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(* Title: HOL/Codatatype/Tools/bnf_fp_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_SUGAR =
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sig
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val datatyp: bool ->
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(mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
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BNF_Def.BNF list -> local_theory ->
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(term list * term list * term list * term list * thm * thm list * thm list * thm list *
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thm list * thm list) * local_theory) ->
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bool * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) *
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(binding * typ) list) * (binding * term) list) * 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 -> typ list * typ list list ->
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BNF_Def.BNF list -> local_theory ->
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(term list * term list * term list * term list * thm * thm list * thm list * thm list *
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thm list * thm list) * local_theory) ->
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(local_theory -> local_theory) parser
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end;
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structure BNF_FP_Sugar : BNF_FP_SUGAR =
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struct
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open BNF_Util
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open BNF_Wrap
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open BNF_Def
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open BNF_FP_Util
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open BNF_FP_Sugar_Tactics
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val simp_attrs = @{attributes [simp]};
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fun split_list10 xs =
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(map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
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map #9 xs, map #10 xs);
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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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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 mk_uncurried2_fun f xss =
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mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
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fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
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fun tack z_name (c, v) f =
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let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
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Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
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end;
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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 type_args_constrained_of (((cAs, _), _), _) = cAs;
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fun type_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 define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
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no_defs_lthy0 =
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let
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(* TODO: sanity checks on arguments *)
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val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
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else ();
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val nn = length specs;
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val fp_bs = map type_binding_of specs;
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val fp_common_name = mk_common_name fp_bs;
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fun prepare_type_arg (ty, c) =
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let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
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TFree (s, prepare_constraint no_defs_lthy0 c)
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end;
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val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
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val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
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val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
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val ((Bs, Cs), no_defs_lthy) =
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no_defs_lthy0
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|> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
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|> mk_TFrees nn
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||>> mk_TFrees nn;
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(* TODO: cleaner handling of fake contexts, without "background_theory" *)
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(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
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locale and shadows an existing global type*)
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val fake_thy =
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Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
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(type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
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val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
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fun mk_fake_T b =
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Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
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unsorted_As);
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val fake_Ts = map mk_fake_T fp_bs;
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val mixfixes = map mixfix_of specs;
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val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
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| b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
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val ctr_specss = map ctr_specs_of specs;
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val disc_bindingss = map (map disc_of) ctr_specss;
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val ctr_bindingss =
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map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
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fp_bs ctr_specss;
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val ctr_argsss = map (map args_of) ctr_specss;
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val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
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val sel_bindingsss = map (map (map fst)) ctr_argsss;
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val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
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val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
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val (As :: _) :: fake_ctr_Tsss =
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burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
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val _ = (case duplicates (op =) unsorted_As of [] => ()
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| A :: _ => error ("Duplicate type parameter " ^
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quote (Syntax.string_of_typ no_defs_lthy A)));
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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
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val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
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[] => ()
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| A' :: _ => error ("Extra type variable on right-hand side: " ^
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quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
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fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
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s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
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quote (Syntax.string_of_typ fake_lthy T)))
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| eq_fpT _ _ = false;
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fun freeze_fp (T as Type (s, Us)) =
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(case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
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| freeze_fp T = T;
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val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
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val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
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val fp_eqs =
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map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
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val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects,
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fp_iter_thms, fp_rec_thms), lthy)) =
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fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
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fun add_nesty_bnf_names Us =
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let
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fun add (Type (s, Ts)) ss =
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let val (needs, ss') = fold_map add Ts ss in
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if exists I needs then (true, insert (op =) s ss') else (false, ss')
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end
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| add T ss = (member (op =) Us T, ss);
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in snd oo add end;
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fun nesty_bnfs Us =
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map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []);
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val nesting_bnfs = nesty_bnfs As;
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val nested_bnfs = nesty_bnfs Bs;
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val timer = time (Timer.startRealTimer ());
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blanchet@50182
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fun mk_unf_or_fld 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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blanchet@50136
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val mk_unf = mk_unf_or_fld domain_type;
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blanchet@50141
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val mk_fld = mk_unf_or_fld range_type;
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blanchet@50139
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blanchet@50218
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val unfs = map (mk_unf As) unfs0;
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blanchet@50218
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val flds = map (mk_fld As) flds0;
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val fpTs = map (domain_type o fastype_of) unfs;
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blanchet@50377
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val exists_fp_subtype = exists_subtype (member (op =) fpTs);
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blanchet@50312
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val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
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blanchet@50218
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val ns = map length ctr_Tsss;
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blanchet@50227
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val kss = map (fn n => 1 upto n) ns;
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blanchet@50218
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val mss = map (map length) ctr_Tsss;
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blanchet@50218
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val Css = map2 replicate ns Cs;
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blanchet@50218
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blanchet@50229
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fun mk_iter_like 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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blanchet@50225
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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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blanchet@50191
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blanchet@50225
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val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
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blanchet@50225
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val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
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blanchet@50225
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blanchet@50227
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val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
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blanchet@50227
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val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
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blanchet@50219
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blanchet@50271
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val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
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blanchet@50291
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(zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
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blanchet@50223
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if lfp then
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blanchet@50223
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let
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blanchet@50223
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val y_Tsss =
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blanchet@50270
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map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
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blanchet@50227
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ns mss fp_iter_fun_Ts;
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blanchet@50223
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val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
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blanchet@50219
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blanchet@50223
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val ((gss, ysss), _) =
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blanchet@50223
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lthy
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blanchet@50223
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|> mk_Freess "f" g_Tss
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blanchet@50223
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||>> mk_Freesss "x" y_Tsss;
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blanchet@50289
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val yssss = map (map (map single)) ysss;
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blanchet@50289
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blanchet@50289
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fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
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blanchet@50289
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if member (op =) Cs U then Us else [T]
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blanchet@50289
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| dest_rec_prodT T = [T];
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blanchet@50219
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blanchet@50223
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val z_Tssss =
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blanchet@50289
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map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
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blanchet@50270
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dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
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blanchet@50223
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val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
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blanchet@50223
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blanchet@50313
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val hss = map2 (map2 retype_free) h_Tss gss;
|
blanchet@50313
|
251 |
val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
|
blanchet@50289
|
252 |
val (zssss_tl, _) =
|
blanchet@50223
|
253 |
lthy
|
blanchet@50289
|
254 |
|> mk_Freessss "y" (map (map (map tl)) z_Tssss);
|
blanchet@50289
|
255 |
val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
|
blanchet@50225
|
256 |
in
|
blanchet@50289
|
257 |
(((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
|
blanchet@50291
|
258 |
([], [], [], (([], []), ([], [])), (([], []), ([], []))))
|
blanchet@50225
|
259 |
end
|
blanchet@50223
|
260 |
else
|
blanchet@50225
|
261 |
let
|
blanchet@50236
|
262 |
(*avoid "'a itself" arguments in coiterators and corecursors*)
|
blanchet@50236
|
263 |
val mss' = map (fn [0] => [1] | ms => ms) mss;
|
blanchet@50236
|
264 |
|
blanchet@50290
|
265 |
val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
|
blanchet@50191
|
266 |
|
blanchet@50291
|
267 |
fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
|
blanchet@50230
|
268 |
|
blanchet@50291
|
269 |
fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
|
blanchet@50291
|
270 |
| zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
|
blanchet@50291
|
271 |
p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
|
blanchet@50289
|
272 |
|
blanchet@50289
|
273 |
fun mk_types maybe_dest_sumT fun_Ts =
|
blanchet@50227
|
274 |
let
|
blanchet@50227
|
275 |
val f_sum_prod_Ts = map range_type fun_Ts;
|
blanchet@50270
|
276 |
val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
|
blanchet@50290
|
277 |
val f_Tssss =
|
blanchet@50290
|
278 |
map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
|
blanchet@50290
|
279 |
Cs mss' f_prod_Tss;
|
blanchet@50290
|
280 |
val q_Tssss =
|
blanchet@50290
|
281 |
map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
|
blanchet@50291
|
282 |
val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
|
blanchet@50290
|
283 |
in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
|
blanchet@50226
|
284 |
|
blanchet@50290
|
285 |
val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
|
blanchet@50226
|
286 |
|
blanchet@50290
|
287 |
val ((((Free (z, _), cs), pss), gssss), _) =
|
blanchet@50225
|
288 |
lthy
|
blanchet@50248
|
289 |
|> yield_singleton (mk_Frees "z") dummyT
|
blanchet@50248
|
290 |
||>> mk_Frees "a" Cs
|
blanchet@50226
|
291 |
||>> mk_Freess "p" p_Tss
|
blanchet@50290
|
292 |
||>> mk_Freessss "g" g_Tssss;
|
blanchet@50290
|
293 |
val rssss = map (map (map (fn [] => []))) r_Tssss;
|
blanchet@50289
|
294 |
|
blanchet@50289
|
295 |
fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
|
blanchet@50289
|
296 |
if member (op =) Cs U then Us else [T]
|
blanchet@50289
|
297 |
| dest_corec_sumT T = [T];
|
blanchet@50289
|
298 |
|
blanchet@50290
|
299 |
val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
|
blanchet@50225
|
300 |
|
blanchet@50313
|
301 |
val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
|
blanchet@50290
|
302 |
val ((sssss, hssss_tl), _) =
|
blanchet@50290
|
303 |
lthy
|
blanchet@50290
|
304 |
|> mk_Freessss "q" s_Tssss
|
blanchet@50290
|
305 |
||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
|
blanchet@50290
|
306 |
val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
|
blanchet@50226
|
307 |
|
blanchet@50227
|
308 |
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
|
blanchet@50227
|
309 |
|
blanchet@50291
|
310 |
fun mk_preds_getters_join [] [cf] = cf
|
blanchet@50291
|
311 |
| mk_preds_getters_join [cq] [cf, cf'] =
|
blanchet@50291
|
312 |
mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
|
blanchet@50291
|
313 |
|
blanchet@50290
|
314 |
fun mk_terms qssss fssss =
|
blanchet@50227
|
315 |
let
|
blanchet@50291
|
316 |
val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
|
blanchet@50290
|
317 |
val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
|
blanchet@50289
|
318 |
val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
|
blanchet@50291
|
319 |
val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
|
blanchet@50291
|
320 |
in (pfss, cqfsss) end;
|
blanchet@50225
|
321 |
in
|
blanchet@50227
|
322 |
((([], [], []), ([], [], [])),
|
blanchet@50290
|
323 |
([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
|
blanchet@50290
|
324 |
(mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
|
blanchet@50225
|
325 |
end;
|
blanchet@50225
|
326 |
|
blanchet@50385
|
327 |
fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), fld), unf), fp_iter), fp_rec),
|
blanchet@50385
|
328 |
fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
|
blanchet@50385
|
329 |
disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
|
blanchet@50191
|
330 |
let
|
blanchet@50216
|
331 |
val unfT = domain_type (fastype_of fld);
|
blanchet@50225
|
332 |
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
|
blanchet@50270
|
333 |
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
|
blanchet@50149
|
334 |
val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
|
blanchet@50139
|
335 |
|
blanchet@50385
|
336 |
val ((((u, fs), xss), v'), _) =
|
blanchet@50219
|
337 |
no_defs_lthy
|
blanchet@50216
|
338 |
|> yield_singleton (mk_Frees "u") unfT
|
blanchet@50191
|
339 |
||>> mk_Frees "f" case_Ts
|
blanchet@50385
|
340 |
||>> mk_Freess "x" ctr_Tss
|
blanchet@50385
|
341 |
||>> yield_singleton (Variable.variant_fixes) (Binding.name_of fp_b);
|
blanchet@50385
|
342 |
|
blanchet@50385
|
343 |
val v = Free (v', fpT);
|
blanchet@50136
|
344 |
|
blanchet@50144
|
345 |
val ctr_rhss =
|
blanchet@50271
|
346 |
map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
|
blanchet@50271
|
347 |
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
|
blanchet@50136
|
348 |
|
blanchet@50351
|
349 |
val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b;
|
blanchet@50144
|
350 |
|
blanchet@50149
|
351 |
val case_rhs =
|
blanchet@50270
|
352 |
fold_rev Term.lambda (fs @ [v])
|
blanchet@50270
|
353 |
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
|
blanchet@50144
|
354 |
|
blanchet@50216
|
355 |
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
|
blanchet@50184
|
356 |
|> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
|
blanchet@50317
|
357 |
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
|
blanchet@50351
|
358 |
(case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
|
blanchet@50136
|
359 |
||> `Local_Theory.restore;
|
blanchet@50136
|
360 |
|
blanchet@50136
|
361 |
val phi = Proof_Context.export_morphism lthy lthy';
|
blanchet@50136
|
362 |
|
blanchet@50136
|
363 |
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
|
blanchet@50145
|
364 |
val case_def = Morphism.thm phi raw_case_def;
|
blanchet@50145
|
365 |
|
blanchet@50218
|
366 |
val ctrs0 = map (Morphism.term phi) raw_ctrs;
|
blanchet@50218
|
367 |
val casex0 = Morphism.term phi raw_case;
|
blanchet@50218
|
368 |
|
blanchet@50218
|
369 |
val ctrs = map (mk_ctr As) ctrs0;
|
blanchet@50136
|
370 |
|
blanchet@50150
|
371 |
fun exhaust_tac {context = ctxt, ...} =
|
blanchet@50138
|
372 |
let
|
blanchet@50150
|
373 |
val fld_iff_unf_thm =
|
blanchet@50150
|
374 |
let
|
blanchet@50150
|
375 |
val goal =
|
blanchet@50150
|
376 |
fold_rev Logic.all [u, v]
|
blanchet@50150
|
377 |
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
|
blanchet@50150
|
378 |
in
|
blanchet@50150
|
379 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
|
blanchet@50216
|
380 |
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
|
blanchet@50191
|
381 |
(certify lthy fld) (certify lthy unf) fld_unf unf_fld)
|
blanchet@50150
|
382 |
|> Thm.close_derivation
|
blanchet@50150
|
383 |
|> Morphism.thm phi
|
blanchet@50150
|
384 |
end;
|
blanchet@50150
|
385 |
|
blanchet@50150
|
386 |
val sumEN_thm' =
|
blanchet@50150
|
387 |
Local_Defs.unfold lthy @{thms all_unit_eq}
|
blanchet@50270
|
388 |
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
|
blanchet@50270
|
389 |
(mk_sumEN_balanced n))
|
blanchet@50150
|
390 |
|> Morphism.thm phi;
|
blanchet@50138
|
391 |
in
|
blanchet@50176
|
392 |
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
|
blanchet@50138
|
393 |
end;
|
blanchet@50136
|
394 |
|
blanchet@50141
|
395 |
val inject_tacss =
|
blanchet@50220
|
396 |
map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
|
blanchet@50220
|
397 |
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
|
blanchet@50141
|
398 |
|
blanchet@50142
|
399 |
val half_distinct_tacss =
|
blanchet@50142
|
400 |
map (map (fn (def, def') => fn {context = ctxt, ...} =>
|
blanchet@50142
|
401 |
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
|
blanchet@50142
|
402 |
|
blanchet@50145
|
403 |
val case_tacs =
|
blanchet@50145
|
404 |
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
|
blanchet@50145
|
405 |
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
|
blanchet@50136
|
406 |
|
blanchet@50136
|
407 |
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
|
blanchet@50149
|
408 |
|
blanchet@50302
|
409 |
fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
|
blanchet@50149
|
410 |
let
|
blanchet@50223
|
411 |
val fpT_to_C = fpT --> C;
|
blanchet@50214
|
412 |
|
blanchet@50230
|
413 |
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
|
blanchet@50230
|
414 |
let
|
blanchet@50230
|
415 |
val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
|
blanchet@50351
|
416 |
val binding = Binding.suffix_name ("_" ^ suf) fp_b;
|
blanchet@50230
|
417 |
val spec =
|
blanchet@50351
|
418 |
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
|
blanchet@50230
|
419 |
Term.list_comb (fp_iter_like,
|
blanchet@50270
|
420 |
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
|
blanchet@50351
|
421 |
in (binding, spec) end;
|
blanchet@50230
|
422 |
|
blanchet@50315
|
423 |
val iter_like_infos =
|
blanchet@50230
|
424 |
[(iterN, fp_iter, iter_only),
|
blanchet@50230
|
425 |
(recN, fp_rec, rec_only)];
|
blanchet@50230
|
426 |
|
blanchet@50351
|
427 |
val (bindings, specs) = map generate_iter_like iter_like_infos |> split_list;
|
blanchet@50230
|
428 |
|
blanchet@50230
|
429 |
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|
blanchet@50216
|
430 |
|> apfst split_list o fold_map2 (fn b => fn spec =>
|
blanchet@50214
|
431 |
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
|
blanchet@50351
|
432 |
#>> apsnd snd) bindings specs
|
blanchet@50214
|
433 |
||> `Local_Theory.restore;
|
blanchet@50216
|
434 |
|
blanchet@50216
|
435 |
val phi = Proof_Context.export_morphism lthy lthy';
|
blanchet@50216
|
436 |
|
blanchet@50230
|
437 |
val [iter_def, rec_def] = map (Morphism.thm phi) defs;
|
blanchet@50216
|
438 |
|
blanchet@50230
|
439 |
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
|
blanchet@50149
|
440 |
in
|
blanchet@50385
|
441 |
((ctrs, selss0, iter, recx, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def), lthy)
|
blanchet@50149
|
442 |
end;
|
blanchet@50149
|
443 |
|
blanchet@50302
|
444 |
fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
|
blanchet@50225
|
445 |
let
|
blanchet@50225
|
446 |
val B_to_fpT = C --> fpT;
|
blanchet@50225
|
447 |
|
blanchet@50291
|
448 |
fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
|
blanchet@50291
|
449 |
Term.lambda c (mk_IfN sum_prod_T cps
|
blanchet@50291
|
450 |
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
|
blanchet@50290
|
451 |
|
blanchet@50291
|
452 |
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
|
blanchet@50289
|
453 |
pf_Tss))) =
|
blanchet@50226
|
454 |
let
|
blanchet@50226
|
455 |
val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
|
blanchet@50351
|
456 |
val binding = Binding.suffix_name ("_" ^ suf) fp_b;
|
blanchet@50226
|
457 |
val spec =
|
blanchet@50351
|
458 |
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
|
blanchet@50226
|
459 |
Term.list_comb (fp_iter_like,
|
blanchet@50291
|
460 |
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
|
blanchet@50351
|
461 |
in (binding, spec) end;
|
blanchet@50225
|
462 |
|
blanchet@50315
|
463 |
val coiter_like_infos =
|
blanchet@50230
|
464 |
[(coiterN, fp_iter, coiter_only),
|
blanchet@50230
|
465 |
(corecN, fp_rec, corec_only)];
|
blanchet@50227
|
466 |
|
blanchet@50351
|
467 |
val (bindings, specs) = map generate_coiter_like coiter_like_infos |> split_list;
|
blanchet@50226
|
468 |
|
blanchet@50226
|
469 |
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|
blanchet@50225
|
470 |
|> apfst split_list o fold_map2 (fn b => fn spec =>
|
blanchet@50225
|
471 |
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
|
blanchet@50351
|
472 |
#>> apsnd snd) bindings specs
|
blanchet@50225
|
473 |
||> `Local_Theory.restore;
|
blanchet@50225
|
474 |
|
blanchet@50225
|
475 |
val phi = Proof_Context.export_morphism lthy lthy';
|
blanchet@50225
|
476 |
|
blanchet@50226
|
477 |
val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
|
blanchet@50225
|
478 |
|
blanchet@50226
|
479 |
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
|
blanchet@50225
|
480 |
in
|
blanchet@50385
|
481 |
((ctrs, selss0, coiter, corec, xss, ctr_defs, discIs, sel_thmss, coiter_def, corec_def),
|
blanchet@50385
|
482 |
lthy)
|
blanchet@50225
|
483 |
end;
|
blanchet@50301
|
484 |
|
blanchet@50302
|
485 |
fun wrap lthy =
|
blanchet@50302
|
486 |
let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
|
blanchet@50351
|
487 |
wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss,
|
blanchet@50302
|
488 |
sel_defaultss))) lthy
|
blanchet@50302
|
489 |
end;
|
blanchet@50302
|
490 |
|
blanchet@50302
|
491 |
val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
|
blanchet@50134
|
492 |
in
|
blanchet@50302
|
493 |
((wrap, define_iter_likes), lthy')
|
blanchet@50134
|
494 |
end;
|
blanchet@50182
|
495 |
|
blanchet@50241
|
496 |
val pre_map_defs = map map_def_of_bnf pre_bnfs;
|
blanchet@50357
|
497 |
val pre_set_defss = map set_defs_of_bnf pre_bnfs;
|
blanchet@50383
|
498 |
val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
|
blanchet@50378
|
499 |
val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
|
blanchet@50241
|
500 |
|
blanchet@50408
|
501 |
fun mk_map live Ts Us t =
|
blanchet@50441
|
502 |
let
|
blanchet@50441
|
503 |
val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last
|
blanchet@50441
|
504 |
in
|
blanchet@50229
|
505 |
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
|
blanchet@50229
|
506 |
end;
|
blanchet@50229
|
507 |
|
blanchet@50396
|
508 |
fun build_map build_arg (T as Type (s, Ts)) (U as Type (_, Us)) =
|
blanchet@50249
|
509 |
let
|
blanchet@50407
|
510 |
val bnf = the (bnf_of lthy s);
|
blanchet@50408
|
511 |
val live = live_of_bnf bnf;
|
blanchet@50408
|
512 |
val mapx = mk_map live Ts Us (map_of_bnf bnf);
|
blanchet@50408
|
513 |
val TUs = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
|
blanchet@50249
|
514 |
val args = map build_arg TUs;
|
blanchet@50249
|
515 |
in Term.list_comb (mapx, args) end;
|
blanchet@50249
|
516 |
|
blanchet@50385
|
517 |
fun derive_induct_iter_rec_thms_for_types ((ctrss, _, iters, recs, xsss, ctr_defss, _, _,
|
blanchet@50352
|
518 |
iter_defs, rec_defs), lthy) =
|
blanchet@50217
|
519 |
let
|
blanchet@50385
|
520 |
val (((phis, phis'), vs'), names_lthy) =
|
blanchet@50385
|
521 |
lthy
|
blanchet@50385
|
522 |
|> mk_Frees' "P" (map mk_predT fpTs)
|
blanchet@50385
|
523 |
||>> Variable.variant_fixes (map Binding.name_of fp_bs);
|
blanchet@50385
|
524 |
|
blanchet@50385
|
525 |
val vs = map2 (curry Free) vs' fpTs;
|
blanchet@50385
|
526 |
|
blanchet@50377
|
527 |
fun mk_sets_nested bnf =
|
blanchet@50377
|
528 |
let
|
blanchet@50377
|
529 |
val Type (T_name, Us) = T_of_bnf bnf;
|
blanchet@50377
|
530 |
val lives = lives_of_bnf bnf;
|
blanchet@50377
|
531 |
val sets = sets_of_bnf bnf;
|
blanchet@50377
|
532 |
fun mk_set U =
|
blanchet@50377
|
533 |
(case find_index (curry (op =) U) lives of
|
blanchet@50377
|
534 |
~1 => Term.dummy
|
blanchet@50377
|
535 |
| i => nth sets i);
|
blanchet@50377
|
536 |
in
|
blanchet@50377
|
537 |
(T_name, map mk_set Us)
|
blanchet@50377
|
538 |
end;
|
blanchet@50377
|
539 |
|
blanchet@50377
|
540 |
val setss_nested = map mk_sets_nested nested_bnfs;
|
blanchet@50377
|
541 |
|
blanchet@50352
|
542 |
val (induct_thms, induct_thm) =
|
blanchet@50352
|
543 |
let
|
blanchet@50377
|
544 |
fun mk_set Ts t =
|
blanchet@50377
|
545 |
let val Type (_, Ts0) = domain_type (fastype_of t) in
|
blanchet@50377
|
546 |
Term.subst_atomic_types (Ts0 ~~ Ts) t
|
blanchet@50377
|
547 |
end;
|
blanchet@50377
|
548 |
|
blanchet@50390
|
549 |
fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
|
blanchet@50376
|
550 |
(case find_index (curry (op =) T) fpTs of
|
blanchet@50377
|
551 |
~1 =>
|
blanchet@50377
|
552 |
(case AList.lookup (op =) setss_nested T_name of
|
blanchet@50377
|
553 |
NONE => []
|
blanchet@50377
|
554 |
| SOME raw_sets0 =>
|
blanchet@50377
|
555 |
let
|
blanchet@50377
|
556 |
val (Ts, raw_sets) =
|
blanchet@50377
|
557 |
split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
|
blanchet@50377
|
558 |
val sets = map (mk_set Ts0) raw_sets;
|
blanchet@50377
|
559 |
val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
|
blanchet@50390
|
560 |
val xysets = map (pair x) (ys ~~ sets);
|
blanchet@50390
|
561 |
val ppremss = map (mk_raw_prem_prems names_lthy') ys;
|
blanchet@50377
|
562 |
in
|
blanchet@50390
|
563 |
flat (map2 (map o apfst o cons) xysets ppremss)
|
blanchet@50377
|
564 |
end)
|
blanchet@50391
|
565 |
| i => [([], (i + 1, x))])
|
blanchet@50390
|
566 |
| mk_raw_prem_prems _ _ = [];
|
blanchet@50357
|
567 |
|
blanchet@50393
|
568 |
fun close_prem_prem xs t =
|
blanchet@50393
|
569 |
fold_rev Logic.all (map Free (drop (nn + length xs)
|
blanchet@50393
|
570 |
(rev (Term.add_frees t (map dest_Free xs @ phis'))))) t;
|
blanchet@50377
|
571 |
|
blanchet@50393
|
572 |
fun mk_prem_prem xs (xysets, (j, x)) =
|
blanchet@50393
|
573 |
close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
|
blanchet@50391
|
574 |
HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
|
blanchet@50391
|
575 |
HOLogic.mk_Trueprop (nth phis (j - 1) $ x)));
|
blanchet@50390
|
576 |
|
blanchet@50387
|
577 |
fun mk_raw_prem phi ctr ctr_Ts =
|
blanchet@50377
|
578 |
let
|
blanchet@50377
|
579 |
val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
|
blanchet@50391
|
580 |
val pprems = maps (mk_raw_prem_prems names_lthy') xs;
|
blanchet@50393
|
581 |
in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
|
blanchet@50357
|
582 |
|
blanchet@50391
|
583 |
fun mk_prem (xs, raw_pprems, concl) =
|
blanchet@50393
|
584 |
fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
|
blanchet@50383
|
585 |
|
blanchet@50404
|
586 |
val raw_premss = map3 (map2 o mk_raw_prem) phis ctrss ctr_Tsss;
|
blanchet@50404
|
587 |
|
blanchet@50376
|
588 |
val goal =
|
blanchet@50387
|
589 |
Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
|
blanchet@50383
|
590 |
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
|
blanchet@50383
|
591 |
(map2 (curry (op $)) phis vs)));
|
blanchet@50383
|
592 |
|
blanchet@50392
|
593 |
fun mk_raw_prem_prems_indices pprems =
|
blanchet@50391
|
594 |
let
|
blanchet@50392
|
595 |
fun has_index kk (_, (kk', _)) = kk' = kk;
|
blanchet@50392
|
596 |
val buckets = Library.partition_list has_index 1 nn pprems;
|
blanchet@50392
|
597 |
val pps = map length buckets;
|
blanchet@50391
|
598 |
in
|
blanchet@50393
|
599 |
map (fn pprem as (xysets, (kk, _)) =>
|
blanchet@50392
|
600 |
((nth pps (kk - 1), find_index (curry (op =) pprem) (nth buckets (kk - 1)) + 1),
|
blanchet@50393
|
601 |
(length xysets, kk))) pprems
|
blanchet@50391
|
602 |
end;
|
blanchet@50391
|
603 |
|
blanchet@50404
|
604 |
val ppjjqqkksss = map (map (mk_raw_prem_prems_indices o #2)) raw_premss;
|
blanchet@50442
|
605 |
val _ = tracing ("val ppjjqqkksss = " ^ PolyML.makestring ppjjqqkksss) (*###*)
|
blanchet@50383
|
606 |
|
blanchet@50383
|
607 |
val fld_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
|
blanchet@50357
|
608 |
|
blanchet@50357
|
609 |
val induct_thm =
|
blanchet@50376
|
610 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
|
blanchet@50404
|
611 |
mk_induct_tac ctxt ns mss ppjjqqkksss (flat ctr_defss) fld_induct'
|
blanchet@50404
|
612 |
nested_set_natural's pre_set_defss)
|
blanchet@50383
|
613 |
|> singleton (Proof_Context.export names_lthy lthy)
|
blanchet@50352
|
614 |
in
|
blanchet@50382
|
615 |
`(conj_dests nn) induct_thm
|
blanchet@50352
|
616 |
end;
|
blanchet@50216
|
617 |
|
blanchet@50217
|
618 |
val (iter_thmss, rec_thmss) =
|
blanchet@50222
|
619 |
let
|
blanchet@50352
|
620 |
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
|
blanchet@50352
|
621 |
val giters = map (lists_bmoc gss) iters;
|
blanchet@50352
|
622 |
val hrecs = map (lists_bmoc hss) recs;
|
blanchet@50352
|
623 |
|
blanchet@50227
|
624 |
fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
|
blanchet@50222
|
625 |
fold_rev (fold_rev Logic.all) (xs :: fss)
|
blanchet@50227
|
626 |
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
|
blanchet@50216
|
627 |
|
blanchet@50249
|
628 |
fun build_call fiter_likes maybe_tick (T, U) =
|
blanchet@50249
|
629 |
if T = U then
|
blanchet@50383
|
630 |
id_const T
|
blanchet@50249
|
631 |
else
|
blanchet@50249
|
632 |
(case find_index (curry (op =) T) fpTs of
|
blanchet@50249
|
633 |
~1 => build_map (build_call fiter_likes maybe_tick) T U
|
blanchet@50249
|
634 |
| j => maybe_tick (nth vs j) (nth fiter_likes j));
|
blanchet@50248
|
635 |
|
blanchet@50289
|
636 |
fun mk_U maybe_mk_prodT =
|
blanchet@50289
|
637 |
typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
|
blanchet@50229
|
638 |
|
blanchet@50357
|
639 |
fun intr_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
|
blanchet@50229
|
640 |
if member (op =) fpTs T then
|
blanchet@50248
|
641 |
maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
|
blanchet@50377
|
642 |
else if exists_fp_subtype T then
|
blanchet@50289
|
643 |
[build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
|
blanchet@50229
|
644 |
else
|
blanchet@50229
|
645 |
[x];
|
blanchet@50229
|
646 |
|
blanchet@50357
|
647 |
val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss;
|
blanchet@50357
|
648 |
val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
|
blanchet@50219
|
649 |
|
blanchet@50227
|
650 |
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
|
blanchet@50227
|
651 |
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
|
blanchet@50219
|
652 |
|
blanchet@50218
|
653 |
val iter_tacss =
|
blanchet@50378
|
654 |
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms
|
blanchet@50378
|
655 |
ctr_defss;
|
blanchet@50218
|
656 |
val rec_tacss =
|
blanchet@50378
|
657 |
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms
|
blanchet@50378
|
658 |
ctr_defss;
|
blanchet@50217
|
659 |
in
|
blanchet@50291
|
660 |
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
|
blanchet@50220
|
661 |
goal_iterss iter_tacss,
|
blanchet@50291
|
662 |
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
|
blanchet@50220
|
663 |
goal_recss rec_tacss)
|
blanchet@50217
|
664 |
end;
|
blanchet@50216
|
665 |
|
blanchet@50352
|
666 |
val common_notes =
|
blanchet@50382
|
667 |
(if nn > 1 then [(inductN, [induct_thm], [])] (* FIXME: attribs *) else [])
|
blanchet@50352
|
668 |
|> map (fn (thmN, thms, attrs) =>
|
blanchet@50352
|
669 |
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
|
blanchet@50352
|
670 |
|
blanchet@50241
|
671 |
val notes =
|
blanchet@50357
|
672 |
[(inductN, map single induct_thms, []), (* FIXME: attribs *)
|
blanchet@50357
|
673 |
(itersN, iter_thmss, simp_attrs),
|
blanchet@50315
|
674 |
(recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
|
blanchet@50315
|
675 |
|> maps (fn (thmN, thmss, attrs) =>
|
blanchet@50217
|
676 |
map2 (fn b => fn thms =>
|
blanchet@50315
|
677 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
|
blanchet@50317
|
678 |
[(thms, [])])) fp_bs thmss);
|
blanchet@50217
|
679 |
in
|
blanchet@50352
|
680 |
lthy |> Local_Theory.notes (common_notes @ notes) |> snd
|
blanchet@50217
|
681 |
end;
|
blanchet@50217
|
682 |
|
blanchet@50385
|
683 |
fun derive_coinduct_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, _, ctr_defss,
|
blanchet@50385
|
684 |
discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
|
blanchet@50227
|
685 |
let
|
blanchet@50387
|
686 |
val (vs', _) =
|
blanchet@50385
|
687 |
lthy
|
blanchet@50385
|
688 |
|> Variable.variant_fixes (map Binding.name_of fp_bs);
|
blanchet@50385
|
689 |
|
blanchet@50385
|
690 |
val vs = map2 (curry Free) vs' fpTs;
|
blanchet@50385
|
691 |
|
blanchet@50352
|
692 |
val (coinduct_thms, coinduct_thm) =
|
blanchet@50352
|
693 |
let
|
blanchet@50352
|
694 |
val coinduct_thm = fp_induct;
|
blanchet@50352
|
695 |
in
|
blanchet@50382
|
696 |
`(conj_dests nn) coinduct_thm
|
blanchet@50352
|
697 |
end;
|
blanchet@50227
|
698 |
|
blanchet@50227
|
699 |
val (coiter_thmss, corec_thmss) =
|
blanchet@50227
|
700 |
let
|
blanchet@50352
|
701 |
val z = the_single zs;
|
blanchet@50352
|
702 |
val gcoiters = map (lists_bmoc pgss) coiters;
|
blanchet@50352
|
703 |
val hcorecs = map (lists_bmoc phss) corecs;
|
blanchet@50352
|
704 |
|
blanchet@50247
|
705 |
fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
|
blanchet@50227
|
706 |
|
blanchet@50291
|
707 |
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
|
blanchet@50227
|
708 |
fold_rev (fold_rev Logic.all) ([c] :: pfss)
|
blanchet@50247
|
709 |
(Logic.list_implies (seq_conds mk_goal_cond n k cps,
|
blanchet@50291
|
710 |
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
|
blanchet@50227
|
711 |
|
blanchet@50249
|
712 |
fun build_call fiter_likes maybe_tack (T, U) =
|
blanchet@50249
|
713 |
if T = U then
|
blanchet@50383
|
714 |
id_const T
|
blanchet@50249
|
715 |
else
|
blanchet@50249
|
716 |
(case find_index (curry (op =) U) fpTs of
|
blanchet@50249
|
717 |
~1 => build_map (build_call fiter_likes maybe_tack) T U
|
blanchet@50249
|
718 |
| j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
|
blanchet@50248
|
719 |
|
blanchet@50289
|
720 |
fun mk_U maybe_mk_sumT =
|
blanchet@50289
|
721 |
typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
|
blanchet@50227
|
722 |
|
blanchet@50357
|
723 |
fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
|
blanchet@50291
|
724 |
let val T = fastype_of cqf in
|
blanchet@50291
|
725 |
if exists_subtype (member (op =) Cs) T then
|
blanchet@50291
|
726 |
build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
|
blanchet@50291
|
727 |
else
|
blanchet@50291
|
728 |
cqf
|
blanchet@50291
|
729 |
end;
|
blanchet@50247
|
730 |
|
blanchet@50357
|
731 |
val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss;
|
blanchet@50357
|
732 |
val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
|
blanchet@50227
|
733 |
|
blanchet@50227
|
734 |
val goal_coiterss =
|
blanchet@50291
|
735 |
map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
|
blanchet@50248
|
736 |
val goal_corecss =
|
blanchet@50291
|
737 |
map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
|
blanchet@50228
|
738 |
|
blanchet@50228
|
739 |
val coiter_tacss =
|
blanchet@50378
|
740 |
map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs
|
blanchet@50241
|
741 |
ctr_defss;
|
blanchet@50248
|
742 |
val corec_tacss =
|
blanchet@50378
|
743 |
map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs
|
blanchet@50248
|
744 |
ctr_defss;
|
blanchet@50227
|
745 |
in
|
blanchet@50291
|
746 |
(map2 (map2 (fn goal => fn tac =>
|
blanchet@50291
|
747 |
Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
|
blanchet@50228
|
748 |
goal_coiterss coiter_tacss,
|
blanchet@50291
|
749 |
map2 (map2 (fn goal => fn tac =>
|
blanchet@50291
|
750 |
Skip_Proof.prove lthy [] [] goal (tac o #context)
|
blanchet@50291
|
751 |
|> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
|
blanchet@50248
|
752 |
goal_corecss corec_tacss)
|
blanchet@50227
|
753 |
end;
|
blanchet@50227
|
754 |
|
blanchet@50281
|
755 |
fun mk_disc_coiter_like_thms [_] = K []
|
blanchet@50281
|
756 |
| mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
|
blanchet@50281
|
757 |
|
blanchet@50281
|
758 |
val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
|
blanchet@50281
|
759 |
val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
|
blanchet@50281
|
760 |
|
blanchet@50282
|
761 |
fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
|
blanchet@50281
|
762 |
let
|
blanchet@50282
|
763 |
val (domT, ranT) = dest_funT (fastype_of sel0);
|
blanchet@50281
|
764 |
val arg_cong' =
|
blanchet@50281
|
765 |
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
|
blanchet@50282
|
766 |
[NONE, NONE, SOME (certify lthy sel0)] arg_cong
|
blanchet@50282
|
767 |
|> Thm.varifyT_global;
|
blanchet@50281
|
768 |
val sel_thm' = sel_thm RSN (2, trans);
|
blanchet@50281
|
769 |
in
|
blanchet@50282
|
770 |
coiter_like_thm RS arg_cong' RS sel_thm'
|
blanchet@50281
|
771 |
end;
|
blanchet@50281
|
772 |
|
blanchet@50281
|
773 |
val sel_coiter_thmsss =
|
blanchet@50281
|
774 |
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
|
blanchet@50281
|
775 |
val sel_corec_thmsss =
|
blanchet@50282
|
776 |
map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
|
blanchet@50281
|
777 |
|
blanchet@50357
|
778 |
val common_notes =
|
blanchet@50382
|
779 |
(if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
|
blanchet@50357
|
780 |
|> map (fn (thmN, thms, attrs) =>
|
blanchet@50357
|
781 |
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
|
blanchet@50357
|
782 |
|
blanchet@50227
|
783 |
val notes =
|
blanchet@50357
|
784 |
[(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
|
blanchet@50357
|
785 |
(coitersN, coiter_thmss, []),
|
blanchet@50315
|
786 |
(disc_coitersN, disc_coiter_thmss, []),
|
blanchet@50315
|
787 |
(sel_coitersN, map flat sel_coiter_thmsss, []),
|
blanchet@50315
|
788 |
(corecsN, corec_thmss, []),
|
blanchet@50315
|
789 |
(disc_corecsN, disc_corec_thmss, []),
|
blanchet@50315
|
790 |
(sel_corecsN, map flat sel_corec_thmsss, [])]
|
blanchet@50315
|
791 |
|> maps (fn (thmN, thmss, attrs) =>
|
blanchet@50281
|
792 |
map_filter (fn (_, []) => NONE | (b, thms) =>
|
blanchet@50315
|
793 |
SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
|
blanchet@50317
|
794 |
[(thms, [])])) (fp_bs ~~ thmss));
|
blanchet@50227
|
795 |
in
|
blanchet@50376
|
796 |
lthy |> Local_Theory.notes (common_notes @ notes) |> snd
|
blanchet@50227
|
797 |
end;
|
blanchet@50227
|
798 |
|
blanchet@50302
|
799 |
fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
|
blanchet@50385
|
800 |
fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list10
|
blanchet@50302
|
801 |
|
blanchet@50219
|
802 |
val lthy' = lthy
|
blanchet@50385
|
803 |
|> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
|
blanchet@50385
|
804 |
fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
|
blanchet@50385
|
805 |
ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
|
blanchet@50302
|
806 |
|>> split_list |> wrap_types_and_define_iter_likes
|
blanchet@50352
|
807 |
|> (if lfp then derive_induct_iter_rec_thms_for_types
|
blanchet@50352
|
808 |
else derive_coinduct_coiter_corec_thms_for_types);
|
blanchet@50182
|
809 |
|
blanchet@50182
|
810 |
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
|
blanchet@50223
|
811 |
(if lfp then "" else "co") ^ "datatype"));
|
blanchet@50127
|
812 |
in
|
blanchet@50323
|
813 |
timer; lthy'
|
blanchet@50127
|
814 |
end;
|
blanchet@50127
|
815 |
|
blanchet@50313
|
816 |
val datatyp = define_datatype (K I) (K I) (K I);
|
blanchet@50312
|
817 |
|
blanchet@50313
|
818 |
val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
|
blanchet@50134
|
819 |
|
blanchet@50344
|
820 |
val parse_binding_colon = Parse.binding --| @{keyword ":"};
|
blanchet@50351
|
821 |
val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binding;
|
blanchet@50134
|
822 |
|
blanchet@50127
|
823 |
val parse_ctr_arg =
|
blanchet@50344
|
824 |
@{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
|
blanchet@50351
|
825 |
(Parse.typ >> pair no_binding);
|
blanchet@50127
|
826 |
|
blanchet@50301
|
827 |
val parse_defaults =
|
blanchet@50301
|
828 |
@{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
|
blanchet@50301
|
829 |
|
blanchet@50127
|
830 |
val parse_single_spec =
|
blanchet@50127
|
831 |
Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
|
blanchet@50134
|
832 |
(@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
|
blanchet@50301
|
833 |
Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
|
blanchet@50127
|
834 |
|
blanchet@50293
|
835 |
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
|
blanchet@50293
|
836 |
|
blanchet@50323
|
837 |
fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;
|
blanchet@50127
|
838 |
|
blanchet@50127
|
839 |
end;
|