src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Tue Sep 11 22:13:22 2012 +0200 (2012-09-11)
changeset 49297 47fbf2e3e89c
parent 49287 ebe2a5cec4bf
child 49298 36e551d3af3b
permissions -rw-r--r--
provide a programmatic interface for FP sugar
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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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  val datatyp: bool ->
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    bool * ((((typ * typ option) list * binding) * mixfix) * ((((binding * binding) *
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      (binding * typ) list) * (binding * term) list) * mixfix) list) list ->
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    local_theory -> local_theory
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end;
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structure BNF_FP_Sugar : BNF_FP_SUGAR =
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struct
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open BNF_Util
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open BNF_Wrap
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open BNF_Def
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open BNF_FP_Util
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open BNF_LFP
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open BNF_GFP
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open BNF_FP_Sugar_Tactics
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val caseN = "case";
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val coitersN = "coiters";
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val corecsN = "corecs";
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val disc_coitersN = "disc_coiters";
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val disc_corecsN = "disc_corecs";
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val itersN = "iters";
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val recsN = "recs";
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val sel_coitersN = "sel_coiters";
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val sel_corecsN = "sel_corecs";
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fun split_list11 xs =
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  (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
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   map #9 xs, map #10 xs, map #11 xs);
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fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
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  | strip_map_type T = ([], T);
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fun typ_subst inst (T as Type (s, Ts)) =
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    (case AList.lookup (op =) inst T of
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      NONE => Type (s, map (typ_subst inst) Ts)
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    | SOME T' => T')
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  | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
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fun retype_free (Free (s, _)) T = Free (s, T);
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun mk_predT T = T --> HOLogic.boolT;
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fun mk_id T = Const (@{const_name id}, T --> T);
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fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
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fun mk_uncurried2_fun f xss =
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  mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
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fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
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fun tack z_name (c, v) f =
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  let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
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    Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
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  end;
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fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
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fun merge_type_arg_constrained ctxt (T, c) (T', c') =
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  if T = T' then
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    (case (c, c') of
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      (_, NONE) => (T, c)
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    | (NONE, _) => (T, c')
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    | _ =>
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      if c = c' then
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        (T, c)
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      else
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        error ("Inconsistent sort constraints for type variable " ^
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          quote (Syntax.string_of_typ ctxt T)))
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  else
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    cannot_merge_types ();
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fun merge_type_args_constrained ctxt (cAs, cAs') =
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  if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
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  else cannot_merge_types ();
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fun type_args_constrained_of (((cAs, _), _), _) = cAs;
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val type_args_of = map fst o type_args_constrained_of;
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fun type_binder_of (((_, b), _), _) = b;
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fun mixfix_of ((_, mx), _) = mx;
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fun ctr_specs_of (_, ctr_specs) = ctr_specs;
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fun disc_of ((((disc, _), _), _), _) = disc;
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fun ctr_of ((((_, ctr), _), _), _) = ctr;
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fun args_of (((_, args), _), _) = args;
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fun defaults_of ((_, ds), _) = ds;
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fun ctr_mixfix_of (_, mx) = mx;
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fun prepare_datatype prepare_typ prepare_term lfp (no_dests, specs) fake_lthy no_defs_lthy =
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  let
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    val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
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      else ();
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    val 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 raw_sel_defaultsss = map (map defaults_of) ctr_specss;
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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 ((Bs, Cs), _) =
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      no_defs_lthy
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      |> fold Variable.declare_typ As
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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 Bs j)
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      | freeze_fp T = T;
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    val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
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    val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
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    val eqs = map dest_TFree Bs ~~ ctr_sum_prod_TsBs;
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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_TsssBs []);
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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 (Bs ~~ fpTs)))) ctr_TsssBs;
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    val ns = map length ctr_Tsss;
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    val kss = map (fn n => 1 upto n) ns;
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    val mss = map (map length) ctr_Tsss;
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    val Css = map2 replicate ns Cs;
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    fun mk_iter_like Ts Us t =
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      let
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        val (binders, body) = strip_type (fastype_of t);
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        val (f_Us, prebody) = split_last binders;
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        val Type (_, Ts0) = if lfp then prebody else body;
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        val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
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      in
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        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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      end;
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    val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
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    val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
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    val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
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    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
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    val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
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         (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
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      if lfp then
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        let
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          val y_Tsss =
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            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
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              ns mss fp_iter_fun_Ts;
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          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
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          val ((gss, ysss), _) =
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            lthy
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            |> mk_Freess "f" g_Tss
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            ||>> mk_Freesss "x" y_Tsss;
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          val yssss = map (map (map single)) ysss;
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          fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
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              if member (op =) Cs U then Us else [T]
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            | dest_rec_prodT T = [T];
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          val z_Tssss =
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            map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
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              dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
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          val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
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          val hss = map2 (map2 retype_free) gss h_Tss;
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          val zssss_hd = map2 (map2 (map2 (fn y => fn T :: _ => retype_free y T))) ysss z_Tssss;
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          val (zssss_tl, _) =
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            lthy
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            |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
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          val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
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        in
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          (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
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           ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
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        end
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      else
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        let
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          (*avoid "'a itself" arguments in coiterators and corecursors*)
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          val mss' =  map (fn [0] => [1] | ms => ms) mss;
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          val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
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          fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
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          fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
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            | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
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              p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
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          fun mk_types maybe_dest_sumT fun_Ts =
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            let
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              val f_sum_prod_Ts = map range_type fun_Ts;
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              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
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              val f_Tssss =
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                map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
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                  Cs mss' f_prod_Tss;
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              val q_Tssss =
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                map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
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              val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
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            in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
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          val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
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          val ((((Free (z, _), cs), pss), gssss), _) =
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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_Freessss "g" g_Tssss;
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          val rssss = map (map (map (fn [] => []))) r_Tssss;
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          fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
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              if member (op =) Cs U then Us else [T]
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            | dest_corec_sumT T = [T];
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   297
          val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
blanchet@49210
   298
blanchet@49275
   299
          val hssss_hd = map2 (map2 (map2 (fn [g] => fn T :: _ => retype_free g T))) gssss h_Tssss;
blanchet@49275
   300
          val ((sssss, hssss_tl), _) =
blanchet@49275
   301
            lthy
blanchet@49275
   302
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   303
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   304
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   305
blanchet@49212
   306
          val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
blanchet@49212
   307
blanchet@49276
   308
          fun mk_preds_getters_join [] [cf] = cf
blanchet@49276
   309
            | mk_preds_getters_join [cq] [cf, cf'] =
blanchet@49276
   310
              mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
blanchet@49276
   311
blanchet@49275
   312
          fun mk_terms qssss fssss =
blanchet@49212
   313
            let
blanchet@49276
   314
              val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
blanchet@49275
   315
              val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
blanchet@49274
   316
              val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
blanchet@49276
   317
              val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
blanchet@49276
   318
            in (pfss, cqfsss) end;
blanchet@49210
   319
        in
blanchet@49212
   320
          ((([], [], []), ([], [], [])),
blanchet@49275
   321
           ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
blanchet@49275
   322
            (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
blanchet@49210
   323
        end;
blanchet@49210
   324
blanchet@49287
   325
    fun define_ctrs_case_for_type ((((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec),
blanchet@49212
   326
          fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss),
blanchet@49286
   327
        disc_binders), sel_binderss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   328
      let
blanchet@49201
   329
        val unfT = domain_type (fastype_of fld);
blanchet@49210
   330
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   331
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   332
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   333
blanchet@49176
   334
        val ((((u, v), fs), xss), _) =
blanchet@49204
   335
          no_defs_lthy
blanchet@49201
   336
          |> yield_singleton (mk_Frees "u") unfT
blanchet@49201
   337
          ||>> yield_singleton (mk_Frees "v") fpT
blanchet@49176
   338
          ||>> mk_Frees "f" case_Ts
blanchet@49124
   339
          ||>> mk_Freess "x" ctr_Tss;
blanchet@49121
   340
blanchet@49129
   341
        val ctr_rhss =
blanchet@49256
   342
          map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
blanchet@49256
   343
            mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
blanchet@49121
   344
blanchet@49130
   345
        val case_binder = Binding.suffix_name ("_" ^ caseN) b;
blanchet@49129
   346
blanchet@49134
   347
        val case_rhs =
blanchet@49255
   348
          fold_rev Term.lambda (fs @ [v])
blanchet@49255
   349
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
blanchet@49129
   350
blanchet@49201
   351
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   352
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49169
   353
               Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49201
   354
             (case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   355
          ||> `Local_Theory.restore;
blanchet@49121
   356
blanchet@49121
   357
        (*transforms defined frees into consts (and more)*)
blanchet@49121
   358
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   359
blanchet@49121
   360
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   361
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   362
blanchet@49203
   363
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   364
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   365
blanchet@49203
   366
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   367
blanchet@49135
   368
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   369
          let
blanchet@49135
   370
            val fld_iff_unf_thm =
blanchet@49135
   371
              let
blanchet@49135
   372
                val goal =
blanchet@49135
   373
                  fold_rev Logic.all [u, v]
blanchet@49135
   374
                    (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
blanchet@49135
   375
              in
blanchet@49135
   376
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49201
   377
                  mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
blanchet@49176
   378
                    (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
blanchet@49135
   379
                |> Thm.close_derivation
blanchet@49135
   380
                |> Morphism.thm phi
blanchet@49135
   381
              end;
blanchet@49135
   382
blanchet@49135
   383
            val sumEN_thm' =
blanchet@49135
   384
              Local_Defs.unfold lthy @{thms all_unit_eq}
blanchet@49255
   385
                (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49255
   386
                   (mk_sumEN_balanced n))
blanchet@49135
   387
              |> Morphism.thm phi;
blanchet@49123
   388
          in
blanchet@49161
   389
            mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
blanchet@49123
   390
          end;
blanchet@49121
   391
blanchet@49126
   392
        val inject_tacss =
blanchet@49205
   393
          map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49205
   394
              mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
blanchet@49126
   395
blanchet@49127
   396
        val half_distinct_tacss =
blanchet@49127
   397
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49127
   398
            mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   399
blanchet@49130
   400
        val case_tacs =
blanchet@49130
   401
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49130
   402
            mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
blanchet@49121
   403
blanchet@49121
   404
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   405
blanchet@49287
   406
        fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
blanchet@49134
   407
          let
blanchet@49208
   408
            val fpT_to_C = fpT --> C;
blanchet@49199
   409
blanchet@49215
   410
            fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
blanchet@49215
   411
              let
blanchet@49215
   412
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49215
   413
blanchet@49215
   414
                val binder = Binding.suffix_name ("_" ^ suf) b;
blanchet@49199
   415
blanchet@49215
   416
                val spec =
blanchet@49215
   417
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)),
blanchet@49215
   418
                    Term.list_comb (fp_iter_like,
blanchet@49255
   419
                      map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
blanchet@49215
   420
              in (binder, spec) end;
blanchet@49199
   421
blanchet@49274
   422
            val iter_like_bundles =
blanchet@49215
   423
              [(iterN, fp_iter, iter_only),
blanchet@49215
   424
               (recN, fp_rec, rec_only)];
blanchet@49215
   425
blanchet@49274
   426
            val (binders, specs) = map generate_iter_like iter_like_bundles |> split_list;
blanchet@49215
   427
blanchet@49215
   428
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   429
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   430
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49215
   431
                #>> apsnd snd) binders specs
blanchet@49199
   432
              ||> `Local_Theory.restore;
blanchet@49201
   433
blanchet@49201
   434
            (*transforms defined frees into consts (and more)*)
blanchet@49201
   435
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   436
blanchet@49215
   437
            val [iter_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   438
blanchet@49215
   439
            val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49134
   440
          in
blanchet@49267
   441
            ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
blanchet@49266
   442
             lthy)
blanchet@49134
   443
          end;
blanchet@49134
   444
blanchet@49287
   445
        fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
blanchet@49210
   446
          let
blanchet@49210
   447
            val B_to_fpT = C --> fpT;
blanchet@49211
   448
blanchet@49276
   449
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   450
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   451
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   452
blanchet@49276
   453
            fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
blanchet@49274
   454
                pf_Tss))) =
blanchet@49211
   455
              let
blanchet@49211
   456
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49210
   457
blanchet@49211
   458
                val binder = Binding.suffix_name ("_" ^ suf) b;
blanchet@49210
   459
blanchet@49211
   460
                val spec =
blanchet@49212
   461
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)),
blanchet@49211
   462
                    Term.list_comb (fp_iter_like,
blanchet@49276
   463
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49211
   464
              in (binder, spec) end;
blanchet@49210
   465
blanchet@49274
   466
            val coiter_like_bundles =
blanchet@49215
   467
              [(coiterN, fp_iter, coiter_only),
blanchet@49215
   468
               (corecN, fp_rec, corec_only)];
blanchet@49212
   469
blanchet@49274
   470
            val (binders, specs) = map generate_coiter_like coiter_like_bundles |> split_list;
blanchet@49211
   471
blanchet@49211
   472
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   473
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   474
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49211
   475
                #>> apsnd snd) binders specs
blanchet@49210
   476
              ||> `Local_Theory.restore;
blanchet@49210
   477
blanchet@49210
   478
            (*transforms defined frees into consts (and more)*)
blanchet@49210
   479
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   480
blanchet@49211
   481
            val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   482
blanchet@49211
   483
            val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49210
   484
          in
blanchet@49267
   485
            ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
blanchet@49266
   486
              corec_def), lthy)
blanchet@49210
   487
          end;
blanchet@49286
   488
blanchet@49287
   489
        fun wrap lthy =
blanchet@49287
   490
          let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
blanchet@49287
   491
            wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_binders, (sel_binderss,
blanchet@49287
   492
              sel_defaultss))) lthy
blanchet@49287
   493
          end;
blanchet@49287
   494
blanchet@49287
   495
        val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
blanchet@49119
   496
      in
blanchet@49287
   497
        ((wrap, define_iter_likes), lthy')
blanchet@49119
   498
      end;
blanchet@49167
   499
blanchet@49226
   500
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49229
   501
    val map_ids = map map_id_of_bnf nested_bnfs;
blanchet@49226
   502
blanchet@49214
   503
    fun mk_map Ts Us t =
blanchet@49217
   504
      let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
blanchet@49214
   505
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49214
   506
      end;
blanchet@49214
   507
blanchet@49234
   508
    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
blanchet@49234
   509
      let
traytel@49236
   510
        val map0 = map_of_bnf (the (bnf_of lthy s));
blanchet@49234
   511
        val mapx = mk_map Ts Us map0;
blanchet@49234
   512
        val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
blanchet@49234
   513
        val args = map build_arg TUs;
blanchet@49234
   514
      in Term.list_comb (mapx, args) end;
blanchet@49234
   515
blanchet@49287
   516
    fun derive_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs,
blanchet@49266
   517
        rec_defs), lthy) =
blanchet@49202
   518
      let
blanchet@49202
   519
        val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49212
   520
        val giters = map (lists_bmoc gss) iters;
blanchet@49212
   521
        val hrecs = map (lists_bmoc hss) recs;
blanchet@49201
   522
blanchet@49202
   523
        val (iter_thmss, rec_thmss) =
blanchet@49207
   524
          let
blanchet@49212
   525
            fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
blanchet@49207
   526
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49212
   527
                (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   528
blanchet@49234
   529
            fun build_call fiter_likes maybe_tick (T, U) =
blanchet@49234
   530
              if T = U then
blanchet@49234
   531
                mk_id T
blanchet@49234
   532
              else
blanchet@49234
   533
                (case find_index (curry (op =) T) fpTs of
blanchet@49234
   534
                  ~1 => build_map (build_call fiter_likes maybe_tick) T U
blanchet@49234
   535
                | j => maybe_tick (nth vs j) (nth fiter_likes j));
blanchet@49233
   536
blanchet@49274
   537
            fun mk_U maybe_mk_prodT =
blanchet@49274
   538
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
blanchet@49214
   539
blanchet@49274
   540
            fun repair_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
blanchet@49214
   541
              if member (op =) fpTs T then
blanchet@49233
   542
                maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49214
   543
              else if exists_subtype (member (op =) fpTs) T then
blanchet@49274
   544
                [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
blanchet@49214
   545
              else
blanchet@49214
   546
                [x];
blanchet@49214
   547
blanchet@49214
   548
            val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss;
blanchet@49214
   549
            val hxsss =
blanchet@49214
   550
              map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   551
blanchet@49212
   552
            val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
blanchet@49212
   553
            val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   554
blanchet@49203
   555
            val iter_tacss =
blanchet@49229
   556
              map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
blanchet@49203
   557
            val rec_tacss =
blanchet@49229
   558
              map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
blanchet@49202
   559
          in
blanchet@49276
   560
            (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   561
               goal_iterss iter_tacss,
blanchet@49276
   562
             map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   563
               goal_recss rec_tacss)
blanchet@49202
   564
          end;
blanchet@49201
   565
blanchet@49226
   566
        val notes =
blanchet@49202
   567
          [(itersN, iter_thmss),
blanchet@49202
   568
           (recsN, rec_thmss)]
blanchet@49202
   569
          |> maps (fn (thmN, thmss) =>
blanchet@49202
   570
            map2 (fn b => fn thms =>
blanchet@49202
   571
                ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]))
blanchet@49202
   572
              bs thmss);
blanchet@49202
   573
      in
blanchet@49202
   574
        lthy |> Local_Theory.notes notes |> snd
blanchet@49202
   575
      end;
blanchet@49202
   576
blanchet@49287
   577
    fun derive_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss,
blanchet@49287
   578
        discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
blanchet@49212
   579
      let
blanchet@49233
   580
        val z = the_single zs;
blanchet@49233
   581
blanchet@49212
   582
        val gcoiters = map (lists_bmoc pgss) coiters;
blanchet@49212
   583
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49212
   584
blanchet@49212
   585
        val (coiter_thmss, corec_thmss) =
blanchet@49212
   586
          let
blanchet@49232
   587
            fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
blanchet@49212
   588
blanchet@49276
   589
            fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
blanchet@49212
   590
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49232
   591
                (Logic.list_implies (seq_conds mk_goal_cond n k cps,
blanchet@49276
   592
                   mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
   593
blanchet@49234
   594
            fun build_call fiter_likes maybe_tack (T, U) =
blanchet@49234
   595
              if T = U then
blanchet@49234
   596
                mk_id T
blanchet@49234
   597
              else
blanchet@49234
   598
                (case find_index (curry (op =) U) fpTs of
blanchet@49234
   599
                  ~1 => build_map (build_call fiter_likes maybe_tack) T U
blanchet@49234
   600
                | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
blanchet@49233
   601
blanchet@49274
   602
            fun mk_U maybe_mk_sumT =
blanchet@49274
   603
              typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
   604
blanchet@49276
   605
            fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
blanchet@49276
   606
              let val T = fastype_of cqf in
blanchet@49276
   607
                if exists_subtype (member (op =) Cs) T then
blanchet@49276
   608
                  build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
blanchet@49276
   609
                else
blanchet@49276
   610
                  cqf
blanchet@49276
   611
              end;
blanchet@49232
   612
blanchet@49276
   613
            val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss;
blanchet@49276
   614
            val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
blanchet@49212
   615
blanchet@49212
   616
            val goal_coiterss =
blanchet@49276
   617
              map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
blanchet@49233
   618
            val goal_corecss =
blanchet@49276
   619
              map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@49213
   620
blanchet@49213
   621
            val coiter_tacss =
blanchet@49229
   622
              map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
blanchet@49226
   623
                ctr_defss;
blanchet@49233
   624
            val corec_tacss =
blanchet@49233
   625
              map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
blanchet@49233
   626
                ctr_defss;
blanchet@49212
   627
          in
blanchet@49276
   628
            (map2 (map2 (fn goal => fn tac =>
blanchet@49276
   629
                 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
blanchet@49213
   630
               goal_coiterss coiter_tacss,
blanchet@49276
   631
             map2 (map2 (fn goal => fn tac =>
blanchet@49276
   632
                 Skip_Proof.prove lthy [] [] goal (tac o #context)
blanchet@49276
   633
                 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
blanchet@49233
   634
               goal_corecss corec_tacss)
blanchet@49212
   635
          end;
blanchet@49212
   636
blanchet@49266
   637
        fun mk_disc_coiter_like_thms [_] = K []
blanchet@49266
   638
          | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
blanchet@49266
   639
blanchet@49266
   640
        val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
blanchet@49266
   641
        val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
blanchet@49266
   642
blanchet@49267
   643
        fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
blanchet@49266
   644
          let
blanchet@49267
   645
            val (domT, ranT) = dest_funT (fastype_of sel0);
blanchet@49266
   646
            val arg_cong' =
blanchet@49266
   647
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49267
   648
                [NONE, NONE, SOME (certify lthy sel0)] arg_cong
blanchet@49267
   649
              |> Thm.varifyT_global;
blanchet@49266
   650
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
   651
          in
blanchet@49267
   652
            coiter_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
   653
          end;
blanchet@49266
   654
blanchet@49266
   655
        val sel_coiter_thmsss =
blanchet@49266
   656
          map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
blanchet@49266
   657
        val sel_corec_thmsss =
blanchet@49267
   658
          map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
blanchet@49266
   659
blanchet@49212
   660
        val notes =
blanchet@49233
   661
          [(coitersN, coiter_thmss),
blanchet@49266
   662
           (disc_coitersN, disc_coiter_thmss),
blanchet@49266
   663
           (sel_coitersN, map flat sel_coiter_thmsss),
blanchet@49266
   664
           (corecsN, corec_thmss),
blanchet@49266
   665
           (disc_corecsN, disc_corec_thmss),
blanchet@49266
   666
           (sel_corecsN, map flat sel_corec_thmsss)]
blanchet@49212
   667
          |> maps (fn (thmN, thmss) =>
blanchet@49266
   668
            map_filter (fn (_, []) => NONE | (b, thms) =>
blanchet@49266
   669
              SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []),
blanchet@49266
   670
                [(thms, [])])) (bs ~~ thmss));
blanchet@49212
   671
      in
blanchet@49230
   672
        lthy |> Local_Theory.notes notes |> snd
blanchet@49212
   673
      end;
blanchet@49212
   674
blanchet@49287
   675
    fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
blanchet@49287
   676
      fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
blanchet@49287
   677
blanchet@49204
   678
    val lthy' = lthy
blanchet@49287
   679
      |> fold_map define_ctrs_case_for_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
blanchet@49212
   680
        fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~
blanchet@49286
   681
        ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss ~~ raw_sel_defaultsss)
blanchet@49287
   682
      |>> split_list |> wrap_types_and_define_iter_likes
blanchet@49287
   683
      |> (if lfp then derive_iter_rec_thms_for_types else derive_coiter_corec_thms_for_types);
blanchet@49167
   684
blanchet@49167
   685
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
   686
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
   687
  in
blanchet@49204
   688
    (timer; lthy')
blanchet@49112
   689
  end;
blanchet@49112
   690
blanchet@49297
   691
fun datatyp lfp bundle lthy = prepare_datatype (K I) (K I) lfp bundle lthy lthy;
blanchet@49297
   692
blanchet@49278
   693
fun datatype_cmd lfp (bundle as (_, specs)) lthy =
blanchet@49121
   694
  let
blanchet@49209
   695
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49184
   696
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49184
   697
      locale and shadows an existing global type*)
blanchet@49179
   698
    val fake_thy = Theory.copy
blanchet@49184
   699
      #> fold (fn spec => perhaps (try (Sign.add_type lthy
blanchet@49184
   700
        (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
blanchet@49179
   701
    val fake_lthy = Proof_Context.background_theory fake_thy lthy;
blanchet@49121
   702
  in
blanchet@49286
   703
    prepare_datatype Syntax.read_typ Syntax.read_term lfp bundle fake_lthy lthy
blanchet@49121
   704
  end;
blanchet@49119
   705
blanchet@49277
   706
val parse_opt_binding_colon = Scan.optional (Parse.binding --| @{keyword ":"}) no_binder
blanchet@49119
   707
blanchet@49112
   708
val parse_ctr_arg =
blanchet@49277
   709
  @{keyword "("} |-- parse_opt_binding_colon -- Parse.typ --| @{keyword ")"} ||
blanchet@49129
   710
  (Parse.typ >> pair no_binder);
blanchet@49112
   711
blanchet@49286
   712
val parse_defaults =
blanchet@49286
   713
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
   714
blanchet@49112
   715
val parse_single_spec =
blanchet@49112
   716
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   717
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49286
   718
    Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
blanchet@49112
   719
blanchet@49278
   720
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
blanchet@49278
   721
blanchet@49112
   722
val _ =
blanchet@49112
   723
  Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
blanchet@49278
   724
    (parse_datatype >> datatype_cmd true);
blanchet@49112
   725
blanchet@49112
   726
val _ =
blanchet@49112
   727
  Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
blanchet@49278
   728
    (parse_datatype >> datatype_cmd false);
blanchet@49112
   729
blanchet@49112
   730
end;