907  530 
mk_coiter_body lthy0 cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter); 
51897  531 
in (binding, spec) end; 
532 

533 
val binding_specs = 

534 
map generate_coiter [(unfoldN, dtor_unfold, unfold_only), (corecN, dtor_corec, corec_only)]; 

535 

51907  536 
val ((csts, defs), (lthy', lthy)) = lthy0 
51897  537 
> apfst split_list o fold_map (fn (b, spec) => 
538 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

539 
#>> apsnd snd) binding_specs 

540 
> `Local_Theory.restore; 

541 

542 
val phi = Proof_Context.export_morphism lthy lthy'; 

543 

544 
val [unfold_def, corec_def] = map (Morphism.thm phi) defs; 

545 

52207
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

546 
val [unfold, corec] = map (mk_co_iter thy Greatest_FP fpT Cs o Morphism.term phi) csts; 
51897  547 
in 
548 
((unfold, corec, unfold_def, corec_def), lthy') 

52172  549 
end ; 
51897  550 

52171  551 
fun derive_induct_fold_rec_thms_for_types pre_bnfs ctor_folds ctor_recs ctor_induct ctor_fold_thms 
51912  552 
ctor_rec_thms nesting_bnfs nested_bnfs fpTs Cs ctrss ctr_defss folds recs fold_defs rec_defs 
51827  553 
lthy = 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

554 
let 
51827  555 
val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss; 
556 

51815  557 
val nn = length pre_bnfs; 
51827  558 
val ns = map length ctr_Tsss; 
559 
val mss = map (map length) ctr_Tsss; 

51815  560 

51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

561 
val pre_map_defs = map map_def_of_bnf pre_bnfs; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

562 
val pre_set_defss = map set_defs_of_bnf pre_bnfs; 
51830  563 
val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs; 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

564 
val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

565 
val nested_set_map's = maps set_map'_of_bnf nested_bnfs; 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

566 

51816  567 
val fp_b_names = map base_name_of_typ fpTs; 
51811  568 

52171  569 
val ctor_fold_fun_Ts = mk_fp_iter_fun_types (hd ctor_folds); 
570 
val ctor_rec_fun_Ts = mk_fp_iter_fun_types (hd ctor_recs); 

51827  571 

51835
56523caf372f
Added maps, sets, rels to "simps" thm collection
blanchet
parents:
51833
diff
changeset

572 
val (((gss, _, _), (hss, _, _)), names_lthy0) = 
52296  573 
mk_fold_rec_args_types Cs ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy; 
51827  574 

51832  575 
val ((((ps, ps'), xsss), us'), names_lthy) = 
576 
names_lthy0 

51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

577 
> mk_Frees' "P" (map mk_pred1T fpTs) 
51827  578 
>> mk_Freesss "x" ctr_Tsss 
51816  579 
>> Variable.variant_fixes fp_b_names; 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

580 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

581 
val us = map2 (curry Free) us' fpTs; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

582 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

583 
fun mk_sets_nested bnf = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

584 
let 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

585 
val Type (T_name, Us) = T_of_bnf bnf; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

586 
val lives = lives_of_bnf bnf; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

587 
val sets = sets_of_bnf bnf; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

588 
fun mk_set U = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

589 
(case find_index (curry (op =) U) lives of 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

590 
~1 => Term.dummy 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

591 
 i => nth sets i); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

592 
in 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

593 
(T_name, map mk_set Us) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

594 
end; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

595 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

596 
val setss_nested = map mk_sets_nested nested_bnfs; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

597 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

598 
val (induct_thms, induct_thm) = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

599 
let 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

600 
fun mk_set Ts t = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

601 
let val Type (_, Ts0) = domain_type (fastype_of t) in 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

602 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

603 
end; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

604 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

605 
fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

606 
(case find_index (curry (op =) T) fpTs of 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

607 
~1 => 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

608 
(case AList.lookup (op =) setss_nested T_name of 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

609 
NONE => [] 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

610 
 SOME raw_sets0 => 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

611 
let 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

612 
val (Ts, raw_sets) = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

613 
split_list (filter (exists_subtype_in fpTs o fst) (Ts0 ~~ raw_sets0)); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

614 
val sets = map (mk_set Ts0) raw_sets; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

615 
val (ys, names_lthy') = names_lthy > mk_Frees s Ts; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

616 
val xysets = map (pair x) (ys ~~ sets); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

617 
val ppremss = map (mk_raw_prem_prems names_lthy') ys; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

618 
in 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

619 
flat (map2 (map o apfst o cons) xysets ppremss) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

620 
end) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

621 
 kk => [([], (kk + 1, x))]) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

622 
 mk_raw_prem_prems _ _ = []; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

623 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

624 
fun close_prem_prem xs t = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

625 
fold_rev Logic.all (map Free (drop (nn + length xs) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

626 
(rev (Term.add_frees t (map dest_Free xs @ ps'))))) t; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

627 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

628 
fun mk_prem_prem xs (xysets, (j, x)) = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

629 
close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) => 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

630 
HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets, 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

631 
HOLogic.mk_Trueprop (nth ps (j  1) $ x))); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

632 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

633 
fun mk_raw_prem phi ctr ctr_Ts = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

634 
let 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

635 
val (xs, names_lthy') = names_lthy > mk_Frees "x" ctr_Ts; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

636 
val pprems = maps (mk_raw_prem_prems names_lthy') xs; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

637 
in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

638 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

639 
fun mk_prem (xs, raw_pprems, concl) = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

640 
fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl)); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

641 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

642 
val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

643 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

644 
val goal = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

645 
Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss, 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

646 
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us))); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

647 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

648 
val kksss = map (map (map (fst o snd) o #2)) raw_premss; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

649 

51814  650 
val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss); 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

651 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

652 
val thm = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

653 
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} => 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

654 
mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

655 
pre_set_defss) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

656 
> singleton (Proof_Context.export names_lthy lthy) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

657 
> Thm.close_derivation; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

658 
in 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

659 
`(conj_dests nn) thm 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

660 
end; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

661 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

662 
val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

663 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

664 
val (fold_thmss, rec_thmss) = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

665 
let 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

666 
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

667 
val gfolds = map (lists_bmoc gss) folds; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

668 
val hrecs = map (lists_bmoc hss) recs; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

669 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

670 
fun mk_goal fss fiter xctr f xs fxs = 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

671 
fold_rev (fold_rev Logic.all) (xs :: fss) 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

672 
(mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs))); 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

673 

51845  674 
val mk_U = typ_subst_nonatomic (map2 pair fpTs Cs); 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

675 

52217  676 
fun mk_nested_U maybe_mk_prodT = 
677 
typ_subst_nonatomic (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs); 

52214
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

678 

52300  679 
fun unzip_iters fiters maybe_tick maybe_mk_prodT x = 
680 
let val Free (_, T) = x in 

681 
if member (op =) fpTs T then 

682 
[x, build_map lthy (indexify_fst fpTs (K o nth fiters)) (T, mk_U T) $ x] 

683 
else if exists_subtype_in fpTs T then 

684 
[build_map lthy (indexify_fst fpTs (fn kk => fn _ => 

685 
maybe_tick (nth us kk) (nth fiters kk))) (T, mk_nested_U maybe_mk_prodT T) $ x] 

686 
else 

687 
[x] 

688 
end; 

52214
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

689 

4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

690 
fun tick u f = Term.lambda u (HOLogic.mk_prod (u, f $ u)); 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

691 

52215
7facaee8586f
tuning (use lists rather than pairs of lists throughout)
blanchet
parents:
52214
diff
changeset

692 
val gxsss = map (map (flat_rec (single o List.last o unzip_iters gfolds (K I) (K I)))) xsss; 
52214
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

693 
val hxsss = map (map (flat_rec (unzip_iters hrecs tick (curry HOLogic.mk_prodT)))) xsss; 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

694 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

695 
val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

696 
val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

697 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

698 
val fold_tacss = 
52214
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

699 
map2 (map o mk_iter_tac pre_map_defs nesting_map_ids'' fold_defs) 
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

700 
ctor_fold_thms ctr_defss; 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

701 
val rec_tacss = 
52214
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

702 
map2 (map o mk_iter_tac pre_map_defs (nested_map_ids'' @ nesting_map_ids'') rec_defs) 
4cc5a80bba80
generalized recursors, effectively reverting inductive half of c7a034d01936
blanchet
parents:
52213
diff
changeset

703 
ctor_rec_thms ctr_defss; 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

704 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

705 
fun prove goal tac = 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

706 
Goal.prove_sorry lthy [] [] goal (tac o #context) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

707 
> Thm.close_derivation; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

708 
in 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

709 
(map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

710 
end; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

711 

355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

712 
val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases)); 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

713 
in 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

714 
((induct_thm, induct_thms, [induct_case_names_attr]), 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

715 
(fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs)) 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

716 
end; 
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

717 

52171  718 
fun derive_coinduct_unfold_corec_thms_for_types pre_bnfs dtor_unfolds dtor_corecs dtor_coinduct 
51814  719 
dtor_strong_induct dtor_ctors dtor_unfold_thms dtor_corec_thms nesting_bnfs nested_bnfs fpTs Cs 
51840  720 
As kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy = 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

721 
let 
51815  722 
val nn = length pre_bnfs; 
723 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

724 
val pre_map_defs = map map_def_of_bnf pre_bnfs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

725 
val pre_rel_defs = map rel_def_of_bnf pre_bnfs; 
51830  726 
val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs; 
727 
val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs; 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

728 
val nested_map_comp's = map map_comp'_of_bnf nested_bnfs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

729 
val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

730 
val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

731 

51816  732 
val fp_b_names = map base_name_of_typ fpTs; 
51811  733 

52171  734 
val dtor_unfold_fun_Ts = mk_fp_iter_fun_types (hd dtor_unfolds); 
735 
val dtor_corec_fun_Ts = mk_fp_iter_fun_types (hd dtor_corecs); 

51829  736 

51840  737 
val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars; 
738 
val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars; 

739 
val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars; 

740 
val exhausts = map #exhaust ctr_sugars; 

741 
val disc_thmsss = map #disc_thmss ctr_sugars; 

742 
val discIss = map #discIs ctr_sugars; 

743 
val sel_thmsss = map #sel_thmss ctr_sugars; 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

744 

51831  745 
val ((cs, cpss, ((pgss, crssss, cgssss), _), ((phss, csssss, chssss), _)), names_lthy0) = 
52297  746 
mk_unfold_corec_args_types Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy; 
51831  747 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

748 
val (((rs, us'), vs'), names_lthy) = 
51831  749 
names_lthy0 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

750 
> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs) 
51816  751 
>> Variable.variant_fixes fp_b_names 
752 
>> Variable.variant_fixes (map (suffix "'") fp_b_names); 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

753 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

754 
val us = map2 (curry Free) us' fpTs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

755 
val udiscss = map2 (map o rapp) us discss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

756 
val uselsss = map2 (map o map o rapp) us selsss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

757 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

758 
val vs = map2 (curry Free) vs' fpTs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

759 
val vdiscss = map2 (map o rapp) vs discss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

760 
val vselsss = map2 (map o map o rapp) vs selsss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

761 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

762 
val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

763 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

764 
val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

765 
val uv_eqs = map2 (curry HOLogic.mk_eq) us vs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

766 
val strong_rs = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

767 
map4 (fn u => fn v => fn uvr => fn uv_eq => 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

768 
fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

769 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

770 
fun build_rel rs' T = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

771 
(case find_index (curry (op =) T) fpTs of 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

772 
~1 => 
51856  773 
if exists_subtype_in fpTs T then 
774 
let 

775 
val Type (s, Ts) = T 

776 
val bnf = the (bnf_of lthy s); 

777 
val live = live_of_bnf bnf; 

778 
val rel = mk_rel live Ts Ts (rel_of_bnf bnf); 

779 
val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel))); 

780 
in Term.list_comb (rel, map (build_rel rs') Ts') end 

781 
else 

782 
HOLogic.eq_const T 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

783 
 kk => nth rs' kk); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

784 

51856  785 
fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel)); 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

786 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

787 
fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

788 
(if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @ 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

789 
(if null usels then 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

790 
[] 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

791 
else 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

792 
[Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc], 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

793 
Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

794 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

795 
fun mk_prem_concl rs' n udiscs uselss vdiscs vselss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

796 
Library.foldr1 HOLogic.mk_conj 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

797 
(flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss)) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

798 
handle List.Empty => @{term True}; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

799 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

800 
fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

801 
fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr, 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

802 
HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss))); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

803 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

804 
val concl = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

805 
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

806 
(map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v))) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

807 
uvrs us vs)); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

808 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

809 
fun mk_goal rs' = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

810 
Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss, 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

811 
concl); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

812 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

813 
val goal = mk_goal rs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

814 
val strong_goal = mk_goal strong_rs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

815 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

816 
fun prove dtor_coinduct' goal = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

817 
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} => 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

818 
mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors 
51819  819 
exhausts ctr_defss disc_thmsss sel_thmsss) 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

820 
> singleton (Proof_Context.export names_lthy lthy) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

821 
> Thm.close_derivation; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

822 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

823 
fun postproc nn thm = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

824 
Thm.permute_prems 0 nn 
51828  825 
(if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm) 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

826 
> Drule.zero_var_indexes 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

827 
> `(conj_dests nn); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

828 
in 
51814  829 
(postproc nn (prove dtor_coinduct goal), postproc nn (prove dtor_strong_induct strong_goal)) 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

830 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

831 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

832 
fun mk_coinduct_concls ms discs ctrs = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

833 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

834 
fun mk_disc_concl disc = [name_of_disc disc]; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

835 
fun mk_ctr_concl 0 _ = [] 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

836 
 mk_ctr_concl _ ctor = [name_of_ctr ctor]; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

837 
val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]]; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

838 
val ctr_concls = map2 mk_ctr_concl ms ctrs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

839 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

840 
flat (map2 append disc_concls ctr_concls) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

841 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

842 

51816  843 
val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names); 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

844 
val coinduct_conclss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

845 
map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

846 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

847 
fun mk_maybe_not pos = not pos ? HOLogic.mk_not; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

848 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

849 
val gunfolds = map (lists_bmoc pgss) unfolds; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

850 
val hcorecs = map (lists_bmoc phss) corecs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

851 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

852 
val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

853 
let 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

854 
fun mk_goal pfss c cps fcoiter n k ctr m cfs' = 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

855 
fold_rev (fold_rev Logic.all) ([c] :: pfss) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

856 
(Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps, 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

857 
mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs')))); 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

858 

51845  859 
val mk_U = typ_subst_nonatomic (map2 pair Cs fpTs); 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

860 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

861 
fun intr_coiters fcoiters [] [cf] = 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

862 
let val T = fastype_of cf in 
51855  863 
if exists_subtype_in Cs T then 
864 
build_map lthy (indexify_fst Cs (K o nth fcoiters)) (T, mk_U T) $ cf 

865 
else 

866 
cf 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

867 
end 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

868 
 intr_coiters fcoiters [cq] [cf, cf'] = 
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

869 
mk_If cq (intr_coiters fcoiters [] [cf]) (intr_coiters fcoiters [] [cf']); 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

870 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

871 
val crgsss = map2 (map2 (map2 (intr_coiters gunfolds))) crssss cgssss; 
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

872 
val cshsss = map2 (map2 (map2 (intr_coiters hcorecs))) csssss chssss; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

873 

51828  874 
val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss; 
875 
val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss; 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

876 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

877 
fun mk_map_if_distrib bnf = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

878 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

879 
val mapx = map_of_bnf bnf; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

880 
val live = live_of_bnf bnf; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

881 
val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) >> split_last; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

882 
val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

883 
val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

884 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

885 
Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)] 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

886 
@{thm if_distrib} 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

887 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

888 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

889 
val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

890 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

891 
val unfold_tacss = 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

892 
map3 (map oo mk_coiter_tac unfold_defs [] [] nesting_map_ids'' []) 
51814  893 
dtor_unfold_thms pre_map_defs ctr_defss; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

894 
val corec_tacss = 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

895 
map3 (map oo mk_coiter_tac corec_defs nested_map_comps'' nested_map_comp's 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

896 
(nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs) 
51814  897 
dtor_corec_thms pre_map_defs ctr_defss; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

898 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

899 
fun prove goal tac = 
51815  900 
Goal.prove_sorry lthy [] [] goal (tac o #context) 
901 
> Thm.close_derivation; 

51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

902 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

903 
val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

904 
val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

905 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

906 
val filter_safesss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

907 
map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

908 
curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

909 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

910 
val safe_unfold_thmss = filter_safesss unfold_thmss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

911 
val safe_corec_thmss = filter_safesss corec_thmss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

912 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

913 
(unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

914 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

915 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

916 
val (disc_unfold_iff_thmss, disc_corec_iff_thmss) = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

917 
let 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

918 
fun mk_goal c cps fcoiter n k disc = 
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

919 
mk_Trueprop_eq (disc $ (fcoiter $ c), 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

920 
if n = 1 then @{const True} 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

921 
else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps)); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

922 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

923 
val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

924 
val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

925 

51828  926 
fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split}; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

927 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

928 
val case_splitss' = map (map mk_case_split') cpss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

929 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

930 
val unfold_tacss = 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

931 
map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

932 
val corec_tacss = 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

933 
map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

934 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

935 
fun prove goal tac = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

936 
Goal.prove_sorry lthy [] [] goal (tac o #context) 
51829  937 
> singleton (Proof_Context.export names_lthy lthy) 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

938 
> Thm.close_derivation; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

939 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

940 
fun proves [_] [_] = [] 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

941 
 proves goals tacs = map2 prove goals tacs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

942 
in 
51828  943 
(map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss) 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

944 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

945 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

946 
val is_triv_discI = is_triv_implies orf is_concl_refl; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

947 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

948 
fun mk_disc_coiter_thms coiters discIs = 
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

949 
map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs)); 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

950 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

951 
val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss; 
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

952 
val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

953 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

954 
fun mk_sel_coiter_thm coiter_thm sel sel_thm = 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

955 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

956 
val (domT, ranT) = dest_funT (fastype_of sel); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

957 
val arg_cong' = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

958 
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT]) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

959 
[NONE, NONE, SOME (certify lthy sel)] arg_cong 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

960 
> Thm.varifyT_global; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

961 
val sel_thm' = sel_thm RSN (2, trans); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

962 
in 
51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

963 
coiter_thm RS arg_cong' RS sel_thm' 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

964 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

965 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

966 
fun mk_sel_coiter_thms coiterss = 
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

967 
map3 (map3 (map2 o mk_sel_coiter_thm)) coiterss selsss sel_thmsss > map flat; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

968 

51843
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

969 
val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss; 
899663644482
rationalized terminology (iterator = fold or rec, xxfoo = (co)foo or (un)foo)
blanchet
parents:
51842
diff
changeset

970 
val sel_corec_thmss = mk_sel_coiter_thms corec_thmss; 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

971 

7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

972 
val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn)); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

973 
val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases)); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

974 
val coinduct_case_concl_attrs = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

975 
map2 (fn casex => fn concls => 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

976 
Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls)))) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

977 
coinduct_cases coinduct_conclss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

978 
val coinduct_case_attrs = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

979 
coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

980 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

981 
((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms, coinduct_case_attrs), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

982 
(unfold_thmss, corec_thmss, []), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

983 
(safe_unfold_thmss, safe_corec_thmss), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

984 
(disc_unfold_thmss, disc_corec_thmss, simp_attrs), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

985 
(disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

986 
(sel_unfold_thmss, sel_corec_thmss, simp_attrs)) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

987 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

988 

52207
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

989 
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp 
49633  990 
(wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 = 
49112  991 
let 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

992 
(* TODO: sanity checks on arguments *) 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

993 

52207
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

994 
val _ = if fp = Greatest_FP andalso no_dests then 
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

995 
error "Cannot define destructorless codatatypes" 
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

996 
else 
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
blanchet
parents:
52197
diff
changeset

997 
(); 
49278  998 

49633  999 
fun qualify mandatory fp_b_name = 
1000 
Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix); 

1001 

49367  1002 
val nn = length specs; 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

1003 
val fp_bs = map type_binding_of specs; 
49498  1004 
val fp_b_names = map Binding.name_of fp_bs; 
1005 
val fp_common_name = mk_common_name fp_b_names; 

51758  1006 
val map_bs = map map_binding_of specs; 
51767
bbcdd8519253
honor userspecified name for relator + generalize syntax
blanchet
parents:
51766
diff
changeset

1007 
val rel_bs = map rel_binding_of specs; 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1008 

51758  1009 
fun prepare_type_arg (_, (ty, c)) = 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1010 
let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1011 
TFree (s, prepare_constraint no_defs_lthy0 c) 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1012 
end; 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1013 

51758  1014 
val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs; 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1015 
val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0; 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1016 
val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0; 
51758  1017 
val set_bss = map (map fst o type_args_named_constrained_of) specs; 
49119  1018 

49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1019 
val (((Bs0, Cs), Xs), no_defs_lthy) = 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1020 
no_defs_lthy0 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1021 
> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1022 
> mk_TFrees (length unsorted_As) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1023 
>> mk_TFrees nn 
51858
7a08fe1e19b1
added and moved library functions (used in primrec code)
blanchet
parents:
51857
diff
changeset

1024 
>> variant_tfrees fp_b_names; 
49119  1025 

52195  1026 
(* TODO: Cleaner handling of fake contexts, without "background_theory". The case where the new 
1027 
type is defined in a locale and shadows an existing global type is currently not handled. *) 

51768  1028 

51769
5c657ca97d99
simplified code  no need for two attempts, the error we get from mixfix the first time is good (and better to get than a parse error in the specification because the user tries to use a mixfix that silently failed)
blanchet
parents:
51768
diff
changeset

1029 
fun add_fake_type spec = 
51768  1030 
Sign.add_type no_defs_lthy (type_binding_of spec, 
51769
5c657ca97d99
simplified code  no need for two attempts, the error we get from mixfix the first time is good (and better to get than a parse error in the specification because the user tries to use a mixfix that silently failed)
blanchet
parents:
51768
diff
changeset

1031 
length (type_args_named_constrained_of spec), mixfix_of spec); 
51768  1032 

51769
5c657ca97d99
simplified code  no need for two attempts, the error we get from mixfix the first time is good (and better to get than a parse error in the specification because the user tries to use a mixfix that silently failed)
blanchet
parents:
51768
diff
changeset

1033 
val fake_thy = Theory.copy #> fold add_fake_type specs; 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1034 
val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy; 
49119  1035 

49182
b8517107ffc5
read the real types off the constant types, rather than using the fake parser types (second step of sugar localization)
blanchet
parents:
49181
diff
changeset

1036 
fun mk_fake_T b = 
49121  1037 
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1038 
unsorted_As); 
49121  1039 

49302
f5bd87aac224
added optional qualifiers for constructors and destructors, similarly to the old package
blanchet
parents:
49300
diff
changeset

1040 
val fake_Ts = map mk_fake_T fp_bs; 
49121  1041 

49181  1042 
val mixfixes = map mixfix_of specs; 
49119  1043 

49302
f5bd87aac224
added optional qualifiers for constructors and destructors, similarly to the old package
blanchet
parents:
49300
diff
changeset

1044 
val _ = (case duplicates Binding.eq_name fp_bs of [] => () 
49119  1045 
 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 
1046 

49121  1047 
val ctr_specss = map ctr_specs_of specs; 
49119  1048 

49336  1049 
val disc_bindingss = map (map disc_of) ctr_specss; 
1050 
val ctr_bindingss = 

49633  1051 
map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss; 
49121  1052 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  1053 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  1054 

49336  1055 
val sel_bindingsss = map (map (map fst)) ctr_argsss; 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1056 
val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; 
49286  1057 
val raw_sel_defaultsss = map (map defaults_of) ctr_specss; 
1058 

49308
6190b701e4f4
reorganized dependencies so that the sugar does not depend on GFP  this will be essential for bootstrapping
blanchet
parents:
49302
diff
changeset

1059 
val (As :: _) :: fake_ctr_Tsss = 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1060 
burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0); 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1061 

36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1062 
val _ = (case duplicates (op =) unsorted_As of [] => () 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1063 
 A :: _ => error ("Duplicate type parameter " ^ 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1064 
quote (Syntax.string_of_typ no_defs_lthy A))); 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1065 

49183
0cc46e2dee7e
careful about constructor types w.r.t. fake context (third step of localization)
blanchet
parents:
49182
diff
changeset

1066 
val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1067 
val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of 
49165  1068 
[] => () 
49342  1069 
 A' :: _ => error ("Extra type variable on righthand side: " ^ 
49204  1070 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  1071 

49591
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

1072 
fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) = 
49146  1073 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
1074 
quote (Syntax.string_of_typ fake_lthy T))) 

49591
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

1075 
 eq_fpT_check _ _ = false; 
49146  1076 

49204  1077 
fun freeze_fp (T as Type (s, Us)) = 
49591
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

1078 
(case find_index (eq_fpT_check T) fake_Ts of 
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

1079 
~1 => Type (s, map freeze_fp Us) 
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

1080 
 kk => nth Xs kk) 
49204  1081 
 freeze_fp T = T; 
49121  1082 

49536  1083 
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; 
1084 
val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs; 

49119  1085 

49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

1086 
val fp_eqs = 
49536  1087 
map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs; 
49121  1088 

51839  1089 
val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0, 
51869  1090 
un_folds = fp_folds0, co_recs = fp_recs0, co_induct = fp_induct, 
1091 
strong_co_induct = fp_strong_induct, dtor_ctors, ctor_dtors, ctor_injects, 

1092 
map_thms = fp_map_thms, set_thmss = fp_set_thmss, rel_thms = fp_rel_thms, 

1093 
un_fold_thms = fp_fold_thms, co_rec_thms = fp_rec_thms, ...}, lthy)) = 

51868  1094 
fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs 
1095 
no_defs_lthy0; 

49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1096 

5c4a12550491
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1097 
val timer = time (Timer.startRealTimer ()); 
49121  1098 

51907  1099 
val nesting_bnfs = nesty_bnfs lthy ctr_TsssXs As; 
1100 
val nested_bnfs = nesty_bnfs lthy ctr_TsssXs Xs; 

49226  1101 

49585
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1102 
val pre_map_defs = map map_def_of_bnf pre_bnfs; 
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1103 
val pre_set_defss = map set_defs_of_bnf pre_bnfs; 
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1104 
val pre_rel_defs = map rel_def_of_bnf pre_bnfs; 
51830  1105 
val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs; 
51766
f19a4d0ab1bf
renamed "set_natural" to "set_map", reflecting {Bl,Po,Tr} concensus
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1106 
val nested_set_map's = maps set_map'_of_bnf nested_bnfs; 
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1107 

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1108 
val live = live_of_bnf any_fp_bnf; 
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1109 

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1110 
val Bs = 
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1111 
map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A) 
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1112 
(liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0; 
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1113 

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1114 
val B_ify = Term.typ_subst_atomic (As ~~ Bs); 
49167  1115 

49501  1116 
val ctors = map (mk_ctor As) ctors0; 
1117 
val dtors = map (mk_dtor As) dtors0; 

49124  1118 

49501  1119 
val fpTs = map (domain_type o fastype_of) dtors; 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
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1120 

51780  1121 
fun massage_simple_notes base = 
1122 
filter_out (null o #2) 

1123 
#> map (fn (thmN, thms, attrs) => 

1124 
((qualify true base (Binding.name thmN), attrs), [(thms, [])])); 

1125 

1126 
val massage_multi_notes = 

1127 
maps (fn (thmN, thmss, attrs) => 

1128 
if forall null thmss then 

1129 
[] 

1130 
else 

1131 
map3 (fn fp_b_name => fn Type (T_name, _) => fn thms => 

1132 
((qualify true fp_b_name (Binding.name thmN), attrs T_name), 

1133 
[(thms, [])])) fp_b_names fpTs thmss); 

1134 

49536  1135 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; 
49203  1136 
val ns = map length ctr_Tsss; 
49212  1137 
val kss = map (fn n => 1 upto n) ns; 
49203  1138 
val mss = map (map length) ctr_Tsss; 
1139 

51903  1140 
val ((fp_folds, fp_recs, fold_rec_args_types, unfold_corec_args_types), lthy) = 
52207
21026c312cc3
tuning  avoided unreadable true/false all over the place for LFP/GFP
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1141 
mk_un_fold_co_rec_prelims fp fpTs Cs ns mss fp_folds0 fp_recs0 lthy; 
49210  1142 

49585
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1143 
fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor), 
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1144 
fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs), 
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1145 
pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings), 
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1146 
ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy = 
49176  1147 
let 
49498  1148 
val fp_b_name = Binding.name_of fp_b; 
1149 

49501  1150 
val dtorT = domain_type (fastype_of ctor); 
49210  1151 
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
49255
2ecc533d6697
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1152 
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts; 
49134
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1153 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  1154 

49593  1155 
val (((((w, fs), xss), yss), u'), names_lthy) = 
49204  1156 
no_defs_lthy 
49501  1157 
> yield_singleton (mk_Frees "w") dtorT 
49176  1158 
>> mk_Frees "f" case_Ts 
49370  1159 
>> mk_Freess "x" ctr_Tss 
49585
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1160 
>> mk_Freess "y" (map (map B_ify) ctr_Tss) 
49498  1161 
>> yield_singleton Variable.variant_fixes fp_b_name; 
49370  1162 

49498  1163 
val u = Free (u', fpT); 
49121  1164 

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1165 
val tuple_xs = map HOLogic.mk_tuple xss; 
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1166 
val tuple_ys = map HOLogic.mk_tuple yss; 
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1167 

49129  1168 
val ctr_rhss = 
49585
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1169 
map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $ 
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1170 
mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs; 
49121  1171 

49633  1172 
val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b); 
49129  1173 

49134
846264f80f16
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1174 
val case_rhs = 
49498  1175 
fold_rev Term.lambda (fs @ [u]) 
49501  1176 
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u)); 
49129  1177 

49201  1178 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  1179 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
49302
f5bd87aac224
added optional qualifiers for constructors and destructors, similarly to the old package
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1180 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 
49336  1181 
(case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  1182 
> `Local_Theory.restore; 
1183 

1184 
val phi = Proof_Context.export_morphism lthy lthy'; 

1185 

1186 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

49585
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1187 
val ctr_defs' = 
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1188 
map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs; 
49130
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
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1189 
val case_def = Morphism.thm phi raw_case_def; 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
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1190 
