src/HOL/Tools/inductive_package.ML
author berghofe
Fri, 03 Jul 1998 11:02:01 +0200
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Removed disjE from list of rules used to simplify elimination rules because it made mk_cases fail if elimination rules contained disjunctive side conditions.
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(*  Title:      HOL/Tools/inductive_package.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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                Stefan Berghofer,   TU Muenchen
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    Copyright   1994  University of Cambridge
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                1998  TU Muenchen     
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(Co)Inductive Definition module for HOL
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Features:
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* least or greatest fixedpoints
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* user-specified product and sum constructions
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* mutually recursive definitions
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* definitions involving arbitrary monotone operators
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* automatically proves introduction and elimination rules
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The recursive sets must *already* be declared as constants in parent theory!
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  Introduction rules have the form
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  [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk |]
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  where M is some monotone operator (usually the identity)
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  P(x) is any side condition on the free variables
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  ti, t are any terms
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  Sj, Sk are two of the sets being defined in mutual recursion
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Sums are used only for mutual recursion;
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Products are used only to derive "streamlined" induction rules for relations
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*)
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signature INDUCTIVE_PACKAGE =
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sig
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  val add_inductive_i : bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
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    term list -> thm list -> thm list -> theory -> theory *
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      {defs:thm list, elims:thm list, raw_induct:thm, induct:thm,
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       intrs:thm list,
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       mk_cases:thm list -> string -> thm, mono:thm,
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       unfold:thm}
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  val add_inductive : bool -> bool -> string list -> string list
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    -> thm list -> thm list -> theory -> theory *
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      {defs:thm list, elims:thm list, raw_induct:thm, induct:thm,
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       intrs:thm list,
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       mk_cases:thm list -> string -> thm, mono:thm,
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       unfold:thm}
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end;
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structure InductivePackage : INDUCTIVE_PACKAGE =
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struct
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(*For proving monotonicity of recursion operator*)
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val basic_monos = [subset_refl, imp_refl, disj_mono, conj_mono, 
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                   ex_mono, Collect_mono, in_mono, vimage_mono];
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val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (concl_of vimageD);
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(*Delete needless equality assumptions*)
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val refl_thin = prove_goal HOL.thy "!!P. [| a=a;  P |] ==> P"
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     (fn _ => [assume_tac 1]);
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(*For simplifying the elimination rule*)
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val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
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val vimage_name = Sign.intern_const (sign_of Vimage.thy) "op -``";
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val mono_name = Sign.intern_const (sign_of Ord.thy) "mono";
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(* make injections needed in mutually recursive definitions *)
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fun mk_inj cs sumT c 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 cs) (1 + find_index_eq c cs)
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  end;
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(* make "vimage" terms for selecting out components of mutually rec.def. *)
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fun mk_vimage cs sumT t c = if length cs < 2 then t else
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  let
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    val cT = HOLogic.dest_setT (fastype_of c);
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    val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
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  in
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    Const (vimage_name, vimageT) $
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      Abs ("y", cT, mk_inj cs sumT c (Bound 0)) $ t
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  end;
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(**************************** well-formedness checks **************************)
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fun err_in_rule sign t msg = error ("Ill-formed introduction rule\n" ^
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  (Sign.string_of_term sign t) ^ "\n" ^ msg);
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fun err_in_prem sign t p msg = error ("Ill-formed premise\n" ^
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  (Sign.string_of_term sign p) ^ "\nin introduction rule\n" ^
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  (Sign.string_of_term sign t) ^ "\n" ^ msg);
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val msg1 = "Conclusion of introduction rule must have form\
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          \ ' t : S_i '";
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val msg2 = "Premises mentioning recursive sets must have form\
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          \ ' t : M S_i '";
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val msg3 = "Recursion term on left of member symbol";
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fun check_rule sign cs r =
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  let
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    fun check_prem prem = if exists (Logic.occs o (rpair prem)) cs then
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         (case prem of
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           (Const ("op :", _) $ t $ u) =>
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             if exists (Logic.occs o (rpair t)) cs then
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               err_in_prem sign r prem msg3 else ()
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         | _ => err_in_prem sign r prem msg2)
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        else ()
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  in (case (HOLogic.dest_Trueprop o Logic.strip_imp_concl) r of
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        (Const ("op :", _) $ _ $ u) =>
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          if u mem cs then map (check_prem o HOLogic.dest_Trueprop)
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            (Logic.strip_imp_prems r)
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          else err_in_rule sign r msg1
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      | _ => err_in_rule sign r msg1)
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  end;
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fun try' f msg sign t = (f t) handle _ => error (msg ^ Sign.string_of_term sign t);
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(*********************** properties of (co)inductive sets *********************)
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(***************************** elimination rules ******************************)
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fun mk_elims cs cTs params intr_ts =
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  let
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    val used = foldr add_term_names (intr_ts, []);
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    val [aname, pname] = variantlist (["a", "P"], used);
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    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
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    fun dest_intr r =
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      let val Const ("op :", _) $ t $ u =
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        HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
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      in (u, t, Logic.strip_imp_prems r) end;
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    val intrs = map dest_intr intr_ts;
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    fun mk_elim (c, T) =
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      let
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        val a = Free (aname, T);
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        fun mk_elim_prem (_, t, ts) =
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          list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
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            Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
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      in
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        Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
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          map mk_elim_prem (filter (equal c o #1) intrs), P)
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      end
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  in
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    map mk_elim (cs ~~ cTs)
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  end;
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(***************** premises and conclusions of induction rules ****************)
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fun mk_indrule cs cTs params intr_ts =
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  let
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    val used = foldr add_term_names (intr_ts, []);
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    (* predicates for induction rule *)
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    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
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      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
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        map (fn T => T --> HOLogic.boolT) cTs);
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    (* transform an introduction rule into a premise for induction rule *)
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    fun mk_ind_prem r =
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      let
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        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
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        fun subst (prem as (Const ("op :", T) $ t $ u), prems) =
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              let val n = find_index_eq u cs in
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                if n >= 0 then prem :: (nth_elem (n, preds)) $ t :: prems else
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                  (subst_free (map (fn (c, P) => (c, HOLogic.mk_binop "op Int"
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                    (c, HOLogic.Collect_const (HOLogic.dest_setT
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                      (fastype_of c)) $ P))) (cs ~~ preds)) prem)::prems
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              end
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          | subst (prem, prems) = prem::prems;
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        val Const ("op :", _) $ t $ u =
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          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
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      in list_all_free (frees,
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           Logic.list_implies (map HOLogic.mk_Trueprop (foldr subst
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             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
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               HOLogic.mk_Trueprop (nth_elem (find_index_eq u cs, preds) $ t)))
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      end;
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    val ind_prems = map mk_ind_prem intr_ts;
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    (* make conclusions for induction rules *)
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    fun mk_ind_concl ((c, P), (ts, x)) =
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      let val T = HOLogic.dest_setT (fastype_of c);
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          val Ts = HOLogic.prodT_factors T;
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          val (frees, x') = foldr (fn (T', (fs, s)) =>
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            ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
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          val tuple = HOLogic.mk_tuple T frees;
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      in ((HOLogic.mk_binop "op -->"
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        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
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      end;
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    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 (app HOLogic.conj)
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        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
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  in (preds, ind_prems, mutual_ind_concl)
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  end;
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(********************** proofs for (co)inductive sets *************************)
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(**************************** prove monotonicity ******************************)
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fun prove_mono setT fp_fun monos thy =
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  let
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    val _ = writeln "  Proving monotonicity...";
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    val mono = prove_goalw_cterm [] (cterm_of (sign_of thy) (HOLogic.mk_Trueprop
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      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
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        (fn _ => [rtac monoI 1, REPEAT (ares_tac (basic_monos @ monos) 1)])
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  in mono end;
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(************************* prove introduction rules ***************************)
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fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
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  let
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    val _ = writeln "  Proving the introduction rules...";
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    val unfold = standard (mono RS (fp_def RS
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      (if coind then def_gfp_Tarski else def_lfp_Tarski)));
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    fun select_disj 1 1 = []
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      | select_disj _ 1 = [rtac disjI1]
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      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
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    val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
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      (cterm_of (sign_of thy) intr) (fn prems =>
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       [(*insert prems and underlying sets*)
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       cut_facts_tac prems 1,
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       stac unfold 1,
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       REPEAT (resolve_tac [vimageI2, CollectI] 1),
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       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
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       EVERY1 (select_disj (length intr_ts) i),
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       (*Not ares_tac, since refl must be tried before any equality assumptions;
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         backtracking may occur if the premises have extra variables!*)
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       DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
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       (*Now solve the equations like Inl 0 = Inl ?b2*)
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       rewrite_goals_tac con_defs,
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       REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
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  in (intrs, unfold) end;
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(*************************** prove elimination rules **************************)
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fun prove_elims cs cTs params intr_ts unfold rec_sets_defs thy =
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  let
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    val _ = writeln "  Proving the elimination rules...";
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    val rules1 = [CollectE, disjE, make_elim vimageD];
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    val rules2 = [exE, conjE, Inl_neq_Inr, Inr_neq_Inl] @
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      map make_elim [Inl_inject, Inr_inject];
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    val elims = map (fn t => prove_goalw_cterm rec_sets_defs
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      (cterm_of (sign_of thy) t) (fn prems =>
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        [cut_facts_tac [hd prems] 1,
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         dtac (unfold RS subst) 1,
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         REPEAT (FIRSTGOAL (eresolve_tac rules1)),
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         REPEAT (FIRSTGOAL (eresolve_tac rules2)),
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         EVERY (map (fn prem =>
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           DEPTH_SOLVE_1 (ares_tac (prem::[conjI]) 1)) (tl prems))]))
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      (mk_elims cs cTs params intr_ts)
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  in elims end;
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(** derivation of simplified elimination rules **)
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(*Applies freeness of the given constructors, which *must* be unfolded by
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  the given defs.  Cannot simply use the local con_defs because con_defs=[] 
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  for inference systems.
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 *)
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fun con_elim_tac simps =
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  let val elim_tac = REPEAT o (eresolve_tac elim_rls)
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  in ALLGOALS(EVERY'[elim_tac,
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                 asm_full_simp_tac (simpset_of Nat.thy addsimps simps),
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                 elim_tac,
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                 REPEAT o bound_hyp_subst_tac])
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     THEN prune_params_tac
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  end;
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(*String s should have the form t:Si where Si is an inductive set*)
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fun mk_cases elims simps s =
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  let val prem = assume (read_cterm (sign_of_thm (hd elims)) (s, propT));
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      val elims' = map (try (fn r =>
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        rule_by_tactic (con_elim_tac simps) (prem RS r) |> standard)) elims
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  in case find_first is_some elims' of
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       Some (Some r) => r
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     | None => error ("mk_cases: string '" ^ s ^ "' not of form 't : S_i'")
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  end;
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(**************************** prove induction rule ****************************)
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fun prove_indrule cs cTs sumT rec_const params intr_ts mono
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    fp_def rec_sets_defs thy =
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  let
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    val _ = writeln "  Proving the induction rule...";
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    val sign = sign_of thy;
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    val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
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    (* make predicate for instantiation of abstract induction rule *)
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    fun mk_ind_pred _ [P] = P
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      | mk_ind_pred T Ps =
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         let val n = (length Ps) div 2;
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             val Type (_, [T1, T2]) = T
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         in Const ("sum_case",
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           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
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             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
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         end;
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    val ind_pred = mk_ind_pred sumT preds;
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    val ind_concl = HOLogic.mk_Trueprop
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      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
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        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
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    (* simplification rules for vimage and Collect *)
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    val vimage_simps = if length cs < 2 then [] else
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      map (fn c => prove_goalw_cterm [] (cterm_of sign
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        (HOLogic.mk_Trueprop (HOLogic.mk_eq
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          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
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           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
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             nth_elem (find_index_eq c cs, preds)))))
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        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac
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           (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
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          rtac refl 1])) cs;
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    val induct = prove_goalw_cterm [] (cterm_of sign
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      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
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        [rtac (impI RS allI) 1,
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         DETERM (etac (mono RS (fp_def RS def_induct)) 1),
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         rewrite_goals_tac (map mk_meta_eq (vimage_Int::vimage_simps)),
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         fold_goals_tac rec_sets_defs,
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         (*This CollectE and disjE separates out the introduction rules*)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   354
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   355
         (*Now break down the individual cases.  No disjE here in case
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   356
           some premise involves disjunction.*)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   357
         REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE] 
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   358
                     ORELSE' hyp_subst_tac)),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   359
         rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   360
         EVERY (map (fn prem =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   361
           DEPTH_SOLVE_1 (ares_tac (prem::[conjI, refl]) 1)) prems)]);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   362
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   363
    val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   364
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   365
        [cut_facts_tac prems 1,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   366
         REPEAT (EVERY
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   367
           [REPEAT (resolve_tac [conjI, impI] 1),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   368
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   369
            rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   370
            atac 1])])
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   371
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   372
  in standard (split_rule (induct RS lemma))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   373
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   374
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   375
(*************** definitional introduction of (co)inductive sets **************)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   376
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   377
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   378
    intr_ts monos con_defs thy params paramTs cTs cnames =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   379
  let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   380
    val _ = if verbose then writeln ("Proofs for " ^
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   381
      (if coind then "co" else "") ^ "inductive set(s) " ^ commas cnames) else ();
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   382
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   383
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   384
    val setT = HOLogic.mk_setT sumT;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   385
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   386
    val fp_name = if coind then Sign.intern_const (sign_of Gfp.thy) "gfp"
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   387
      else Sign.intern_const (sign_of Lfp.thy) "lfp";
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   388
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   389
    (* transform an introduction rule into a conjunction  *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   390
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   391
    (* is transformed into                                *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   392
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   393
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   394
    fun transform_rule r =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   395
      let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   396
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   397
        val idx = length frees;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   398
        val subst = subst_free (cs ~~ (map (mk_vimage cs sumT (Bound (idx + 1))) cs));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   399
        val Const ("op :", _) $ t $ u =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   400
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   401
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   402
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   403
        (frees, foldr1 (app HOLogic.conj)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   404
          (((HOLogic.eq_const sumT) $ Bound idx $ (mk_inj cs sumT u t))::
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   405
            (map (subst o HOLogic.dest_Trueprop)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   406
              (Logic.strip_imp_prems r))))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   407
      end
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   408
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   409
    (* make a disjunction of all introduction rules *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   410
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   411
    val fp_fun = Abs ("S", setT, (HOLogic.Collect_const sumT) $
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   412
      Abs ("x", sumT, foldr1 (app HOLogic.disj) (map transform_rule intr_ts)));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   413
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   414
    (* add definiton of recursive sets to theory *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   415
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   416
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   417
    val full_rec_name = Sign.full_name (sign_of thy) rec_name;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   418
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   419
    val rec_const = list_comb
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   420
      (Const (full_rec_name, paramTs ---> setT), params);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   421
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   422
    val fp_def_term = Logic.mk_equals (rec_const,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   423
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   424
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   425
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   426
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   427
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   428
    val thy' = thy |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   429
      (if declare_consts then
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   430
        Theory.add_consts_i (map (fn (c, n) =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   431
          (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   432
       else I) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   433
      (if length cs < 2 then I else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   434
       Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)]) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   435
      Theory.add_path rec_name |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   436
      PureThy.add_defss_i [(("defs", def_terms), [])];
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   437
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   438
    (* get definitions from theory *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   439
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   440
    val fp_def::rec_sets_defs = get_thms thy' "defs";
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   441
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   442
    (* prove and store theorems *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   443
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   444
    val mono = prove_mono setT fp_fun monos thy';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   445
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   446
      rec_sets_defs thy';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   447
    val elims = if no_elim then [] else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   448
      prove_elims cs cTs params intr_ts unfold rec_sets_defs thy';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   449
    val raw_induct = if no_ind then TrueI else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   450
      if coind then standard (rule_by_tactic
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   451
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   452
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   453
      else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   454
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   455
          rec_sets_defs thy';
5108
4074c7d86d44 Fixed bug (improper handling of flag no_ind).
berghofe
parents: 5094
diff changeset
   456
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   457
      else standard (raw_induct RSN (2, rev_mp));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   458
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   459
    val thy'' = thy' |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   460
      PureThy.add_tthmss [(("intrs", map Attribute.tthm_of intrs), [])] |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   461
      (if no_elim then I else PureThy.add_tthmss
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   462
        [(("elims", map Attribute.tthm_of elims), [])]) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   463
      (if no_ind then I else PureThy.add_tthms
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   464
        [(((if coind then "co" else "") ^ "induct",
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   465
          Attribute.tthm_of induct), [])]) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   466
      Theory.parent_path;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   467
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   468
  in (thy'',
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   469
    {defs = fp_def::rec_sets_defs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   470
     mono = mono,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   471
     unfold = unfold,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   472
     intrs = intrs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   473
     elims = elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   474
     mk_cases = mk_cases elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   475
     raw_induct = raw_induct,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   476
     induct = induct})
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   477
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   478
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   479
(***************** axiomatic introduction of (co)inductive sets ***************)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   480
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   481
fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   482
    intr_ts monos con_defs thy params paramTs cTs cnames =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   483
  let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   484
    val _ = if verbose then writeln ("Adding axioms for " ^
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   485
      (if coind then "co" else "") ^ "inductive set(s) " ^ commas cnames) else ();
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   486
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   487
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   488
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   489
    val elim_ts = mk_elims cs cTs params intr_ts;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   490
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   491
    val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   492
    val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   493
    
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   494
    val thy' = thy |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   495
      (if declare_consts then
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   496
        Theory.add_consts_i (map (fn (c, n) =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   497
          (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   498
       else I) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   499
      Theory.add_path rec_name |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   500
      PureThy.add_axiomss_i [(("intrs", intr_ts), []), (("elims", elim_ts), [])] |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   501
      (if coind then I
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   502
       else PureThy.add_axioms_i [(("internal_induct", ind_t), [])]);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   503
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   504
    val intrs = get_thms thy' "intrs";
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   505
    val elims = get_thms thy' "elims";
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   506
    val raw_induct = if coind then TrueI else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   507
      standard (split_rule (get_thm thy' "internal_induct"));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   508
    val induct = if coind orelse length cs > 1 then raw_induct
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   509
      else standard (raw_induct RSN (2, rev_mp));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   510
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   511
    val thy'' = thy' |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   512
      (if coind then I
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   513
       else PureThy.add_tthms [(("induct", Attribute.tthm_of induct), [])]) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   514
      Theory.parent_path
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   515
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   516
  in (thy'',
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   517
    {defs = [],
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   518
     mono = TrueI,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   519
     unfold = TrueI,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   520
     intrs = intrs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   521
     elims = elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   522
     mk_cases = mk_cases elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   523
     raw_induct = raw_induct,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   524
     induct = induct})
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   525
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   526
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   527
(********************** introduction of (co)inductive sets ********************)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   528
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   529
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   530
    intr_ts monos con_defs thy =
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   531
  let
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   532
    val _ = Theory.requires thy "Inductive"
ddcc3c114a0e New inductive definition package
berghofe
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   533
      ((if coind then "co" else "") ^ "inductive definitions");
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   534
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   535
    val sign = sign_of thy;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   536
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   537
    (*parameters should agree for all mutually recursive components*)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   538
    val (_, params) = strip_comb (hd cs);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   539
    val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   540
      \ component is not a free variable: " sign) params;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   541
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   542
    val cTs = map (try' (HOLogic.dest_setT o fastype_of)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   543
      "Recursive component not of type set: " sign) cs;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   544
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   545
    val cnames = map (try' (Sign.base_name o fst o dest_Const o head_of)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   546
      "Recursive set not previously declared as constant: " sign) cs;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   547
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   548
    val _ = assert_all Syntax.is_identifier cnames
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   549
       (fn a => "Base name of recursive set not an identifier: " ^ a);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   550
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   551
    val _ = map (check_rule sign cs) intr_ts;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   552
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   553
  in
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   554
    (if !quick_and_dirty then add_ind_axm else add_ind_def)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   555
      verbose declare_consts alt_name coind no_elim no_ind cs intr_ts monos
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   556
        con_defs thy params paramTs cTs cnames
ddcc3c114a0e New inductive definition package
berghofe
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   557
  end;
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   558
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   559
(***************************** external interface *****************************)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   560
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   561
fun add_inductive verbose coind c_strings intr_strings monos con_defs thy =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   562
  let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   563
    val sign = sign_of thy;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   564
    val cs = map (readtm (sign_of thy) HOLogic.termTVar) c_strings;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   565
    val intr_ts = map (readtm (sign_of thy) propT) intr_strings;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   566
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   567
    (* the following code ensures that each recursive set *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   568
    (* always has the same type in all introduction rules *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   569
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   570
    val {tsig, ...} = Sign.rep_sg sign;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   571
    val add_term_consts_2 =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   572
      foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   573
    fun varify (t, (i, ts)) =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   574
      let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   575
      in (maxidx_of_term t', t'::ts) end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   576
    val (i, cs') = foldr varify (cs, (~1, []));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   577
    val (i', intr_ts') = foldr varify (intr_ts, (i, []));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   578
    val rec_consts = foldl add_term_consts_2 ([], cs');
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   579
    val intr_consts = foldl add_term_consts_2 ([], intr_ts');
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   580
    fun unify (env, (cname, cT)) =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   581
      let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   582
      in (foldl (fn ((env', j'), Tp) => Type.unify tsig j' env' Tp)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   583
        (env, (replicate (length consts) cT) ~~ consts)) handle _ =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   584
          error ("Occurrences of constant '" ^ cname ^
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   585
            "' have incompatible types")
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   586
      end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   587
    val (env, _) = foldl unify (([], i'), rec_consts);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   588
    fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars env T
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   589
      in if T = T' then T else typ_subst_TVars_2 env T' end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   590
    val subst = fst o Type.freeze_thaw o
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   591
      (map_term_types (typ_subst_TVars_2 env));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   592
    val cs'' = map subst cs';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   593
    val intr_ts'' = map subst intr_ts';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   594
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   595
  in add_inductive_i verbose false "" coind false false cs'' intr_ts''
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   596
    monos con_defs thy
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   597
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   598
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   599
end;