src/HOL/Tools/datatype_rep_proofs.ML
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(*  Title:      HOL/Tools/datatype_rep_proofs.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer
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    Copyright   1998  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 (internal version)
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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 -> (int * (string * DatatypeAux.dtyp list *
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      (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
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        (string * mixfix) list -> (string * mixfix) list list -> theory ->
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          theory * thm list list * thm list list * thm list list *
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            DatatypeAux.simproc_dist list * thm
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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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(* figure out internal names *)
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val image_name = Sign.intern_const (Theory.sign_of Set.thy) "op ``";
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val UNIV_name = Sign.intern_const (Theory.sign_of Set.thy) "UNIV";
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val inj_on_name = Sign.intern_const (Theory.sign_of Fun.thy) "inj_on";
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val inv_name = Sign.intern_const (Theory.sign_of Fun.thy) "inv";
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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 thy =
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  let
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    val Datatype_thy = theory "Datatype";
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    val node_name = Sign.intern_tycon (Theory.sign_of Datatype_thy) "node";
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    val [In0_name, In1_name, Scons_name, Leaf_name, Numb_name, Lim_name,
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      Funs_name, o_name] =
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      map (Sign.intern_const (Theory.sign_of Datatype_thy))
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        ["In0", "In1", "Scons", "Leaf", "Numb", "Lim", "Funs", "op o"];
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    val [In0_inject, In1_inject, Scons_inject, Leaf_inject, In0_eq, In1_eq,
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         In0_not_In1, In1_not_In0, Funs_mono, FunsI, Lim_inject,
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         Funs_inv, FunsD, Funs_rangeE, Funs_nonempty] = map (get_thm Datatype_thy)
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        ["In0_inject", "In1_inject", "Scons_inject", "Leaf_inject", "In0_eq", "In1_eq",
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         "In0_not_In1", "In1_not_In0", "Funs_mono", "FunsI", "Lim_inject",
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         "Funs_inv", "FunsD", "Funs_rangeE", "Funs_nonempty"];
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    val Funs_IntE = (Int_lower2 RS Funs_mono RS
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      (Int_lower1 RS Funs_mono RS Int_greatest) RS subsetD) RS IntE;
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    val descr' = flat 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 unneeded_vars = hd tyvars \\ foldr add_typ_tfree_names (leafTs' @ branchTs, []);
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    val leafTs = leafTs' @ (map (fn n => TFree (n, the (assoc (sorts, n)))) unneeded_vars);
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    val recTs = get_rec_types descr' sorts;
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    val newTs = take (length (hd descr), recTs);
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    val oldTs = 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 ("Inl", T1 --> T) $ (mk_inj' T1 n2 i)
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            else
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              Const ("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 (ap In0, ap In1, 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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            val sum_case = Const ("sum_case", [T1 --> Univ_elT, T2 --> Univ_elT, T] ---> Univ_elT)
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          in
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            if i <= n2 then
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              sum_case $ (mk_inj T1 n2 i) $ Const ("arbitrary", T2 --> Univ_elT)
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            else
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              sum_case $ Const ("arbitrary", T1 --> Univ_elT) $ 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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    (************** 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 (DtRec k, (j, prems, ts)) =
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              let val free_t = mk_Free "x" Univ_elT j
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              in (j + 1, (HOLogic.mk_mem (free_t,
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                Const (nth_elem (k, rep_set_names), UnivT)))::prems, free_t::ts)
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              end
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          | mk_prem (DtType ("fun", [T, DtRec k]), (j, prems, ts)) =
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              let val T' = typ_of_dtyp descr' sorts T;
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                  val free_t = mk_Free "x" (T' --> Univ_elT) j
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              in (j + 1, (HOLogic.mk_mem (free_t,
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                Const (Funs_name, UnivT --> HOLogic.mk_setT (T' --> Univ_elT)) $
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                  Const (nth_elem (k, rep_set_names), UnivT)))::prems,
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                    Lim $ mk_fun_inj T' free_t::ts)
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              end
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          | mk_prem (dt, (j, prems, ts)) =
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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 (cargs, (1, [], []));
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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 (map HOLogic.mk_Trueprop 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 = flat (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) [Funs_mono] []) thy1;
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    (********************************* typedef ********************************)
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    val thy3 = add_path flat_names big_name (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_no_def name' (name, tvs, mx) c [] []
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          (Some (QUIET_BREADTH_FIRST (has_fewer_prems 1)
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            (resolve_tac (Funs_nonempty::rep_intrs) 1)))) thy)
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              (parent_path flat_names thy2, types_syntax ~~ tyvars ~~
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                (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 (flat (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 dt of
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              DtRec m => (j + 1, free_t::l_args, (Const (nth_elem (m, all_rep_names),
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                T --> Univ_elT) $ free_t)::r_args)
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            | DtType ("fun", [T', DtRec m]) =>
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                let val ([T''], T''') = strip_type T
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                in (j + 1, free_t::l_args, (Lim $ mk_fun_inj T''
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                  (Const (o_name, [T''' --> Univ_elT, T, T''] ---> Univ_elT) $
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                    Const (nth_elem (m, all_rep_names), T''' --> Univ_elT) $ free_t))::r_args)
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                end
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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 (cargs, (1, [], []));
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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 thy' = thy |>
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          Theory.add_consts_i [(cname', constrT, mx)] |>
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          Theory.add_defs_i [(def_name, def)];
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      in (thy', defs @ [get_axiom thy' def_name], eqns @ [eqn], i + 1)
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      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', _) = 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) = 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_axiom thy4 ("Abs_" ^ s ^ "_inverse"),
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       get_axiom thy4 ("Rep_" ^ s ^ "_inverse"),
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       get_axiom thy4 ("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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	    prove_goalw_cterm [] 
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	      (cterm_of sg
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	       (HOLogic.mk_Trueprop 
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		(Const (inj_on_name, [AbsT, UnivT] ---> HOLogic.boolT) $
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		 Const (Abs_name, AbsT) $ Const (rep_set_name, UnivT))))
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              (fn _ => [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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	    prove_goalw_cterm []
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	      (cterm_of sg
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	       (HOLogic.mk_Trueprop
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		(Const (inj_on_name, [RepT, setT] ---> HOLogic.boolT) $
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		 Const (Rep_name, RepT) $ Const (UNIV_name, setT))))
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              (fn _ => [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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        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 ((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 ((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 = nth_elem (k, recTs);
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        val rep_name = nth_elem (k, all_rep_names);
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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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        fun process_arg ks' ((i2, i2', ts, Ts), dt) =
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          let val T' = typ_of_dtyp descr' sorts dt
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          in (case dt of
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              DtRec j => if j mem ks' then
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                  (i2 + 1, i2' + 1, ts @ [mk_Free "y" Univ_elT i2'], Ts @ [Univ_elT])
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                else
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                  (i2 + 1, i2', ts @ [Const (nth_elem (j, all_rep_names),
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                    T' --> Univ_elT) $ mk_Free "x" T' i2], Ts)
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            | (DtType ("fun", [_, DtRec j])) =>
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                let val ([T''], T''') = strip_type T'
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                in if j mem ks' then
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                    (i2 + 1, i2' + 1, ts @ [Lim $ mk_fun_inj T''
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                      (mk_Free "y" (T'' --> Univ_elT) i2')], Ts @ [T'' --> Univ_elT])
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                  else
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                    (i2 + 1, i2', ts @ [Lim $ mk_fun_inj T''
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                      (Const (o_name, [T''' --> Univ_elT, T', T''] ---> Univ_elT) $
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                        Const (nth_elem (j, all_rep_names), T''' --> Univ_elT) $
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                          mk_Free "x" T' i2)], Ts)
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                end
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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) = 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', _) = 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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    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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        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', _) = foldl (make_iso_def k ks (length constrs))
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              ((fs, eqns, 1), constrs);
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            val iso = (nth_elem (k, recTs), nth_elem (k, all_rep_names))
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          in (fs', eqns', isos @ [iso]) end;
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   379
        
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        val (fs, eqns, isos) = foldl process_dt (([], [], []), ds);
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        val fTs = map fastype_of fs;
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   382
        val defs = map (fn (rec_name, (T, iso_name)) => ((Sign.base_name iso_name) ^ "_def",
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   383
          equals (T --> Univ_elT) $ Const (iso_name, T --> Univ_elT) $
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   384
            list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs))) (rec_names ~~ isos);
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   385
        val thy' = Theory.add_defs_i defs thy;
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   386
        val def_thms = map (get_axiom thy') (map fst defs);
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   387
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   388
        (* prove characteristic equations *)
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   389
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   390
        val rewrites = def_thms @ (map mk_meta_eq rec_rewrites);
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   391
        val char_thms' = map (fn eqn => prove_goalw_cterm rewrites
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3d9fd50fcc43 Theory.sign_of;
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   392
          (cterm_of (Theory.sign_of thy') eqn) (fn _ => [rtac refl 1])) eqns;
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   393
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      in (thy', char_thms' @ char_thms) end;
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   395
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   396
    val (thy5, iso_char_thms) = foldr make_iso_defs
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   397
      (tl descr, (add_path flat_names big_name thy4, []));
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   398
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   399
    (* prove isomorphism properties *)
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   400
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   401
    fun mk_funs_inv thm =
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   402
      let
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   403
        val [_, t] = prems_of Funs_inv;
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   404
        val [_ $ (_ $ _ $ R)] = Logic.strip_assums_hyp t;
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   405
        val _ $ (_ $ (r $ (a $ _)) $ _) = Logic.strip_assums_concl t;
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   406
        val [_ $ (_ $ _ $ R')] = prems_of thm;
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   407
        val _ $ (_ $ (r' $ (a' $ _)) $ _) = concl_of thm;
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   408
        val inv' = cterm_instantiate (map 
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   409
          ((pairself (cterm_of (sign_of_thm thm))) o
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   410
           (apsnd (map_term_types (incr_tvar 1))))
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   411
             [(R, R'), (r, r'), (a, a')]) Funs_inv
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   412
      in
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   413
        rule_by_tactic (atac 2) (thm RSN (2, inv'))
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   414
      end;
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   415
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   416
    (* prove  x : dt_rep_set_i --> x : range dt_Rep_i *)
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   417
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   418
    fun mk_iso_t (((set_name, iso_name), i), T) =
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   419
      let val isoT = T --> Univ_elT
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   420
      in HOLogic.imp $ 
0d3a168e4d44 New datatype definition package
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   421
        HOLogic.mk_mem (mk_Free "x" Univ_elT i, Const (set_name, UnivT)) $
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   422
          (if i < length newTs then Const ("True", HOLogic.boolT)
0d3a168e4d44 New datatype definition package
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   423
           else HOLogic.mk_mem (mk_Free "x" Univ_elT i,
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   424
             Const (image_name, [isoT, HOLogic.mk_setT T] ---> UnivT) $
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   425
               Const (iso_name, isoT) $ Const (UNIV_name, HOLogic.mk_setT T)))
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   426
      end;
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   427
0d3a168e4d44 New datatype definition package
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   428
    val iso_t = HOLogic.mk_Trueprop (mk_conj (map mk_iso_t
0d3a168e4d44 New datatype definition package
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   429
      (rep_set_names ~~ all_rep_names ~~ (0 upto (length descr' - 1)) ~~ recTs)));
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   430
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   431
    (* all the theorems are proved by one single simultaneous induction *)
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   432
0d3a168e4d44 New datatype definition package
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   433
    val iso_thms = if length descr = 1 then [] else
0d3a168e4d44 New datatype definition package
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   434
      drop (length newTs, split_conj_thm
6394
3d9fd50fcc43 Theory.sign_of;
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   435
        (prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) iso_t) (fn _ =>
5177
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   436
           [indtac rep_induct 1,
0d3a168e4d44 New datatype definition package
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   437
            REPEAT (rtac TrueI 1),
0d3a168e4d44 New datatype definition package
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   438
            REPEAT (EVERY
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85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   439
              [rewrite_goals_tac [mk_meta_eq Collect_mem_eq],
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   440
               REPEAT (etac Funs_IntE 1),
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   441
               REPEAT (eresolve_tac [rangeE, Funs_rangeE] 1),
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   442
               REPEAT (eresolve_tac (map (fn (iso, _, _) => iso RS subst) newT_iso_axms @
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
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   443
                 map (fn (iso, _, _) => mk_funs_inv iso RS subst) newT_iso_axms) 1),
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   444
               TRY (hyp_subst_tac 1),
0d3a168e4d44 New datatype definition package
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   445
               rtac (sym RS range_eqI) 1,
0d3a168e4d44 New datatype definition package
berghofe
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   446
               resolve_tac iso_char_thms 1])])));
0d3a168e4d44 New datatype definition package
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   447
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   448
    val Abs_inverse_thms' = (map #1 newT_iso_axms) @ map (fn r => r RS mp RS f_inv_f) iso_thms;
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   449
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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diff changeset
   450
    val Abs_inverse_thms = map (fn r => r RS subst) (Abs_inverse_thms' @
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
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   451
      map mk_funs_inv Abs_inverse_thms');
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   452
0d3a168e4d44 New datatype definition package
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   453
    (* prove  inj dt_Rep_i  and  dt_Rep_i x : dt_rep_set_i *)
0d3a168e4d44 New datatype definition package
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   454
0d3a168e4d44 New datatype definition package
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   455
    fun prove_iso_thms (ds, (inj_thms, elem_thms)) =
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berghofe
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   456
      let
0d3a168e4d44 New datatype definition package
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   457
        val (_, (tname, _, _)) = hd ds;
0d3a168e4d44 New datatype definition package
berghofe
parents:
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   458
        val {induction, ...} = the (Symtab.lookup (dt_info, tname));
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   459
0d3a168e4d44 New datatype definition package
berghofe
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   460
        fun mk_ind_concl (i, _) =
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   461
          let
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   462
            val T = nth_elem (i, recTs);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   463
            val Rep_t = Const (nth_elem (i, all_rep_names), T --> Univ_elT);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   464
            val rep_set_name = nth_elem (i, rep_set_names)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   465
          in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   466
                HOLogic.mk_eq (Rep_t $ mk_Free "x" T i, Rep_t $ Bound 0) $
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   467
                  HOLogic.mk_eq (mk_Free "x" T i, Bound 0)),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   468
              HOLogic.mk_mem (Rep_t $ mk_Free "x" T i, Const (rep_set_name, UnivT)))
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   469
          end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   470
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   471
        val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   472
5553
ae42b36a50c2 renamed mk_meta_eq to mk_eq
oheimb
parents: 5303
diff changeset
   473
        val rewrites = map mk_meta_eq iso_char_thms;
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   474
        val inj_thms' = flat (map (fn r => [r RS injD, r RS inj_o]) inj_thms);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   475
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   476
        val inj_thm = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   477
          (HOLogic.mk_Trueprop (mk_conj ind_concl1))) (fn _ =>
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   478
            [indtac induction 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   479
             REPEAT (EVERY
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   480
               [rtac allI 1, rtac impI 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   481
                exh_tac (exh_thm_of dt_info) 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   482
                REPEAT (EVERY
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   483
                  [hyp_subst_tac 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   484
                   rewrite_goals_tac rewrites,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   485
                   REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   486
                   (eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   487
                   ORELSE (EVERY
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   488
                     [REPEAT (etac Scons_inject 1),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   489
                      REPEAT (dresolve_tac
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   490
                        (inj_thms' @ [Leaf_inject, Lim_inject, Inl_inject, Inr_inject]) 1),
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   491
                      REPEAT ((EVERY [etac allE 1, dtac mp 1, atac 1]) ORELSE
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   492
                              (dtac inj_fun_lemma 1 THEN atac 1)),
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   493
                      TRY (hyp_subst_tac 1),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   494
                      rtac refl 1])])])]);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   495
6171
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   496
        val inj_thms'' = map (fn r => r RS datatype_injI)
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   497
                             (split_conj_thm inj_thm);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   498
6171
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   499
        val elem_thm = 
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   500
	    prove_goalw_cterm []
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   501
	      (cterm_of (Theory.sign_of thy5)
6171
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   502
	       (HOLogic.mk_Trueprop (mk_conj ind_concl2)))
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   503
	      (fn _ =>
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   504
	       [indtac induction 1,
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   505
		rewrite_goals_tac (o_def :: rewrites),
6171
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   506
		REPEAT (EVERY
cd237a10cbf8 inj is now a translation of inj_on
paulson
parents: 6092
diff changeset
   507
			[resolve_tac rep_intrs 1,
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   508
			 REPEAT (FIRST [atac 1, etac spec 1,
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   509
				 resolve_tac (FunsI :: elem_thms) 1])])]);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   510
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   511
      in (inj_thms @ inj_thms'', elem_thms @ (split_conj_thm elem_thm))
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   512
      end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   513
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   514
    val (iso_inj_thms, iso_elem_thms) = foldr prove_iso_thms
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   515
      (tl descr, (map snd newT_iso_inj_thms, map #3 newT_iso_axms));
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   516
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   517
    (******************* freeness theorems for constructors *******************)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   518
6427
fd36b2e7d80e tuned messages;
wenzelm
parents: 6422
diff changeset
   519
    val _ = message "Proving freeness of constructors ...";
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   520
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   521
    (* prove theorem  Rep_i (Constr_j ...) = Inj_j ...  *)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   522
    
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   523
    fun prove_constr_rep_thm eqn =
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   524
      let
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   525
        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
   526
        val rewrites = o_def :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms)
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   527
      in prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) eqn) (fn _ =>
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   528
        [resolve_tac inj_thms 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   529
         rewrite_goals_tac rewrites,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   530
         rtac refl 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   531
         resolve_tac rep_intrs 2,
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   532
         REPEAT (resolve_tac (FunsI :: iso_elem_thms) 1)])
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   533
      end;
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
    (* 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
   537
    (* of constructors.                                             *)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   538
    (*--------------------------------------------------------------*)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   539
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   540
    val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   541
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   542
    val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   543
      dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   544
        (constr_rep_thms ~~ dist_lemmas);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   545
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   546
    fun prove_distinct_thms (_, []) = []
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   547
      | prove_distinct_thms (dist_rewrites', t::_::ts) =
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   548
          let
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   549
            val dist_thm = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) t) (fn _ =>
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   550
              [simp_tac (HOL_ss addsimps dist_rewrites') 1])
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   551
          in dist_thm::(standard (dist_thm RS not_sym))::
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   552
            (prove_distinct_thms (dist_rewrites', ts))
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   553
          end;
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   554
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   555
    val distinct_thms = map prove_distinct_thms (dist_rewrites ~~
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   556
      DatatypeProp.make_distincts new_type_names descr sorts thy5);
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   557
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   558
    val simproc_dists = map (fn ((((_, (_, _, constrs)), rep_thms), congr), dists) =>
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   559
      if length constrs < !DatatypeProp.dtK then FewConstrs dists
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   560
      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
   561
        constr_rep_thms ~~ rep_congs ~~ distinct_thms);
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   562
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   563
    (* prove injectivity of constructors *)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   564
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   565
    fun prove_constr_inj_thm rep_thms t =
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   566
      let val inj_thms = Scons_inject::sum_case_inject::(map make_elim
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   567
        ((map (fn r => r RS injD) iso_inj_thms) @
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   568
          [In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject, Lim_inject]))
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   569
      in prove_goalw_cterm [] (cterm_of (Theory.sign_of thy5) t) (fn _ =>
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   570
        [rtac iffI 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   571
         REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   572
         dresolve_tac rep_congs 1, dtac box_equals 1,
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   573
         REPEAT (resolve_tac rep_thms 1), rewrite_goals_tac [o_def],
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   574
         REPEAT (eresolve_tac inj_thms 1),
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   575
         REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [rtac ext 1, dtac fun_cong 1,
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   576
                  eresolve_tac inj_thms 1, atac 1]))])
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   577
      end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   578
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   579
    val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   580
      ((DatatypeProp.make_injs descr sorts) ~~ constr_rep_thms);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   581
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   582
    val thy6 = thy5 |> parent_path flat_names |>
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   583
      store_thmss "inject" new_type_names constr_inject |>
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
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) @
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   591
      (map (fn r => r RS inv_f_f RS subst) (drop (length newTs, iso_inj_thms)));
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   592
    val Rep_inverse_thms' = map (fn r => r RS inv_f_f)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   593
      (drop (length newTs, iso_inj_thms));
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   594
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   595
    fun mk_indrule_lemma ((prems, concls), ((i, _), T)) =
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   596
      let
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   597
        val Rep_t = Const (nth_elem (i, all_rep_names), T --> Univ_elT) $
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   598
          mk_Free "x" T i;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   599
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   600
        val Abs_t = if i < length newTs then
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   601
            Const (Sign.intern_const (Theory.sign_of thy6)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   602
              ("Abs_" ^ (nth_elem (i, new_type_names))), Univ_elT --> T)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   603
          else Const (inv_name, [T --> Univ_elT, Univ_elT] ---> T) $
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   604
            Const (nth_elem (i, all_rep_names), T --> Univ_elT)
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   605
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   606
      in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   607
            Const (nth_elem (i, rep_set_names), UnivT)) $
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   608
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   609
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   610
      end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   611
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   612
    val (indrule_lemma_prems, indrule_lemma_concls) =
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   613
      foldl mk_indrule_lemma (([], []), (descr' ~~ recTs));
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   614
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6171
diff changeset
   615
    val cert = cterm_of (Theory.sign_of thy6);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   616
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   617
    val indrule_lemma = prove_goalw_cterm [] (cert
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   618
      (Logic.mk_implies
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   619
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   620
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls)))) (fn prems =>
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   621
           [cut_facts_tac prems 1, REPEAT (etac conjE 1),
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   622
            REPEAT (EVERY
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   623
              [TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   624
               etac mp 1, resolve_tac iso_elem_thms 1])]);
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   625
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   626
    val Ps = map head_of (dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   627
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   628
      map (Free o apfst fst o dest_Var) Ps;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   629
    val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   630
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   631
    val dt_induct = prove_goalw_cterm [] (cert
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   632
      (DatatypeProp.make_ind descr sorts)) (fn prems =>
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   633
        [rtac indrule_lemma' 1, indtac rep_induct 1,
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   634
         EVERY (map (fn (prem, r) => (EVERY
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   635
           [REPEAT (eresolve_tac (Funs_IntE::Abs_inverse_thms) 1),
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   636
            simp_tac (HOL_basic_ss addsimps ((symmetric r)::Rep_inverse_thms')) 1,
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   637
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE (EVERY [rewrite_goals_tac [o_def],
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   638
              rtac allI 1, dtac FunsD 1, etac CollectD 1]))]))
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   639
                (prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]);
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   640
5661
6ecb6ea25f19 - Changed structure of name spaces
berghofe
parents: 5553
diff changeset
   641
    val thy7 = thy6 |>
6ecb6ea25f19 - Changed structure of name spaces
berghofe
parents: 5553
diff changeset
   642
      Theory.add_path big_name |>
6092
d9db67970c73 eliminated tthm type and Attribute structure;
wenzelm
parents: 5696
diff changeset
   643
      PureThy.add_thms [(("induct", dt_induct), [])] |>
5661
6ecb6ea25f19 - Changed structure of name spaces
berghofe
parents: 5553
diff changeset
   644
      Theory.parent_path;
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   645
7015
85be09eb136c - Datatype package now also supports arbitrarily branching datatypes
berghofe
parents: 6522
diff changeset
   646
  in (thy7, constr_inject, distinct_thms, dist_rewrites, simproc_dists, dt_induct)
5177
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   647
  end;
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   648
0d3a168e4d44 New datatype definition package
berghofe
parents:
diff changeset
   649
end;