src/HOL/Tools/inductive_package.ML
author wenzelm
Fri Dec 22 18:24:39 2000 +0100 (2000-12-22)
changeset 10729 1b3350c4ee92
parent 10569 e8346dad78e1
child 10735 dfaf75f0076f
permissions -rw-r--r--
handle proper rules;
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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 the
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current 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.  Products are used only to
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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 quiet_mode: bool ref
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  val unify_consts: Sign.sg -> term list -> term list -> term list * term list
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  val get_inductive: theory -> string -> ({names: string list, coind: bool} *
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    {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
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     intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}) option
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  val print_inductives: theory -> unit
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  val mono_add_global: theory attribute
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  val mono_del_global: theory attribute
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  val get_monos: theory -> thm list
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  val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
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    theory attribute list -> ((bstring * term) * theory attribute list) 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, mk_cases: string -> thm, mono: thm, unfold: thm}
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  val add_inductive: bool -> bool -> string list -> Args.src list ->
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    ((bstring * string) * Args.src list) list -> (xstring * Args.src list) list ->
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      (xstring * Args.src list) 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, mk_cases: string -> thm, mono: thm, unfold: thm}
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  val inductive_cases: ((bstring * Args.src list) * string list) * Comment.text
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    -> theory -> theory
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  val inductive_cases_i: ((bstring * theory attribute list) * term list) * Comment.text
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    -> theory -> theory
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  val setup: (theory -> theory) list
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end;
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structure InductivePackage: INDUCTIVE_PACKAGE =
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struct
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(** theory context references **)
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val mk_inductive_conj = HOLogic.mk_binop "Inductive.conj";
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val inductive_conj_def = thm "conj_def";
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val inductive_conj = thms "inductive_conj";
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val inductive_atomize = thms "inductive_atomize";
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val inductive_rulify1 = thms "inductive_rulify1";
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val inductive_rulify2 = thms "inductive_rulify2";
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(*** theory data ***)
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(* data kind 'HOL/inductive' *)
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type inductive_info =
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  {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
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    induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
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structure InductiveArgs =
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struct
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  val name = "HOL/inductive";
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  type T = inductive_info Symtab.table * thm list;
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  val empty = (Symtab.empty, []);
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  val copy = I;
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  val prep_ext = I;
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  fun merge ((tab1, monos1), (tab2, monos2)) = (Symtab.merge (K true) (tab1, tab2),
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    Library.generic_merge Thm.eq_thm I I monos1 monos2);
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  fun print sg (tab, monos) =
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    [Pretty.strs ("(co)inductives:" :: map #1 (Sign.cond_extern_table sg Sign.constK tab)),
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     Pretty.big_list "monotonicity rules:" (map (Display.pretty_thm_sg sg) monos)]
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    |> Pretty.chunks |> Pretty.writeln;
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end;
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structure InductiveData = TheoryDataFun(InductiveArgs);
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val print_inductives = InductiveData.print;
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(* get and put data *)
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fun get_inductive thy name = Symtab.lookup (fst (InductiveData.get thy), name);
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fun the_inductive thy name =
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  (case get_inductive thy name of
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    None => error ("Unknown (co)inductive set " ^ quote name)
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  | Some info => info);
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fun put_inductives names info thy =
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  let
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    fun upd ((tab, monos), name) = (Symtab.update_new ((name, info), tab), monos);
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    val tab_monos = foldl upd (InductiveData.get thy, names)
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      handle Symtab.DUP name => error ("Duplicate definition of (co)inductive set " ^ quote name);
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  in InductiveData.put tab_monos thy end;
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(** monotonicity rules **)
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val get_monos = #2 o InductiveData.get;
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fun map_monos f = InductiveData.map (Library.apsnd f);
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fun mk_mono thm =
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  let
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    fun eq2mono thm' = [standard (thm' RS (thm' RS eq_to_mono))] @
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      (case concl_of thm of
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          (_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
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        | _ => [standard (thm' RS (thm' RS eq_to_mono2))]);
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    val concl = concl_of thm
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  in
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    if Logic.is_equals concl then
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      eq2mono (thm RS meta_eq_to_obj_eq)
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    else if can (HOLogic.dest_eq o HOLogic.dest_Trueprop) concl then
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      eq2mono thm
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    else [thm]
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  end;
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(* attributes *)
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fun mono_add_global (thy, thm) = (map_monos (Drule.add_rules (mk_mono thm)) thy, thm);
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fun mono_del_global (thy, thm) = (map_monos (Drule.del_rules (mk_mono thm)) thy, thm);
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val mono_attr =
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 (Attrib.add_del_args mono_add_global mono_del_global,
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  Attrib.add_del_args Attrib.undef_local_attribute Attrib.undef_local_attribute);
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(** utilities **)
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(* messages *)
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val quiet_mode = ref false;
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fun message s = if !quiet_mode then () else writeln s;
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fun coind_prefix true = "co"
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  | coind_prefix false = "";
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(* the following code ensures that each recursive set *)
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(* always has the same type in all introduction rules *)
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fun unify_consts sign cs intr_ts =
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  (let
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    val {tsig, ...} = Sign.rep_sg sign;
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    val add_term_consts_2 =
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      foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
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    fun varify (t, (i, ts)) =
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      let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
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      in (maxidx_of_term t', t'::ts) end;
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    val (i, cs') = foldr varify (cs, (~1, []));
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    val (i', intr_ts') = foldr varify (intr_ts, (i, []));
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    val rec_consts = foldl add_term_consts_2 ([], cs');
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    val intr_consts = foldl add_term_consts_2 ([], intr_ts');
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    fun unify (env, (cname, cT)) =
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      let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
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      in foldl (fn ((env', j'), Tp) => (Type.unify tsig j' env' Tp))
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          (env, (replicate (length consts) cT) ~~ consts)
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      end;
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    val (env, _) = foldl unify ((Vartab.empty, i'), rec_consts);
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    fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars_Vartab env T
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      in if T = T' then T else typ_subst_TVars_2 env T' end;
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    val subst = fst o Type.freeze_thaw o
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      (map_term_types (typ_subst_TVars_2 env))
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  in (map subst cs', map subst intr_ts')
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  end) handle Type.TUNIFY =>
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    (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
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(* misc *)
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val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (concl_of vimageD);
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val vimage_name = Sign.intern_const (Theory.sign_of Inverse_Image.thy) "vimage";
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val mono_name = Sign.intern_const (Theory.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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(** process rules **)
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local
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fun err_in_rule sg name t msg =
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  error (cat_lines ["Ill-formed introduction rule " ^ quote name, Sign.string_of_term sg t, msg]);
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fun err_in_prem sg name t p msg =
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  error (cat_lines ["Ill-formed premise", Sign.string_of_term sg p,
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    "in introduction rule " ^ quote name, Sign.string_of_term sg t, msg]);
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val bad_concl = "Conclusion of introduction rule must have form \"t : S_i\"";
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val atomize_cterm = InductMethod.rewrite_cterm inductive_atomize;
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fun full_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews);
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in
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fun check_rule sg cs ((name, rule), att) =
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  let
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    val concl = Logic.strip_imp_concl rule;
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    val prems = Logic.strip_imp_prems rule;
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    val aprems = prems |> map (Thm.term_of o atomize_cterm o Thm.cterm_of sg);
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    val arule = Logic.list_implies (aprems, concl);
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    fun check_prem (prem, aprem) =
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      if can HOLogic.dest_Trueprop aprem then ()
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      else err_in_prem sg name rule prem "Non-atomic premise";
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  in
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    (case HOLogic.dest_Trueprop concl of
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      (Const ("op :", _) $ t $ u) =>
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        if u mem cs then
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          if exists (Logic.occs o rpair t) cs then
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            err_in_rule sg name rule "Recursion term on left of member symbol"
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          else seq check_prem (prems ~~ aprems)
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        else err_in_rule sg name rule bad_concl
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      | _ => err_in_rule sg name rule bad_concl);
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    ((name, arule), att)
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  end;
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val rulify =
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  standard o full_simplify [Drule.norm_hhf_eq] o
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  full_simplify inductive_rulify2 o full_simplify inductive_rulify1 o
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  full_simplify inductive_conj;
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fun rulified x = Drule.rule_attribute (K rulify) x;
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end;
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fun try' f msg sign t = (case (try f t) of
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      Some x => x
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    | None => 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 intr_names =
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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 ~~ intr_names;
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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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        val c_intrs = (filter (equal c o #1 o #1) intrs);
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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 (map #1 c_intrs), P), map #2 c_intrs)
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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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   331
    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
berghofe@5094
   332
      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
berghofe@5094
   333
        map (fn T => T --> HOLogic.boolT) cTs);
berghofe@5094
   334
berghofe@5094
   335
    (* transform an introduction rule into a premise for induction rule *)
berghofe@5094
   336
berghofe@5094
   337
    fun mk_ind_prem r =
berghofe@5094
   338
      let
berghofe@5094
   339
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5094
   340
berghofe@7710
   341
        val pred_of = curry (Library.gen_assoc (op aconv)) (cs ~~ preds);
berghofe@5094
   342
berghofe@7710
   343
        fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
berghofe@7710
   344
              (case pred_of u of
berghofe@7710
   345
                  None => (m $ fst (subst t) $ fst (subst u), None)
wenzelm@10729
   346
                | Some P => (mk_inductive_conj (s, P $ t), Some (s, P $ t)))
berghofe@7710
   347
          | subst s =
berghofe@7710
   348
              (case pred_of s of
berghofe@7710
   349
                  Some P => (HOLogic.mk_binop "op Int"
berghofe@7710
   350
                    (s, HOLogic.Collect_const (HOLogic.dest_setT
berghofe@7710
   351
                      (fastype_of s)) $ P), None)
berghofe@7710
   352
                | None => (case s of
berghofe@7710
   353
                     (t $ u) => (fst (subst t) $ fst (subst u), None)
berghofe@7710
   354
                   | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), None)
berghofe@7710
   355
                   | _ => (s, None)));
berghofe@7710
   356
berghofe@7710
   357
        fun mk_prem (s, prems) = (case subst s of
berghofe@7710
   358
              (_, Some (t, u)) => t :: u :: prems
berghofe@7710
   359
            | (t, _) => t :: prems);
wenzelm@9598
   360
berghofe@5094
   361
        val Const ("op :", _) $ t $ u =
berghofe@5094
   362
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   363
berghofe@5094
   364
      in list_all_free (frees,
berghofe@7710
   365
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
berghofe@5094
   366
             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
berghofe@7710
   367
               HOLogic.mk_Trueprop (the (pred_of u) $ t)))
berghofe@5094
   368
      end;
berghofe@5094
   369
berghofe@5094
   370
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@5094
   371
berghofe@5094
   372
    (* make conclusions for induction rules *)
berghofe@5094
   373
berghofe@5094
   374
    fun mk_ind_concl ((c, P), (ts, x)) =
berghofe@5094
   375
      let val T = HOLogic.dest_setT (fastype_of c);
berghofe@5094
   376
          val Ts = HOLogic.prodT_factors T;
berghofe@5094
   377
          val (frees, x') = foldr (fn (T', (fs, s)) =>
berghofe@5094
   378
            ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
berghofe@5094
   379
          val tuple = HOLogic.mk_tuple T frees;
berghofe@5094
   380
      in ((HOLogic.mk_binop "op -->"
berghofe@5094
   381
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
berghofe@5094
   382
      end;
berghofe@5094
   383
berghofe@7710
   384
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@5094
   385
        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
berghofe@5094
   386
berghofe@5094
   387
  in (preds, ind_prems, mutual_ind_concl)
berghofe@5094
   388
  end;
berghofe@5094
   389
wenzelm@6424
   390
berghofe@5094
   391
wenzelm@8316
   392
(** prepare cases and induct rules **)
wenzelm@8316
   393
wenzelm@8316
   394
(*
wenzelm@8316
   395
  transform mutual rule:
wenzelm@8316
   396
    HH ==> (x1:A1 --> P1 x1) & ... & (xn:An --> Pn xn)
wenzelm@8316
   397
  into i-th projection:
wenzelm@8316
   398
    xi:Ai ==> HH ==> Pi xi
wenzelm@8316
   399
*)
wenzelm@8316
   400
wenzelm@8316
   401
fun project_rules [name] rule = [(name, rule)]
wenzelm@8316
   402
  | project_rules names mutual_rule =
wenzelm@8316
   403
      let
wenzelm@8316
   404
        val n = length names;
wenzelm@8316
   405
        fun proj i =
wenzelm@8316
   406
          (if i < n then (fn th => th RS conjunct1) else I)
wenzelm@8316
   407
            (Library.funpow (i - 1) (fn th => th RS conjunct2) mutual_rule)
wenzelm@8316
   408
            RS mp |> Thm.permute_prems 0 ~1 |> Drule.standard;
wenzelm@8316
   409
      in names ~~ map proj (1 upto n) end;
wenzelm@8316
   410
wenzelm@8375
   411
fun add_cases_induct no_elim no_ind names elims induct induct_cases =
wenzelm@8316
   412
  let
wenzelm@9405
   413
    fun cases_spec (name, elim) thy =
wenzelm@9405
   414
      thy
wenzelm@9405
   415
      |> Theory.add_path (Sign.base_name name)
wenzelm@10279
   416
      |> (#1 o PureThy.add_thms [(("cases", elim), [InductAttrib.cases_set_global name])])
wenzelm@9405
   417
      |> Theory.parent_path;
wenzelm@8375
   418
    val cases_specs = if no_elim then [] else map2 cases_spec (names, elims);
wenzelm@8316
   419
wenzelm@9405
   420
    fun induct_spec (name, th) = (#1 o PureThy.add_thms
wenzelm@10279
   421
      [(("", th), [RuleCases.case_names induct_cases, InductAttrib.induct_set_global name])]);
wenzelm@8401
   422
    val induct_specs = if no_ind then [] else map induct_spec (project_rules names induct);
wenzelm@9405
   423
  in Library.apply (cases_specs @ induct_specs) end;
wenzelm@8316
   424
wenzelm@8316
   425
wenzelm@8316
   426
wenzelm@6424
   427
(*** proofs for (co)inductive sets ***)
wenzelm@6424
   428
wenzelm@6424
   429
(** prove monotonicity **)
berghofe@5094
   430
berghofe@5094
   431
fun prove_mono setT fp_fun monos thy =
berghofe@5094
   432
  let
wenzelm@6427
   433
    val _ = message "  Proving monotonicity ...";
berghofe@5094
   434
wenzelm@6394
   435
    val mono = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
berghofe@5094
   436
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
berghofe@7710
   437
        (fn _ => [rtac monoI 1, REPEAT (ares_tac (get_monos thy @ flat (map mk_mono monos)) 1)])
berghofe@5094
   438
berghofe@5094
   439
  in mono end;
berghofe@5094
   440
wenzelm@6424
   441
wenzelm@6424
   442
wenzelm@6424
   443
(** prove introduction rules **)
berghofe@5094
   444
berghofe@5094
   445
fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
berghofe@5094
   446
  let
wenzelm@6427
   447
    val _ = message "  Proving the introduction rules ...";
berghofe@5094
   448
berghofe@5094
   449
    val unfold = standard (mono RS (fp_def RS
nipkow@10186
   450
      (if coind then def_gfp_unfold else def_lfp_unfold)));
berghofe@5094
   451
berghofe@5094
   452
    fun select_disj 1 1 = []
berghofe@5094
   453
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   454
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   455
berghofe@5094
   456
    val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   457
      (cterm_of (Theory.sign_of thy) intr) (fn prems =>
berghofe@5094
   458
       [(*insert prems and underlying sets*)
berghofe@5094
   459
       cut_facts_tac prems 1,
berghofe@5094
   460
       stac unfold 1,
berghofe@5094
   461
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
berghofe@5094
   462
       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
berghofe@5094
   463
       EVERY1 (select_disj (length intr_ts) i),
berghofe@5094
   464
       (*Not ares_tac, since refl must be tried before any equality assumptions;
berghofe@5094
   465
         backtracking may occur if the premises have extra variables!*)
berghofe@5094
   466
       DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
berghofe@5094
   467
       (*Now solve the equations like Inl 0 = Inl ?b2*)
berghofe@5094
   468
       rewrite_goals_tac con_defs,
wenzelm@10729
   469
       REPEAT (rtac refl 1)])
wenzelm@10729
   470
      |> rulify) (1 upto (length intr_ts) ~~ intr_ts)
berghofe@5094
   471
berghofe@5094
   472
  in (intrs, unfold) end;
berghofe@5094
   473
wenzelm@6424
   474
wenzelm@6424
   475
wenzelm@6424
   476
(** prove elimination rules **)
berghofe@5094
   477
wenzelm@8375
   478
fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy =
berghofe@5094
   479
  let
wenzelm@6427
   480
    val _ = message "  Proving the elimination rules ...";
berghofe@5094
   481
berghofe@7710
   482
    val rules1 = [CollectE, disjE, make_elim vimageD, exE];
berghofe@7710
   483
    val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @
berghofe@5094
   484
      map make_elim [Inl_inject, Inr_inject];
wenzelm@8375
   485
  in
wenzelm@8375
   486
    map (fn (t, cases) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   487
      (cterm_of (Theory.sign_of thy) t) (fn prems =>
berghofe@5094
   488
        [cut_facts_tac [hd prems] 1,
berghofe@5094
   489
         dtac (unfold RS subst) 1,
berghofe@5094
   490
         REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@5094
   491
         REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@5094
   492
         EVERY (map (fn prem =>
wenzelm@8375
   493
           DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))])
wenzelm@10729
   494
      |> rulify
wenzelm@8375
   495
      |> RuleCases.name cases)
wenzelm@8375
   496
      (mk_elims cs cTs params intr_ts intr_names)
wenzelm@8375
   497
  end;
berghofe@5094
   498
wenzelm@6424
   499
berghofe@5094
   500
(** derivation of simplified elimination rules **)
berghofe@5094
   501
berghofe@5094
   502
(*Applies freeness of the given constructors, which *must* be unfolded by
wenzelm@9598
   503
  the given defs.  Cannot simply use the local con_defs because con_defs=[]
berghofe@5094
   504
  for inference systems.
berghofe@5094
   505
 *)
berghofe@5094
   506
wenzelm@7107
   507
(*cprop should have the form t:Si where Si is an inductive set*)
wenzelm@9598
   508
wenzelm@9598
   509
val mk_cases_err = "mk_cases: proposition not of form 't : S_i'";
wenzelm@9598
   510
wenzelm@9598
   511
fun mk_cases_i elims ss cprop =
wenzelm@7107
   512
  let
wenzelm@7107
   513
    val prem = Thm.assume cprop;
wenzelm@9598
   514
    val tac = ALLGOALS (InductMethod.simp_case_tac false ss) THEN prune_params_tac;
wenzelm@9298
   515
    fun mk_elim rl = Drule.standard (Tactic.rule_by_tactic tac (prem RS rl));
wenzelm@7107
   516
  in
wenzelm@7107
   517
    (case get_first (try mk_elim) elims of
wenzelm@7107
   518
      Some r => r
wenzelm@7107
   519
    | None => error (Pretty.string_of (Pretty.block
wenzelm@9598
   520
        [Pretty.str mk_cases_err, Pretty.fbrk, Display.pretty_cterm cprop])))
wenzelm@7107
   521
  end;
wenzelm@7107
   522
paulson@6141
   523
fun mk_cases elims s =
wenzelm@9598
   524
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.sign_of_thm (hd elims)) (s, propT));
wenzelm@9598
   525
wenzelm@9598
   526
fun smart_mk_cases thy ss cprop =
wenzelm@9598
   527
  let
wenzelm@9598
   528
    val c = #1 (Term.dest_Const (Term.head_of (#2 (HOLogic.dest_mem (HOLogic.dest_Trueprop
wenzelm@9598
   529
      (Logic.strip_imp_concl (Thm.term_of cprop))))))) handle TERM _ => error mk_cases_err;
wenzelm@9598
   530
    val (_, {elims, ...}) = the_inductive thy c;
wenzelm@9598
   531
  in mk_cases_i elims ss cprop end;
wenzelm@7107
   532
wenzelm@7107
   533
wenzelm@7107
   534
(* inductive_cases(_i) *)
wenzelm@7107
   535
wenzelm@7107
   536
fun gen_inductive_cases prep_att prep_const prep_prop
wenzelm@9598
   537
    (((name, raw_atts), raw_props), comment) thy =
wenzelm@9598
   538
  let
wenzelm@9598
   539
    val ss = Simplifier.simpset_of thy;
wenzelm@9598
   540
    val sign = Theory.sign_of thy;
wenzelm@9598
   541
    val cprops = map (Thm.cterm_of sign o prep_prop (ProofContext.init thy)) raw_props;
wenzelm@9598
   542
    val atts = map (prep_att thy) raw_atts;
wenzelm@9598
   543
    val thms = map (smart_mk_cases thy ss) cprops;
wenzelm@9598
   544
  in thy |> IsarThy.have_theorems_i [(((name, atts), map Thm.no_attributes thms), comment)] end;
berghofe@5094
   545
wenzelm@7107
   546
val inductive_cases =
wenzelm@7107
   547
  gen_inductive_cases Attrib.global_attribute Sign.intern_const ProofContext.read_prop;
wenzelm@7107
   548
wenzelm@7107
   549
val inductive_cases_i = gen_inductive_cases (K I) (K I) ProofContext.cert_prop;
wenzelm@7107
   550
wenzelm@6424
   551
wenzelm@9598
   552
(* mk_cases_meth *)
wenzelm@9598
   553
wenzelm@9598
   554
fun mk_cases_meth (ctxt, raw_props) =
wenzelm@9598
   555
  let
wenzelm@9598
   556
    val thy = ProofContext.theory_of ctxt;
wenzelm@9598
   557
    val ss = Simplifier.get_local_simpset ctxt;
wenzelm@9598
   558
    val cprops = map (Thm.cterm_of (Theory.sign_of thy) o ProofContext.read_prop ctxt) raw_props;
wenzelm@9598
   559
  in Method.erule (map (smart_mk_cases thy ss) cprops) end;
wenzelm@9598
   560
wenzelm@9598
   561
val mk_cases_args = Method.syntax (Scan.lift (Scan.repeat1 Args.name));
wenzelm@9598
   562
wenzelm@9598
   563
wenzelm@6424
   564
wenzelm@6424
   565
(** prove induction rule **)
berghofe@5094
   566
berghofe@5094
   567
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   568
    fp_def rec_sets_defs thy =
berghofe@5094
   569
  let
wenzelm@6427
   570
    val _ = message "  Proving the induction rule ...";
berghofe@5094
   571
wenzelm@6394
   572
    val sign = Theory.sign_of thy;
berghofe@5094
   573
berghofe@7293
   574
    val sum_case_rewrites = (case ThyInfo.lookup_theory "Datatype" of
berghofe@7293
   575
        None => []
berghofe@7293
   576
      | Some thy' => map mk_meta_eq (PureThy.get_thms thy' "sum.cases"));
berghofe@7293
   577
berghofe@5094
   578
    val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   579
berghofe@5094
   580
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   581
berghofe@5094
   582
    fun mk_ind_pred _ [P] = P
berghofe@5094
   583
      | mk_ind_pred T Ps =
berghofe@5094
   584
         let val n = (length Ps) div 2;
berghofe@5094
   585
             val Type (_, [T1, T2]) = T
berghofe@7293
   586
         in Const ("Datatype.sum.sum_case",
berghofe@5094
   587
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
berghofe@5094
   588
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
berghofe@5094
   589
         end;
berghofe@5094
   590
berghofe@5094
   591
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   592
berghofe@5094
   593
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   594
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   595
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   596
berghofe@5094
   597
    (* simplification rules for vimage and Collect *)
berghofe@5094
   598
berghofe@5094
   599
    val vimage_simps = if length cs < 2 then [] else
berghofe@5094
   600
      map (fn c => prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   601
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   602
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   603
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
berghofe@5094
   604
             nth_elem (find_index_eq c cs, preds)))))
berghofe@7293
   605
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   606
          rtac refl 1])) cs;
berghofe@5094
   607
wenzelm@10729
   608
    val induct = prove_goalw_cterm [inductive_conj_def] (cterm_of sign
berghofe@5094
   609
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
berghofe@5094
   610
        [rtac (impI RS allI) 1,
nipkow@10202
   611
         DETERM (etac (mono RS (fp_def RS def_lfp_induct)) 1),
berghofe@7710
   612
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
berghofe@5094
   613
         fold_goals_tac rec_sets_defs,
berghofe@5094
   614
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@7710
   615
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE])),
berghofe@5094
   616
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   617
           some premise involves disjunction.*)
berghofe@7710
   618
         REPEAT (FIRSTGOAL (etac conjE ORELSE' hyp_subst_tac)),
berghofe@7293
   619
         rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   620
         EVERY (map (fn prem =>
berghofe@5149
   621
           DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
berghofe@5094
   622
berghofe@5094
   623
    val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
berghofe@5094
   624
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
berghofe@5094
   625
        [cut_facts_tac prems 1,
berghofe@5094
   626
         REPEAT (EVERY
berghofe@5094
   627
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   628
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
berghofe@7293
   629
            rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   630
            atac 1])])
berghofe@5094
   631
wenzelm@10729
   632
  in standard (split_rule (induct RS lemma)) end;
berghofe@5094
   633
wenzelm@6424
   634
wenzelm@6424
   635
wenzelm@6424
   636
(*** specification of (co)inductive sets ****)
wenzelm@6424
   637
wenzelm@6424
   638
(** definitional introduction of (co)inductive sets **)
berghofe@5094
   639
wenzelm@10729
   640
fun cond_declare_consts declare_consts cs paramTs cnames =
wenzelm@10729
   641
  if declare_consts then
wenzelm@10729
   642
    Theory.add_consts_i (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@10729
   643
  else I;
wenzelm@10729
   644
berghofe@9072
   645
fun mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   646
      params paramTs cTs cnames =
berghofe@5094
   647
  let
berghofe@5094
   648
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   649
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   650
wenzelm@6394
   651
    val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
wenzelm@6394
   652
      else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
berghofe@5094
   653
berghofe@5149
   654
    val used = foldr add_term_names (intr_ts, []);
berghofe@5149
   655
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   656
berghofe@5094
   657
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   658
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   659
    (* is transformed into                                *)
berghofe@5094
   660
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   661
berghofe@5094
   662
    fun transform_rule r =
berghofe@5094
   663
      let
berghofe@5094
   664
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   665
        val subst = subst_free
berghofe@5149
   666
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   667
        val Const ("op :", _) $ t $ u =
berghofe@5094
   668
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   669
berghofe@5094
   670
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
berghofe@7710
   671
        (frees, foldr1 HOLogic.mk_conj
berghofe@5149
   672
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   673
            (map (subst o HOLogic.dest_Trueprop)
berghofe@5094
   674
              (Logic.strip_imp_prems r))))
berghofe@5094
   675
      end
berghofe@5094
   676
berghofe@5094
   677
    (* make a disjunction of all introduction rules *)
berghofe@5094
   678
berghofe@5149
   679
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@7710
   680
      absfree (xname, sumT, foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
berghofe@5094
   681
berghofe@5094
   682
    (* add definiton of recursive sets to theory *)
berghofe@5094
   683
berghofe@5094
   684
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
wenzelm@6394
   685
    val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
berghofe@5094
   686
berghofe@5094
   687
    val rec_const = list_comb
berghofe@5094
   688
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   689
berghofe@5094
   690
    val fp_def_term = Logic.mk_equals (rec_const,
berghofe@5094
   691
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun)
berghofe@5094
   692
berghofe@5094
   693
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   694
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   695
wenzelm@8433
   696
    val (thy', [fp_def :: rec_sets_defs]) =
wenzelm@8433
   697
      thy
wenzelm@10729
   698
      |> cond_declare_consts declare_consts cs paramTs cnames
wenzelm@8433
   699
      |> (if length cs < 2 then I
wenzelm@8433
   700
          else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
wenzelm@8433
   701
      |> Theory.add_path rec_name
wenzelm@9315
   702
      |> PureThy.add_defss_i false [(("defs", def_terms), [])];
berghofe@5094
   703
berghofe@9072
   704
    val mono = prove_mono setT fp_fun monos thy'
berghofe@5094
   705
berghofe@9072
   706
  in
wenzelm@9598
   707
    (thy', mono, fp_def, rec_sets_defs, rec_const, sumT)
berghofe@9072
   708
  end;
berghofe@5094
   709
berghofe@9072
   710
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
berghofe@9072
   711
    atts intros monos con_defs thy params paramTs cTs cnames induct_cases =
berghofe@9072
   712
  let
berghofe@9072
   713
    val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
berghofe@9072
   714
      commas_quote cnames) else ();
berghofe@9072
   715
berghofe@9072
   716
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
berghofe@9072
   717
wenzelm@9939
   718
    val (thy1, mono, fp_def, rec_sets_defs, rec_const, sumT) =
berghofe@9072
   719
      mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   720
        params paramTs cTs cnames;
berghofe@9072
   721
berghofe@5094
   722
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
wenzelm@9939
   723
      rec_sets_defs thy1;
berghofe@5094
   724
    val elims = if no_elim then [] else
wenzelm@9939
   725
      prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy1;
wenzelm@8312
   726
    val raw_induct = if no_ind then Drule.asm_rl else
berghofe@5094
   727
      if coind then standard (rule_by_tactic
oheimb@5553
   728
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   729
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   730
      else
berghofe@5094
   731
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
wenzelm@9939
   732
          rec_sets_defs thy1;
berghofe@5108
   733
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
berghofe@5094
   734
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   735
wenzelm@9939
   736
    val (thy2, intrs') =
wenzelm@9939
   737
      thy1 |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts);
wenzelm@9939
   738
    val (thy3, [intrs'']) =
wenzelm@9939
   739
      thy2      
wenzelm@9939
   740
      |> PureThy.add_thmss [(("intros", intrs'), atts)]
wenzelm@8433
   741
      |>> (if no_elim then I else #1 o PureThy.add_thmss [(("elims", elims), [])])
wenzelm@8433
   742
      |>> (if no_ind then I else #1 o PureThy.add_thms
wenzelm@10729
   743
        [((coind_prefix coind ^ "induct", rulify induct), [RuleCases.case_names induct_cases])])
wenzelm@8433
   744
      |>> Theory.parent_path;
wenzelm@9939
   745
    val elims' = if no_elim then elims else PureThy.get_thms thy3 "elims";  (* FIXME improve *)
wenzelm@9939
   746
    val induct' = if no_ind then induct else PureThy.get_thm thy3 (coind_prefix coind ^ "induct");  (* FIXME improve *)
wenzelm@9939
   747
  in (thy3,
berghofe@5094
   748
    {defs = fp_def::rec_sets_defs,
berghofe@5094
   749
     mono = mono,
berghofe@5094
   750
     unfold = unfold,
wenzelm@9939
   751
     intrs = intrs'',
wenzelm@7798
   752
     elims = elims',
wenzelm@7798
   753
     mk_cases = mk_cases elims',
wenzelm@10729
   754
     raw_induct = rulify raw_induct,
wenzelm@7798
   755
     induct = induct'})
berghofe@5094
   756
  end;
berghofe@5094
   757
wenzelm@6424
   758
wenzelm@6424
   759
wenzelm@6424
   760
(** axiomatic introduction of (co)inductive sets **)
berghofe@5094
   761
berghofe@5094
   762
fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@8401
   763
    atts intros monos con_defs thy params paramTs cTs cnames induct_cases =
berghofe@5094
   764
  let
berghofe@9072
   765
    val _ = message (coind_prefix coind ^ "inductive set(s) " ^ commas_quote cnames);
berghofe@5094
   766
wenzelm@6424
   767
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
wenzelm@9939
   768
    val (thy1, _, fp_def, rec_sets_defs, _, _) =
berghofe@9072
   769
      mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   770
        params paramTs cTs cnames;
wenzelm@8375
   771
    val (elim_ts, elim_cases) = Library.split_list (mk_elims cs cTs params intr_ts intr_names);
berghofe@5094
   772
    val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   773
    val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
wenzelm@9598
   774
wenzelm@9939
   775
    val (thy2, [intrs, raw_elims]) =
wenzelm@9939
   776
      thy1
wenzelm@10729
   777
      |> PureThy.add_axiomss_i
wenzelm@10729
   778
        [(("raw_intros", intr_ts), [rulified]),
wenzelm@10729
   779
          (("raw_elims", elim_ts), [rulified])]
wenzelm@9598
   780
      |>> (if coind then I else
wenzelm@8433
   781
            #1 o PureThy.add_axioms_i [(("raw_induct", ind_t), [apsnd (standard o split_rule)])]);
berghofe@5094
   782
wenzelm@9598
   783
    val elims = map2 (fn (th, cases) => RuleCases.name cases th) (raw_elims, elim_cases);
wenzelm@9939
   784
    val raw_induct = if coind then Drule.asm_rl else PureThy.get_thm thy2 "raw_induct";
berghofe@5094
   785
    val induct = if coind orelse length cs > 1 then raw_induct
berghofe@5094
   786
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   787
wenzelm@9939
   788
    val (thy3, intrs') =
wenzelm@9939
   789
      thy2 |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts);
wenzelm@9939
   790
    val (thy4, [intrs'', elims']) =
wenzelm@9939
   791
      thy3
wenzelm@9939
   792
      |> PureThy.add_thmss [(("intros", intrs'), atts), (("elims", elims), [])]
wenzelm@8433
   793
      |>> (if coind then I
wenzelm@10729
   794
          else #1 o PureThy.add_thms [(("induct", rulify induct),
wenzelm@10729
   795
            [RuleCases.case_names induct_cases])])
wenzelm@8433
   796
      |>> Theory.parent_path;
wenzelm@9939
   797
    val induct' = if coind then raw_induct else PureThy.get_thm thy4 "induct";
wenzelm@9939
   798
  in (thy4,
wenzelm@9235
   799
    {defs = fp_def :: rec_sets_defs,
wenzelm@8312
   800
     mono = Drule.asm_rl,
wenzelm@8312
   801
     unfold = Drule.asm_rl,
wenzelm@9939
   802
     intrs = intrs'',
wenzelm@8433
   803
     elims = elims',
wenzelm@8433
   804
     mk_cases = mk_cases elims',
wenzelm@10729
   805
     raw_induct = rulify raw_induct,
wenzelm@7798
   806
     induct = induct'})
berghofe@5094
   807
  end;
berghofe@5094
   808
wenzelm@6424
   809
wenzelm@6424
   810
wenzelm@6424
   811
(** introduction of (co)inductive sets **)
berghofe@5094
   812
berghofe@5094
   813
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@10729
   814
    atts pre_intros monos con_defs thy =
berghofe@5094
   815
  let
wenzelm@6424
   816
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
wenzelm@6394
   817
    val sign = Theory.sign_of thy;
berghofe@5094
   818
berghofe@5094
   819
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   820
    val (_, params) = strip_comb (hd cs);
berghofe@5094
   821
    val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
berghofe@5094
   822
      \ component is not a free variable: " sign) params;
berghofe@5094
   823
berghofe@5094
   824
    val cTs = map (try' (HOLogic.dest_setT o fastype_of)
berghofe@5094
   825
      "Recursive component not of type set: " sign) cs;
berghofe@5094
   826
wenzelm@6437
   827
    val full_cnames = map (try' (fst o dest_Const o head_of)
berghofe@5094
   828
      "Recursive set not previously declared as constant: " sign) cs;
wenzelm@6437
   829
    val cnames = map Sign.base_name full_cnames;
berghofe@5094
   830
wenzelm@10729
   831
    val save_sign =
wenzelm@10729
   832
      thy |> Theory.copy |> cond_declare_consts declare_consts cs paramTs cnames |> Theory.sign_of;
wenzelm@10729
   833
    val intros = map (check_rule save_sign cs) pre_intros;
wenzelm@8401
   834
    val induct_cases = map (#1 o #1) intros;
wenzelm@6437
   835
wenzelm@9405
   836
    val (thy1, result as {elims, induct, ...}) =
wenzelm@10569
   837
      (if ! quick_and_dirty andalso not coind (* FIXME *) then add_ind_axm else add_ind_def)
wenzelm@6521
   838
        verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
wenzelm@8401
   839
        con_defs thy params paramTs cTs cnames induct_cases;
wenzelm@8307
   840
    val thy2 = thy1
wenzelm@8307
   841
      |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result)
wenzelm@9405
   842
      |> add_cases_induct no_elim (no_ind orelse coind) full_cnames elims induct induct_cases;
wenzelm@6437
   843
  in (thy2, result) end;
berghofe@5094
   844
wenzelm@6424
   845
berghofe@5094
   846
wenzelm@6424
   847
(** external interface **)
wenzelm@6424
   848
wenzelm@6521
   849
fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
berghofe@5094
   850
  let
wenzelm@6394
   851
    val sign = Theory.sign_of thy;
wenzelm@8100
   852
    val cs = map (term_of o Thm.read_cterm sign o rpair HOLogic.termT) c_strings;
wenzelm@6424
   853
wenzelm@6521
   854
    val atts = map (Attrib.global_attribute thy) srcs;
wenzelm@6424
   855
    val intr_names = map (fst o fst) intro_srcs;
wenzelm@9405
   856
    fun read_rule s = Thm.read_cterm sign (s, propT)
wenzelm@9405
   857
      handle ERROR => error ("The error(s) above occurred for " ^ s);
wenzelm@9405
   858
    val intr_ts = map (Thm.term_of o read_rule o snd o fst) intro_srcs;
wenzelm@6424
   859
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
berghofe@7020
   860
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
berghofe@5094
   861
wenzelm@6424
   862
    val ((thy', con_defs), monos) = thy
wenzelm@6424
   863
      |> IsarThy.apply_theorems raw_monos
wenzelm@6424
   864
      |> apfst (IsarThy.apply_theorems raw_con_defs);
wenzelm@6424
   865
  in
berghofe@7020
   866
    add_inductive_i verbose false "" coind false false cs'
berghofe@7020
   867
      atts ((intr_names ~~ intr_ts') ~~ intr_atts) monos con_defs thy'
berghofe@5094
   868
  end;
berghofe@5094
   869
wenzelm@6424
   870
wenzelm@6424
   871
wenzelm@6437
   872
(** package setup **)
wenzelm@6437
   873
wenzelm@6437
   874
(* setup theory *)
wenzelm@6437
   875
wenzelm@8634
   876
val setup =
wenzelm@8634
   877
 [InductiveData.init,
wenzelm@9625
   878
  Method.add_methods [("ind_cases", mk_cases_meth oo mk_cases_args,
wenzelm@9598
   879
    "dynamic case analysis on sets")],
wenzelm@9893
   880
  Attrib.add_attributes [("mono", mono_attr, "declaration of monotonicity rule")]];
wenzelm@6437
   881
wenzelm@6437
   882
wenzelm@6437
   883
(* outer syntax *)
wenzelm@6424
   884
wenzelm@6723
   885
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6424
   886
wenzelm@6521
   887
fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
wenzelm@6723
   888
  #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
wenzelm@6424
   889
wenzelm@6424
   890
fun ind_decl coind =
wenzelm@6729
   891
  (Scan.repeat1 P.term --| P.marg_comment) --
wenzelm@9598
   892
  (P.$$$ "intros" |--
wenzelm@7152
   893
    P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop --| P.marg_comment))) --
wenzelm@6729
   894
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
wenzelm@6729
   895
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
wenzelm@6424
   896
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   897
wenzelm@6723
   898
val inductiveP =
wenzelm@6723
   899
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   900
wenzelm@6723
   901
val coinductiveP =
wenzelm@6723
   902
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   903
wenzelm@7107
   904
wenzelm@7107
   905
val ind_cases =
wenzelm@9625
   906
  P.opt_thm_name ":" -- Scan.repeat1 P.prop -- P.marg_comment
wenzelm@7107
   907
  >> (Toplevel.theory o inductive_cases);
wenzelm@7107
   908
wenzelm@7107
   909
val inductive_casesP =
wenzelm@9804
   910
  OuterSyntax.command "inductive_cases"
wenzelm@9598
   911
    "create simplified instances of elimination rules (improper)" K.thy_script ind_cases;
wenzelm@7107
   912
wenzelm@9643
   913
val _ = OuterSyntax.add_keywords ["intros", "monos", "con_defs"];
wenzelm@7107
   914
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   915
berghofe@5094
   916
end;
wenzelm@6424
   917
wenzelm@6424
   918
wenzelm@6424
   919
end;