src/HOL/Tools/datatype_rep_proofs.ML
author haftmann
Tue, 06 Dec 2005 09:04:09 +0100
changeset 18358 0a733e11021a
parent 18330 444f16d232a2
child 18377 0e1d025d57b3
permissions -rw-r--r--
re-oriented some result tuples in PureThy
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(*  Title:      HOL/Tools/datatype_rep_proofs.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer, TU Muenchen
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Definitional introduction of datatypes
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Proof of characteristic theorems:
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 - injectivity of constructors
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 - distinctness of constructors
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 - induction theorem
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*)
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signature DATATYPE_REP_PROOFS =
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sig
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  val representation_proofs : bool -> DatatypeAux.datatype_info Symtab.table ->
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    string list -> DatatypeAux.descr list -> (string * sort) list ->
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      (string * mixfix) list -> (string * mixfix) list list -> theory attribute
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        -> theory -> (thm list list * thm list list * thm list list *
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          DatatypeAux.simproc_dist list * thm) * theory
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end;
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structure DatatypeRepProofs : DATATYPE_REP_PROOFS =
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struct
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open DatatypeAux;
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
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(** theory context references **)
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val f_myinv_f = thm "f_myinv_f";
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val myinv_f_f = thm "myinv_f_f";
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fun exh_thm_of (dt_info : datatype_info Symtab.table) tname =
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  #exhaustion (the (Symtab.lookup dt_info tname));
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(******************************************************************************)
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fun representation_proofs flat_names (dt_info : datatype_info Symtab.table)
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      new_type_names descr sorts types_syntax constr_syntax case_names_induct thy =
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  let
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    val Datatype_thy =
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      if Context.theory_name thy = "Datatype" then thy
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      else theory "Datatype";
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    val node_name = "Datatype_Universe.node";
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    val In0_name = "Datatype_Universe.In0";
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    val In1_name = "Datatype_Universe.In1";
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    val Scons_name = "Datatype_Universe.Scons";
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    val Leaf_name = "Datatype_Universe.Leaf";
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    val Numb_name = "Datatype_Universe.Numb";
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    val Lim_name = "Datatype_Universe.Lim";
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    val Suml_name = "Datatype.Suml";
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    val Sumr_name = "Datatype.Sumr";
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    val [In0_inject, In1_inject, Scons_inject, Leaf_inject,
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         In0_eq, In1_eq, In0_not_In1, In1_not_In0,
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         Lim_inject, Suml_inject, Sumr_inject] = map (get_thm Datatype_thy o Name)
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        ["In0_inject", "In1_inject", "Scons_inject", "Leaf_inject",
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         "In0_eq", "In1_eq", "In0_not_In1", "In1_not_In0",
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         "Lim_inject", "Suml_inject", "Sumr_inject"];
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    val descr' = List.concat descr;
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    val big_name = space_implode "_" new_type_names;
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    val thy1 = add_path flat_names big_name thy;
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    val big_rec_name = big_name ^ "_rep_set";
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    val rep_set_names = map (Sign.full_name (Theory.sign_of thy1))
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      (if length descr' = 1 then [big_rec_name] else
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        (map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int)
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          (1 upto (length descr'))));
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    val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
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    val leafTs' = get_nonrec_types descr' sorts;
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    val branchTs = get_branching_types descr' sorts;
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    val branchT = if null branchTs then HOLogic.unitT
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      else fold_bal (fn (T, U) => Type ("+", [T, U])) branchTs;
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    val arities = get_arities descr' \ 0;
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    val unneeded_vars = hd tyvars \\ foldr add_typ_tfree_names [] (leafTs' @ branchTs);
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    val leafTs = leafTs' @ (map (fn n => TFree (n, (the o AList.lookup (op =) sorts) n)) unneeded_vars);
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    val recTs = get_rec_types descr' sorts;
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    val newTs = Library.take (length (hd descr), recTs);
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    val oldTs = Library.drop (length (hd descr), recTs);
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    val sumT = if null leafTs then HOLogic.unitT
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      else fold_bal (fn (T, U) => Type ("+", [T, U])) leafTs;
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    val Univ_elT = HOLogic.mk_setT (Type (node_name, [sumT, branchT]));
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    val UnivT = HOLogic.mk_setT Univ_elT;
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    val In0 = Const (In0_name, Univ_elT --> Univ_elT);
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    val In1 = Const (In1_name, Univ_elT --> Univ_elT);
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    val Leaf = Const (Leaf_name, sumT --> Univ_elT);
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    val Lim = Const (Lim_name, (branchT --> Univ_elT) --> Univ_elT);
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    (* make injections needed for embedding types in leaves *)
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    fun mk_inj T' x =
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      let
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        fun mk_inj' T n i =
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          if n = 1 then x else
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          let val n2 = n div 2;
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              val Type (_, [T1, T2]) = T
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          in
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            if i <= n2 then
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              Const ("Sum_Type.Inl", T1 --> T) $ (mk_inj' T1 n2 i)
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            else
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              Const ("Sum_Type.Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
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          end
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      in mk_inj' sumT (length leafTs) (1 + find_index_eq T' leafTs)
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      end;
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    (* make injections for constructors *)
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    fun mk_univ_inj ts = access_bal (fn t => In0 $ t, fn t => In1 $ t, if ts = [] then
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        Const ("arbitrary", Univ_elT)
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      else
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        foldr1 (HOLogic.mk_binop Scons_name) ts);
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    (* function spaces *)
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    fun mk_fun_inj T' x =
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      let
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        fun mk_inj T n i =
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          if n = 1 then x else
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          let
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            val n2 = n div 2;
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            val Type (_, [T1, T2]) = T;
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            fun mkT U = (U --> Univ_elT) --> T --> Univ_elT
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          in
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            if i <= n2 then Const (Suml_name, mkT T1) $ mk_inj T1 n2 i
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            else Const (Sumr_name, mkT T2) $ mk_inj T2 (n - n2) (i - n2)
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          end
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      in mk_inj branchT (length branchTs) (1 + find_index_eq T' branchTs)
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      end;
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    val mk_lim = foldr (fn (T, t) => Lim $ mk_fun_inj T (Abs ("x", T, t)));
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    (************** generate introduction rules for representing set **********)
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    val _ = message "Constructing representing sets ...";
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    (* make introduction rule for a single constructor *)
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    fun make_intr s n (i, (_, cargs)) =
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      let
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        fun mk_prem (dt, (j, prems, ts)) = (case strip_dtyp dt of
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            (dts, DtRec k) =>
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              let
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                val Ts = map (typ_of_dtyp descr' sorts) dts;
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                val free_t =
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                  app_bnds (mk_Free "x" (Ts ---> Univ_elT) j) (length Ts)
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              in (j + 1, list_all (map (pair "x") Ts,
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                  HOLogic.mk_Trueprop (HOLogic.mk_mem (free_t,
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                    Const (List.nth (rep_set_names, k), UnivT)))) :: prems,
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                mk_lim free_t Ts :: ts)
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              end
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          | _ =>
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              let val T = typ_of_dtyp descr' sorts dt
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              in (j + 1, prems, (Leaf $ mk_inj T (mk_Free "x" T j))::ts)
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              end);
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        val (_, prems, ts) = foldr mk_prem (1, [], []) cargs;
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        val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem
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          (mk_univ_inj ts n i, Const (s, UnivT)))
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      in Logic.list_implies (prems, concl)
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      end;
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    val consts = map (fn s => Const (s, UnivT)) rep_set_names;
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    val intr_ts = List.concat (map (fn ((_, (_, _, constrs)), rep_set_name) =>
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      map (make_intr rep_set_name (length constrs))
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        ((1 upto (length constrs)) ~~ constrs)) (descr' ~~ rep_set_names));
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    val (thy2, {raw_induct = rep_induct, intrs = rep_intrs, ...}) =
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      setmp InductivePackage.quiet_mode (!quiet_mode)
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        (InductivePackage.add_inductive_i false true big_rec_name false true false
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           consts (map (fn x => (("", x), [])) intr_ts) []) thy1;
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    (********************************* typedef ********************************)
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    val thy3 = add_path flat_names big_name (Library.foldl (fn (thy, ((((name, mx), tvs), c), name')) =>
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      setmp TypedefPackage.quiet_mode true
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        (TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE
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          (rtac exI 1 THEN
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            QUIET_BREADTH_FIRST (has_fewer_prems 1)
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            (resolve_tac rep_intrs 1))) thy |> #1)
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              (parent_path flat_names thy2, types_syntax ~~ tyvars ~~
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                (Library.take (length newTs, consts)) ~~ new_type_names));
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    (*********************** definition of constructors ***********************)
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    val big_rep_name = (space_implode "_" new_type_names) ^ "_Rep_";
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    val rep_names = map (curry op ^ "Rep_") new_type_names;
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    val rep_names' = map (fn i => big_rep_name ^ (string_of_int i))
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      (1 upto (length (List.concat (tl descr))));
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    val all_rep_names = map (Sign.intern_const (Theory.sign_of thy3)) rep_names @
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      map (Sign.full_name (Theory.sign_of thy3)) rep_names';
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    (* isomorphism declarations *)
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    val iso_decls = map (fn (T, s) => (s, T --> Univ_elT, NoSyn))
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      (oldTs ~~ rep_names');
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    (* constructor definitions *)
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    fun make_constr_def tname T n ((thy, defs, eqns, i), ((cname, cargs), (cname', mx))) =
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      let
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        fun constr_arg (dt, (j, l_args, r_args)) =
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          let val T = typ_of_dtyp descr' sorts dt;
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              val free_t = mk_Free "x" T j
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          in (case (strip_dtyp dt, strip_type T) of
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              ((_, DtRec m), (Us, U)) => (j + 1, free_t :: l_args, mk_lim
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                (Const (List.nth (all_rep_names, m), U --> Univ_elT) $
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                   app_bnds free_t (length Us)) Us :: r_args)
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            | _ => (j + 1, free_t::l_args, (Leaf $ mk_inj T free_t)::r_args))
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          end;
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        val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs;
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        val constrT = (map (typ_of_dtyp descr' sorts) cargs) ---> T;
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        val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname);
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        val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname);
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        val lhs = list_comb (Const (cname, constrT), l_args);
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        val rhs = mk_univ_inj r_args n i;
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        val def = equals T $ lhs $ (Const (abs_name, Univ_elT --> T) $ rhs);
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        val def_name = (Sign.base_name cname) ^ "_def";
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        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
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          (Const (rep_name, T --> Univ_elT) $ lhs, rhs));
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        val ([def_thm], thy') = thy |>
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          Theory.add_consts_i [(cname', constrT, mx)] |>
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          (PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)];
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      in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end;
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    (* constructor definitions for datatype *)
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    fun dt_constr_defs ((thy, defs, eqns, rep_congs, dist_lemmas),
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        ((((_, (_, _, constrs)), tname), T), constr_syntax)) =
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      let
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        val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong;
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        val sg = Theory.sign_of thy;
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        val rep_const = cterm_of sg
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          (Const (Sign.intern_const sg ("Rep_" ^ tname), T --> Univ_elT));
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        val cong' = standard (cterm_instantiate [(cterm_of sg cong_f, rep_const)] arg_cong);
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        val dist = standard (cterm_instantiate [(cterm_of sg distinct_f, rep_const)] distinct_lemma);
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        val (thy', defs', eqns', _) = Library.foldl ((make_constr_def tname T) (length constrs))
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          ((add_path flat_names tname thy, defs, [], 1), constrs ~~ constr_syntax)
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      in
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        (parent_path flat_names thy', defs', eqns @ [eqns'],
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          rep_congs @ [cong'], dist_lemmas @ [dist])
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      end;
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    val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) = Library.foldl dt_constr_defs
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      ((thy3 |> Theory.add_consts_i iso_decls |> parent_path flat_names, [], [], [], []),
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        hd descr ~~ new_type_names ~~ newTs ~~ constr_syntax);
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    (*********** isomorphisms for new types (introduced by typedef) ***********)
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    val _ = message "Proving isomorphism properties ...";
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    (* get axioms from theory *)
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    val newT_iso_axms = map (fn s =>
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      (get_thm thy4 (Name ("Abs_" ^ s ^ "_inverse")),
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       get_thm thy4 (Name ("Rep_" ^ s ^ "_inverse")),
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       get_thm thy4 (Name ("Rep_" ^ s)))) new_type_names;
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    (*------------------------------------------------*)
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    (* prove additional theorems:                     *)
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    (*  inj_on dt_Abs_i rep_set_i  and  inj dt_Rep_i  *)
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    (*------------------------------------------------*)
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    fun prove_newT_iso_inj_thm (((s, (thm1, thm2, _)), T), rep_set_name) =
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      let
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        val sg = Theory.sign_of thy4;
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        val RepT = T --> Univ_elT;
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        val Rep_name = Sign.intern_const sg ("Rep_" ^ s);
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        val AbsT = Univ_elT --> T;
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        val Abs_name = Sign.intern_const sg ("Abs_" ^ s);
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        val inj_Abs_thm = 
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	    standard (Goal.prove sg [] []
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	      (HOLogic.mk_Trueprop 
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		(Const ("Fun.inj_on", [AbsT, UnivT] ---> HOLogic.boolT) $
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		 Const (Abs_name, AbsT) $ Const (rep_set_name, UnivT)))
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              (fn _ => EVERY [rtac inj_on_inverseI 1, etac thm1 1]));
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        val setT = HOLogic.mk_setT T
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        val inj_Rep_thm =
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	    standard (Goal.prove sg [] []
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	      (HOLogic.mk_Trueprop
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		(Const ("Fun.inj_on", [RepT, setT] ---> HOLogic.boolT) $
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		 Const (Rep_name, RepT) $ Const ("UNIV", setT)))
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              (fn _ => EVERY [rtac inj_inverseI 1, rtac thm2 1]));
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      in (inj_Abs_thm, inj_Rep_thm) end;
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    val newT_iso_inj_thms = map prove_newT_iso_inj_thm
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      (new_type_names ~~ newT_iso_axms ~~ newTs ~~
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        Library.take (length newTs, rep_set_names));
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    (********* isomorphisms between existing types and "unfolded" types *******)
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    (*---------------------------------------------------------------------*)
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    (* isomorphisms are defined using primrec-combinators:                 *)
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    (* generate appropriate functions for instantiating primrec-combinator *)
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    (*                                                                     *)
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    (*   e.g.  dt_Rep_i = list_rec ... (%h t y. In1 (Scons (Leaf h) y))    *)
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    (*                                                                     *)
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    (* also generate characteristic equations for isomorphisms             *)
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    (*                                                                     *)
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    (*   e.g.  dt_Rep_i (cons h t) = In1 (Scons (dt_Rep_j h) (dt_Rep_i t)) *)
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    (*---------------------------------------------------------------------*)
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    fun make_iso_def k ks n ((fs, eqns, i), (cname, cargs)) =
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      let
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        val argTs = map (typ_of_dtyp descr' sorts) cargs;
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        val T = List.nth (recTs, k);
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        val rep_name = List.nth (all_rep_names, k);
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        val rep_const = Const (rep_name, T --> Univ_elT);
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        val constr = Const (cname, argTs ---> T);
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   323
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        fun process_arg ks' ((i2, i2', ts, Ts), dt) =
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          let
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            val T' = typ_of_dtyp descr' sorts dt;
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            val (Us, U) = strip_type T'
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          in (case strip_dtyp dt of
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              (_, DtRec j) => if j mem ks' then
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                  (i2 + 1, i2' + 1, ts @ [mk_lim (app_bnds
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                     (mk_Free "y" (Us ---> Univ_elT) i2') (length Us)) Us],
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                   Ts @ [Us ---> Univ_elT])
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                else
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                  (i2 + 1, i2', ts @ [mk_lim
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                     (Const (List.nth (all_rep_names, j), U --> Univ_elT) $
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                        app_bnds (mk_Free "x" T' i2) (length Us)) Us], Ts)
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            | _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (mk_Free "x" T' i2)], Ts))
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          end;
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        val (i2, i2', ts, Ts) = Library.foldl (process_arg ks) ((1, 1, [], []), cargs);
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        val xs = map (uncurry (mk_Free "x")) (argTs ~~ (1 upto (i2 - 1)));
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        val ys = map (uncurry (mk_Free "y")) (Ts ~~ (1 upto (i2' - 1)));
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        val f = list_abs_free (map dest_Free (xs @ ys), mk_univ_inj ts n i);
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        val (_, _, ts', _) = Library.foldl (process_arg []) ((1, 1, [], []), cargs);
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        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
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          (rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i))
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      in (fs @ [f], eqns @ [eqn], i + 1) end;
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    (* define isomorphisms for all mutually recursive datatypes in list ds *)
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   353
    fun make_iso_defs (ds, (thy, char_thms)) =
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      let
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        val ks = map fst ds;
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   356
        val (_, (tname, _, _)) = hd ds;
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        val {rec_rewrites, rec_names, ...} = the (Symtab.lookup dt_info tname);
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        fun process_dt ((fs, eqns, isos), (k, (tname, _, constrs))) =
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          let
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            val (fs', eqns', _) = Library.foldl (make_iso_def k ks (length constrs))
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              ((fs, eqns, 1), constrs);
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            val iso = (List.nth (recTs, k), List.nth (all_rep_names, k))
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          in (fs', eqns', isos @ [iso]) end;
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   365
        
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        val (fs, eqns, isos) = Library.foldl process_dt (([], [], []), ds);
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        val fTs = map fastype_of fs;
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   368
        val defs = map (fn (rec_name, (T, iso_name)) => ((Sign.base_name iso_name) ^ "_def",
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          equals (T --> Univ_elT) $ Const (iso_name, T --> Univ_elT) $
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            list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs))) (rec_names ~~ isos);
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        val (def_thms, thy') = (PureThy.add_defs_i false o map Thm.no_attributes) defs thy;
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        (* prove characteristic equations *)
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   374
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        val rewrites = def_thms @ (map mk_meta_eq rec_rewrites);
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        val char_thms' = map (fn eqn => standard (Goal.prove thy' [] [] eqn
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          (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1]))) eqns;
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   378
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   379
      in (thy', char_thms' @ char_thms) end;
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   380
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   381
    val (thy5, iso_char_thms) = foldr make_iso_defs
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   382
      (add_path flat_names big_name thy4, []) (tl descr);
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   383
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   384
    (* prove isomorphism properties *)
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   385
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   386
    fun mk_funs_inv thm =
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   387
      let
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   388
        val {sign, prop, ...} = rep_thm thm;
16287
7a03b4b4df67 Type.freeze;
wenzelm
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   389
        val _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ S)) $
7a03b4b4df67 Type.freeze;
wenzelm
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   390
          (_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop;
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63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
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   391
        val used = add_term_tfree_names (a, []);
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   392
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   393
        fun mk_thm i =
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   394
          let
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   395
            val Ts = map (TFree o rpair HOLogic.typeS)
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
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   396
              (variantlist (replicate i "'t", used));
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
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   397
            val f = Free ("f", Ts ---> U)
17985
d5d576b72371 avoid legacy goals;
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   398
          in standard (Goal.prove sign [] [] (Logic.mk_implies
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
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parents: 13585
diff changeset
   399
            (HOLogic.mk_Trueprop (HOLogic.list_all
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berghofe
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   400
               (map (pair "x") Ts, HOLogic.mk_mem (app_bnds f i, S))),
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
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diff changeset
   401
             HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts,
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   402
               r $ (a $ app_bnds f i)), f))))
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   403
            (fn _ => EVERY [REPEAT (rtac ext 1), REPEAT (etac allE 1), rtac thm 1, atac 1]))
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
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diff changeset
   404
          end
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   405
      in map (fn r => r RS subst) (thm :: map mk_thm arities) end;
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   406
5177
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   407
    (* prove  inj dt_Rep_i  and  dt_Rep_i x : dt_rep_set_i *)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   408
0d3a168e4d44 New datatype definition package
berghofe
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diff changeset
   409
    fun prove_iso_thms (ds, (inj_thms, elem_thms)) =
0d3a168e4d44 New datatype definition package
berghofe
parents:
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   410
      let
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   411
        val (_, (tname, _, _)) = hd ds;
17412
e26cb20ef0cc TableFun/Symtab: curried lookup and update;
wenzelm
parents: 17261
diff changeset
   412
        val {induction, ...} = the (Symtab.lookup dt_info tname);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   413
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   414
        fun mk_ind_concl (i, _) =
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   415
          let
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   416
            val T = List.nth (recTs, i);
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   417
            val Rep_t = Const (List.nth (all_rep_names, i), T --> Univ_elT);
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   418
            val rep_set_name = List.nth (rep_set_names, i)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
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   419
          in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   420
                HOLogic.mk_eq (Rep_t $ mk_Free "x" T i, Rep_t $ Bound 0) $
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   421
                  HOLogic.mk_eq (mk_Free "x" T i, Bound 0)),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   422
              HOLogic.mk_mem (Rep_t $ mk_Free "x" T i, Const (rep_set_name, UnivT)))
0d3a168e4d44 New datatype definition package
berghofe
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   423
          end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   424
0d3a168e4d44 New datatype definition package
berghofe
parents:
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   425
        val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   426
5553
ae42b36a50c2 renamed mk_meta_eq to mk_eq
oheimb
parents: 5303
diff changeset
   427
        val rewrites = map mk_meta_eq iso_char_thms;
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   428
        val inj_thms' = map (fn r => r RS injD)
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   429
          (map snd newT_iso_inj_thms @ inj_thms);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   430
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   431
        val inj_thm = standard (Goal.prove thy5 [] []
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   432
          (HOLogic.mk_Trueprop (mk_conj ind_concl1)) (fn _ => EVERY
11951
381135c295ef Fixed several bugs concerning arbitrarily branching datatypes.
berghofe
parents: 11827
diff changeset
   433
            [(indtac induction THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   434
             REPEAT (EVERY
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   435
               [rtac allI 1, rtac impI 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   436
                exh_tac (exh_thm_of dt_info) 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   437
                REPEAT (EVERY
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   438
                  [hyp_subst_tac 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   439
                   rewrite_goals_tac rewrites,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   440
                   REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   441
                   (eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   442
                   ORELSE (EVERY
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   443
                     [REPEAT (eresolve_tac (Scons_inject ::
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   444
                        map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1),
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   445
                      REPEAT (cong_tac 1), rtac refl 1,
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   446
                      REPEAT (atac 1 ORELSE (EVERY
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   447
                        [REPEAT (rtac ext 1),
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   448
                         REPEAT (eresolve_tac (mp :: allE ::
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   449
                           map make_elim (Suml_inject :: Sumr_inject ::
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   450
                             Lim_inject :: fun_cong :: inj_thms')) 1),
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   451
                         atac 1]))])])])]));
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   452
6171
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   453
        val inj_thms'' = map (fn r => r RS datatype_injI)
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   454
                             (split_conj_thm inj_thm);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   455
6171
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   456
        val elem_thm = 
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   457
	    standard (Goal.prove thy5 [] [] (HOLogic.mk_Trueprop (mk_conj ind_concl2))
6171
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   458
	      (fn _ =>
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   459
	       EVERY [(indtac induction THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   460
		rewrite_goals_tac rewrites,
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   461
		REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   462
                  ((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]));
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   463
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   464
      in (inj_thms'' @ inj_thms, elem_thms @ (split_conj_thm elem_thm))
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   465
      end;
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   466
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   467
    val (iso_inj_thms_unfolded, iso_elem_thms) = foldr prove_iso_thms
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   468
      ([], map #3 newT_iso_axms) (tl descr);
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   469
    val iso_inj_thms = map snd newT_iso_inj_thms @ iso_inj_thms_unfolded;
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   470
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   471
    (* prove  x : dt_rep_set_i --> x : range dt_Rep_i *)
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   472
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   473
    fun mk_iso_t (((set_name, iso_name), i), T) =
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   474
      let val isoT = T --> Univ_elT
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   475
      in HOLogic.imp $ 
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   476
        HOLogic.mk_mem (mk_Free "x" Univ_elT i, Const (set_name, UnivT)) $
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   477
          (if i < length newTs then Const ("True", HOLogic.boolT)
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   478
           else HOLogic.mk_mem (mk_Free "x" Univ_elT i,
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   479
             Const ("image", [isoT, HOLogic.mk_setT T] ---> UnivT) $
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   480
               Const (iso_name, isoT) $ Const ("UNIV", HOLogic.mk_setT T)))
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   481
      end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   482
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   483
    val iso_t = HOLogic.mk_Trueprop (mk_conj (map mk_iso_t
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   484
      (rep_set_names ~~ all_rep_names ~~ (0 upto (length descr' - 1)) ~~ recTs)));
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   485
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   486
    (* all the theorems are proved by one single simultaneous induction *)
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   487
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   488
    val range_eqs = map (fn r => mk_meta_eq (r RS range_ex1_eq))
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   489
      iso_inj_thms_unfolded;
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   490
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   491
    val iso_thms = if length descr = 1 then [] else
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   492
      Library.drop (length newTs, split_conj_thm
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   493
        (standard (Goal.prove thy5 [] [] iso_t (fn _ => EVERY
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   494
           [(indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   495
            REPEAT (rtac TrueI 1),
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   496
            rewrite_goals_tac (mk_meta_eq choice_eq ::
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   497
              symmetric (mk_meta_eq expand_fun_eq) :: range_eqs),
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   498
            rewrite_goals_tac (map symmetric range_eqs),
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   499
            REPEAT (EVERY
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   500
              [REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   501
                 List.concat (map (mk_funs_inv o #1) newT_iso_axms)) 1),
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   502
               TRY (hyp_subst_tac 1),
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   503
               rtac (sym RS range_eqI) 1,
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   504
               resolve_tac iso_char_thms 1])]))));
11435
bd1a7f53c11b replaced "Eps" by "The";
wenzelm
parents: 10911
diff changeset
   505
bd1a7f53c11b replaced "Eps" by "The";
wenzelm
parents: 10911
diff changeset
   506
    val Abs_inverse_thms' =
bd1a7f53c11b replaced "Eps" by "The";
wenzelm
parents: 10911
diff changeset
   507
      map #1 newT_iso_axms @
18330
444f16d232a2 introduced new map2, fold
haftmann
parents: 18314
diff changeset
   508
      map2 (fn r_inj => fn r => f_myinv_f OF [r_inj, r RS mp])
444f16d232a2 introduced new map2, fold
haftmann
parents: 18314
diff changeset
   509
        iso_inj_thms_unfolded iso_thms;
11435
bd1a7f53c11b replaced "Eps" by "The";
wenzelm
parents: 10911
diff changeset
   510
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   511
    val Abs_inverse_thms = List.concat (map mk_funs_inv Abs_inverse_thms');
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   512
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   513
    (******************* freeness theorems for constructors *******************)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   514
6427
fd36b2e7d80e tuned messages;
wenzelm
parents: 6422
diff changeset
   515
    val _ = message "Proving freeness of constructors ...";
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   516
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   517
    (* prove theorem  Rep_i (Constr_j ...) = Inj_j ...  *)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   518
    
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   519
    fun prove_constr_rep_thm eqn =
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   520
      let
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   521
        val inj_thms = map (fn (r, _) => r RS inj_onD) newT_iso_inj_thms;
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   522
        val rewrites = o_def :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms)
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   523
      in standard (Goal.prove thy5 [] [] eqn (fn _ => EVERY
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   524
        [resolve_tac inj_thms 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   525
         rewrite_goals_tac rewrites,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   526
         rtac refl 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   527
         resolve_tac rep_intrs 2,
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   528
         REPEAT (resolve_tac iso_elem_thms 1)]))
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   529
      end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   530
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   531
    (*--------------------------------------------------------------*)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   532
    (* constr_rep_thms and rep_congs are used to prove distinctness *)
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   533
    (* of constructors.                                             *)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   534
    (*--------------------------------------------------------------*)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   535
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   536
    val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   537
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   538
    val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   539
      dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   540
        (constr_rep_thms ~~ dist_lemmas);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   541
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   542
    fun prove_distinct_thms (_, []) = []
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   543
      | prove_distinct_thms (dist_rewrites', t::_::ts) =
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   544
          let
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   545
            val dist_thm = standard (Goal.prove thy5 [] [] t (fn _ =>
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   546
              EVERY [simp_tac (HOL_ss addsimps dist_rewrites') 1]))
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   547
          in dist_thm::(standard (dist_thm RS not_sym))::
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   548
            (prove_distinct_thms (dist_rewrites', ts))
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   549
          end;
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   550
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   551
    val distinct_thms = map prove_distinct_thms (dist_rewrites ~~
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   552
      DatatypeProp.make_distincts new_type_names descr sorts thy5);
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   553
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   554
    val simproc_dists = map (fn ((((_, (_, _, constrs)), rep_thms), congr), dists) =>
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   555
      if length constrs < !DatatypeProp.dtK then FewConstrs dists
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   556
      else ManyConstrs (congr, HOL_basic_ss addsimps rep_thms)) (hd descr ~~
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   557
        constr_rep_thms ~~ rep_congs ~~ distinct_thms);
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   558
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   559
    (* prove injectivity of constructors *)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   560
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   561
    fun prove_constr_inj_thm rep_thms t =
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   562
      let val inj_thms = Scons_inject :: (map make_elim
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   563
        ((map (fn r => r RS injD) iso_inj_thms) @
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   564
          [In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject,
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   565
           Lim_inject, Suml_inject, Sumr_inject]))
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   566
      in standard (Goal.prove thy5 [] [] t (fn _ => EVERY
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   567
        [rtac iffI 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   568
         REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   569
         dresolve_tac rep_congs 1, dtac box_equals 1,
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   570
         REPEAT (resolve_tac rep_thms 1),
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   571
         REPEAT (eresolve_tac inj_thms 1),
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   572
         REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [REPEAT (rtac ext 1),
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   573
           REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1),
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   574
           atac 1]))]))
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   575
      end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   576
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   577
    val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   578
      ((DatatypeProp.make_injs descr sorts) ~~ constr_rep_thms);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   579
18314
4595eb4627fa oriented pairs theory * 'a to 'a * theory
haftmann
parents: 17985
diff changeset
   580
    val ((constr_inject', distinct_thms'), thy6) =
4595eb4627fa oriented pairs theory * 'a to 'a * theory
haftmann
parents: 17985
diff changeset
   581
      thy5
4595eb4627fa oriented pairs theory * 'a to 'a * theory
haftmann
parents: 17985
diff changeset
   582
      |> parent_path flat_names
4595eb4627fa oriented pairs theory * 'a to 'a * theory
haftmann
parents: 17985
diff changeset
   583
      |> store_thmss "inject" new_type_names constr_inject
4595eb4627fa oriented pairs theory * 'a to 'a * theory
haftmann
parents: 17985
diff changeset
   584
      ||>> store_thmss "distinct" new_type_names distinct_thms;
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   585
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   586
    (*************************** induction theorem ****************************)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   587
6427
fd36b2e7d80e tuned messages;
wenzelm
parents: 6422
diff changeset
   588
    val _ = message "Proving induction rule for datatypes ...";
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   589
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   590
    val Rep_inverse_thms = (map (fn (_, iso, _) => iso RS subst) newT_iso_axms) @
11471
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   591
      (map (fn r => r RS myinv_f_f RS subst) iso_inj_thms_unfolded);
ba2c252b55ad - Fixed bug in isomorphism proofs (caused by migration from SOME to THE)
berghofe
parents: 11435
diff changeset
   592
    val Rep_inverse_thms' = map (fn r => r RS myinv_f_f) iso_inj_thms_unfolded;
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   593
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   594
    fun mk_indrule_lemma ((prems, concls), ((i, _), T)) =
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   595
      let
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   596
        val Rep_t = Const (List.nth (all_rep_names, i), T --> Univ_elT) $
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   597
          mk_Free "x" T i;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   598
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   599
        val Abs_t = if i < length newTs then
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   600
            Const (Sign.intern_const (Theory.sign_of thy6)
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   601
              ("Abs_" ^ (List.nth (new_type_names, i))), Univ_elT --> T)
11435
bd1a7f53c11b replaced "Eps" by "The";
wenzelm
parents: 10911
diff changeset
   602
          else Const ("Inductive.myinv", [T --> Univ_elT, Univ_elT] ---> T) $
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   603
            Const (List.nth (all_rep_names, i), T --> Univ_elT)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   604
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   605
      in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t,
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   606
            Const (List.nth (rep_set_names, i), UnivT)) $
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   607
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   608
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   609
      end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   610
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   611
    val (indrule_lemma_prems, indrule_lemma_concls) =
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   612
      Library.foldl mk_indrule_lemma (([], []), (descr' ~~ recTs));
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   613
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   614
    val cert = cterm_of (Theory.sign_of thy6);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   615
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   616
    val indrule_lemma = standard (Goal.prove thy6 [] []
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   617
      (Logic.mk_implies
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   618
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   619
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   620
           [REPEAT (etac conjE 1),
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   621
            REPEAT (EVERY
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   622
              [TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1,
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   623
               etac mp 1, resolve_tac iso_elem_thms 1])]));
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   624
8305
93aa21ec5494 HOLogic.dest_conj;
wenzelm
parents: 8005
diff changeset
   625
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   626
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   627
      map (Free o apfst fst o dest_Var) Ps;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   628
    val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   629
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   630
    val dt_induct_prop = DatatypeProp.make_ind descr sorts;
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   631
    val dt_induct = standard (Goal.prove thy6 []
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   632
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   633
      (fn prems => EVERY
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   634
        [rtac indrule_lemma' 1,
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   635
         (indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   636
         EVERY (map (fn (prem, r) => (EVERY
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   637
           [REPEAT (eresolve_tac Abs_inverse_thms 1),
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   638
            simp_tac (HOL_basic_ss addsimps ((symmetric r)::Rep_inverse_thms')) 1,
13641
63d1790a43ed Reimplemented parts of datatype package dealing with datatypes involving
berghofe
parents: 13585
diff changeset
   639
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   640
                (prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]));
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   641
8436
8a87fa482baf adapted to new PureThy.add_thms etc.;
wenzelm
parents: 8305
diff changeset
   642
    val (thy7, [dt_induct']) = thy6 |>
5661
6ecb6ea25f19 - Changed structure of name spaces
berghofe
parents: 5553
diff changeset
   643
      Theory.add_path big_name |>
13340
9b0332344ae2 Simplified proof of induction rule for datatypes involving function types.
berghofe
parents: 12922
diff changeset
   644
      PureThy.add_thms [(("induct", dt_induct), [case_names_induct])] |>>
5661
6ecb6ea25f19 - Changed structure of name spaces
berghofe
parents: 5553
diff changeset
   645
      Theory.parent_path;
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   646
18314
4595eb4627fa oriented pairs theory * 'a to 'a * theory
haftmann
parents: 17985
diff changeset
   647
  in
4595eb4627fa oriented pairs theory * 'a to 'a * theory
haftmann
parents: 17985
diff changeset
   648
    ((constr_inject', distinct_thms', dist_rewrites, simproc_dists, dt_induct'), thy7)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   649
  end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   650
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   651
end;