author  blanchet 
Mon, 29 Apr 2013 13:42:54 +0200  
changeset 51813  ca201253e7bb 
parent 51811  1461426e2bf1 
child 51814  8b89afea27e7 
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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val derive_induct_fold_rec_thms_for_types: int > BNF_Def.BNF list > thm > thm list > 
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thm list > BNF_Def.BNF list > BNF_Def.BNF list > typ list > typ list > 

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typ list list list > int list list > int list > term list list > term list list > 

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term list list > term list list list > thm list list > term list > term list > thm list > 

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thm list > Proof.context > 

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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: Proof.context > Proof.context > int > 

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BNF_Def.BNF list > thm > thm > thm list > thm list > thm list > BNF_Def.BNF list > 

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BNF_Def.BNF list > typ list > typ list > typ list > int list list > int list list > 

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int list > term list > term list list > term list list > term list list list list > 

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term list list list list > term list list > term list list list list > 

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term list list list list > term list list > thm list list > 

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BNF_Ctr_Sugar.ctr_wrap_result list > term list > term list > thm list > thm list > 
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Proof.context > 

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(thm * thm list * thm * thm list * Args.src list) * (thm list list * thm list list * 'e 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 datatypes: bool > 
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(mixfix list > (string * sort) list option > binding list > binding list > binding list > 
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binding list list > typ list * typ list list > BNF_Def.BNF list > local_theory > 
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BNF_FP.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_datatype_cmd: bool > 
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(mixfix list > (string * sort) list option > binding list > binding list > binding list > 
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binding list list > typ list * typ list list > BNF_Def.BNF list > local_theory > 
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BNF_FP.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 
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open BNF_FP_Def_Sugar_Tactics 
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val EqN = "Eq_"; 
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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 split_list4 [] = ([], [], [], []) 
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 split_list4 ((x1, x2, x3, x4) :: xs) = 

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let val (xs1, xs2, xs3, xs4) = split_list4 xs; 

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in (x1 :: xs1, x2 :: xs2, x3 :: xs3, x4 :: xs4) end; 

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fun add_components_of_typ (Type (s, Ts)) = 
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fold add_components_of_typ Ts 

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#> cons s 

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 add_components_of_typ _ = I; 

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fun name_of_typ T = space_implode "_" (add_components_of_typ T []); 

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fun exists_subtype_in Ts = exists_subtype (member (op =) Ts); 
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fun resort_tfree S (TFree (s, _)) = TFree (s, S); 
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fun typ_subst 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 inst) Ts) 
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 SOME T' => T') 
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 typ_subst inst T = the_default T (AList.lookup (op =) inst T); 
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fun variant_types ss Ss ctxt = 
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let 

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val (tfrees, _) = 

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fold_map2 (fn s => fn S => Name.variant s #> apfst (rpair S)) ss Ss (Variable.names_of ctxt); 

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val ctxt' = fold (Variable.declare_constraints o Logic.mk_type o TFree) tfrees ctxt; 

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in (tfrees, ctxt') end; 

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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)); 
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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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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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maps (op @) ps 
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*) 
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maps fst ps @ maps snd ps 
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end; 
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fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) = 
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Abs ("x", T1, Abs ("y", T2, Var (x, T2 > T1 > T3) $ Bound 0 $ Bound 1)); 
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fun flip_rels lthy n thm = 
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let 
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val Rs = Term.add_vars (prop_of thm) []; 
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val Rs' = rev (drop (length Rs  n) Rs); 
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val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs'; 
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in 
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Drule.cterm_instantiate cRs thm 
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end; 
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fun mk_ctor_or_dtor get_T Ts t = 
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let val Type (_, Ts0) = get_T (fastype_of t) in 

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Term.subst_atomic_types (Ts0 ~~ Ts) t 

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end; 

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val mk_ctor = mk_ctor_or_dtor range_type; 

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val mk_dtor = mk_ctor_or_dtor domain_type; 

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fun mk_rec_like lfp Ts Us t = 

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let 

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val (bindings, body) = strip_type (fastype_of t); 

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val (f_Us, prebody) = split_last bindings; 

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val Type (_, Ts0) = if lfp then prebody else body; 

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val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); 

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in 

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

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end; 

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fun mk_map live Ts Us t = 

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let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) >> List.last in 

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

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end; 

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fun mk_rel live Ts Us t = 
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let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in 
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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
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end; 
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fun liveness_of_fp_bnf n bnf = 
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(case T_of_bnf bnf of 
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Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts 
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 _ => replicate n false); 
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fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
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fun merge_type_arg T T' = if T = T' then T else cannot_merge_types (); 
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fun merge_type_args (As, As') = 
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if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types (); 
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fun reassoc_conjs thm = 
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reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]}) 
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handle THM _ => thm; 
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fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs; 
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fun type_binding_of ((((_, b), _), _), _) = b; 
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fun map_binding_of (((_, (b, _)), _), _) = b; 
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fun rel_binding_of (((_, (_, b)), _), _) = b; 
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fun mixfix_of ((_, mx), _) = mx; 
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fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
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fun disc_of ((((disc, _), _), _), _) = disc; 
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fun ctr_of ((((_, ctr), _), _), _) = ctr; 

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

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

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fun ctr_mixfix_of (_, mx) = mx; 
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fun build_map lthy build_arg (Type (s, Ts)) (Type (_, Us)) = 
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let 
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val bnf = the (bnf_of lthy s); 
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val live = live_of_bnf bnf; 
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val mapx = mk_map live Ts Us (map_of_bnf bnf); 
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val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx))); 
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in Term.list_comb (mapx, map build_arg TUs') end; 
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fun build_rel_step lthy build_arg (Type (s, Ts)) = 
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let 
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val bnf = the (bnf_of lthy s); 
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val live = live_of_bnf bnf; 
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val rel = mk_rel live Ts Ts (rel_of_bnf bnf); 
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val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel))); 
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in Term.list_comb (rel, map build_arg Ts') end; 
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fun derive_induct_fold_rec_thms_for_types nn pre_bnfs fp_induct fp_fold_thms fp_rec_thms 
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nesting_bnfs nested_bnfs fpTs Cs ctr_Tsss mss ns gss hss ctrss xsss ctr_defss folds recs 

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fold_defs rec_defs lthy = 

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let 
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val pre_map_defs = map map_def_of_bnf pre_bnfs; 
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val pre_set_defss = map set_defs_of_bnf pre_bnfs; 
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val nested_map_comp's = map map_comp'_of_bnf nested_bnfs; 
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val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs; 
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val nested_set_map's = maps set_map'_of_bnf nested_bnfs; 
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val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs; 
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val fp_T_names = map name_of_typ fpTs; 
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val (((ps, ps'), us'), names_lthy) = 
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lthy 
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> mk_Frees' "P" (map mk_pred1T fpTs) 
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>> Variable.variant_fixes fp_T_names; 
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219 

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val us = map2 (curry Free) us' fpTs; 
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221 

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fun mk_sets_nested bnf = 
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let 
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val Type (T_name, Us) = T_of_bnf bnf; 
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val lives = lives_of_bnf bnf; 
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val sets = sets_of_bnf bnf; 
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fun mk_set U = 
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(case find_index (curry (op =) U) lives of 
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~1 => Term.dummy 
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 i => nth sets i); 
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231 
in 
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(T_name, map mk_set Us) 
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233 
end; 
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234 

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val setss_nested = map mk_sets_nested nested_bnfs; 
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236 

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val (induct_thms, induct_thm) = 
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let 
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fun mk_set Ts t = 
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let val Type (_, Ts0) = domain_type (fastype_of t) in 
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Term.subst_atomic_types (Ts0 ~~ Ts) t 
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end; 
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243 

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fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) = 
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(case find_index (curry (op =) T) fpTs of 
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~1 => 
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(case AList.lookup (op =) setss_nested T_name of 
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NONE => [] 
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 SOME raw_sets0 => 
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let 
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val (Ts, raw_sets) = 
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split_list (filter (exists_subtype_in fpTs o fst) (Ts0 ~~ raw_sets0)); 
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val sets = map (mk_set Ts0) raw_sets; 
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val (ys, names_lthy') = names_lthy > mk_Frees s Ts; 
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val xysets = map (pair x) (ys ~~ sets); 
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val ppremss = map (mk_raw_prem_prems names_lthy') ys; 
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in 
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flat (map2 (map o apfst o cons) xysets ppremss) 
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end) 
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 kk => [([], (kk + 1, x))]) 
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 mk_raw_prem_prems _ _ = []; 
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262 

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fun close_prem_prem xs t = 
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fold_rev Logic.all (map Free (drop (nn + length xs) 
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(rev (Term.add_frees t (map dest_Free xs @ ps'))))) t; 
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266 

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fun mk_prem_prem xs (xysets, (j, x)) = 
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close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) => 
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HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets, 
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HOLogic.mk_Trueprop (nth ps (j  1) $ x))); 
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271 

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fun mk_raw_prem phi ctr ctr_Ts = 
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let 
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val (xs, names_lthy') = names_lthy > mk_Frees "x" ctr_Ts; 
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val pprems = maps (mk_raw_prem_prems names_lthy') xs; 
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in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end; 
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277 

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fun mk_prem (xs, raw_pprems, concl) = 
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fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl)); 
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280 

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val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss; 
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282 

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val goal = 
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Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss, 
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HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us))); 
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286 

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val kksss = map (map (map (fst o snd) o #2)) raw_premss; 
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288 

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val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss); 
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val thm = 
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Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} => 
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mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's 
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pre_set_defss) 
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> singleton (Proof_Context.export names_lthy lthy) 
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> Thm.close_derivation; 
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in 
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`(conj_dests nn) thm 
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end; 
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300 

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val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss); 
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302 

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val (fold_thmss, rec_thmss) = 
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let 
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val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
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val gfolds = map (lists_bmoc gss) folds; 
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val hrecs = map (lists_bmoc hss) recs; 
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308 

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fun mk_goal fss frec_like xctr f xs fxs = 
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fold_rev (fold_rev Logic.all) (xs :: fss) 
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(mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs))); 
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fun build_rec_like frec_likes (T, U) = 
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if T = U then 
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id_const T 
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else 
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(case find_index (curry (op =) T) fpTs of 
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~1 => build_map lthy (build_rec_like frec_likes) T U 
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 kk => nth frec_likes kk); 
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val mk_U = typ_subst (map2 pair fpTs Cs); 
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fun unzip_rec_likes frec_likes combine (x as Free (_, T)) = 
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if exists_subtype_in fpTs T then 
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combine (x, build_rec_like frec_likes (T, mk_U T) $ x) 
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else 
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([x], []); 
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val gxsss = map (map (flat_rec (unzip_rec_likes gfolds (fn (_, t) => ([t], []))))) xsss; 
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val hxsss = map (map (flat_rec (unzip_rec_likes hrecs (pairself single)))) xsss; 
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val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss; 
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333 
val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss; 
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334 

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335 
val fold_tacss = 
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336 
map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) fp_fold_thms 
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337 
ctr_defss; 
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338 
val rec_tacss = 
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339 
map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's 
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340 
(nested_map_ids'' @ nesting_map_ids'') rec_defs) fp_rec_thms ctr_defss; 
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341 

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342 
fun prove goal tac = 
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343 
Goal.prove_sorry lthy [] [] goal (tac o #context) 
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344 
> Thm.close_derivation; 
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345 
in 
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346 
(map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss) 
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347 
end; 
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348 

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349 
val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases)); 
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350 
in 
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351 
((induct_thm, induct_thms, [induct_case_names_attr]), 
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352 
(fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs)) 
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353 
end; 
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354 

51811  355 
fun derive_coinduct_unfold_corec_thms_for_types names_lthy0 no_defs_lthy nn pre_bnfs fp_induct 
356 
fp_strong_induct dtor_ctors fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As kss mss 

357 
ns cs cpss pgss crssss cgssss phss csssss chssss ctrss ctr_defss ctr_wrap_ress unfolds corecs 

358 
unfold_defs corec_defs lthy = 

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359 
let 
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360 
val pre_map_defs = map map_def_of_bnf pre_bnfs; 
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361 
val pre_rel_defs = map rel_def_of_bnf pre_bnfs; 
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362 
val nested_map_comp's = map map_comp'_of_bnf nested_bnfs; 
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363 
val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs; 
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364 
val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs; 
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365 
val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs; 
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366 
val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs; 
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367 

51811  368 
val fp_T_names = map name_of_typ fpTs; 
369 

51810
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370 
val discss = map (map (mk_disc_or_sel As) o #1) ctr_wrap_ress; 
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371 
val selsss = map (map (map (mk_disc_or_sel As)) o #2) ctr_wrap_ress; 
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372 
val exhaust_thms = map #3 ctr_wrap_ress; 
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373 
val disc_thmsss = map #7 ctr_wrap_ress; 
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374 
val discIss = map #8 ctr_wrap_ress; 
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375 
val sel_thmsss = map #9 ctr_wrap_ress; 
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376 

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377 
val (((rs, us'), vs'), names_lthy) = 
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378 
lthy 
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379 
> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs) 
51811  380 
>> Variable.variant_fixes fp_T_names 
381 
>> Variable.variant_fixes (map (suffix "'") fp_T_names); 

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382 

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383 
val us = map2 (curry Free) us' fpTs; 
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384 
val udiscss = map2 (map o rapp) us discss; 
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385 
val uselsss = map2 (map o map o rapp) us selsss; 
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386 

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387 
val vs = map2 (curry Free) vs' fpTs; 
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388 
val vdiscss = map2 (map o rapp) vs discss; 
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389 
val vselsss = map2 (map o map o rapp) vs selsss; 
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390 

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391 
val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) = 
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392 
let 
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393 
val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs; 
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394 
val uv_eqs = map2 (curry HOLogic.mk_eq) us vs; 
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395 
val strong_rs = 
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396 
map4 (fn u => fn v => fn uvr => fn uv_eq => 
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397 
fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs; 
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398 

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399 
fun build_rel rs' T = 
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400 
(case find_index (curry (op =) T) fpTs of 
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401 
~1 => 
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402 
if exists_subtype_in fpTs T then build_rel_step lthy (build_rel rs') T 
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403 
else HOLogic.eq_const T 
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404 
 kk => nth rs' kk); 
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405 

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406 
fun build_rel_app rs' usel vsel = 
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407 
fold rapp [usel, vsel] (build_rel rs' (fastype_of usel)); 
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408 

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409 
fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels = 
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410 
(if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @ 
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411 
(if null usels then 
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412 
[] 
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413 
else 
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414 
[Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc], 
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415 
Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]); 
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416 

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417 
fun mk_prem_concl rs' n udiscs uselss vdiscs vselss = 
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418 
Library.foldr1 HOLogic.mk_conj 
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419 
(flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss)) 
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420 
handle List.Empty => @{term True}; 
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421 

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422 
fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss = 
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423 
fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr, 
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424 
HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss))); 
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425 

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426 
val concl = 
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427 
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 
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428 
(map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v))) 
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429 
uvrs us vs)); 
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430 

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431 
fun mk_goal rs' = 
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432 
Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss, 
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433 
concl); 
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434 

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435 
val goal = mk_goal rs; 
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436 
val strong_goal = mk_goal strong_rs; 
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437 

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438 
fun prove dtor_coinduct' goal = 
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439 
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} => 
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440 
mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors 
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441 
exhaust_thms ctr_defss disc_thmsss sel_thmsss) 
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442 
> singleton (Proof_Context.export names_lthy lthy) 
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443 
> Thm.close_derivation; 
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444 

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445 
fun postproc nn thm = 
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446 
Thm.permute_prems 0 nn 
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447 
(if nn = 1 then thm RS mp 
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448 
else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm) 
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449 
> Drule.zero_var_indexes 
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450 
> `(conj_dests nn); 
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451 
in 
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452 
(postproc nn (prove fp_induct goal), postproc nn (prove fp_strong_induct strong_goal)) 
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453 
end; 
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454 

7b75fab5ebf5
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455 
fun mk_coinduct_concls ms discs ctrs = 
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456 
let 
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457 
fun mk_disc_concl disc = [name_of_disc disc]; 
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458 
fun mk_ctr_concl 0 _ = [] 
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459 
 mk_ctr_concl _ ctor = [name_of_ctr ctor]; 
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460 
val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]]; 
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changeset

461 
val ctr_concls = map2 mk_ctr_concl ms ctrs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

462 
in 
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factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
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463 
flat (map2 append disc_concls ctr_concls) 
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factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
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464 
end; 
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factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

465 

51811  466 
val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_T_names); 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

467 
val coinduct_conclss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

468 
map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

469 

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

470 
fun mk_maybe_not pos = not pos ? HOLogic.mk_not; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

471 

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

472 
val gunfolds = map (lists_bmoc pgss) unfolds; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

473 
val hcorecs = map (lists_bmoc phss) corecs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

474 

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

475 
val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) = 
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factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

476 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

477 
fun mk_goal pfss c cps fcorec_like n k ctr m cfs' = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

478 
fold_rev (fold_rev Logic.all) ([c] :: pfss) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

479 
(Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps, 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

480 
mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs')))); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

481 

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

482 
fun build_corec_like fcorec_likes (T, U) = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

483 
if T = U then 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
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484 
id_const T 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

485 
else 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

486 
(case find_index (curry (op =) U) fpTs of 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

487 
~1 => build_map lthy (build_corec_like fcorec_likes) T U 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

488 
 kk => nth fcorec_likes kk); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

489 

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

490 
val mk_U = typ_subst (map2 pair Cs fpTs); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

491 

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

492 
fun intr_corec_likes fcorec_likes [] [cf] = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

493 
let val T = fastype_of cf in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

494 
if exists_subtype_in Cs T then build_corec_like fcorec_likes (T, mk_U T) $ cf 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

495 
else cf 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
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parents:
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diff
changeset

496 
end 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

497 
 intr_corec_likes fcorec_likes [cq] [cf, cf'] = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
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parents:
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diff
changeset

498 
mk_If cq (intr_corec_likes fcorec_likes [] [cf]) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

499 
(intr_corec_likes fcorec_likes [] [cf']); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

500 

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

501 
val crgsss = map2 (map2 (map2 (intr_corec_likes gunfolds))) crssss cgssss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

502 
val cshsss = map2 (map2 (map2 (intr_corec_likes hcorecs))) csssss chssss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

503 

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

504 
val unfold_goalss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

505 
map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

506 
val corec_goalss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

507 
map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

508 

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

509 
fun mk_map_if_distrib bnf = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

510 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

511 
val mapx = map_of_bnf bnf; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

512 
val live = live_of_bnf bnf; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

513 
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

514 
val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

515 
val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
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diff
changeset

516 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

517 
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

518 
@{thm if_distrib} 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

519 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

520 

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

521 
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

522 

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

523 
val unfold_tacss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

524 
map3 (map oo mk_corec_like_tac unfold_defs [] [] nesting_map_ids'' []) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

525 
fp_fold_thms pre_map_defs ctr_defss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

526 
val corec_tacss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

527 
map3 (map oo mk_corec_like_tac corec_defs nested_map_comps'' nested_map_comp's 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

528 
(nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

529 
fp_rec_thms pre_map_defs ctr_defss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

530 

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

531 
fun prove goal tac = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

532 
Goal.prove_sorry lthy [] [] goal (tac o #context) > Thm.close_derivation; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

533 

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

534 
val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

535 
val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

536 

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

537 
val filter_safesss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

538 
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

539 
curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

540 

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

541 
val safe_unfold_thmss = filter_safesss unfold_thmss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

542 
val safe_corec_thmss = filter_safesss corec_thmss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

543 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

544 
(unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

545 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

546 

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

547 
val (disc_unfold_iff_thmss, disc_corec_iff_thmss) = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

548 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

549 
fun mk_goal c cps fcorec_like n k disc = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

550 
mk_Trueprop_eq (disc $ (fcorec_like $ c), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

551 
if n = 1 then @{const True} 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

552 
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

553 

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

554 
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

555 
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

556 

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

557 
fun mk_case_split' cp = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

558 
Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split}; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

559 

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

560 
val case_splitss' = map (map mk_case_split') cpss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

561 

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

562 
val unfold_tacss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

563 
map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

564 
val corec_tacss = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

565 
map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

566 

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

567 
fun prove goal tac = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

568 
Goal.prove_sorry lthy [] [] goal (tac o #context) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

569 
> singleton (Proof_Context.export names_lthy0 no_defs_lthy) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

570 
> Thm.close_derivation; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

571 

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

572 
fun proves [_] [_] = [] 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

573 
 proves goals tacs = map2 prove goals tacs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

574 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

575 
(map2 proves unfold_goalss unfold_tacss, 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

576 
map2 proves corec_goalss corec_tacss) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

577 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

578 

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

579 
val is_triv_discI = is_triv_implies orf is_concl_refl; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

580 

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

581 
fun mk_disc_corec_like_thms corec_likes discIs = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

582 
map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs)); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

583 

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

584 
val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

585 
val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

586 

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

587 
fun mk_sel_corec_like_thm corec_like_thm sel sel_thm = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

588 
let 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

589 
val (domT, ranT) = dest_funT (fastype_of sel); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

590 
val arg_cong' = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

591 
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT]) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

592 
[NONE, NONE, SOME (certify lthy sel)] arg_cong 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

593 
> Thm.varifyT_global; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

594 
val sel_thm' = sel_thm RSN (2, trans); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

595 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

596 
corec_like_thm RS arg_cong' RS sel_thm' 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

597 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

598 

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

599 
fun mk_sel_corec_like_thms corec_likess = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

600 
map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss > map flat; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

601 

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

602 
val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

603 
val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

604 

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

605 
val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn)); 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

606 
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

607 
val coinduct_case_concl_attrs = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

608 
map2 (fn casex => fn concls => 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

609 
Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls)))) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

610 
coinduct_cases coinduct_conclss; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

611 
val coinduct_case_attrs = 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

612 
coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

613 
in 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

614 
((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

615 
(unfold_thmss, corec_thmss, []), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

616 
(safe_unfold_thmss, safe_corec_thmss), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
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parents:
51808
diff
changeset

617 
(disc_unfold_thmss, disc_corec_thmss, simp_attrs), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
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parents:
51808
diff
changeset

618 
(disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs), 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
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parents:
51808
diff
changeset

619 
(sel_unfold_thmss, sel_corec_thmss, simp_attrs)) 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

620 
end; 
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

621 

49633  622 
fun define_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp 
623 
(wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 = 

49112  624 
let 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
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parents:
49297
diff
changeset

625 
(* TODO: sanity checks on arguments *) 
36e551d3af3b
support for sort constraints in new (co)data commands
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parents:
49297
diff
changeset

626 

49286  627 
val _ = if not lfp andalso no_dests then error "Cannot define destructorless codatatypes" 
49278  628 
else (); 
629 

49633  630 
fun qualify mandatory fp_b_name = 
631 
Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix); 

632 

49367  633 
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

634 
val fp_bs = map type_binding_of specs; 
49498  635 
val fp_b_names = map Binding.name_of fp_bs; 
636 
val fp_common_name = mk_common_name fp_b_names; 

51758  637 
val map_bs = map map_binding_of specs; 
51767
bbcdd8519253
honor userspecified name for relator + generalize syntax
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parents:
51766
diff
changeset

638 
val rel_bs = map rel_binding_of specs; 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

639 

51758  640 
fun prepare_type_arg (_, (ty, c)) = 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
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parents:
49297
diff
changeset

641 
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

642 
TFree (s, prepare_constraint no_defs_lthy0 c) 
36e551d3af3b
support for sort constraints in new (co)data commands
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parents:
49297
diff
changeset

643 
end; 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

644 

51758  645 
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

646 
val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0; 
36e551d3af3b
support for sort constraints in new (co)data commands
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parents:
49297
diff
changeset

647 
val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0; 
51758  648 
val set_bss = map (map fst o type_args_named_constrained_of) specs; 
49119  649 

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

650 
val (((Bs0, Cs), Xs), no_defs_lthy) = 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
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parents:
49297
diff
changeset

651 
no_defs_lthy0 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

652 
> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

653 
> mk_TFrees (length unsorted_As) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

654 
>> mk_TFrees nn 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

655 
>> apfst (map TFree) o 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

656 
variant_types (map (prefix "'") fp_b_names) (replicate nn HOLogic.typeS); 
49119  657 

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

658 
(* TODO: cleaner handling of fake contexts, without "background_theory" *) 
36e551d3af3b
support for sort constraints in new (co)data commands
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parents:
49297
diff
changeset

659 
(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

660 
locale and shadows an existing global type*) 
51768  661 

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

662 
fun add_fake_type spec = 
51768  663 
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

664 
length (type_args_named_constrained_of spec), mixfix_of spec); 
51768  665 

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

666 
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

667 
val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy; 
49119  668 

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

669 
fun mk_fake_T b = 
49121  670 
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

671 
unsorted_As); 
49121  672 

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

673 
val fake_Ts = map mk_fake_T fp_bs; 
49121  674 

49181  675 
val mixfixes = map mixfix_of specs; 
49119  676 

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

677 
val _ = (case duplicates Binding.eq_name fp_bs of [] => () 
49119  678 
 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 
679 

49121  680 
val ctr_specss = map ctr_specs_of specs; 
49119  681 

49336  682 
val disc_bindingss = map (map disc_of) ctr_specss; 
683 
val ctr_bindingss = 

49633  684 
map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss; 
49121  685 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  686 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  687 

49336  688 
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

689 
val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; 
49286  690 
val raw_sel_defaultsss = map (map defaults_of) ctr_specss; 
691 

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

692 
val (As :: _) :: fake_ctr_Tsss = 
49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

693 
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

694 

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

695 
val _ = (case duplicates (op =) unsorted_As of [] => () 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

696 
 A :: _ => error ("Duplicate type parameter " ^ 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

697 
quote (Syntax.string_of_typ no_defs_lthy A))); 
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

698 

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

699 
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

700 
val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of 
49165  701 
[] => () 
49342  702 
 A' :: _ => error ("Extra type variable on righthand side: " ^ 
49204  703 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  704 

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

705 
fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) = 
49146  706 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
707 
quote (Syntax.string_of_typ fake_lthy T))) 

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

708 
 eq_fpT_check _ _ = false; 
49146  709 

49204  710 
fun freeze_fp (T as Type (s, Us)) = 
49591
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

711 
(case find_index (eq_fpT_check T) fake_Ts of 
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

712 
~1 => Type (s, map freeze_fp Us) 
91b228e26348
generate highlevel "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset

713 
 kk => nth Xs kk) 
49204  714 
 freeze_fp T = T; 
49121  715 

49536  716 
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; 
717 
val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs; 

49119  718 

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

719 
val fp_eqs = 
49536  720 
map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs; 
49121  721 

51805  722 
val (pre_bnfs, ({bnfs = fp_bnfs as any_fp_bnf :: _, dtors = dtors0, ctors = ctors0, 
723 
folds = fp_folds0, recs = fp_recs0, induct = fp_induct, strong_induct = fp_strong_induct, 

724 
dtor_ctors, ctor_dtors, ctor_injects, map_thms = fp_map_thms, set_thmss = fp_set_thmss, 

725 
rel_thms = fp_rel_thms, fold_thms = fp_fold_thms, rec_thms = fp_rec_thms}, lthy)) = 

51767
bbcdd8519253
honor userspecified name for relator + generalize syntax
blanchet
parents:
51766
diff
changeset

726 
fp_bnf construct_fp fp_bs mixfixes map_bs rel_bs set_bss (map dest_TFree unsorted_As) fp_eqs 
51758  727 
no_defs_lthy0; 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

728 

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

729 
val timer = time (Timer.startRealTimer ()); 
49121  730 

49363  731 
fun add_nesty_bnf_names Us = 
49226  732 
let 
733 
fun add (Type (s, Ts)) ss = 

734 
let val (needs, ss') = fold_map add Ts ss in 

735 
if exists I needs then (true, insert (op =) s ss') else (false, ss') 

736 
end 

49363  737 
 add T ss = (member (op =) Us T, ss); 
49226  738 
in snd oo add end; 
739 

49363  740 
fun nesty_bnfs Us = 
49536  741 
map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssXs []); 
49363  742 

743 
val nesting_bnfs = nesty_bnfs As; 

49536  744 
val nested_bnfs = nesty_bnfs Xs; 
49226  745 

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

746 
val pre_map_defs = map map_def_of_bnf pre_bnfs; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

747 
val pre_set_defss = map set_defs_of_bnf pre_bnfs; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

748 
val pre_rel_defs = map rel_def_of_bnf pre_bnfs; 
51766
f19a4d0ab1bf
renamed "set_natural" to "set_map", reflecting {Bl,Po,Tr} concensus
blanchet
parents:
51758
diff
changeset

749 
val nested_set_map's = maps set_map'_of_bnf nested_bnfs; 
f19a4d0ab1bf
renamed "set_natural" to "set_map", reflecting {Bl,Po,Tr} concensus
blanchet
parents:
51758
diff
changeset

750 
val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs; 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

751 

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

752 
val live = live_of_bnf any_fp_bnf; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

753 

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

754 
val Bs = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

755 
map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

756 
(liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

757 

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

758 
val B_ify = Term.typ_subst_atomic (As ~~ Bs); 
49167  759 

49501  760 
val ctors = map (mk_ctor As) ctors0; 
761 
val dtors = map (mk_dtor As) dtors0; 

49124  762 

49501  763 
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
blanchet
parents:
49361
diff
changeset

764 

51780  765 
fun massage_simple_notes base = 
766 
filter_out (null o #2) 

767 
#> map (fn (thmN, thms, attrs) => 

768 
((qualify true base (Binding.name thmN), attrs), [(thms, [])])); 

769 

770 
val massage_multi_notes = 

771 
maps (fn (thmN, thmss, attrs) => 

772 
if forall null thmss then 

773 
[] 

774 
else 

775 
map3 (fn fp_b_name => fn Type (T_name, _) => fn thms => 

776 
((qualify true fp_b_name (Binding.name thmN), attrs T_name), 

777 
[(thms, [])])) fp_b_names fpTs thmss); 

778 

49536  779 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; 
49203  780 
val ns = map length ctr_Tsss; 
49212  781 
val kss = map (fn n => 1 upto n) ns; 
49203  782 
val mss = map (map length) ctr_Tsss; 
783 
val Css = map2 replicate ns Cs; 

784 

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

785 
val fp_folds as any_fp_fold :: _ = map (mk_rec_like lfp As Cs) fp_folds0; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

786 
val fp_recs as any_fp_rec :: _ = map (mk_rec_like lfp As Cs) fp_recs0; 
49210  787 

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

788 
val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_fold))); 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

789 
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_rec))); 
49204  790 

49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

791 
val (((fold_only as (gss, _, _), rec_only as (hss, _, _)), 
49683  792 
(cs, cpss, unfold_only as ((pgss, crssss, cgssss), (_, g_Tsss, _)), 
793 
corec_only as ((phss, csssss, chssss), (_, h_Tsss, _)))), names_lthy0) = 

49208  794 
if lfp then 
795 
let 

796 
val y_Tsss = 

49255
2ecc533d6697
use balanced sums for constructors (to gracefully handle 100 constructors or more)
blanchet
parents:
49254
diff
changeset

797 
map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type) 
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

798 
ns mss fp_fold_fun_Ts; 
49208  799 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 
800 

49484  801 
val ((gss, ysss), lthy) = 
49208  802 
lthy 
803 
> mk_Freess "f" g_Tss 

804 
>> mk_Freesss "x" y_Tsss; 

49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

805 

c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

806 
fun proj_recT proj (Type (s as @{type_name prod}, Ts as [T, U])) = 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

807 
if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_recT proj) Ts) 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

808 
 proj_recT proj (Type (s, Ts)) = Type (s, map (proj_recT proj) Ts) 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

809 
 proj_recT _ T = T; 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

810 

51794  811 
fun unzip_recT T = 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

812 
if exists_subtype_in fpTs T then ([proj_recT fst T], [proj_recT snd T]) else ([T], []); 
49204  813 

49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

814 
val z_Tsss = 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

815 
map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type) 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

816 
ns mss fp_rec_fun_Ts; 
51794  817 
val z_Tsss' = map (map (flat_rec unzip_recT)) z_Tsss; 
818 
val h_Tss = map2 (map2 (curry (op >))) z_Tsss' Css; 

49204  819 

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

820 
val hss = map2 (map2 retype_free) h_Tss gss; 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

821 
val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss; 
49210  822 
in 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

823 
((((gss, g_Tss, ysss), (hss, h_Tss, zsss)), 
49683  824 
([], [], (([], [], []), ([], [], [])), (([], [], []), ([], [], [])))), lthy) 
49210  825 
end 
49208  826 
else 
49210  827 
let 
49221
6d8d5fe9f3a2
fixed bug with onevalue types with phantom type arguments
blanchet
parents:
49220
diff
changeset

828 
(*avoid "'a itself" arguments in coiterators and corecursors*) 
6d8d5fe9f3a2
fixed bug with onevalue types with phantom type arguments
blanchet
parents:
49220
diff
changeset

829 
val mss' = map (fn [0] => [1]  ms => ms) mss; 
6d8d5fe9f3a2
fixed bug with onevalue types with phantom type arguments
blanchet
parents:
49220
diff
changeset

830 

49463  831 
val p_Tss = map2 (fn n => replicate (Int.max (0, n  1)) o mk_pred1T) ns Cs; 
49275  832 

49587  833 
fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss); 
49211  834 

49587  835 
fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss 
836 
 flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) = 

837 
p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss; 

49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

838 

49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

839 
fun mk_types maybe_unzipT fun_Ts = 
49212  840 
let 
841 
val f_sum_prod_Ts = map range_type fun_Ts; 

49255
2ecc533d6697
use balanced sums for constructors (to gracefully handle 100 constructors or more)
blanchet
parents:
49254
diff
changeset

842 
val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts; 
49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

843 
val f_Tsss = map2 (map2 dest_tupleT) mss' f_prod_Tss; 
49275  844 
val f_Tssss = 
49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

845 
map2 (fn C => map (map (map (curry (op >) C) o maybe_unzipT))) Cs f_Tsss; 
49275  846 
val q_Tssss = 
49463  847 
map (map (map (fn [_] => []  [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss; 
49587  848 
val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss; 
49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

849 
in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end; 
49176  850 

49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

851 
val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts; 
49211  852 

49683  853 
val (((cs, pss), gssss), lthy) = 
49210  854 
lthy 
49683  855 
> mk_Frees "a" Cs 
49211  856 
>> mk_Freess "p" p_Tss 
49275  857 
>> mk_Freessss "g" g_Tssss; 
858 
val rssss = map (map (map (fn [] => []))) r_Tssss; 

49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

859 

49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

860 
fun proj_corecT proj (Type (s as @{type_name sum}, Ts as [T, U])) = 
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

861 
if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_corecT proj) Ts) 
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

862 
 proj_corecT proj (Type (s, Ts)) = Type (s, map (proj_corecT proj) Ts) 
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

863 
 proj_corecT _ T = T; 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

864 

49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

865 
fun unzip_corecT T = 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

866 
if exists_subtype_in fpTs T then [proj_corecT fst T, proj_corecT snd T] else [T]; 
49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

867 

aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

868 
val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) = 
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

869 
mk_types unzip_corecT fp_rec_fun_Ts; 
49210  870 

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

871 
val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss; 
49484  872 
val ((sssss, hssss_tl), lthy) = 
49275  873 
lthy 
874 
> mk_Freessss "q" s_Tssss 

875 
>> mk_Freessss "h" (map (map (map tl)) h_Tssss); 

876 
val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl; 

49211  877 

49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

878 
val cpss = map2 (map o rapp) cs pss; 
49212  879 

49683  880 
fun mk_terms qssss fssss = 
49212  881 
let 
49587  882 
val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss; 
49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

883 
val cqssss = map2 (map o map o map o rapp) cs qssss; 
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

884 
val cfssss = map2 (map o map o map o rapp) cs fssss; 
49683  885 
in (pfss, cqssss, cfssss) end; 
49210  886 
in 
49484  887 
(((([], [], []), ([], [], [])), 
49683  888 
(cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, g_Tsss, pg_Tss)), 
889 
(mk_terms sssss hssss, (h_sum_prod_Ts, h_Tsss, ph_Tss)))), lthy) 

49210  890 
end; 
891 

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

892 
fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor), 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

893 
fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs), 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

894 
pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings), 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

895 
ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy = 
49176  896 
let 
49498  897 
val fp_b_name = Binding.name_of fp_b; 
898 

49501  899 
val dtorT = domain_type (fastype_of ctor); 
49210  900 
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
49255
2ecc533d6697
use balanced sums for constructors (to gracefully handle 100 constructors or more)
blanchet
parents:
49254
diff
changeset

901 
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

902 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  903 

49593  904 
val (((((w, fs), xss), yss), u'), names_lthy) = 
49204  905 
no_defs_lthy 
49501  906 
> yield_singleton (mk_Frees "w") dtorT 
49176  907 
>> mk_Frees "f" case_Ts 
49370  908 
>> mk_Freess "x" ctr_Tss 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

909 
>> mk_Freess "y" (map (map B_ify) ctr_Tss) 
49498  910 
>> yield_singleton Variable.variant_fixes fp_b_name; 
49370  911 

49498  912 
val u = Free (u', fpT); 
49121  913 

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

914 
val tuple_xs = map HOLogic.mk_tuple xss; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

915 
val tuple_ys = map HOLogic.mk_tuple yss; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

916 

49129  917 
val ctr_rhss = 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

918 
map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $ 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

919 
mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs; 
49121  920 

49633  921 
val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b); 
49129  922 

49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

923 
val case_rhs = 
49498  924 
fold_rev Term.lambda (fs @ [u]) 
49501  925 
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u)); 
49129  926 

49201  927 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  928 
> 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
blanchet
parents:
49300
diff
changeset

929 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 
49336  930 
(case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  931 
> `Local_Theory.restore; 
932 

933 
val phi = Proof_Context.export_morphism lthy lthy'; 

934 

935 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

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

936 
val ctr_defs' = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

937 
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"
blanchet
parents:
49129
diff
changeset

938 
val case_def = Morphism.thm phi raw_case_def; 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

939 

49203  940 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
941 
val casex0 = Morphism.term phi raw_case; 

942 

943 
val ctrs = map (mk_ctr As) ctrs0; 

49121  944 

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

945 
fun wrap lthy = 
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

946 
let 
50170  947 
fun exhaust_tac {context = ctxt, prems = _} = 
49135  948 
let 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

949 
val ctor_iff_dtor_thm = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

950 
let 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

951 
val goal = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

952 
fold_rev Logic.all [w, u] 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

953 
(mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w))); 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

954 
in 
51551  955 
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} => 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

956 
mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT]) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

957 
(certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

958 
> Thm.close_derivation 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

959 
> Morphism.thm phi 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

960 
end; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

961 

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

962 
val sumEN_thm' = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

963 
unfold_thms lthy @{thms all_unit_eq} 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

964 
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

965 
(mk_sumEN_balanced n)) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

966 
> Morphism.thm phi; 
49135  967 
in 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

968 
mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm' 
49135  969 
end; 
970 

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

971 
val inject_tacss = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

972 
map2 (fn 0 => K []  _ => fn ctr_def => [fn {context = ctxt, ...} => 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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changeset

973 
mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

974 

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

975 
val half_distinct_tacss = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

976 
map (map (fn (def, def') => fn {context = ctxt, ...} => 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

977 
mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs)); 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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diff
changeset

978 

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

979 
val case_tacs = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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changeset

980 
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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changeset

981 
mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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diff
changeset

982 

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

983 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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diff
changeset

984 

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

985 
val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss 
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

986 
in 
51781  987 
wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings, 
988 
(sel_bindingss, sel_defaultss))) lthy 

49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

989 
end; 
49121  990 

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

991 
fun derive_maps_sets_rels (ctr_wrap_res, lthy) = 
49585
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generate highlevel "maps", "sets", and "rels" properties
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changeset

992 
let 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

993 
val rel_flip = rel_flip_of_bnf fp_bnf; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

994 
val nones = replicate live NONE; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

995 

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

996 
val ctor_cong = 
51746
5af40820948b
avoid accidental specialization of the types in the "map" property of codatatypes
blanchet
parents:
51745
diff
changeset

997 
if lfp then 
5af40820948b
avoid accidental specialization of the types in the "map" property of codatatypes
blanchet
parents:
51745
diff
changeset

998 
Drule.dummy_thm 
5af40820948b
avoid accidental specialization of the types in the "map" property of codatatypes
blanchet
parents:
51745
diff
changeset

999 
else 
5af40820948b
avoid accidental specialization of the types in the "map" property of codatatypes
blanchet
parents:
51745
diff
changeset

1000 
let val ctor' = mk_ctor Bs ctor in 
5af40820948b
avoid accidental specialization of the types in the "map" property of codatatypes
blanchet
parents:
51745
diff
changeset

1001 
cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong 
5af40820948b
avoid accidental specialization of the types in the "map" property of codatatypes
blanchet
parents:
51745
diff
changeset

1002 
end; 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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diff
changeset

1003 

5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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diff
changeset

1004 
fun mk_cIn ify = 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1005 
certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1006 
mk_InN_balanced (ify ctr_sum_prod_T) n; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1007 

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

1008 
val cxIns = map2 (mk_cIn I) tuple_xs ks; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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diff
changeset

1009 
val cyIns = map2 (mk_cIn B_ify) tuple_ys ks; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
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diff
changeset

1010 

49682  1011 
fun mk_map_thm ctr_def' cxIn = 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1012 
fold_thms lthy [ctr_def'] 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1013 
(unfold_thms lthy (pre_map_def :: 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1014 
(if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1015 
(cterm_instantiate_pos (nones @ [SOME cxIn]) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1016 
(if lfp then fp_map_thm else fp_map_thm RS ctor_cong))) 
49593  1017 
> singleton (Proof_Context.export names_lthy no_defs_lthy); 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
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diff
changeset

1018 

49682  1019 
fun mk_set_thm fp_set_thm ctr_def' cxIn = 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1020 
fold_thms lthy [ctr_def'] 
51766
f19a4d0ab1bf
renamed "set_natural" to "set_map", reflecting {Bl,Po,Tr} concensus
blanchet
parents:
51758
diff
changeset

1021 
(unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @ 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1022 
(if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set) 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
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diff
changeset

1023 
(cterm_instantiate_pos [SOME cxIn] fp_set_thm)) 
49593  1024 
> singleton (Proof_Context.export names_lthy no_defs_lthy); 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1025 

49682  1026 
fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns; 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
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diff
changeset

1027 

49682  1028 
val map_thms = map2 mk_map_thm ctr_defs' cxIns; 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
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diff
changeset

1029 
val set_thmss = map mk_set_thms fp_set_thms; 
49127  1030 

49682  1031 
val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns); 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1032 

49682  1033 
fun mk_rel_thm postproc ctr_defs' cxIn cyIn = 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1034 
fold_thms lthy ctr_defs' 
51745
a06a3c777add
simplify "Inl () = Inr ()" as well (not entirely clear why this is necessary)
blanchet
parents:
51551
diff
changeset

1035 
(unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def :: 
a06a3c777add
simplify "Inl () = Inr ()" as well (not entirely clear why this is necessary)
blanchet
parents:
51551
diff
changeset

1036 
(if lfp then [] else [dtor_ctor]) @ sum_prod_thms_rel) 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1037 
(cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm)) 
49593  1038 
> postproc 
1039 
> singleton (Proof_Context.export names_lthy no_defs_lthy); 

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

1040 

49682  1041 
fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) = 
1042 
mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn; 

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

1043 

49592
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1044 
val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos); 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1045 

49682  1046 
fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) = 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
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parents:
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diff
changeset

1047 
mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def'] 
49682  1048 
cxIn cyIn; 
49121  1049 

49592
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1050 
fun mk_other_half_rel_distinct_thm thm = 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1051 
flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2); 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
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diff
changeset

1052 

49592
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1053 
val half_rel_distinct_thmss = 
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1054 
map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos); 
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1055 
val other_half_rel_distinct_thmss = 
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1056 
map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss; 
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1057 
val (rel_distinct_thms, _) = 
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1058 
join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

1059 

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

1060 
val notes = 
49594
55e798614c45
tweaked theorem names (in particular, dropped s's)
blanchet
parents:
49593
diff
changeset

1061 
[(mapN, map_thms, code_simp_attrs), 
49592
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1062 
(rel_distinctN, rel_distinct_thms, code_simp_attrs), 
b859a02c1150
fixed "rels" + split them into injectivity and distinctness
blanchet
parents:
49591
diff
changeset

1063 
(rel_injectN, rel_inject_thms, code_simp_attrs), 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1064 
(setsN, flat set_thmss, code_simp_attrs)] 
51780  1065 
> massage_simple_notes fp_b_name; 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1066 
in 
51810
7b75fab5ebf5
factored out derivation of coinduction, unfold, corec
blanchet
parents:
51808
diff
changeset

1067 
(ctr_wrap_res, lthy > Local_Theory.notes notes > snd) 
49585
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1068 
end; 
5c4a12550491
generate highlevel "maps", "sets", and "rels" properties
blanchet
parents:
49583
diff
changeset

1069 

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

1070 
fun define_fold_rec no_defs_lthy = 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

1071 
let 
49208  1072 
val fpT_to_C = fpT > C; 
49199  1073 

49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

1074 
fun build_prod_proj mk_proj (T, U) = 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1075 
if T = U then 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1076 
id_const T 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1077 
else 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1078 
(case (T, U) of 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1079 
(Type (s, _), Type (s', _)) => 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

1080 
if s = s' then build_map lthy (build_prod_proj mk_proj) T U else mk_proj T 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1081 
 _ => mk_proj T); 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1082 

49681
aa66ea552357
changed type of corecursor for the nested recursion case
blanchet
parents:
49672
diff
changeset

1083 
(* TODO: Avoid these complications; cf. corec case *) 
49672
902b24e0ffb4
fixed recursor definition for datatypes with inner products (e.g. "'a trm" from the lambdaterm example)
blanchet
parents:
49671
diff
changeset

1084 
fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) = 
902b24e0ffb4
fixed recursor definition for datatypes with inner products (e.g. "'a trm" from the lambdaterm example)
blanchet
parents:
49671
diff
changeset

1085 
if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts) 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1086 
 mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts) 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1087 
 mk_U _ T = T; 
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1088 

51794  1089 
fun unzip_rec (x as Free (_, T)) = 
51808
355dcd6a9b3c
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
blanchet
parents:
51805
diff
changeset

1090 
if exists_subtype_in fpTs T then 
51794  1091 
([build_prod_proj fst_const (T, mk_U fst T) $ x], 
1092 
[build_prod_proj snd_const (T, mk_U snd T) $ x]) 

49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1093 
else 
51794  1094 
([x], []); 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1095 

51793
22f22172a361
started working on compatibility with old package's recursor
blanchet
parents:
51790
diff
changeset

1096 
fun mk_rec_like_arg f xs = 
51794  1097 
mk_tupled_fun (HOLogic.mk_tuple xs) f (flat_rec unzip_rec xs); 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1098 

c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1099 
fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xsss)) = 
49215  1100 
let 
1101 
val res_T = fold_rev (curry (op >)) f_Tss fpT_to_C; 

49633  1102 
val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b); 
49215  1103 
val spec = 
49336  1104 
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)), 
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1105 
Term.list_comb (fp_rec_like, 
49670
c7a034d01936
changed the type of the recursor for nested recursion
blanchet
parents:
49636
diff
changeset

1106 
map2 (mk_sum_caseN_balanced oo map2 mk_rec_like_arg) fss xsss)); 
49336  1107 
in (binding, spec) end; 
49199  1108 

49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1109 
val rec_like_infos = 
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1110 
[(foldN, fp_fold, fold_only), 
49215  1111 
(recN, fp_rec, rec_only)]; 
1112 

49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1113 
val (bindings, specs) = map generate_rec_like rec_like_infos > split_list; 
49215  1114 

1115 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49201  1116 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  1117 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49336  1118 
#>> apsnd snd) bindings specs 
49199  1119 
> `Local_Theory.restore; 
49201  1120 

1121 
val phi = Proof_Context.export_morphism lthy lthy'; 

1122 

49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1123 
val [fold_def, rec_def] = map (Morphism.thm phi) defs; 
49201  1124 

49536  1125 
val [foldx, recx] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

1126 
in 
49693
393d7242adaf
thread the right local theory through + reenable parallel proofs for previously problematic theories
blanchet
parents:
49683
diff
changeset

1127 
((foldx, recx, fold_def, rec_def), lthy') 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

1128 
end; 
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

1129 

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

1130 
fun define_unfold_corec no_defs_lthy = 
49210  1131 
let 
1132 
val B_to_fpT = C > fpT; 

49211  1133 

49683  1134 
fun build_sum_inj mk_inj (T, U) = 
1135 
if T = U then 

1136 
id_const T 

1137 
else 

1138 
(case (T, U) of 

1139 
(Type (s, _), Type (s', _)) => 

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

1140 
if s = s' then build_map lthy (build_sum_inj mk_inj) T U 
49683  1141 
else uncurry mk_inj (dest_sumT U) 
1142 
 _ => uncurry mk_inj (dest_sumT U)); 

1143 

1144 
fun build_dtor_corec_like_arg _ [] [cf] = cf 

1145 
 build_dtor_corec_like_arg T [cq] [cf, cf'] = 

1146 
mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf) 

1147 
(build_sum_inj Inr_const (fastype_of cf', T) $ cf') 

1148 

1149 
val crgsss = map3 (map3 (map3 build_dtor_corec_like_arg)) g_Tsss crssss cgssss; 

1150 
val cshsss = map3 (map3 (map3 build_dtor_corec_like_arg)) h_Tsss csssss chssss; 

1151 

49276  1152 
fun mk_preds_getterss_join c n cps sum_prod_T cqfss = 
1153 
Term.lambda c (mk_IfN sum_prod_T cps 

1154 
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n))); 

49275  1155 

49683  1156 
fun generate_corec_like (suf, fp_rec_like, (cqfsss, ((pfss, _, _), (f_sum_prod_Ts, _, 
1157 
pf_Tss)))) = 

49211  1158 
let 
1159 
val res_T = fold_rev (curry (op >)) pf_Tss B_to_fpT; 

49633  1160 
val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b); 
49211  1161 
val spec = 
49336  1162 
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)), 
49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1163 
Term.list_comb (fp_rec_like, 
49276  1164 
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss)); 
49336  1165 
in (binding, spec) end; 
49210  1166 

49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1167 
val corec_like_infos = 
49683  1168 
[(unfoldN, fp_fold, (crgsss, unfold_only)), 
1169 
(corecN, fp_rec, (cshsss, corec_only))]; 

49212  1170 

49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1171 
val (bindings, specs) = map generate_corec_like corec_like_infos > split_list; 
49211  1172 

1173 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49210  1174 
> apfst split_list o fold_map2 (fn b => fn spec => 
1175 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

49336  1176 
#>> apsnd snd) bindings specs 
49210  1177 
> `Local_Theory.restore; 
1178 

1179 
val phi = Proof_Context.export_morphism lthy lthy'; 

1180 

49504
df9b897fb254
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
blanchet
parents:
49502
diff
changeset

1181 
val [unfold_def, corec_def] = map (Morphism.thm phi) defs; 
49210  1182 

49536  1183 
val [unfold, corec] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts; 
49210  1184 
in 
49693
393d7242adaf
thread the right local theory through + reenable parallel proofs for previously problematic theories
blanchet
parents:
49683
diff
changeset

1185 
((unfold, corec, unfold_def, corec_def), lthy') 
49287
