src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Mon Sep 10 17:36:02 2012 +0200 (2012-09-10)
changeset 49256 df98aeb80a19
parent 49255 2ecc533d6697
child 49261 4bf74375b4f7
permissions -rw-r--r--
avoid type inference + tuning
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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 itersN = "iters";
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val recsN = "recs";
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fun split_list8 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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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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val mk_sumTN_balanced = Balanced_Tree.make mk_sumT;
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val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT;
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fun mk_InN_balanced sum_T n t k =
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  let
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    fun repair_types T (Const (s as @{const_name Inl}, _) $ t) = repair_inj_types T s fst t
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      | repair_types T (Const (s as @{const_name Inr}, _) $ t) = repair_inj_types T s snd t
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      | repair_types _ t = t
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    and repair_inj_types T s get t =
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      let val T' = get (dest_sumT T) in
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        Const (s, T' --> T) $ repair_types T' t
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      end;
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  in
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    Balanced_Tree.access {left = mk_Inl dummyT, right = mk_Inr dummyT, init = t} n k
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    |> repair_types sum_T
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  end;
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val mk_sum_caseN_balanced = Balanced_Tree.make mk_sum_case;
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fun mk_sumEN_balanced n =
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  let
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    val thm =
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      Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f})))
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        (replicate n asm_rl) OF (replicate n (impI RS allI));
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    val f as (_, f_T) =
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      Term.add_vars (prop_of thm) []
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      |> filter (fn ((s, _), _) => s = "f") |> the_single;
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    val inst = [pairself (cterm_of @{theory}) (Var f, Abs (Name.uu, domain_type f_T, Bound 0))];
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  in cterm_instantiate inst thm end;
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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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    fun dest_rec_pair (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_pair T = [T];
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    val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
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         (zs, cs, cpss, coiter_only as ((pgss, cgsss), _), corec_only as ((phss, chsss), _))) =
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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 z_Tssss =
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            map3 (fn n => fn ms => map2 (map dest_rec_pair 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, _) =
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            lthy
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            |> mk_Freessss "x" z_Tssss;
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        in
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          (((gss, g_Tss, map (map (map single)) ysss), (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_preds_getters [] [fs] = fs
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            | zip_preds_getters (p :: ps) (fs :: fss) = p :: fs @ zip_preds_getters ps fss;
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          fun mk_types 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 pf_Tss = map2 zip_preds_getters p_Tss f_Tsss
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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 fp_iter_fun_Ts;
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          val (h_sum_prod_Ts, h_Tsss, ph_Tss) = mk_types fp_rec_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 hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss;
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          val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
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          fun mk_terms fsss =
blanchet@49212
   304
            let
blanchet@49254
   305
              val pfss = map2 zip_preds_getters pss fsss;
blanchet@49212
   306
              val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss
blanchet@49212
   307
            in (pfss, cfsss) end;
blanchet@49210
   308
        in
blanchet@49212
   309
          ((([], [], []), ([], [], [])),
blanchet@49256
   310
           ([z], cs, cpss, (mk_terms gsss, (g_sum_prod_Ts, pg_Tss)),
blanchet@49256
   311
            (mk_terms hsss, (h_sum_prod_Ts, ph_Tss))))
blanchet@49210
   312
        end;
blanchet@49210
   313
blanchet@49212
   314
    fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
blanchet@49212
   315
          fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
blanchet@49212
   316
        disc_binders), sel_binderss) no_defs_lthy =
blanchet@49176
   317
      let
blanchet@49201
   318
        val unfT = domain_type (fastype_of fld);
blanchet@49210
   319
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   320
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   321
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   322
blanchet@49176
   323
        val ((((u, v), fs), xss), _) =
blanchet@49204
   324
          no_defs_lthy
blanchet@49201
   325
          |> yield_singleton (mk_Frees "u") unfT
blanchet@49201
   326
          ||>> yield_singleton (mk_Frees "v") fpT
blanchet@49176
   327
          ||>> mk_Frees "f" case_Ts
blanchet@49124
   328
          ||>> mk_Freess "x" ctr_Tss;
blanchet@49121
   329
blanchet@49129
   330
        val ctr_rhss =
blanchet@49256
   331
          map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
blanchet@49256
   332
            mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
blanchet@49121
   333
blanchet@49130
   334
        val case_binder = Binding.suffix_name ("_" ^ caseN) b;
blanchet@49129
   335
blanchet@49134
   336
        val case_rhs =
blanchet@49255
   337
          fold_rev Term.lambda (fs @ [v])
blanchet@49255
   338
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
blanchet@49129
   339
blanchet@49201
   340
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   341
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49169
   342
               Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49201
   343
             (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   344
          ||> `Local_Theory.restore;
blanchet@49121
   345
blanchet@49121
   346
        (*transforms defined frees into consts (and more)*)
blanchet@49121
   347
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   348
blanchet@49121
   349
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   350
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   351
blanchet@49203
   352
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   353
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   354
blanchet@49203
   355
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   356
blanchet@49135
   357
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   358
          let
blanchet@49135
   359
            val fld_iff_unf_thm =
blanchet@49135
   360
              let
blanchet@49135
   361
                val goal =
blanchet@49135
   362
                  fold_rev Logic.all [u, v]
blanchet@49135
   363
                    (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
blanchet@49135
   364
              in
blanchet@49135
   365
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49201
   366
                  mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
blanchet@49176
   367
                    (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
blanchet@49135
   368
                |> Thm.close_derivation
blanchet@49135
   369
                |> Morphism.thm phi
blanchet@49135
   370
              end;
blanchet@49135
   371
blanchet@49135
   372
            val sumEN_thm' =
blanchet@49135
   373
              Local_Defs.unfold lthy @{thms all_unit_eq}
blanchet@49255
   374
                (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49255
   375
                   (mk_sumEN_balanced n))
blanchet@49135
   376
              |> Morphism.thm phi;
blanchet@49123
   377
          in
blanchet@49161
   378
            mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
blanchet@49123
   379
          end;
blanchet@49121
   380
blanchet@49126
   381
        val inject_tacss =
blanchet@49205
   382
          map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49205
   383
              mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
blanchet@49126
   384
blanchet@49127
   385
        val half_distinct_tacss =
blanchet@49127
   386
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49127
   387
            mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   388
blanchet@49130
   389
        val case_tacs =
blanchet@49130
   390
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49130
   391
            mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
blanchet@49121
   392
blanchet@49121
   393
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   394
blanchet@49210
   395
        fun some_lfp_sugar no_defs_lthy =
blanchet@49134
   396
          let
blanchet@49208
   397
            val fpT_to_C = fpT --> C;
blanchet@49199
   398
blanchet@49215
   399
            fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
blanchet@49215
   400
              let
blanchet@49215
   401
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49215
   402
blanchet@49215
   403
                val binder = Binding.suffix_name ("_" ^ suf) b;
blanchet@49199
   404
blanchet@49215
   405
                val spec =
blanchet@49215
   406
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
blanchet@49215
   407
                    Term.list_comb (fp_iter_like,
blanchet@49255
   408
                      map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
blanchet@49215
   409
              in (binder, spec) end;
blanchet@49199
   410
blanchet@49215
   411
            val iter_likes =
blanchet@49215
   412
              [(iterN, fp_iter, iter_only),
blanchet@49215
   413
               (recN, fp_rec, rec_only)];
blanchet@49215
   414
blanchet@49215
   415
            val (binders, specs) = map generate_iter_like iter_likes |> split_list;
blanchet@49215
   416
blanchet@49215
   417
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   418
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   419
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49215
   420
                #>> apsnd snd) binders specs
blanchet@49199
   421
              ||> `Local_Theory.restore;
blanchet@49201
   422
blanchet@49201
   423
            (*transforms defined frees into consts (and more)*)
blanchet@49201
   424
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   425
blanchet@49215
   426
            val [iter_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   427
blanchet@49215
   428
            val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49134
   429
          in
blanchet@49214
   430
            ((ctrs, iter, recx, v, xss, ctr_defs, iter_def, rec_def), lthy)
blanchet@49134
   431
          end;
blanchet@49134
   432
blanchet@49210
   433
        fun some_gfp_sugar no_defs_lthy =
blanchet@49210
   434
          let
blanchet@49210
   435
            val B_to_fpT = C --> fpT;
blanchet@49211
   436
blanchet@49256
   437
            fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), (f_sum_prod_Ts, pf_Tss))) =
blanchet@49211
   438
              let
blanchet@49211
   439
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49210
   440
blanchet@49211
   441
                val binder = Binding.suffix_name ("_" ^ suf) b;
blanchet@49210
   442
blanchet@49256
   443
                fun mk_preds_getters_join c n cps sum_prod_T cfss =
blanchet@49211
   444
                  Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49256
   445
                    (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cfss) (1 upto n)));
blanchet@49210
   446
blanchet@49211
   447
                val spec =
blanchet@49212
   448
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
blanchet@49211
   449
                    Term.list_comb (fp_iter_like,
blanchet@49256
   450
                      map5 mk_preds_getters_join cs ns cpss f_sum_prod_Ts cfsss));
blanchet@49211
   451
              in (binder, spec) end;
blanchet@49210
   452
blanchet@49212
   453
            val coiter_likes =
blanchet@49215
   454
              [(coiterN, fp_iter, coiter_only),
blanchet@49215
   455
               (corecN, fp_rec, corec_only)];
blanchet@49212
   456
blanchet@49211
   457
            val (binders, specs) = map generate_coiter_like coiter_likes |> split_list;
blanchet@49211
   458
blanchet@49211
   459
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   460
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   461
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49211
   462
                #>> apsnd snd) binders specs
blanchet@49210
   463
              ||> `Local_Theory.restore;
blanchet@49210
   464
blanchet@49210
   465
            (*transforms defined frees into consts (and more)*)
blanchet@49210
   466
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   467
blanchet@49211
   468
            val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   469
blanchet@49211
   470
            val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49210
   471
          in
blanchet@49214
   472
            ((ctrs, coiter, corec, v, xss, ctr_defs, coiter_def, corec_def), lthy)
blanchet@49210
   473
          end;
blanchet@49119
   474
      in
blanchet@49203
   475
        wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy'
blanchet@49210
   476
        |> (if lfp then some_lfp_sugar else some_gfp_sugar)
blanchet@49119
   477
      end;
blanchet@49167
   478
blanchet@49226
   479
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49229
   480
    val map_ids = map map_id_of_bnf nested_bnfs;
blanchet@49226
   481
blanchet@49214
   482
    fun mk_map Ts Us t =
blanchet@49217
   483
      let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
blanchet@49214
   484
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49214
   485
      end;
blanchet@49214
   486
blanchet@49234
   487
    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
blanchet@49234
   488
      let
traytel@49236
   489
        val map0 = map_of_bnf (the (bnf_of lthy s));
blanchet@49234
   490
        val mapx = mk_map Ts Us map0;
blanchet@49234
   491
        val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
blanchet@49234
   492
        val args = map build_arg TUs;
blanchet@49234
   493
      in Term.list_comb (mapx, args) end;
blanchet@49234
   494
blanchet@49214
   495
    fun pour_more_sugar_on_lfps ((ctrss, iters, recs, vs, xsss, ctr_defss, iter_defs, rec_defs),
blanchet@49205
   496
        lthy) =
blanchet@49202
   497
      let
blanchet@49202
   498
        val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49212
   499
        val giters = map (lists_bmoc gss) iters;
blanchet@49212
   500
        val hrecs = map (lists_bmoc hss) recs;
blanchet@49201
   501
blanchet@49202
   502
        val (iter_thmss, rec_thmss) =
blanchet@49207
   503
          let
blanchet@49212
   504
            fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
blanchet@49207
   505
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49212
   506
                (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   507
blanchet@49234
   508
            fun build_call fiter_likes maybe_tick (T, U) =
blanchet@49234
   509
              if T = U then
blanchet@49234
   510
                mk_id T
blanchet@49234
   511
              else
blanchet@49234
   512
                (case find_index (curry (op =) T) fpTs of
blanchet@49234
   513
                  ~1 => build_map (build_call fiter_likes maybe_tick) T U
blanchet@49234
   514
                | j => maybe_tick (nth vs j) (nth fiter_likes j));
blanchet@49233
   515
blanchet@49214
   516
            fun mk_U maybe_prodT =
blanchet@49214
   517
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs);
blanchet@49214
   518
blanchet@49214
   519
            fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) =
blanchet@49214
   520
              if member (op =) fpTs T then
blanchet@49233
   521
                maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49214
   522
              else if exists_subtype (member (op =) fpTs) T then
blanchet@49233
   523
                [build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x]
blanchet@49214
   524
              else
blanchet@49214
   525
                [x];
blanchet@49214
   526
blanchet@49214
   527
            val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
blanchet@49214
   528
            val hxsss =
blanchet@49214
   529
              map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   530
blanchet@49212
   531
            val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
blanchet@49212
   532
            val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   533
blanchet@49203
   534
            val iter_tacss =
blanchet@49229
   535
              map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
blanchet@49203
   536
            val rec_tacss =
blanchet@49229
   537
              map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
blanchet@49202
   538
          in
blanchet@49205
   539
            (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   540
               goal_iterss iter_tacss,
blanchet@49205
   541
             map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   542
               goal_recss rec_tacss)
blanchet@49202
   543
          end;
blanchet@49201
   544
blanchet@49226
   545
        val notes =
blanchet@49202
   546
          [(itersN, iter_thmss),
blanchet@49202
   547
           (recsN, rec_thmss)]
blanchet@49202
   548
          |> maps (fn (thmN, thmss) =>
blanchet@49202
   549
            map2 (fn b => fn thms =>
blanchet@49202
   550
                ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
blanchet@49202
   551
              bs thmss);
blanchet@49202
   552
      in
blanchet@49202
   553
        lthy |> Local_Theory.notes notes |> snd
blanchet@49202
   554
      end;
blanchet@49202
   555
blanchet@49256
   556
    fun pour_more_sugar_on_gfps ((ctrss, coiters, corecs, vs, _, ctr_defss, coiter_defs,
blanchet@49214
   557
        corec_defs), lthy) =
blanchet@49212
   558
      let
blanchet@49233
   559
        val z = the_single zs;
blanchet@49233
   560
blanchet@49212
   561
        val gcoiters = map (lists_bmoc pgss) coiters;
blanchet@49212
   562
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49212
   563
blanchet@49212
   564
        val (coiter_thmss, corec_thmss) =
blanchet@49212
   565
          let
blanchet@49232
   566
            fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
blanchet@49212
   567
blanchet@49235
   568
            fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
blanchet@49212
   569
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49232
   570
                (Logic.list_implies (seq_conds mk_goal_cond n k cps,
blanchet@49235
   571
                   mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
   572
blanchet@49234
   573
            fun build_call fiter_likes maybe_tack (T, U) =
blanchet@49234
   574
              if T = U then
blanchet@49234
   575
                mk_id T
blanchet@49234
   576
              else
blanchet@49234
   577
                (case find_index (curry (op =) U) fpTs of
blanchet@49234
   578
                  ~1 => build_map (build_call fiter_likes maybe_tack) T U
blanchet@49234
   579
                | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
blanchet@49233
   580
blanchet@49232
   581
            fun mk_U maybe_sumT =
blanchet@49233
   582
              typ_subst (map2 (fn C => fn fpT => (maybe_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
   583
blanchet@49232
   584
            fun repair_calls fiter_likes maybe_sumT maybe_tack
blanchet@49232
   585
                (cf as Free (_, Type (_, [_, T])) $ _) =
blanchet@49232
   586
              if exists_subtype (member (op =) Cs) T then
blanchet@49233
   587
                build_call fiter_likes maybe_tack (T, mk_U maybe_sumT T) $ cf
blanchet@49232
   588
              else
blanchet@49232
   589
                cf;
blanchet@49232
   590
blanchet@49235
   591
            val cgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) cgsss;
blanchet@49235
   592
            val chsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) chsss;
blanchet@49212
   593
blanchet@49212
   594
            val goal_coiterss =
blanchet@49235
   595
              map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss cgsss';
blanchet@49233
   596
            val goal_corecss =
blanchet@49235
   597
              map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss chsss';
blanchet@49213
   598
blanchet@49213
   599
            val coiter_tacss =
blanchet@49229
   600
              map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
blanchet@49226
   601
                ctr_defss;
blanchet@49233
   602
            val corec_tacss =
blanchet@49233
   603
              map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
blanchet@49233
   604
                ctr_defss;
blanchet@49212
   605
          in
blanchet@49213
   606
            (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49213
   607
               goal_coiterss coiter_tacss,
blanchet@49233
   608
             map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49233
   609
               goal_corecss corec_tacss)
blanchet@49212
   610
          end;
blanchet@49212
   611
blanchet@49212
   612
        val notes =
blanchet@49233
   613
          [(coitersN, coiter_thmss),
blanchet@49233
   614
           (corecsN, corec_thmss)]
blanchet@49212
   615
          |> maps (fn (thmN, thmss) =>
blanchet@49212
   616
            map2 (fn b => fn thms =>
blanchet@49212
   617
                ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
blanchet@49212
   618
              bs thmss);
blanchet@49212
   619
      in
blanchet@49230
   620
        lthy |> Local_Theory.notes notes |> snd
blanchet@49212
   621
      end;
blanchet@49212
   622
blanchet@49204
   623
    val lthy' = lthy
blanchet@49210
   624
      |> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
blanchet@49212
   625
        fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
blanchet@49212
   626
        ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
blanchet@49214
   627
      |>> split_list8
blanchet@49212
   628
      |> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
blanchet@49167
   629
blanchet@49167
   630
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
   631
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
   632
  in
blanchet@49204
   633
    (timer; lthy')
blanchet@49112
   634
  end;
blanchet@49112
   635
blanchet@49199
   636
fun datatype_cmd info specs lthy =
blanchet@49121
   637
  let
blanchet@49209
   638
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49184
   639
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49184
   640
      locale and shadows an existing global type*)
blanchet@49179
   641
    val fake_thy = Theory.copy
blanchet@49184
   642
      #> fold (fn spec => perhaps (try (Sign.add_type lthy
blanchet@49184
   643
        (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
blanchet@49179
   644
    val fake_lthy = Proof_Context.background_theory fake_thy lthy;
blanchet@49121
   645
  in
blanchet@49199
   646
    prepare_datatype Syntax.read_typ info specs fake_lthy lthy
blanchet@49121
   647
  end;
blanchet@49119
   648
blanchet@49129
   649
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
blanchet@49119
   650
blanchet@49112
   651
val parse_ctr_arg =
blanchet@49119
   652
  Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
blanchet@49129
   653
  (Parse.typ >> pair no_binder);
blanchet@49112
   654
blanchet@49112
   655
val parse_single_spec =
blanchet@49112
   656
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   657
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49119
   658
    Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
blanchet@49112
   659
blanchet@49112
   660
val _ =
blanchet@49112
   661
  Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
blanchet@49208
   662
    (Parse.and_list1 parse_single_spec >> datatype_cmd true);
blanchet@49112
   663
blanchet@49112
   664
val _ =
blanchet@49112
   665
  Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
blanchet@49208
   666
    (Parse.and_list1 parse_single_spec >> datatype_cmd false);
blanchet@49112
   667
blanchet@49112
   668
end;