blanchet@50127
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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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Sugar for constructing LFPs and GFPs.
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*)
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signature BNF_FP_SUGAR =
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sig
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(* TODO: programmatic interface *)
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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_LFP
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open BNF_GFP
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open BNF_FP_Sugar_Tactics
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val caseN = "case";
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val coitersN = "coiters";
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val corecsN = "corecs";
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val disc_coitersN = "disc_coiters";
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val disc_corecsN = "disc_corecs";
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val itersN = "iters";
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val recsN = "recs";
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val sel_coitersN = "sel_coiters";
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val sel_corecsN = "sel_corecs";
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fun split_list11 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, map #11 xs);
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fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
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| strip_map_type T = ([], T);
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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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blanchet@50214
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fun retype_free (Free (s, _)) T = Free (s, T);
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs))
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fun mk_id T = Const (@{const_name id}, T --> T);
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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
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val T = fastype_of v;
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val z = Free (z_name, mk_sumT (T, fastype_of c))
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in Term.lambda z (mk_sum_case (mk_id T, Term.lambda c (f $ c)) $ z) 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_constrained ctxt (T, c) (T', c') =
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if T = T' then
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(case (c, c') of
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(_, NONE) => (T, c)
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| (NONE, _) => (T, c')
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| _ =>
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if c = c' then
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(T, c)
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else
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error ("Inconsistent sort constraints for type variable " ^
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quote (Syntax.string_of_typ ctxt T)))
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else
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cannot_merge_types ();
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fun merge_type_args_constrained ctxt (cAs, cAs') =
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if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
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else cannot_merge_types ();
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fun type_args_constrained_of (((cAs, _), _), _) = cAs;
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val type_args_of = map fst o type_args_constrained_of;
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fun type_binder_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 ctr_mixfix_of (_, mx) = mx;
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fun prepare_datatype prepare_typ lfp specs fake_lthy no_defs_lthy =
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let
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val constrained_As =
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map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
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|> Library.foldr1 (merge_type_args_constrained no_defs_lthy);
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val As = map fst constrained_As;
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val As' = map dest_TFree As;
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val _ = (case duplicates (op =) 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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(* TODO: use sort constraints on type args *)
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val N = length specs;
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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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As);
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val bs = map type_binder_of specs;
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val fakeTs = map mk_fake_T bs;
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val mixfixes = map mixfix_of specs;
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val _ = (case duplicates Binding.eq_name 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_binderss = map (map disc_of) ctr_specss;
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val ctr_binderss = map (map ctr_of) 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_bindersss = map (map (map fst)) ctr_argsss;
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val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
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val _ = (case subtract (op =) As' rhs_As' of
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[] => ()
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| A' :: _ => error ("Extra type variables on rhs: " ^
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quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
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val ((Cs, Xs), _) =
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no_defs_lthy
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|> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
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|> mk_TFrees N
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||>> mk_TFrees N;
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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) fakeTs of ~1 => Type (s, map freeze_fp Us) | j => nth Xs j)
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| freeze_fp T = T;
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val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
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val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
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val eqs = map dest_TFree Xs ~~ ctr_sum_prod_TsXs;
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val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects,
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fp_iter_thms, fp_rec_thms), lthy)) =
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fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy;
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val add_nested_bnf_names =
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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 =) As T, ss);
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in snd oo add end;
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blanchet@50241
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val nested_bnfs =
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traytel@50251
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map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []);
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blanchet@50241
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blanchet@50182
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val timer = time (Timer.startRealTimer ());
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blanchet@50182
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blanchet@50191
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fun mk_unf_or_fld get_T Ts t =
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blanchet@50191
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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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blanchet@50141
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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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blanchet@50136
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blanchet@50216
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val fpTs = map (domain_type o fastype_of) unfs;
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blanchet@50219
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blanchet@50216
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val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
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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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blanchet@50134
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let
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blanchet@50229
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val (binders, body) = strip_type (fastype_of t);
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blanchet@50225
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val (f_Us, prebody) = split_last binders;
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blanchet@50225
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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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blanchet@50191
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in
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blanchet@50229
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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@50219
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fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) =
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blanchet@50219
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if member (op =) Cs U then Us else [T]
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blanchet@50219
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| dest_rec_pair T = [T];
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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@50271
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(zs, cs, cpss, coiter_only as ((pgss, cgsss), _), corec_only as ((phss, chsss), _))) =
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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@50219
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blanchet@50223
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val z_Tssss =
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blanchet@50270
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map3 (fn n => fn ms => map2 (map dest_rec_pair 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@50223
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val hss = map2 (map2 retype_free) gss h_Tss;
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blanchet@50223
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val (zssss, _) =
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blanchet@50223
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lthy
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blanchet@50223
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|> mk_Freessss "x" z_Tssss;
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blanchet@50225
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in
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blanchet@50230
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(((gss, g_Tss, map (map (map single)) ysss), (hss, h_Tss, zssss)),
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blanchet@50271
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([], [], [], (([], []), ([], [])), (([], []), ([], []))))
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blanchet@50225
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end
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blanchet@50223
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else
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blanchet@50225
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let
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blanchet@50236
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247 |
(*avoid "'a itself" arguments in coiterators and corecursors*)
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blanchet@50236
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val mss' = map (fn [0] => [1] | ms => ms) mss;
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blanchet@50236
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blanchet@50226
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val p_Tss =
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blanchet@50225
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map2 (fn C => fn n => replicate (Int.max (0, n - 1)) (C --> HOLogic.boolT)) Cs ns;
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blanchet@50191
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blanchet@50269
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fun zip_preds_getters [] [fs] = fs
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blanchet@50269
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254 |
| zip_preds_getters (p :: ps) (fs :: fss) = p :: fs @ zip_preds_getters ps fss;
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blanchet@50230
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255 |
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blanchet@50227
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fun mk_types fun_Ts =
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blanchet@50227
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257 |
let
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blanchet@50227
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258 |
val f_sum_prod_Ts = map range_type fun_Ts;
|
blanchet@50270
|
259 |
val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
|
blanchet@50227
|
260 |
val f_Tsss =
|
blanchet@50236
|
261 |
map3 (fn C => map2 (map (curry (op -->) C) oo dest_tupleT)) Cs mss' f_prod_Tss;
|
blanchet@50269
|
262 |
val pf_Tss = map2 zip_preds_getters p_Tss f_Tsss
|
blanchet@50271
|
263 |
in (f_sum_prod_Ts, f_Tsss, pf_Tss) end;
|
blanchet@50226
|
264 |
|
blanchet@50271
|
265 |
val (g_sum_prod_Ts, g_Tsss, pg_Tss) = mk_types fp_iter_fun_Ts;
|
blanchet@50271
|
266 |
val (h_sum_prod_Ts, h_Tsss, ph_Tss) = mk_types fp_rec_fun_Ts;
|
blanchet@50226
|
267 |
|
blanchet@50248
|
268 |
val ((((Free (z, _), cs), pss), gsss), _) =
|
blanchet@50225
|
269 |
lthy
|
blanchet@50248
|
270 |
|> yield_singleton (mk_Frees "z") dummyT
|
blanchet@50248
|
271 |
||>> mk_Frees "a" Cs
|
blanchet@50226
|
272 |
||>> mk_Freess "p" p_Tss
|
blanchet@50225
|
273 |
||>> mk_Freesss "g" g_Tsss;
|
blanchet@50225
|
274 |
|
blanchet@50226
|
275 |
val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss;
|
blanchet@50226
|
276 |
|
blanchet@50227
|
277 |
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
|
blanchet@50227
|
278 |
|
blanchet@50227
|
279 |
fun mk_terms fsss =
|
blanchet@50227
|
280 |
let
|
blanchet@50269
|
281 |
val pfss = map2 zip_preds_getters pss fsss;
|
blanchet@50227
|
282 |
val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss
|
blanchet@50227
|
283 |
in (pfss, cfsss) end;
|
blanchet@50225
|
284 |
in
|
blanchet@50227
|
285 |
((([], [], []), ([], [], [])),
|
blanchet@50271
|
286 |
([z], cs, cpss, (mk_terms gsss, (g_sum_prod_Ts, pg_Tss)),
|
blanchet@50271
|
287 |
(mk_terms hsss, (h_sum_prod_Ts, ph_Tss))))
|
blanchet@50225
|
288 |
end;
|
blanchet@50225
|
289 |
|
blanchet@50227
|
290 |
fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
|
blanchet@50227
|
291 |
fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
|
blanchet@50227
|
292 |
disc_binders), sel_binderss) no_defs_lthy =
|
blanchet@50191
|
293 |
let
|
blanchet@50216
|
294 |
val unfT = domain_type (fastype_of fld);
|
blanchet@50225
|
295 |
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
|
blanchet@50270
|
296 |
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
|
blanchet@50149
|
297 |
val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
|
blanchet@50139
|
298 |
|
blanchet@50191
|
299 |
val ((((u, v), fs), xss), _) =
|
blanchet@50219
|
300 |
no_defs_lthy
|
blanchet@50216
|
301 |
|> yield_singleton (mk_Frees "u") unfT
|
blanchet@50216
|
302 |
||>> yield_singleton (mk_Frees "v") fpT
|
blanchet@50191
|
303 |
||>> mk_Frees "f" case_Ts
|
blanchet@50139
|
304 |
||>> mk_Freess "x" ctr_Tss;
|
blanchet@50136
|
305 |
|
blanchet@50144
|
306 |
val ctr_rhss =
|
blanchet@50271
|
307 |
map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
|
blanchet@50271
|
308 |
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
|
blanchet@50136
|
309 |
|
blanchet@50145
|
310 |
val case_binder = Binding.suffix_name ("_" ^ caseN) b;
|
blanchet@50144
|
311 |
|
blanchet@50149
|
312 |
val case_rhs =
|
blanchet@50270
|
313 |
fold_rev Term.lambda (fs @ [v])
|
blanchet@50270
|
314 |
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
|
blanchet@50144
|
315 |
|
blanchet@50216
|
316 |
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
|
blanchet@50184
|
317 |
|> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
|
blanchet@50184
|
318 |
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
|
blanchet@50216
|
319 |
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
|
blanchet@50136
|
320 |
||> `Local_Theory.restore;
|
blanchet@50136
|
321 |
|
blanchet@50136
|
322 |
(*transforms defined frees into consts (and more)*)
|
blanchet@50136
|
323 |
val phi = Proof_Context.export_morphism lthy lthy';
|
blanchet@50136
|
324 |
|
blanchet@50136
|
325 |
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
|
blanchet@50145
|
326 |
val case_def = Morphism.thm phi raw_case_def;
|
blanchet@50145
|
327 |
|
blanchet@50218
|
328 |
val ctrs0 = map (Morphism.term phi) raw_ctrs;
|
blanchet@50218
|
329 |
val casex0 = Morphism.term phi raw_case;
|
blanchet@50218
|
330 |
|
blanchet@50218
|
331 |
val ctrs = map (mk_ctr As) ctrs0;
|
blanchet@50136
|
332 |
|
blanchet@50150
|
333 |
fun exhaust_tac {context = ctxt, ...} =
|
blanchet@50138
|
334 |
let
|
blanchet@50150
|
335 |
val fld_iff_unf_thm =
|
blanchet@50150
|
336 |
let
|
blanchet@50150
|
337 |
val goal =
|
blanchet@50150
|
338 |
fold_rev Logic.all [u, v]
|
blanchet@50150
|
339 |
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
|
blanchet@50150
|
340 |
in
|
blanchet@50150
|
341 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
|
blanchet@50216
|
342 |
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
|
blanchet@50191
|
343 |
(certify lthy fld) (certify lthy unf) fld_unf unf_fld)
|
blanchet@50150
|
344 |
|> Thm.close_derivation
|
blanchet@50150
|
345 |
|> Morphism.thm phi
|
blanchet@50150
|
346 |
end;
|
blanchet@50150
|
347 |
|
blanchet@50150
|
348 |
val sumEN_thm' =
|
blanchet@50150
|
349 |
Local_Defs.unfold lthy @{thms all_unit_eq}
|
blanchet@50270
|
350 |
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
|
blanchet@50270
|
351 |
(mk_sumEN_balanced n))
|
blanchet@50150
|
352 |
|> Morphism.thm phi;
|
blanchet@50138
|
353 |
in
|
blanchet@50176
|
354 |
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
|
blanchet@50138
|
355 |
end;
|
blanchet@50136
|
356 |
|
blanchet@50141
|
357 |
val inject_tacss =
|
blanchet@50220
|
358 |
map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
|
blanchet@50220
|
359 |
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
|
blanchet@50141
|
360 |
|
blanchet@50142
|
361 |
val half_distinct_tacss =
|
blanchet@50142
|
362 |
map (map (fn (def, def') => fn {context = ctxt, ...} =>
|
blanchet@50142
|
363 |
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
|
blanchet@50142
|
364 |
|
blanchet@50145
|
365 |
val case_tacs =
|
blanchet@50145
|
366 |
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
|
blanchet@50145
|
367 |
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
|
blanchet@50136
|
368 |
|
blanchet@50136
|
369 |
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
|
blanchet@50149
|
370 |
|
blanchet@50282
|
371 |
fun some_lfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) =
|
blanchet@50149
|
372 |
let
|
blanchet@50223
|
373 |
val fpT_to_C = fpT --> C;
|
blanchet@50214
|
374 |
|
blanchet@50230
|
375 |
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
|
blanchet@50230
|
376 |
let
|
blanchet@50230
|
377 |
val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
|
blanchet@50214
|
378 |
|
blanchet@50230
|
379 |
val binder = Binding.suffix_name ("_" ^ suf) b;
|
blanchet@50214
|
380 |
|
blanchet@50230
|
381 |
val spec =
|
blanchet@50230
|
382 |
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
|
blanchet@50230
|
383 |
Term.list_comb (fp_iter_like,
|
blanchet@50270
|
384 |
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
|
blanchet@50230
|
385 |
in (binder, spec) end;
|
blanchet@50230
|
386 |
|
blanchet@50230
|
387 |
val iter_likes =
|
blanchet@50230
|
388 |
[(iterN, fp_iter, iter_only),
|
blanchet@50230
|
389 |
(recN, fp_rec, rec_only)];
|
blanchet@50230
|
390 |
|
blanchet@50230
|
391 |
val (binders, specs) = map generate_iter_like iter_likes |> split_list;
|
blanchet@50230
|
392 |
|
blanchet@50230
|
393 |
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|
blanchet@50216
|
394 |
|> apfst split_list o fold_map2 (fn b => fn spec =>
|
blanchet@50214
|
395 |
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
|
blanchet@50230
|
396 |
#>> apsnd snd) binders specs
|
blanchet@50214
|
397 |
||> `Local_Theory.restore;
|
blanchet@50216
|
398 |
|
blanchet@50216
|
399 |
(*transforms defined frees into consts (and more)*)
|
blanchet@50216
|
400 |
val phi = Proof_Context.export_morphism lthy lthy';
|
blanchet@50216
|
401 |
|
blanchet@50230
|
402 |
val [iter_def, rec_def] = map (Morphism.thm phi) defs;
|
blanchet@50216
|
403 |
|
blanchet@50230
|
404 |
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
|
blanchet@50149
|
405 |
in
|
blanchet@50282
|
406 |
((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
|
blanchet@50281
|
407 |
lthy)
|
blanchet@50149
|
408 |
end;
|
blanchet@50149
|
409 |
|
blanchet@50282
|
410 |
fun some_gfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) =
|
blanchet@50225
|
411 |
let
|
blanchet@50225
|
412 |
val B_to_fpT = C --> fpT;
|
blanchet@50225
|
413 |
|
blanchet@50271
|
414 |
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), (f_sum_prod_Ts, pf_Tss))) =
|
blanchet@50226
|
415 |
let
|
blanchet@50226
|
416 |
val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
|
blanchet@50225
|
417 |
|
blanchet@50226
|
418 |
val binder = Binding.suffix_name ("_" ^ suf) b;
|
blanchet@50225
|
419 |
|
blanchet@50271
|
420 |
fun mk_preds_getters_join c n cps sum_prod_T cfss =
|
blanchet@50226
|
421 |
Term.lambda c (mk_IfN sum_prod_T cps
|
blanchet@50271
|
422 |
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cfss) (1 upto n)));
|
blanchet@50225
|
423 |
|
blanchet@50226
|
424 |
val spec =
|
blanchet@50227
|
425 |
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
|
blanchet@50226
|
426 |
Term.list_comb (fp_iter_like,
|
blanchet@50271
|
427 |
map5 mk_preds_getters_join cs ns cpss f_sum_prod_Ts cfsss));
|
blanchet@50226
|
428 |
in (binder, spec) end;
|
blanchet@50225
|
429 |
|
blanchet@50227
|
430 |
val coiter_likes =
|
blanchet@50230
|
431 |
[(coiterN, fp_iter, coiter_only),
|
blanchet@50230
|
432 |
(corecN, fp_rec, corec_only)];
|
blanchet@50227
|
433 |
|
blanchet@50226
|
434 |
val (binders, specs) = map generate_coiter_like coiter_likes |> split_list;
|
blanchet@50226
|
435 |
|
blanchet@50226
|
436 |
val ((csts, defs), (lthy', lthy)) = no_defs_lthy
|
blanchet@50225
|
437 |
|> apfst split_list o fold_map2 (fn b => fn spec =>
|
blanchet@50225
|
438 |
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
|
blanchet@50226
|
439 |
#>> apsnd snd) binders specs
|
blanchet@50225
|
440 |
||> `Local_Theory.restore;
|
blanchet@50225
|
441 |
|
blanchet@50225
|
442 |
(*transforms defined frees into consts (and more)*)
|
blanchet@50225
|
443 |
val phi = Proof_Context.export_morphism lthy lthy';
|
blanchet@50225
|
444 |
|
blanchet@50226
|
445 |
val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
|
blanchet@50225
|
446 |
|
blanchet@50226
|
447 |
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
|
blanchet@50225
|
448 |
in
|
blanchet@50282
|
449 |
((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
|
blanchet@50281
|
450 |
corec_def), lthy)
|
blanchet@50225
|
451 |
end;
|
blanchet@50134
|
452 |
in
|
blanchet@50218
|
453 |
wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy'
|
blanchet@50225
|
454 |
|> (if lfp then some_lfp_sugar else some_gfp_sugar)
|
blanchet@50134
|
455 |
end;
|
blanchet@50182
|
456 |
|
blanchet@50241
|
457 |
val pre_map_defs = map map_def_of_bnf pre_bnfs;
|
blanchet@50244
|
458 |
val map_ids = map map_id_of_bnf nested_bnfs;
|
blanchet@50241
|
459 |
|
blanchet@50229
|
460 |
fun mk_map Ts Us t =
|
blanchet@50232
|
461 |
let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
|
blanchet@50229
|
462 |
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
|
blanchet@50229
|
463 |
end;
|
blanchet@50229
|
464 |
|
blanchet@50249
|
465 |
fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
|
blanchet@50249
|
466 |
let
|
traytel@50251
|
467 |
val map0 = map_of_bnf (the (bnf_of lthy s));
|
blanchet@50249
|
468 |
val mapx = mk_map Ts Us map0;
|
blanchet@50249
|
469 |
val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
|
blanchet@50249
|
470 |
val args = map build_arg TUs;
|
blanchet@50249
|
471 |
in Term.list_comb (mapx, args) end;
|
blanchet@50249
|
472 |
|
blanchet@50281
|
473 |
fun pour_more_sugar_on_lfps ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
|
blanchet@50281
|
474 |
rec_defs), lthy) =
|
blanchet@50217
|
475 |
let
|
blanchet@50217
|
476 |
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
|
blanchet@50227
|
477 |
val giters = map (lists_bmoc gss) iters;
|
blanchet@50227
|
478 |
val hrecs = map (lists_bmoc hss) recs;
|
blanchet@50216
|
479 |
|
blanchet@50217
|
480 |
val (iter_thmss, rec_thmss) =
|
blanchet@50222
|
481 |
let
|
blanchet@50227
|
482 |
fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
|
blanchet@50222
|
483 |
fold_rev (fold_rev Logic.all) (xs :: fss)
|
blanchet@50227
|
484 |
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
|
blanchet@50216
|
485 |
|
blanchet@50249
|
486 |
fun build_call fiter_likes maybe_tick (T, U) =
|
blanchet@50249
|
487 |
if T = U then
|
blanchet@50249
|
488 |
mk_id T
|
blanchet@50249
|
489 |
else
|
blanchet@50249
|
490 |
(case find_index (curry (op =) T) fpTs of
|
blanchet@50249
|
491 |
~1 => build_map (build_call fiter_likes maybe_tick) T U
|
blanchet@50249
|
492 |
| j => maybe_tick (nth vs j) (nth fiter_likes j));
|
blanchet@50248
|
493 |
|
blanchet@50229
|
494 |
fun mk_U maybe_prodT =
|
blanchet@50229
|
495 |
typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs);
|
blanchet@50229
|
496 |
|
blanchet@50229
|
497 |
fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) =
|
blanchet@50229
|
498 |
if member (op =) fpTs T then
|
blanchet@50248
|
499 |
maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
|
blanchet@50229
|
500 |
else if exists_subtype (member (op =) fpTs) T then
|
blanchet@50248
|
501 |
[build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x]
|
blanchet@50229
|
502 |
else
|
blanchet@50229
|
503 |
[x];
|
blanchet@50229
|
504 |
|
blanchet@50229
|
505 |
val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
|
blanchet@50229
|
506 |
val hxsss =
|
blanchet@50229
|
507 |
map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
|
blanchet@50219
|
508 |
|
blanchet@50227
|
509 |
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
|
blanchet@50227
|
510 |
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
|
blanchet@50219
|
511 |
|
blanchet@50218
|
512 |
val iter_tacss =
|
blanchet@50244
|
513 |
map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
|
blanchet@50218
|
514 |
val rec_tacss =
|
blanchet@50244
|
515 |
map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
|
blanchet@50217
|
516 |
in
|
blanchet@50281
|
517 |
(map2 (map2 (fn goal => fn tac =>
|
blanchet@50281
|
518 |
Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
|
blanchet@50220
|
519 |
goal_iterss iter_tacss,
|
blanchet@50281
|
520 |
map2 (map2 (fn goal => fn tac =>
|
blanchet@50281
|
521 |
Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
|
blanchet@50220
|
522 |
goal_recss rec_tacss)
|
blanchet@50217
|
523 |
end;
|
blanchet@50216
|
524 |
|
blanchet@50241
|
525 |
val notes =
|
blanchet@50217
|
526 |
[(itersN, iter_thmss),
|
blanchet@50217
|
527 |
(recsN, rec_thmss)]
|
blanchet@50217
|
528 |
|> maps (fn (thmN, thmss) =>
|
blanchet@50217
|
529 |
map2 (fn b => fn thms =>
|
blanchet@50217
|
530 |
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
|
blanchet@50217
|
531 |
bs thmss);
|
blanchet@50217
|
532 |
in
|
blanchet@50217
|
533 |
lthy |> Local_Theory.notes notes |> snd
|
blanchet@50217
|
534 |
end;
|
blanchet@50217
|
535 |
|
blanchet@50281
|
536 |
fun pour_more_sugar_on_gfps ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss, discIss,
|
blanchet@50281
|
537 |
sel_thmsss, coiter_defs, corec_defs), lthy) =
|
blanchet@50227
|
538 |
let
|
blanchet@50248
|
539 |
val z = the_single zs;
|
blanchet@50248
|
540 |
|
blanchet@50227
|
541 |
val gcoiters = map (lists_bmoc pgss) coiters;
|
blanchet@50227
|
542 |
val hcorecs = map (lists_bmoc phss) corecs;
|
blanchet@50227
|
543 |
|
blanchet@50227
|
544 |
val (coiter_thmss, corec_thmss) =
|
blanchet@50227
|
545 |
let
|
blanchet@50247
|
546 |
fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
|
blanchet@50227
|
547 |
|
blanchet@50250
|
548 |
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
|
blanchet@50227
|
549 |
fold_rev (fold_rev Logic.all) ([c] :: pfss)
|
blanchet@50247
|
550 |
(Logic.list_implies (seq_conds mk_goal_cond n k cps,
|
blanchet@50250
|
551 |
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
|
blanchet@50227
|
552 |
|
blanchet@50249
|
553 |
fun build_call fiter_likes maybe_tack (T, U) =
|
blanchet@50249
|
554 |
if T = U then
|
blanchet@50249
|
555 |
mk_id T
|
blanchet@50249
|
556 |
else
|
blanchet@50249
|
557 |
(case find_index (curry (op =) U) fpTs of
|
blanchet@50249
|
558 |
~1 => build_map (build_call fiter_likes maybe_tack) T U
|
blanchet@50249
|
559 |
| j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
|
blanchet@50248
|
560 |
|
blanchet@50247
|
561 |
fun mk_U maybe_sumT =
|
blanchet@50248
|
562 |
typ_subst (map2 (fn C => fn fpT => (maybe_sumT fpT C, fpT)) Cs fpTs);
|
blanchet@50227
|
563 |
|
blanchet@50247
|
564 |
fun repair_calls fiter_likes maybe_sumT maybe_tack
|
blanchet@50247
|
565 |
(cf as Free (_, Type (_, [_, T])) $ _) =
|
blanchet@50247
|
566 |
if exists_subtype (member (op =) Cs) T then
|
blanchet@50248
|
567 |
build_call fiter_likes maybe_tack (T, mk_U maybe_sumT T) $ cf
|
blanchet@50247
|
568 |
else
|
blanchet@50247
|
569 |
cf;
|
blanchet@50247
|
570 |
|
blanchet@50250
|
571 |
val cgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) cgsss;
|
blanchet@50250
|
572 |
val chsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) chsss;
|
blanchet@50227
|
573 |
|
blanchet@50227
|
574 |
val goal_coiterss =
|
blanchet@50250
|
575 |
map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss cgsss';
|
blanchet@50248
|
576 |
val goal_corecss =
|
blanchet@50250
|
577 |
map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss chsss';
|
blanchet@50228
|
578 |
|
blanchet@50228
|
579 |
val coiter_tacss =
|
blanchet@50244
|
580 |
map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
|
blanchet@50241
|
581 |
ctr_defss;
|
blanchet@50248
|
582 |
val corec_tacss =
|
blanchet@50248
|
583 |
map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
|
blanchet@50248
|
584 |
ctr_defss;
|
blanchet@50227
|
585 |
in
|
blanchet@50228
|
586 |
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
|
blanchet@50228
|
587 |
goal_coiterss coiter_tacss,
|
blanchet@50248
|
588 |
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
|
blanchet@50248
|
589 |
goal_corecss corec_tacss)
|
blanchet@50227
|
590 |
end;
|
blanchet@50227
|
591 |
|
blanchet@50281
|
592 |
fun mk_disc_coiter_like_thms [_] = K []
|
blanchet@50281
|
593 |
| mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
|
blanchet@50281
|
594 |
|
blanchet@50281
|
595 |
val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
|
blanchet@50281
|
596 |
val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
|
blanchet@50281
|
597 |
|
blanchet@50282
|
598 |
fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
|
blanchet@50281
|
599 |
let
|
blanchet@50282
|
600 |
val (domT, ranT) = dest_funT (fastype_of sel0);
|
blanchet@50281
|
601 |
val arg_cong' =
|
blanchet@50281
|
602 |
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
|
blanchet@50282
|
603 |
[NONE, NONE, SOME (certify lthy sel0)] arg_cong
|
blanchet@50282
|
604 |
|> Thm.varifyT_global;
|
blanchet@50281
|
605 |
val sel_thm' = sel_thm RSN (2, trans);
|
blanchet@50281
|
606 |
in
|
blanchet@50282
|
607 |
coiter_like_thm RS arg_cong' RS sel_thm'
|
blanchet@50281
|
608 |
end;
|
blanchet@50281
|
609 |
|
blanchet@50281
|
610 |
val sel_coiter_thmsss =
|
blanchet@50281
|
611 |
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
|
blanchet@50281
|
612 |
val sel_corec_thmsss =
|
blanchet@50282
|
613 |
map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
|
blanchet@50281
|
614 |
|
blanchet@50227
|
615 |
val notes =
|
blanchet@50248
|
616 |
[(coitersN, coiter_thmss),
|
blanchet@50281
|
617 |
(disc_coitersN, disc_coiter_thmss),
|
blanchet@50281
|
618 |
(sel_coitersN, map flat sel_coiter_thmsss),
|
blanchet@50281
|
619 |
(corecsN, corec_thmss),
|
blanchet@50281
|
620 |
(disc_corecsN, disc_corec_thmss),
|
blanchet@50281
|
621 |
(sel_corecsN, map flat sel_corec_thmsss)]
|
blanchet@50227
|
622 |
|> maps (fn (thmN, thmss) =>
|
blanchet@50281
|
623 |
map_filter (fn (_, []) => NONE | (b, thms) =>
|
blanchet@50281
|
624 |
SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []),
|
blanchet@50281
|
625 |
[(thms, [])])) (bs ~~ thmss));
|
blanchet@50227
|
626 |
in
|
blanchet@50245
|
627 |
lthy |> Local_Theory.notes notes |> snd
|
blanchet@50227
|
628 |
end;
|
blanchet@50227
|
629 |
|
blanchet@50219
|
630 |
val lthy' = lthy
|
blanchet@50225
|
631 |
|> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
|
blanchet@50227
|
632 |
fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
|
blanchet@50227
|
633 |
ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
|
blanchet@50281
|
634 |
|>> split_list11
|
blanchet@50227
|
635 |
|> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
|
blanchet@50182
|
636 |
|
blanchet@50182
|
637 |
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
|
blanchet@50223
|
638 |
(if lfp then "" else "co") ^ "datatype"));
|
blanchet@50127
|
639 |
in
|
blanchet@50219
|
640 |
(timer; lthy')
|
blanchet@50127
|
641 |
end;
|
blanchet@50127
|
642 |
|
blanchet@50214
|
643 |
fun datatype_cmd info specs lthy =
|
blanchet@50136
|
644 |
let
|
blanchet@50224
|
645 |
(* TODO: cleaner handling of fake contexts, without "background_theory" *)
|
blanchet@50199
|
646 |
(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
|
blanchet@50199
|
647 |
locale and shadows an existing global type*)
|
blanchet@50194
|
648 |
val fake_thy = Theory.copy
|
blanchet@50199
|
649 |
#> fold (fn spec => perhaps (try (Sign.add_type lthy
|
blanchet@50199
|
650 |
(type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
|
blanchet@50194
|
651 |
val fake_lthy = Proof_Context.background_theory fake_thy lthy;
|
blanchet@50136
|
652 |
in
|
blanchet@50214
|
653 |
prepare_datatype Syntax.read_typ info specs fake_lthy lthy
|
blanchet@50136
|
654 |
end;
|
blanchet@50134
|
655 |
|
blanchet@50144
|
656 |
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
|
blanchet@50134
|
657 |
|
blanchet@50127
|
658 |
val parse_ctr_arg =
|
blanchet@50134
|
659 |
Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
|
blanchet@50144
|
660 |
(Parse.typ >> pair no_binder);
|
blanchet@50127
|
661 |
|
blanchet@50127
|
662 |
val parse_single_spec =
|
blanchet@50127
|
663 |
Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
|
blanchet@50134
|
664 |
(@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
|
blanchet@50134
|
665 |
Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
|
blanchet@50127
|
666 |
|
blanchet@50127
|
667 |
val _ =
|
blanchet@50127
|
668 |
Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
|
blanchet@50223
|
669 |
(Parse.and_list1 parse_single_spec >> datatype_cmd true);
|
blanchet@50127
|
670 |
|
blanchet@50127
|
671 |
val _ =
|
blanchet@50127
|
672 |
Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
|
blanchet@50223
|
673 |
(Parse.and_list1 parse_single_spec >> datatype_cmd false);
|
blanchet@50127
|
674 |
|
blanchet@50127
|
675 |
end;
|