src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Mon Sep 10 17:35:53 2012 +0200 (2012-09-10)
changeset 49255 2ecc533d6697
parent 49254 edc322ac5279
child 49256 df98aeb80a19
permissions -rw-r--r--
use balanced sums for constructors (to gracefully handle 100 constructors or more)
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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 ctxt sum_T Ts t k =
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  let
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    val u =
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      Balanced_Tree.access {left = mk_Inl dummyT, right = mk_Inr dummyT, init = t} (length Ts) k;
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  in singleton (Type_Infer_Context.infer_types ctxt) (Type.constraint sum_T u) 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, g_Tss, yssss), rec_only as (hss, h_Tss, zssss)),
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         (zs, cs, cpss, p_Tss, coiter_only as ((pgss, cgsss), g_sum_prod_Ts, g_prod_Tss, g_Tsss),
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          corec_only as ((phss, chsss), h_sum_prod_Ts, h_prod_Tss, h_Tsss))) =
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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_prod_Tss, f_Tsss, pf_Tss) end;
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          val (g_sum_prod_Ts, g_prod_Tss, g_Tsss, pg_Tss) = mk_types fp_iter_fun_Ts;
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          val (h_sum_prod_Ts, h_prod_Tss, 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 =
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            let
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              val pfss = map2 zip_preds_getters pss fsss;
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              val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss
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            in (pfss, cfsss) end;
blanchet@49210
   301
        in
blanchet@49212
   302
          ((([], [], []), ([], [], [])),
blanchet@49233
   303
           ([z], cs, cpss, p_Tss, (mk_terms gsss, g_sum_prod_Ts, g_prod_Tss, pg_Tss),
blanchet@49212
   304
            (mk_terms hsss, h_sum_prod_Ts, h_prod_Tss, ph_Tss)))
blanchet@49210
   305
        end;
blanchet@49210
   306
blanchet@49212
   307
    fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
blanchet@49212
   308
          fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
blanchet@49212
   309
        disc_binders), sel_binderss) no_defs_lthy =
blanchet@49176
   310
      let
blanchet@49201
   311
        val unfT = domain_type (fastype_of fld);
blanchet@49210
   312
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   313
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   314
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   315
blanchet@49176
   316
        val ((((u, v), fs), xss), _) =
blanchet@49204
   317
          no_defs_lthy
blanchet@49201
   318
          |> yield_singleton (mk_Frees "u") unfT
blanchet@49201
   319
          ||>> yield_singleton (mk_Frees "v") fpT
blanchet@49176
   320
          ||>> mk_Frees "f" case_Ts
blanchet@49124
   321
          ||>> mk_Freess "x" ctr_Tss;
blanchet@49121
   322
blanchet@49129
   323
        val ctr_rhss =
blanchet@49121
   324
          map2 (fn k => fn xs =>
blanchet@49255
   325
              fold_rev Term.lambda xs (fld $ mk_InN_balanced no_defs_lthy ctr_sum_prod_T ctr_prod_Ts
blanchet@49255
   326
                (HOLogic.mk_tuple xs) k))
blanchet@49255
   327
            ks xss;
blanchet@49121
   328
blanchet@49130
   329
        val case_binder = Binding.suffix_name ("_" ^ caseN) b;
blanchet@49129
   330
blanchet@49134
   331
        val case_rhs =
blanchet@49255
   332
          fold_rev Term.lambda (fs @ [v])
blanchet@49255
   333
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
blanchet@49129
   334
blanchet@49201
   335
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   336
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49169
   337
               Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49201
   338
             (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   339
          ||> `Local_Theory.restore;
blanchet@49121
   340
blanchet@49121
   341
        (*transforms defined frees into consts (and more)*)
blanchet@49121
   342
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   343
blanchet@49121
   344
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   345
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   346
blanchet@49203
   347
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   348
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   349
blanchet@49203
   350
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   351
blanchet@49135
   352
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   353
          let
blanchet@49135
   354
            val fld_iff_unf_thm =
blanchet@49135
   355
              let
blanchet@49135
   356
                val goal =
blanchet@49135
   357
                  fold_rev Logic.all [u, v]
blanchet@49135
   358
                    (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
blanchet@49135
   359
              in
blanchet@49135
   360
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49201
   361
                  mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
blanchet@49176
   362
                    (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
blanchet@49135
   363
                |> Thm.close_derivation
blanchet@49135
   364
                |> Morphism.thm phi
blanchet@49135
   365
              end;
blanchet@49135
   366
blanchet@49135
   367
            val sumEN_thm' =
blanchet@49135
   368
              Local_Defs.unfold lthy @{thms all_unit_eq}
blanchet@49255
   369
                (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49255
   370
                   (mk_sumEN_balanced n))
blanchet@49135
   371
              |> Morphism.thm phi;
blanchet@49123
   372
          in
blanchet@49161
   373
            mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
blanchet@49123
   374
          end;
blanchet@49121
   375
blanchet@49126
   376
        val inject_tacss =
blanchet@49205
   377
          map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49205
   378
              mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
blanchet@49126
   379
blanchet@49127
   380
        val half_distinct_tacss =
blanchet@49127
   381
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49127
   382
            mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   383
blanchet@49130
   384
        val case_tacs =
blanchet@49130
   385
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49130
   386
            mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
blanchet@49121
   387
blanchet@49121
   388
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   389
blanchet@49210
   390
        fun some_lfp_sugar no_defs_lthy =
blanchet@49134
   391
          let
blanchet@49208
   392
            val fpT_to_C = fpT --> C;
blanchet@49199
   393
blanchet@49215
   394
            fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
blanchet@49215
   395
              let
blanchet@49215
   396
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49215
   397
blanchet@49215
   398
                val binder = Binding.suffix_name ("_" ^ suf) b;
blanchet@49199
   399
blanchet@49215
   400
                val spec =
blanchet@49215
   401
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
blanchet@49215
   402
                    Term.list_comb (fp_iter_like,
blanchet@49255
   403
                      map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
blanchet@49215
   404
              in (binder, spec) end;
blanchet@49199
   405
blanchet@49215
   406
            val iter_likes =
blanchet@49215
   407
              [(iterN, fp_iter, iter_only),
blanchet@49215
   408
               (recN, fp_rec, rec_only)];
blanchet@49215
   409
blanchet@49215
   410
            val (binders, specs) = map generate_iter_like iter_likes |> split_list;
blanchet@49215
   411
blanchet@49215
   412
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   413
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   414
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49215
   415
                #>> apsnd snd) binders specs
blanchet@49199
   416
              ||> `Local_Theory.restore;
blanchet@49201
   417
blanchet@49201
   418
            (*transforms defined frees into consts (and more)*)
blanchet@49201
   419
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   420
blanchet@49215
   421
            val [iter_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   422
blanchet@49215
   423
            val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49134
   424
          in
blanchet@49214
   425
            ((ctrs, iter, recx, v, xss, ctr_defs, iter_def, rec_def), lthy)
blanchet@49134
   426
          end;
blanchet@49134
   427
blanchet@49210
   428
        fun some_gfp_sugar no_defs_lthy =
blanchet@49210
   429
          let
blanchet@49210
   430
            val B_to_fpT = C --> fpT;
blanchet@49211
   431
blanchet@49212
   432
            fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), f_sum_prod_Ts, f_prod_Tss,
blanchet@49212
   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@49254
   439
                fun mk_preds_getters_join c n cps sum_prod_T prod_Ts cfss =
blanchet@49211
   440
                  Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49255
   441
                    (map2 (mk_InN_balanced no_defs_lthy sum_prod_T prod_Ts)
blanchet@49255
   442
                      (map HOLogic.mk_tuple cfss) (1 upto n)));
blanchet@49210
   443
blanchet@49211
   444
                val spec =
blanchet@49212
   445
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
blanchet@49211
   446
                    Term.list_comb (fp_iter_like,
blanchet@49254
   447
                      map6 mk_preds_getters_join cs ns cpss f_sum_prod_Ts f_prod_Tss cfsss));
blanchet@49211
   448
              in (binder, spec) end;
blanchet@49210
   449
blanchet@49212
   450
            val coiter_likes =
blanchet@49215
   451
              [(coiterN, fp_iter, coiter_only),
blanchet@49215
   452
               (corecN, fp_rec, corec_only)];
blanchet@49212
   453
blanchet@49211
   454
            val (binders, specs) = map generate_coiter_like coiter_likes |> split_list;
blanchet@49211
   455
blanchet@49211
   456
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   457
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   458
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49211
   459
                #>> apsnd snd) binders specs
blanchet@49210
   460
              ||> `Local_Theory.restore;
blanchet@49210
   461
blanchet@49210
   462
            (*transforms defined frees into consts (and more)*)
blanchet@49210
   463
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   464
blanchet@49211
   465
            val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   466
blanchet@49211
   467
            val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49210
   468
          in
blanchet@49214
   469
            ((ctrs, coiter, corec, v, xss, ctr_defs, coiter_def, corec_def), lthy)
blanchet@49210
   470
          end;
blanchet@49119
   471
      in
blanchet@49203
   472
        wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy'
blanchet@49210
   473
        |> (if lfp then some_lfp_sugar else some_gfp_sugar)
blanchet@49119
   474
      end;
blanchet@49167
   475
blanchet@49226
   476
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49229
   477
    val map_ids = map map_id_of_bnf nested_bnfs;
blanchet@49226
   478
blanchet@49214
   479
    fun mk_map Ts Us t =
blanchet@49217
   480
      let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
blanchet@49214
   481
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49214
   482
      end;
blanchet@49214
   483
blanchet@49234
   484
    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
blanchet@49234
   485
      let
traytel@49236
   486
        val map0 = map_of_bnf (the (bnf_of lthy s));
blanchet@49234
   487
        val mapx = mk_map Ts Us map0;
blanchet@49234
   488
        val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
blanchet@49234
   489
        val args = map build_arg TUs;
blanchet@49234
   490
      in Term.list_comb (mapx, args) end;
blanchet@49234
   491
blanchet@49214
   492
    fun pour_more_sugar_on_lfps ((ctrss, iters, recs, vs, xsss, ctr_defss, iter_defs, rec_defs),
blanchet@49205
   493
        lthy) =
blanchet@49202
   494
      let
blanchet@49202
   495
        val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49212
   496
        val giters = map (lists_bmoc gss) iters;
blanchet@49212
   497
        val hrecs = map (lists_bmoc hss) recs;
blanchet@49201
   498
blanchet@49202
   499
        val (iter_thmss, rec_thmss) =
blanchet@49207
   500
          let
blanchet@49212
   501
            fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
blanchet@49207
   502
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49212
   503
                (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   504
blanchet@49234
   505
            fun build_call fiter_likes maybe_tick (T, U) =
blanchet@49234
   506
              if T = U then
blanchet@49234
   507
                mk_id T
blanchet@49234
   508
              else
blanchet@49234
   509
                (case find_index (curry (op =) T) fpTs of
blanchet@49234
   510
                  ~1 => build_map (build_call fiter_likes maybe_tick) T U
blanchet@49234
   511
                | j => maybe_tick (nth vs j) (nth fiter_likes j));
blanchet@49233
   512
blanchet@49214
   513
            fun mk_U maybe_prodT =
blanchet@49214
   514
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs);
blanchet@49214
   515
blanchet@49214
   516
            fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) =
blanchet@49214
   517
              if member (op =) fpTs T then
blanchet@49233
   518
                maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49214
   519
              else if exists_subtype (member (op =) fpTs) T then
blanchet@49233
   520
                [build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x]
blanchet@49214
   521
              else
blanchet@49214
   522
                [x];
blanchet@49214
   523
blanchet@49214
   524
            val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
blanchet@49214
   525
            val hxsss =
blanchet@49214
   526
              map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   527
blanchet@49212
   528
            val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
blanchet@49212
   529
            val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   530
blanchet@49203
   531
            val iter_tacss =
blanchet@49229
   532
              map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
blanchet@49203
   533
            val rec_tacss =
blanchet@49229
   534
              map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
blanchet@49202
   535
          in
blanchet@49205
   536
            (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   537
               goal_iterss iter_tacss,
blanchet@49205
   538
             map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   539
               goal_recss rec_tacss)
blanchet@49202
   540
          end;
blanchet@49201
   541
blanchet@49226
   542
        val notes =
blanchet@49202
   543
          [(itersN, iter_thmss),
blanchet@49202
   544
           (recsN, rec_thmss)]
blanchet@49202
   545
          |> maps (fn (thmN, thmss) =>
blanchet@49202
   546
            map2 (fn b => fn thms =>
blanchet@49202
   547
                ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
blanchet@49202
   548
              bs thmss);
blanchet@49202
   549
      in
blanchet@49202
   550
        lthy |> Local_Theory.notes notes |> snd
blanchet@49202
   551
      end;
blanchet@49202
   552
blanchet@49214
   553
    fun pour_more_sugar_on_gfps ((ctrss, coiters, corecs, vs, xsss, ctr_defss, coiter_defs,
blanchet@49214
   554
        corec_defs), lthy) =
blanchet@49212
   555
      let
blanchet@49233
   556
        val z = the_single zs;
blanchet@49233
   557
blanchet@49212
   558
        val gcoiters = map (lists_bmoc pgss) coiters;
blanchet@49212
   559
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49212
   560
blanchet@49212
   561
        val (coiter_thmss, corec_thmss) =
blanchet@49212
   562
          let
blanchet@49232
   563
            fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
blanchet@49212
   564
blanchet@49235
   565
            fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
blanchet@49212
   566
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49232
   567
                (Logic.list_implies (seq_conds mk_goal_cond n k cps,
blanchet@49235
   568
                   mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
   569
blanchet@49234
   570
            fun build_call fiter_likes maybe_tack (T, U) =
blanchet@49234
   571
              if T = U then
blanchet@49234
   572
                mk_id T
blanchet@49234
   573
              else
blanchet@49234
   574
                (case find_index (curry (op =) U) fpTs of
blanchet@49234
   575
                  ~1 => build_map (build_call fiter_likes maybe_tack) T U
blanchet@49234
   576
                | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
blanchet@49233
   577
blanchet@49232
   578
            fun mk_U maybe_sumT =
blanchet@49233
   579
              typ_subst (map2 (fn C => fn fpT => (maybe_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
   580
blanchet@49232
   581
            fun repair_calls fiter_likes maybe_sumT maybe_tack
blanchet@49232
   582
                (cf as Free (_, Type (_, [_, T])) $ _) =
blanchet@49232
   583
              if exists_subtype (member (op =) Cs) T then
blanchet@49233
   584
                build_call fiter_likes maybe_tack (T, mk_U maybe_sumT T) $ cf
blanchet@49232
   585
              else
blanchet@49232
   586
                cf;
blanchet@49232
   587
blanchet@49235
   588
            val cgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) cgsss;
blanchet@49235
   589
            val chsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) chsss;
blanchet@49212
   590
blanchet@49212
   591
            val goal_coiterss =
blanchet@49235
   592
              map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss cgsss';
blanchet@49233
   593
            val goal_corecss =
blanchet@49235
   594
              map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss chsss';
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@49212
   609
        val notes =
blanchet@49233
   610
          [(coitersN, coiter_thmss),
blanchet@49233
   611
           (corecsN, corec_thmss)]
blanchet@49212
   612
          |> maps (fn (thmN, thmss) =>
blanchet@49212
   613
            map2 (fn b => fn thms =>
blanchet@49212
   614
                ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
blanchet@49212
   615
              bs thmss);
blanchet@49212
   616
      in
blanchet@49230
   617
        lthy |> Local_Theory.notes notes |> snd
blanchet@49212
   618
      end;
blanchet@49212
   619
blanchet@49204
   620
    val lthy' = lthy
blanchet@49210
   621
      |> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
blanchet@49212
   622
        fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
blanchet@49212
   623
        ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss)
blanchet@49214
   624
      |>> split_list8
blanchet@49212
   625
      |> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps);
blanchet@49167
   626
blanchet@49167
   627
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
   628
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
   629
  in
blanchet@49204
   630
    (timer; lthy')
blanchet@49112
   631
  end;
blanchet@49112
   632
blanchet@49199
   633
fun datatype_cmd info specs lthy =
blanchet@49121
   634
  let
blanchet@49209
   635
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49184
   636
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49184
   637
      locale and shadows an existing global type*)
blanchet@49179
   638
    val fake_thy = Theory.copy
blanchet@49184
   639
      #> fold (fn spec => perhaps (try (Sign.add_type lthy
blanchet@49184
   640
        (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
blanchet@49179
   641
    val fake_lthy = Proof_Context.background_theory fake_thy lthy;
blanchet@49121
   642
  in
blanchet@49199
   643
    prepare_datatype Syntax.read_typ info specs fake_lthy lthy
blanchet@49121
   644
  end;
blanchet@49119
   645
blanchet@49129
   646
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
blanchet@49119
   647
blanchet@49112
   648
val parse_ctr_arg =
blanchet@49119
   649
  Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
blanchet@49129
   650
  (Parse.typ >> pair no_binder);
blanchet@49112
   651
blanchet@49112
   652
val parse_single_spec =
blanchet@49112
   653
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   654
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49119
   655
    Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
blanchet@49112
   656
blanchet@49112
   657
val _ =
blanchet@49112
   658
  Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
blanchet@49208
   659
    (Parse.and_list1 parse_single_spec >> datatype_cmd true);
blanchet@49112
   660
blanchet@49112
   661
val _ =
blanchet@49112
   662
  Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
blanchet@49208
   663
    (Parse.and_list1 parse_single_spec >> datatype_cmd false);
blanchet@49112
   664
blanchet@49112
   665
end;