src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Tue Sep 11 13:06:13 2012 +0200 (2012-09-11)
changeset 49274 ddd606ec45b9
parent 49273 f839ce127a2e
child 49275 ce87d6a901eb
permissions -rw-r--r--
first step towards splitting corecursor function arguments into (p, g, h) triples
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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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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 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_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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    val nested_bnfs =
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      map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []);
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    val timer = time (Timer.startRealTimer ());
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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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    val mk_unf = mk_unf_or_fld domain_type;
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    val mk_fld = mk_unf_or_fld range_type;
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    val unfs = map (mk_unf As) unfs0;
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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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    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
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    val ns = map length ctr_Tsss;
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    val kss = map (fn n => 1 upto n) ns;
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    val mss = map (map length) ctr_Tsss;
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    val Css = map2 replicate ns Cs;
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    fun mk_iter_like Ts Us t =
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      let
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        val (binders, body) = strip_type (fastype_of t);
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        val (f_Us, prebody) = split_last binders;
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        val Type (_, Ts0) = if lfp then prebody else body;
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        val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
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      in
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        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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      end;
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    val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
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    val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
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    val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
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    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
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    val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
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         (zs, cs, cpss, coiter_only as ((pgss, cgssss), _), corec_only as ((phss, chssss), _))) =
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      if lfp then
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        let
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          val y_Tsss =
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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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              ns mss fp_iter_fun_Ts;
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          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
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          val ((gss, ysss), _) =
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            lthy
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            |> mk_Freess "f" g_Tss
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            ||>> mk_Freesss "x" y_Tsss;
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          val yssss = map (map (map single)) ysss;
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          fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
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              if member (op =) Cs U then Us else [T]
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            | dest_rec_prodT T = [T];
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          val z_Tssss =
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            map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
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              dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
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          val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
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          val hss = map2 (map2 retype_free) gss h_Tss;
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          val zssss_hd = map2 (map2 (map2 (fn y => fn T :: _ => retype_free y T))) ysss z_Tssss;
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          val (zssss_tl, _) =
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            lthy
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            |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
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          val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
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        in
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          (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
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           ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
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        end
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      else
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        let
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          (*avoid "'a itself" arguments in coiterators and corecursors*)
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          val mss' =  map (fn [0] => [1] | ms => ms) mss;
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          val p_Tss =
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            map2 (fn C => fn n => replicate (Int.max (0, n - 1)) (C --> HOLogic.boolT)) Cs ns;
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          fun zip_getters fss = flat fss;
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          fun zip_preds_getters [] [fss] = zip_getters fss
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            | zip_preds_getters (p :: ps) (fss :: fsss) =
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              p :: zip_getters fss @ zip_preds_getters ps fsss;
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          fun mk_types maybe_dest_sumT fun_Ts =
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            let
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              val f_sum_prod_Ts = map range_type fun_Ts;
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              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
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              val f_Tsss =
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                map3 (fn C => map2 (map (curry (op -->) C) oo dest_tupleT)) Cs mss' f_prod_Tss;
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              val f_Tssss = map (map (map maybe_dest_sumT)) f_Tsss;
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              val pf_Tss = map2 zip_preds_getters p_Tss f_Tssss;
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            in (f_sum_prod_Ts, f_Tsss, pf_Tss) end;
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          val (g_sum_prod_Ts, g_Tsss, pg_Tss) = mk_types single fp_iter_fun_Ts;
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          val ((((Free (z, _), cs), pss), gsss), _) =
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            lthy
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            |> yield_singleton (mk_Frees "z") dummyT
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            ||>> mk_Frees "a" Cs
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            ||>> mk_Freess "p" p_Tss
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            ||>> mk_Freesss "g" g_Tsss;
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          val gssss = map (map (map single)) gsss;
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          fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
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              if member (op =) Cs U then Us else [T]
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            | dest_corec_sumT T = [T];
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          val (h_sum_prod_Ts, h_Tsss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
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          val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss;
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          val hssss = map (map (map single)) hsss; (*###*)
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          val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
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          fun mk_terms fssss =
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            let
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              val pfss = map2 zip_preds_getters pss fssss;
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              val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
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            in (pfss, cfssss) end;
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        in
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          ((([], [], []), ([], [], [])),
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           ([z], cs, cpss, (mk_terms gssss, (g_sum_prod_Ts, pg_Tss)),
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            (mk_terms hssss, (h_sum_prod_Ts, ph_Tss))))
blanchet@49210
   301
        end;
blanchet@49210
   302
blanchet@49212
   303
    fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
blanchet@49212
   304
          fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
blanchet@49212
   305
        disc_binders), sel_binderss) no_defs_lthy =
blanchet@49176
   306
      let
blanchet@49201
   307
        val unfT = domain_type (fastype_of fld);
blanchet@49210
   308
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   309
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   310
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   311
blanchet@49176
   312
        val ((((u, v), fs), xss), _) =
blanchet@49204
   313
          no_defs_lthy
blanchet@49201
   314
          |> yield_singleton (mk_Frees "u") unfT
blanchet@49201
   315
          ||>> yield_singleton (mk_Frees "v") fpT
blanchet@49176
   316
          ||>> mk_Frees "f" case_Ts
blanchet@49124
   317
          ||>> mk_Freess "x" ctr_Tss;
blanchet@49121
   318
blanchet@49129
   319
        val ctr_rhss =
blanchet@49256
   320
          map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
blanchet@49256
   321
            mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
blanchet@49121
   322
blanchet@49130
   323
        val case_binder = Binding.suffix_name ("_" ^ caseN) b;
blanchet@49129
   324
blanchet@49134
   325
        val case_rhs =
blanchet@49255
   326
          fold_rev Term.lambda (fs @ [v])
blanchet@49255
   327
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
blanchet@49129
   328
blanchet@49201
   329
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   330
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49169
   331
               Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49201
   332
             (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   333
          ||> `Local_Theory.restore;
blanchet@49121
   334
blanchet@49121
   335
        (*transforms defined frees into consts (and more)*)
blanchet@49121
   336
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   337
blanchet@49121
   338
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   339
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   340
blanchet@49203
   341
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   342
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   343
blanchet@49203
   344
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   345
blanchet@49135
   346
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   347
          let
blanchet@49135
   348
            val fld_iff_unf_thm =
blanchet@49135
   349
              let
blanchet@49135
   350
                val goal =
blanchet@49135
   351
                  fold_rev Logic.all [u, v]
blanchet@49135
   352
                    (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
blanchet@49135
   353
              in
blanchet@49135
   354
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49201
   355
                  mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
blanchet@49176
   356
                    (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
blanchet@49135
   357
                |> Thm.close_derivation
blanchet@49135
   358
                |> Morphism.thm phi
blanchet@49135
   359
              end;
blanchet@49135
   360
blanchet@49135
   361
            val sumEN_thm' =
blanchet@49135
   362
              Local_Defs.unfold lthy @{thms all_unit_eq}
blanchet@49255
   363
                (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49255
   364
                   (mk_sumEN_balanced n))
blanchet@49135
   365
              |> Morphism.thm phi;
blanchet@49123
   366
          in
blanchet@49161
   367
            mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
blanchet@49123
   368
          end;
blanchet@49121
   369
blanchet@49126
   370
        val inject_tacss =
blanchet@49205
   371
          map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49205
   372
              mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
blanchet@49126
   373
blanchet@49127
   374
        val half_distinct_tacss =
blanchet@49127
   375
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49127
   376
            mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   377
blanchet@49130
   378
        val case_tacs =
blanchet@49130
   379
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49130
   380
            mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
blanchet@49121
   381
blanchet@49121
   382
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   383
blanchet@49267
   384
        fun some_lfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) =
blanchet@49134
   385
          let
blanchet@49208
   386
            val fpT_to_C = fpT --> C;
blanchet@49199
   387
blanchet@49215
   388
            fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
blanchet@49215
   389
              let
blanchet@49215
   390
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49215
   391
blanchet@49215
   392
                val binder = Binding.suffix_name ("_" ^ suf) b;
blanchet@49199
   393
blanchet@49215
   394
                val spec =
blanchet@49215
   395
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
blanchet@49215
   396
                    Term.list_comb (fp_iter_like,
blanchet@49255
   397
                      map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
blanchet@49215
   398
              in (binder, spec) end;
blanchet@49199
   399
blanchet@49274
   400
            val iter_like_bundles =
blanchet@49215
   401
              [(iterN, fp_iter, iter_only),
blanchet@49215
   402
               (recN, fp_rec, rec_only)];
blanchet@49215
   403
blanchet@49274
   404
            val (binders, specs) = map generate_iter_like iter_like_bundles |> split_list;
blanchet@49215
   405
blanchet@49215
   406
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   407
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   408
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49215
   409
                #>> apsnd snd) binders specs
blanchet@49199
   410
              ||> `Local_Theory.restore;
blanchet@49201
   411
blanchet@49201
   412
            (*transforms defined frees into consts (and more)*)
blanchet@49201
   413
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   414
blanchet@49215
   415
            val [iter_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   416
blanchet@49215
   417
            val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49134
   418
          in
blanchet@49267
   419
            ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
blanchet@49266
   420
             lthy)
blanchet@49134
   421
          end;
blanchet@49134
   422
blanchet@49267
   423
        fun some_gfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) =
blanchet@49210
   424
          let
blanchet@49210
   425
            val B_to_fpT = C --> fpT;
blanchet@49211
   426
blanchet@49274
   427
            fun mk_preds_getters_join c n cps sum_prod_T cfsss =
blanchet@49274
   428
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49274
   429
                (map2 (mk_InN_balanced sum_prod_T n) (map (HOLogic.mk_tuple o flat) cfsss) (*###*)
blanchet@49274
   430
                   (1 upto n)));
blanchet@49274
   431
blanchet@49274
   432
            fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfssss), (f_sum_prod_Ts,
blanchet@49274
   433
                pf_Tss))) =
blanchet@49211
   434
              let
blanchet@49211
   435
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49210
   436
blanchet@49211
   437
                val binder = Binding.suffix_name ("_" ^ suf) b;
blanchet@49210
   438
blanchet@49211
   439
                val spec =
blanchet@49212
   440
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
blanchet@49211
   441
                    Term.list_comb (fp_iter_like,
blanchet@49274
   442
                      map5 mk_preds_getters_join cs ns cpss f_sum_prod_Ts cfssss));
blanchet@49211
   443
              in (binder, spec) end;
blanchet@49210
   444
blanchet@49274
   445
            val coiter_like_bundles =
blanchet@49215
   446
              [(coiterN, fp_iter, coiter_only),
blanchet@49215
   447
               (corecN, fp_rec, corec_only)];
blanchet@49212
   448
blanchet@49274
   449
            val (binders, specs) = map generate_coiter_like coiter_like_bundles |> split_list;
blanchet@49211
   450
blanchet@49211
   451
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   452
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   453
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49211
   454
                #>> apsnd snd) binders specs
blanchet@49210
   455
              ||> `Local_Theory.restore;
blanchet@49210
   456
blanchet@49210
   457
            (*transforms defined frees into consts (and more)*)
blanchet@49210
   458
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   459
blanchet@49211
   460
            val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   461
blanchet@49211
   462
            val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49210
   463
          in
blanchet@49267
   464
            ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
blanchet@49266
   465
              corec_def), lthy)
blanchet@49210
   466
          end;
blanchet@49119
   467
      in
blanchet@49203
   468
        wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy'
blanchet@49210
   469
        |> (if lfp then some_lfp_sugar else some_gfp_sugar)
blanchet@49119
   470
      end;
blanchet@49167
   471
blanchet@49226
   472
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49229
   473
    val map_ids = map map_id_of_bnf nested_bnfs;
blanchet@49226
   474
blanchet@49214
   475
    fun mk_map Ts Us t =
blanchet@49217
   476
      let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
blanchet@49214
   477
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49214
   478
      end;
blanchet@49214
   479
blanchet@49234
   480
    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
blanchet@49234
   481
      let
traytel@49236
   482
        val map0 = map_of_bnf (the (bnf_of lthy s));
blanchet@49234
   483
        val mapx = mk_map Ts Us map0;
blanchet@49234
   484
        val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
blanchet@49234
   485
        val args = map build_arg TUs;
blanchet@49234
   486
      in Term.list_comb (mapx, args) end;
blanchet@49234
   487
blanchet@49266
   488
    fun pour_more_sugar_on_lfps ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
blanchet@49266
   489
        rec_defs), lthy) =
blanchet@49202
   490
      let
blanchet@49202
   491
        val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49212
   492
        val giters = map (lists_bmoc gss) iters;
blanchet@49212
   493
        val hrecs = map (lists_bmoc hss) recs;
blanchet@49201
   494
blanchet@49202
   495
        val (iter_thmss, rec_thmss) =
blanchet@49207
   496
          let
blanchet@49212
   497
            fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
blanchet@49207
   498
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49212
   499
                (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   500
blanchet@49234
   501
            fun build_call fiter_likes maybe_tick (T, U) =
blanchet@49234
   502
              if T = U then
blanchet@49234
   503
                mk_id T
blanchet@49234
   504
              else
blanchet@49234
   505
                (case find_index (curry (op =) T) fpTs of
blanchet@49234
   506
                  ~1 => build_map (build_call fiter_likes maybe_tick) T U
blanchet@49234
   507
                | j => maybe_tick (nth vs j) (nth fiter_likes j));
blanchet@49233
   508
blanchet@49274
   509
            fun mk_U maybe_mk_prodT =
blanchet@49274
   510
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
blanchet@49214
   511
blanchet@49274
   512
            fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
blanchet@49214
   513
              if member (op =) fpTs T then
blanchet@49233
   514
                maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49214
   515
              else if exists_subtype (member (op =) fpTs) T then
blanchet@49274
   516
                [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
blanchet@49214
   517
              else
blanchet@49214
   518
                [x];
blanchet@49214
   519
blanchet@49214
   520
            val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
blanchet@49214
   521
            val hxsss =
blanchet@49214
   522
              map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   523
blanchet@49212
   524
            val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
blanchet@49212
   525
            val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   526
blanchet@49203
   527
            val iter_tacss =
blanchet@49229
   528
              map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
blanchet@49203
   529
            val rec_tacss =
blanchet@49229
   530
              map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
blanchet@49202
   531
          in
blanchet@49266
   532
            (map2 (map2 (fn goal => fn tac =>
blanchet@49266
   533
                 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
blanchet@49205
   534
               goal_iterss iter_tacss,
blanchet@49266
   535
             map2 (map2 (fn goal => fn tac =>
blanchet@49266
   536
                 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
blanchet@49205
   537
               goal_recss rec_tacss)
blanchet@49202
   538
          end;
blanchet@49201
   539
blanchet@49226
   540
        val notes =
blanchet@49202
   541
          [(itersN, iter_thmss),
blanchet@49202
   542
           (recsN, rec_thmss)]
blanchet@49202
   543
          |> maps (fn (thmN, thmss) =>
blanchet@49202
   544
            map2 (fn b => fn thms =>
blanchet@49202
   545
                ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
blanchet@49202
   546
              bs thmss);
blanchet@49202
   547
      in
blanchet@49202
   548
        lthy |> Local_Theory.notes notes |> snd
blanchet@49202
   549
      end;
blanchet@49202
   550
blanchet@49266
   551
    fun pour_more_sugar_on_gfps ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss, discIss,
blanchet@49266
   552
        sel_thmsss, coiter_defs, corec_defs), lthy) =
blanchet@49212
   553
      let
blanchet@49233
   554
        val z = the_single zs;
blanchet@49233
   555
blanchet@49212
   556
        val gcoiters = map (lists_bmoc pgss) coiters;
blanchet@49212
   557
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49212
   558
blanchet@49212
   559
        val (coiter_thmss, corec_thmss) =
blanchet@49212
   560
          let
blanchet@49232
   561
            fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
blanchet@49212
   562
blanchet@49274
   563
            fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfss' =
blanchet@49212
   564
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49232
   565
                (Logic.list_implies (seq_conds mk_goal_cond n k cps,
blanchet@49274
   566
                   mk_Trueprop_eq (fcoiter_like $ c, lists_bmoc (take m cfss') ctr)));
blanchet@49212
   567
blanchet@49234
   568
            fun build_call fiter_likes maybe_tack (T, U) =
blanchet@49234
   569
              if T = U then
blanchet@49234
   570
                mk_id T
blanchet@49234
   571
              else
blanchet@49234
   572
                (case find_index (curry (op =) U) fpTs of
blanchet@49234
   573
                  ~1 => build_map (build_call fiter_likes maybe_tack) T U
blanchet@49234
   574
                | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
blanchet@49233
   575
blanchet@49274
   576
            fun mk_U maybe_mk_sumT =
blanchet@49274
   577
              typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
   578
blanchet@49274
   579
            fun repair_calls fiter_likes maybe_mk_sumT maybe_tack
blanchet@49232
   580
                (cf as Free (_, Type (_, [_, T])) $ _) =
blanchet@49232
   581
              if exists_subtype (member (op =) Cs) T then
blanchet@49274
   582
                build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cf
blanchet@49232
   583
              else
blanchet@49232
   584
                cf;
blanchet@49232
   585
blanchet@49274
   586
            val cgssss' =
blanchet@49274
   587
              map (map (map (map (repair_calls gcoiters (K I) (K I))))) cgssss;
blanchet@49274
   588
            val chssss' =
blanchet@49274
   589
              map (map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z))))) chssss;
blanchet@49212
   590
blanchet@49212
   591
            val goal_coiterss =
blanchet@49274
   592
              map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss cgssss';
blanchet@49233
   593
            val goal_corecss =
blanchet@49274
   594
              map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss chssss';
blanchet@49213
   595
blanchet@49213
   596
            val coiter_tacss =
blanchet@49229
   597
              map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
blanchet@49226
   598
                ctr_defss;
blanchet@49233
   599
            val corec_tacss =
blanchet@49233
   600
              map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
blanchet@49233
   601
                ctr_defss;
blanchet@49212
   602
          in
blanchet@49213
   603
            (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49213
   604
               goal_coiterss coiter_tacss,
blanchet@49233
   605
             map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49233
   606
               goal_corecss corec_tacss)
blanchet@49212
   607
          end;
blanchet@49212
   608
blanchet@49266
   609
        fun mk_disc_coiter_like_thms [_] = K []
blanchet@49266
   610
          | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
blanchet@49266
   611
blanchet@49266
   612
        val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
blanchet@49266
   613
        val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
blanchet@49266
   614
blanchet@49267
   615
        fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
blanchet@49266
   616
          let
blanchet@49267
   617
            val (domT, ranT) = dest_funT (fastype_of sel0);
blanchet@49266
   618
            val arg_cong' =
blanchet@49266
   619
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49267
   620
                [NONE, NONE, SOME (certify lthy sel0)] arg_cong
blanchet@49267
   621
              |> Thm.varifyT_global;
blanchet@49266
   622
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
   623
          in
blanchet@49267
   624
            coiter_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
   625
          end;
blanchet@49266
   626
blanchet@49266
   627
        val sel_coiter_thmsss =
blanchet@49266
   628
          map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
blanchet@49266
   629
        val sel_corec_thmsss =
blanchet@49267
   630
          map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
blanchet@49266
   631
blanchet@49212
   632
        val notes =
blanchet@49233
   633
          [(coitersN, coiter_thmss),
blanchet@49266
   634
           (disc_coitersN, disc_coiter_thmss),
blanchet@49266
   635
           (sel_coitersN, map flat sel_coiter_thmsss),
blanchet@49266
   636
           (corecsN, corec_thmss),
blanchet@49266
   637
           (disc_corecsN, disc_corec_thmss),
blanchet@49266
   638
           (sel_corecsN, map flat sel_corec_thmsss)]
blanchet@49212
   639
          |> maps (fn (thmN, thmss) =>
blanchet@49266
   640
            map_filter (fn (_, []) => NONE | (b, thms) =>
blanchet@49266
   641
              SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []),
blanchet@49266
   642
                [(thms, [])])) (bs ~~ thmss));
blanchet@49212
   643
      in
blanchet@49230
   644
        lthy |> Local_Theory.notes notes |> snd
blanchet@49212
   645
      end;
blanchet@49212
   646
blanchet@49204
   647
    val lthy' = lthy
blanchet@49210
   648
      |> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
blanchet@49212
   649
        fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
blanchet@49212
   650
        ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
blanchet@49266
   651
      |>> split_list11
blanchet@49212
   652
      |> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
blanchet@49167
   653
blanchet@49167
   654
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
   655
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
   656
  in
blanchet@49204
   657
    (timer; lthy')
blanchet@49112
   658
  end;
blanchet@49112
   659
blanchet@49199
   660
fun datatype_cmd info specs lthy =
blanchet@49121
   661
  let
blanchet@49209
   662
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49184
   663
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49184
   664
      locale and shadows an existing global type*)
blanchet@49179
   665
    val fake_thy = Theory.copy
blanchet@49184
   666
      #> fold (fn spec => perhaps (try (Sign.add_type lthy
blanchet@49184
   667
        (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
blanchet@49179
   668
    val fake_lthy = Proof_Context.background_theory fake_thy lthy;
blanchet@49121
   669
  in
blanchet@49199
   670
    prepare_datatype Syntax.read_typ info specs fake_lthy lthy
blanchet@49121
   671
  end;
blanchet@49119
   672
blanchet@49129
   673
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
blanchet@49119
   674
blanchet@49112
   675
val parse_ctr_arg =
blanchet@49119
   676
  Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
blanchet@49129
   677
  (Parse.typ >> pair no_binder);
blanchet@49112
   678
blanchet@49112
   679
val parse_single_spec =
blanchet@49112
   680
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   681
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49119
   682
    Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
blanchet@49112
   683
blanchet@49112
   684
val _ =
blanchet@49112
   685
  Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
blanchet@49208
   686
    (Parse.and_list1 parse_single_spec >> datatype_cmd true);
blanchet@49112
   687
blanchet@49112
   688
val _ =
blanchet@49112
   689
  Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
blanchet@49208
   690
    (Parse.and_list1 parse_single_spec >> datatype_cmd false);
blanchet@49112
   691
blanchet@49112
   692
end;