src/HOL/Tools/inductive_package.ML
author wenzelm
Sat Sep 02 21:50:38 2000 +0200 (2000-09-02)
changeset 9804 ee0c337327cf
parent 9643 c94db1a96f4e
child 9831 9b883c416aef
permissions -rw-r--r--
"inductive_cases": proper command;
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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 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 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 = snd o InductiveData.get;
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fun put_monos thms thy = InductiveData.put (fst (InductiveData.get thy), thms) thy;
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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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local
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fun map_rules_global f thy = put_monos (f (get_monos thy)) thy;
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fun add_mono thm rules = Library.gen_union Thm.eq_thm (mk_mono thm, rules);
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fun del_mono thm rules = Library.gen_rems Thm.eq_thm (rules, mk_mono thm);
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fun mk_att f g (x, thm) = (f (g thm) x, thm);
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in
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  val mono_add_global = mk_att map_rules_global add_mono;
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  val mono_del_global = mk_att map_rules_global del_mono;
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end;
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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 Vimage.thy) "op -``";
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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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(** 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 = "Non-atomic premise";
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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 can HOLogic.dest_Trueprop prem then ()
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      else err_in_prem sign r prem msg2;
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  in (case HOLogic.dest_Trueprop (Logic.strip_imp_concl r) 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 sign r msg3
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            else
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              seq check_prem (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 = (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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    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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        val pred_of = curry (Library.gen_assoc (op aconv)) (cs ~~ preds);
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        fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
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              (case pred_of u of
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                  None => (m $ fst (subst t) $ fst (subst u), None)
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                | Some P => (HOLogic.conj $ s $ (P $ t), Some (s, P $ t)))
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          | subst s =
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              (case pred_of s of
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                  Some P => (HOLogic.mk_binop "op Int"
berghofe@7710
   330
                    (s, HOLogic.Collect_const (HOLogic.dest_setT
berghofe@7710
   331
                      (fastype_of s)) $ P), None)
berghofe@7710
   332
                | None => (case s of
berghofe@7710
   333
                     (t $ u) => (fst (subst t) $ fst (subst u), None)
berghofe@7710
   334
                   | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), None)
berghofe@7710
   335
                   | _ => (s, None)));
berghofe@7710
   336
berghofe@7710
   337
        fun mk_prem (s, prems) = (case subst s of
berghofe@7710
   338
              (_, Some (t, u)) => t :: u :: prems
berghofe@7710
   339
            | (t, _) => t :: prems);
wenzelm@9598
   340
berghofe@5094
   341
        val Const ("op :", _) $ t $ u =
berghofe@5094
   342
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   343
berghofe@5094
   344
      in list_all_free (frees,
berghofe@7710
   345
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
berghofe@5094
   346
             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
berghofe@7710
   347
               HOLogic.mk_Trueprop (the (pred_of u) $ t)))
berghofe@5094
   348
      end;
berghofe@5094
   349
berghofe@5094
   350
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@5094
   351
berghofe@5094
   352
    (* make conclusions for induction rules *)
berghofe@5094
   353
berghofe@5094
   354
    fun mk_ind_concl ((c, P), (ts, x)) =
berghofe@5094
   355
      let val T = HOLogic.dest_setT (fastype_of c);
berghofe@5094
   356
          val Ts = HOLogic.prodT_factors T;
berghofe@5094
   357
          val (frees, x') = foldr (fn (T', (fs, s)) =>
berghofe@5094
   358
            ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
berghofe@5094
   359
          val tuple = HOLogic.mk_tuple T frees;
berghofe@5094
   360
      in ((HOLogic.mk_binop "op -->"
berghofe@5094
   361
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
berghofe@5094
   362
      end;
berghofe@5094
   363
berghofe@7710
   364
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@5094
   365
        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
berghofe@5094
   366
berghofe@5094
   367
  in (preds, ind_prems, mutual_ind_concl)
berghofe@5094
   368
  end;
berghofe@5094
   369
wenzelm@6424
   370
berghofe@5094
   371
wenzelm@8316
   372
(** prepare cases and induct rules **)
wenzelm@8316
   373
wenzelm@8316
   374
(*
wenzelm@8316
   375
  transform mutual rule:
wenzelm@8316
   376
    HH ==> (x1:A1 --> P1 x1) & ... & (xn:An --> Pn xn)
wenzelm@8316
   377
  into i-th projection:
wenzelm@8316
   378
    xi:Ai ==> HH ==> Pi xi
wenzelm@8316
   379
*)
wenzelm@8316
   380
wenzelm@8316
   381
fun project_rules [name] rule = [(name, rule)]
wenzelm@8316
   382
  | project_rules names mutual_rule =
wenzelm@8316
   383
      let
wenzelm@8316
   384
        val n = length names;
wenzelm@8316
   385
        fun proj i =
wenzelm@8316
   386
          (if i < n then (fn th => th RS conjunct1) else I)
wenzelm@8316
   387
            (Library.funpow (i - 1) (fn th => th RS conjunct2) mutual_rule)
wenzelm@8316
   388
            RS mp |> Thm.permute_prems 0 ~1 |> Drule.standard;
wenzelm@8316
   389
      in names ~~ map proj (1 upto n) end;
wenzelm@8316
   390
wenzelm@8375
   391
fun add_cases_induct no_elim no_ind names elims induct induct_cases =
wenzelm@8316
   392
  let
wenzelm@9405
   393
    fun cases_spec (name, elim) thy =
wenzelm@9405
   394
      thy
wenzelm@9405
   395
      |> Theory.add_path (Sign.base_name name)
wenzelm@9405
   396
      |> (#1 o PureThy.add_thms [(("cases", elim), [InductMethod.cases_set_global name])])
wenzelm@9405
   397
      |> Theory.parent_path;
wenzelm@8375
   398
    val cases_specs = if no_elim then [] else map2 cases_spec (names, elims);
wenzelm@8316
   399
wenzelm@9405
   400
    fun induct_spec (name, th) = (#1 o PureThy.add_thms
wenzelm@9405
   401
      [(("", th), [RuleCases.case_names induct_cases, InductMethod.induct_set_global name])]);
wenzelm@8401
   402
    val induct_specs = if no_ind then [] else map induct_spec (project_rules names induct);
wenzelm@9405
   403
  in Library.apply (cases_specs @ induct_specs) end;
wenzelm@8316
   404
wenzelm@8316
   405
wenzelm@8316
   406
wenzelm@6424
   407
(*** proofs for (co)inductive sets ***)
wenzelm@6424
   408
wenzelm@6424
   409
(** prove monotonicity **)
berghofe@5094
   410
berghofe@5094
   411
fun prove_mono setT fp_fun monos thy =
berghofe@5094
   412
  let
wenzelm@6427
   413
    val _ = message "  Proving monotonicity ...";
berghofe@5094
   414
wenzelm@6394
   415
    val mono = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
berghofe@5094
   416
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
berghofe@7710
   417
        (fn _ => [rtac monoI 1, REPEAT (ares_tac (get_monos thy @ flat (map mk_mono monos)) 1)])
berghofe@5094
   418
berghofe@5094
   419
  in mono end;
berghofe@5094
   420
wenzelm@6424
   421
wenzelm@6424
   422
wenzelm@6424
   423
(** prove introduction rules **)
berghofe@5094
   424
berghofe@5094
   425
fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
berghofe@5094
   426
  let
wenzelm@6427
   427
    val _ = message "  Proving the introduction rules ...";
berghofe@5094
   428
berghofe@5094
   429
    val unfold = standard (mono RS (fp_def RS
berghofe@5094
   430
      (if coind then def_gfp_Tarski else def_lfp_Tarski)));
berghofe@5094
   431
berghofe@5094
   432
    fun select_disj 1 1 = []
berghofe@5094
   433
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   434
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   435
berghofe@5094
   436
    val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   437
      (cterm_of (Theory.sign_of thy) intr) (fn prems =>
berghofe@5094
   438
       [(*insert prems and underlying sets*)
berghofe@5094
   439
       cut_facts_tac prems 1,
berghofe@5094
   440
       stac unfold 1,
berghofe@5094
   441
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
berghofe@5094
   442
       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
berghofe@5094
   443
       EVERY1 (select_disj (length intr_ts) i),
berghofe@5094
   444
       (*Not ares_tac, since refl must be tried before any equality assumptions;
berghofe@5094
   445
         backtracking may occur if the premises have extra variables!*)
berghofe@5094
   446
       DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
berghofe@5094
   447
       (*Now solve the equations like Inl 0 = Inl ?b2*)
berghofe@5094
   448
       rewrite_goals_tac con_defs,
berghofe@5094
   449
       REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
berghofe@5094
   450
berghofe@5094
   451
  in (intrs, unfold) end;
berghofe@5094
   452
wenzelm@6424
   453
wenzelm@6424
   454
wenzelm@6424
   455
(** prove elimination rules **)
berghofe@5094
   456
wenzelm@8375
   457
fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy =
berghofe@5094
   458
  let
wenzelm@6427
   459
    val _ = message "  Proving the elimination rules ...";
berghofe@5094
   460
berghofe@7710
   461
    val rules1 = [CollectE, disjE, make_elim vimageD, exE];
berghofe@7710
   462
    val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @
berghofe@5094
   463
      map make_elim [Inl_inject, Inr_inject];
wenzelm@8375
   464
  in
wenzelm@8375
   465
    map (fn (t, cases) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   466
      (cterm_of (Theory.sign_of thy) t) (fn prems =>
berghofe@5094
   467
        [cut_facts_tac [hd prems] 1,
berghofe@5094
   468
         dtac (unfold RS subst) 1,
berghofe@5094
   469
         REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@5094
   470
         REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@5094
   471
         EVERY (map (fn prem =>
wenzelm@8375
   472
           DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))])
wenzelm@8375
   473
      |> RuleCases.name cases)
wenzelm@8375
   474
      (mk_elims cs cTs params intr_ts intr_names)
wenzelm@8375
   475
  end;
berghofe@5094
   476
wenzelm@6424
   477
berghofe@5094
   478
(** derivation of simplified elimination rules **)
berghofe@5094
   479
berghofe@5094
   480
(*Applies freeness of the given constructors, which *must* be unfolded by
wenzelm@9598
   481
  the given defs.  Cannot simply use the local con_defs because con_defs=[]
berghofe@5094
   482
  for inference systems.
berghofe@5094
   483
 *)
berghofe@5094
   484
wenzelm@7107
   485
(*cprop should have the form t:Si where Si is an inductive set*)
wenzelm@9598
   486
wenzelm@9598
   487
val mk_cases_err = "mk_cases: proposition not of form 't : S_i'";
wenzelm@9598
   488
wenzelm@9598
   489
fun mk_cases_i elims ss cprop =
wenzelm@7107
   490
  let
wenzelm@7107
   491
    val prem = Thm.assume cprop;
wenzelm@9598
   492
    val tac = ALLGOALS (InductMethod.simp_case_tac false ss) THEN prune_params_tac;
wenzelm@9298
   493
    fun mk_elim rl = Drule.standard (Tactic.rule_by_tactic tac (prem RS rl));
wenzelm@7107
   494
  in
wenzelm@7107
   495
    (case get_first (try mk_elim) elims of
wenzelm@7107
   496
      Some r => r
wenzelm@7107
   497
    | None => error (Pretty.string_of (Pretty.block
wenzelm@9598
   498
        [Pretty.str mk_cases_err, Pretty.fbrk, Display.pretty_cterm cprop])))
wenzelm@7107
   499
  end;
wenzelm@7107
   500
paulson@6141
   501
fun mk_cases elims s =
wenzelm@9598
   502
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.sign_of_thm (hd elims)) (s, propT));
wenzelm@9598
   503
wenzelm@9598
   504
fun smart_mk_cases thy ss cprop =
wenzelm@9598
   505
  let
wenzelm@9598
   506
    val c = #1 (Term.dest_Const (Term.head_of (#2 (HOLogic.dest_mem (HOLogic.dest_Trueprop
wenzelm@9598
   507
      (Logic.strip_imp_concl (Thm.term_of cprop))))))) handle TERM _ => error mk_cases_err;
wenzelm@9598
   508
    val (_, {elims, ...}) = the_inductive thy c;
wenzelm@9598
   509
  in mk_cases_i elims ss cprop end;
wenzelm@7107
   510
wenzelm@7107
   511
wenzelm@7107
   512
(* inductive_cases(_i) *)
wenzelm@7107
   513
wenzelm@7107
   514
fun gen_inductive_cases prep_att prep_const prep_prop
wenzelm@9598
   515
    (((name, raw_atts), raw_props), comment) thy =
wenzelm@9598
   516
  let
wenzelm@9598
   517
    val ss = Simplifier.simpset_of thy;
wenzelm@9598
   518
    val sign = Theory.sign_of thy;
wenzelm@9598
   519
    val cprops = map (Thm.cterm_of sign o prep_prop (ProofContext.init thy)) raw_props;
wenzelm@9598
   520
    val atts = map (prep_att thy) raw_atts;
wenzelm@9598
   521
    val thms = map (smart_mk_cases thy ss) cprops;
wenzelm@9598
   522
  in thy |> IsarThy.have_theorems_i [(((name, atts), map Thm.no_attributes thms), comment)] end;
berghofe@5094
   523
wenzelm@7107
   524
val inductive_cases =
wenzelm@7107
   525
  gen_inductive_cases Attrib.global_attribute Sign.intern_const ProofContext.read_prop;
wenzelm@7107
   526
wenzelm@7107
   527
val inductive_cases_i = gen_inductive_cases (K I) (K I) ProofContext.cert_prop;
wenzelm@7107
   528
wenzelm@6424
   529
wenzelm@9598
   530
(* mk_cases_meth *)
wenzelm@9598
   531
wenzelm@9598
   532
fun mk_cases_meth (ctxt, raw_props) =
wenzelm@9598
   533
  let
wenzelm@9598
   534
    val thy = ProofContext.theory_of ctxt;
wenzelm@9598
   535
    val ss = Simplifier.get_local_simpset ctxt;
wenzelm@9598
   536
    val cprops = map (Thm.cterm_of (Theory.sign_of thy) o ProofContext.read_prop ctxt) raw_props;
wenzelm@9598
   537
  in Method.erule (map (smart_mk_cases thy ss) cprops) end;
wenzelm@9598
   538
wenzelm@9598
   539
val mk_cases_args = Method.syntax (Scan.lift (Scan.repeat1 Args.name));
wenzelm@9598
   540
wenzelm@9598
   541
wenzelm@6424
   542
wenzelm@6424
   543
(** prove induction rule **)
berghofe@5094
   544
berghofe@5094
   545
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   546
    fp_def rec_sets_defs thy =
berghofe@5094
   547
  let
wenzelm@6427
   548
    val _ = message "  Proving the induction rule ...";
berghofe@5094
   549
wenzelm@6394
   550
    val sign = Theory.sign_of thy;
berghofe@5094
   551
berghofe@7293
   552
    val sum_case_rewrites = (case ThyInfo.lookup_theory "Datatype" of
berghofe@7293
   553
        None => []
berghofe@7293
   554
      | Some thy' => map mk_meta_eq (PureThy.get_thms thy' "sum.cases"));
berghofe@7293
   555
berghofe@5094
   556
    val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   557
berghofe@5094
   558
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   559
berghofe@5094
   560
    fun mk_ind_pred _ [P] = P
berghofe@5094
   561
      | mk_ind_pred T Ps =
berghofe@5094
   562
         let val n = (length Ps) div 2;
berghofe@5094
   563
             val Type (_, [T1, T2]) = T
berghofe@7293
   564
         in Const ("Datatype.sum.sum_case",
berghofe@5094
   565
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
berghofe@5094
   566
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
berghofe@5094
   567
         end;
berghofe@5094
   568
berghofe@5094
   569
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   570
berghofe@5094
   571
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   572
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   573
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   574
berghofe@5094
   575
    (* simplification rules for vimage and Collect *)
berghofe@5094
   576
berghofe@5094
   577
    val vimage_simps = if length cs < 2 then [] else
berghofe@5094
   578
      map (fn c => prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   579
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   580
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   581
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
berghofe@5094
   582
             nth_elem (find_index_eq c cs, preds)))))
berghofe@7293
   583
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   584
          rtac refl 1])) cs;
berghofe@5094
   585
berghofe@5094
   586
    val induct = prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   587
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
berghofe@5094
   588
        [rtac (impI RS allI) 1,
berghofe@5094
   589
         DETERM (etac (mono RS (fp_def RS def_induct)) 1),
berghofe@7710
   590
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
berghofe@5094
   591
         fold_goals_tac rec_sets_defs,
berghofe@5094
   592
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@7710
   593
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE])),
berghofe@5094
   594
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   595
           some premise involves disjunction.*)
berghofe@7710
   596
         REPEAT (FIRSTGOAL (etac conjE ORELSE' hyp_subst_tac)),
berghofe@7293
   597
         rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   598
         EVERY (map (fn prem =>
berghofe@5149
   599
           DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
berghofe@5094
   600
berghofe@5094
   601
    val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
berghofe@5094
   602
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
berghofe@5094
   603
        [cut_facts_tac prems 1,
berghofe@5094
   604
         REPEAT (EVERY
berghofe@5094
   605
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   606
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
berghofe@7293
   607
            rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   608
            atac 1])])
berghofe@5094
   609
berghofe@5094
   610
  in standard (split_rule (induct RS lemma))
berghofe@5094
   611
  end;
berghofe@5094
   612
wenzelm@6424
   613
wenzelm@6424
   614
wenzelm@6424
   615
(*** specification of (co)inductive sets ****)
wenzelm@6424
   616
wenzelm@6424
   617
(** definitional introduction of (co)inductive sets **)
berghofe@5094
   618
berghofe@9072
   619
fun mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   620
      params paramTs cTs cnames =
berghofe@5094
   621
  let
berghofe@5094
   622
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   623
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   624
wenzelm@6394
   625
    val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
wenzelm@6394
   626
      else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
berghofe@5094
   627
berghofe@5149
   628
    val used = foldr add_term_names (intr_ts, []);
berghofe@5149
   629
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   630
berghofe@5094
   631
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   632
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   633
    (* is transformed into                                *)
berghofe@5094
   634
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   635
berghofe@5094
   636
    fun transform_rule r =
berghofe@5094
   637
      let
berghofe@5094
   638
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   639
        val subst = subst_free
berghofe@5149
   640
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   641
        val Const ("op :", _) $ t $ u =
berghofe@5094
   642
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   643
berghofe@5094
   644
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
berghofe@7710
   645
        (frees, foldr1 HOLogic.mk_conj
berghofe@5149
   646
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   647
            (map (subst o HOLogic.dest_Trueprop)
berghofe@5094
   648
              (Logic.strip_imp_prems r))))
berghofe@5094
   649
      end
berghofe@5094
   650
berghofe@5094
   651
    (* make a disjunction of all introduction rules *)
berghofe@5094
   652
berghofe@5149
   653
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@7710
   654
      absfree (xname, sumT, foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
berghofe@5094
   655
berghofe@5094
   656
    (* add definiton of recursive sets to theory *)
berghofe@5094
   657
berghofe@5094
   658
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
wenzelm@6394
   659
    val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
berghofe@5094
   660
berghofe@5094
   661
    val rec_const = list_comb
berghofe@5094
   662
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   663
berghofe@5094
   664
    val fp_def_term = Logic.mk_equals (rec_const,
berghofe@5094
   665
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun)
berghofe@5094
   666
berghofe@5094
   667
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   668
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   669
wenzelm@8433
   670
    val (thy', [fp_def :: rec_sets_defs]) =
wenzelm@8433
   671
      thy
wenzelm@8433
   672
      |> (if declare_consts then
wenzelm@8433
   673
          Theory.add_consts_i (map (fn (c, n) =>
wenzelm@8433
   674
            (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@8433
   675
          else I)
wenzelm@8433
   676
      |> (if length cs < 2 then I
wenzelm@8433
   677
          else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
wenzelm@8433
   678
      |> Theory.add_path rec_name
wenzelm@9315
   679
      |> PureThy.add_defss_i false [(("defs", def_terms), [])];
berghofe@5094
   680
berghofe@9072
   681
    val mono = prove_mono setT fp_fun monos thy'
berghofe@5094
   682
berghofe@9072
   683
  in
wenzelm@9598
   684
    (thy', mono, fp_def, rec_sets_defs, rec_const, sumT)
berghofe@9072
   685
  end;
berghofe@5094
   686
berghofe@9072
   687
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
berghofe@9072
   688
    atts intros monos con_defs thy params paramTs cTs cnames induct_cases =
berghofe@9072
   689
  let
berghofe@9072
   690
    val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
berghofe@9072
   691
      commas_quote cnames) else ();
berghofe@9072
   692
berghofe@9072
   693
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
berghofe@9072
   694
berghofe@9072
   695
    val (thy', mono, fp_def, rec_sets_defs, rec_const, sumT) =
berghofe@9072
   696
      mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   697
        params paramTs cTs cnames;
berghofe@9072
   698
berghofe@5094
   699
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
berghofe@5094
   700
      rec_sets_defs thy';
berghofe@5094
   701
    val elims = if no_elim then [] else
wenzelm@8375
   702
      prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy';
wenzelm@8312
   703
    val raw_induct = if no_ind then Drule.asm_rl else
berghofe@5094
   704
      if coind then standard (rule_by_tactic
oheimb@5553
   705
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   706
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   707
      else
berghofe@5094
   708
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
berghofe@5094
   709
          rec_sets_defs thy';
berghofe@5108
   710
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
berghofe@5094
   711
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   712
wenzelm@8433
   713
    val (thy'', [intrs']) =
wenzelm@8433
   714
      thy'
wenzelm@9598
   715
      |> PureThy.add_thmss [(("intros", intrs), atts)]
wenzelm@8433
   716
      |>> (#1 o PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts))
wenzelm@8433
   717
      |>> (if no_elim then I else #1 o PureThy.add_thmss [(("elims", elims), [])])
wenzelm@8433
   718
      |>> (if no_ind then I else #1 o PureThy.add_thms
wenzelm@8401
   719
        [((coind_prefix coind ^ "induct", induct), [RuleCases.case_names induct_cases])])
wenzelm@8433
   720
      |>> Theory.parent_path;
wenzelm@8312
   721
    val elims' = if no_elim then elims else PureThy.get_thms thy'' "elims";  (* FIXME improve *)
wenzelm@8312
   722
    val induct' = if no_ind then induct else PureThy.get_thm thy'' (coind_prefix coind ^ "induct");  (* FIXME improve *)
berghofe@5094
   723
  in (thy'',
berghofe@5094
   724
    {defs = fp_def::rec_sets_defs,
berghofe@5094
   725
     mono = mono,
berghofe@5094
   726
     unfold = unfold,
wenzelm@7798
   727
     intrs = intrs',
wenzelm@7798
   728
     elims = elims',
wenzelm@7798
   729
     mk_cases = mk_cases elims',
berghofe@5094
   730
     raw_induct = raw_induct,
wenzelm@7798
   731
     induct = induct'})
berghofe@5094
   732
  end;
berghofe@5094
   733
wenzelm@6424
   734
wenzelm@6424
   735
wenzelm@6424
   736
(** axiomatic introduction of (co)inductive sets **)
berghofe@5094
   737
berghofe@5094
   738
fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@8401
   739
    atts intros monos con_defs thy params paramTs cTs cnames induct_cases =
berghofe@5094
   740
  let
berghofe@9072
   741
    val _ = message (coind_prefix coind ^ "inductive set(s) " ^ commas_quote cnames);
berghofe@5094
   742
wenzelm@6424
   743
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
wenzelm@9235
   744
    val (thy', _, fp_def, rec_sets_defs, _, _) =
berghofe@9072
   745
      mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   746
        params paramTs cTs cnames;
wenzelm@8375
   747
    val (elim_ts, elim_cases) = Library.split_list (mk_elims cs cTs params intr_ts intr_names);
berghofe@5094
   748
    val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   749
    val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
wenzelm@9598
   750
wenzelm@9598
   751
    val (thy'', [intrs, raw_elims]) =
berghofe@9072
   752
      thy'
wenzelm@9598
   753
      |> PureThy.add_axiomss_i [(("intros", intr_ts), atts), (("raw_elims", elim_ts), [])]
wenzelm@9598
   754
      |>> (if coind then I else
wenzelm@8433
   755
            #1 o PureThy.add_axioms_i [(("raw_induct", ind_t), [apsnd (standard o split_rule)])]);
berghofe@5094
   756
wenzelm@9598
   757
    val elims = map2 (fn (th, cases) => RuleCases.name cases th) (raw_elims, elim_cases);
berghofe@9072
   758
    val raw_induct = if coind then Drule.asm_rl else PureThy.get_thm thy'' "raw_induct";
berghofe@5094
   759
    val induct = if coind orelse length cs > 1 then raw_induct
berghofe@5094
   760
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   761
berghofe@9072
   762
    val (thy''', ([elims'], intrs')) =
berghofe@9072
   763
      thy''
wenzelm@8375
   764
      |> PureThy.add_thmss [(("elims", elims), [])]
wenzelm@8433
   765
      |>> (if coind then I
wenzelm@8433
   766
          else #1 o PureThy.add_thms [(("induct", induct), [RuleCases.case_names induct_cases])])
wenzelm@8433
   767
      |>>> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
wenzelm@8433
   768
      |>> Theory.parent_path;
berghofe@9072
   769
    val induct' = if coind then raw_induct else PureThy.get_thm thy''' "induct";
berghofe@9072
   770
  in (thy''',
wenzelm@9235
   771
    {defs = fp_def :: rec_sets_defs,
wenzelm@8312
   772
     mono = Drule.asm_rl,
wenzelm@8312
   773
     unfold = Drule.asm_rl,
wenzelm@8433
   774
     intrs = intrs',
wenzelm@8433
   775
     elims = elims',
wenzelm@8433
   776
     mk_cases = mk_cases elims',
berghofe@5094
   777
     raw_induct = raw_induct,
wenzelm@7798
   778
     induct = induct'})
berghofe@5094
   779
  end;
berghofe@5094
   780
wenzelm@6424
   781
wenzelm@6424
   782
wenzelm@6424
   783
(** introduction of (co)inductive sets **)
berghofe@5094
   784
berghofe@5094
   785
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   786
    atts intros monos con_defs thy =
berghofe@5094
   787
  let
wenzelm@6424
   788
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
wenzelm@6394
   789
    val sign = Theory.sign_of thy;
berghofe@5094
   790
berghofe@5094
   791
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   792
    val (_, params) = strip_comb (hd cs);
berghofe@5094
   793
    val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
berghofe@5094
   794
      \ component is not a free variable: " sign) params;
berghofe@5094
   795
berghofe@5094
   796
    val cTs = map (try' (HOLogic.dest_setT o fastype_of)
berghofe@5094
   797
      "Recursive component not of type set: " sign) cs;
berghofe@5094
   798
wenzelm@6437
   799
    val full_cnames = map (try' (fst o dest_Const o head_of)
berghofe@5094
   800
      "Recursive set not previously declared as constant: " sign) cs;
wenzelm@6437
   801
    val cnames = map Sign.base_name full_cnames;
berghofe@5094
   802
wenzelm@6424
   803
    val _ = seq (check_rule sign cs o snd o fst) intros;
wenzelm@8401
   804
    val induct_cases = map (#1 o #1) intros;
wenzelm@6437
   805
wenzelm@9405
   806
    val (thy1, result as {elims, induct, ...}) =
wenzelm@6437
   807
      (if ! quick_and_dirty then add_ind_axm else add_ind_def)
wenzelm@6521
   808
        verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
wenzelm@8401
   809
        con_defs thy params paramTs cTs cnames induct_cases;
wenzelm@8307
   810
    val thy2 = thy1
wenzelm@8307
   811
      |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result)
wenzelm@9405
   812
      |> add_cases_induct no_elim (no_ind orelse coind) full_cnames elims induct induct_cases;
wenzelm@6437
   813
  in (thy2, result) end;
berghofe@5094
   814
wenzelm@6424
   815
berghofe@5094
   816
wenzelm@6424
   817
(** external interface **)
wenzelm@6424
   818
wenzelm@6521
   819
fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
berghofe@5094
   820
  let
wenzelm@6394
   821
    val sign = Theory.sign_of thy;
wenzelm@8100
   822
    val cs = map (term_of o Thm.read_cterm sign o rpair HOLogic.termT) c_strings;
wenzelm@6424
   823
wenzelm@6521
   824
    val atts = map (Attrib.global_attribute thy) srcs;
wenzelm@6424
   825
    val intr_names = map (fst o fst) intro_srcs;
wenzelm@9405
   826
    fun read_rule s = Thm.read_cterm sign (s, propT)
wenzelm@9405
   827
      handle ERROR => error ("The error(s) above occurred for " ^ s);
wenzelm@9405
   828
    val intr_ts = map (Thm.term_of o read_rule o snd o fst) intro_srcs;
wenzelm@6424
   829
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
berghofe@7020
   830
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
berghofe@5094
   831
wenzelm@6424
   832
    val ((thy', con_defs), monos) = thy
wenzelm@6424
   833
      |> IsarThy.apply_theorems raw_monos
wenzelm@6424
   834
      |> apfst (IsarThy.apply_theorems raw_con_defs);
wenzelm@6424
   835
  in
berghofe@7020
   836
    add_inductive_i verbose false "" coind false false cs'
berghofe@7020
   837
      atts ((intr_names ~~ intr_ts') ~~ intr_atts) monos con_defs thy'
berghofe@5094
   838
  end;
berghofe@5094
   839
wenzelm@6424
   840
wenzelm@6424
   841
wenzelm@6437
   842
(** package setup **)
wenzelm@6437
   843
wenzelm@6437
   844
(* setup theory *)
wenzelm@6437
   845
wenzelm@8634
   846
val setup =
wenzelm@8634
   847
 [InductiveData.init,
wenzelm@9625
   848
  Method.add_methods [("ind_cases", mk_cases_meth oo mk_cases_args,
wenzelm@9598
   849
    "dynamic case analysis on sets")],
wenzelm@8634
   850
  Attrib.add_attributes [("mono", mono_attr, "monotonicity rule")]];
wenzelm@6437
   851
wenzelm@6437
   852
wenzelm@6437
   853
(* outer syntax *)
wenzelm@6424
   854
wenzelm@6723
   855
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6424
   856
wenzelm@6521
   857
fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
wenzelm@6723
   858
  #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
wenzelm@6424
   859
wenzelm@6424
   860
fun ind_decl coind =
wenzelm@6729
   861
  (Scan.repeat1 P.term --| P.marg_comment) --
wenzelm@9598
   862
  (P.$$$ "intros" |--
wenzelm@7152
   863
    P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop --| P.marg_comment))) --
wenzelm@6729
   864
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
wenzelm@6729
   865
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
wenzelm@6424
   866
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   867
wenzelm@6723
   868
val inductiveP =
wenzelm@6723
   869
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   870
wenzelm@6723
   871
val coinductiveP =
wenzelm@6723
   872
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   873
wenzelm@7107
   874
wenzelm@7107
   875
val ind_cases =
wenzelm@9625
   876
  P.opt_thm_name ":" -- Scan.repeat1 P.prop -- P.marg_comment
wenzelm@7107
   877
  >> (Toplevel.theory o inductive_cases);
wenzelm@7107
   878
wenzelm@7107
   879
val inductive_casesP =
wenzelm@9804
   880
  OuterSyntax.command "inductive_cases"
wenzelm@9598
   881
    "create simplified instances of elimination rules (improper)" K.thy_script ind_cases;
wenzelm@7107
   882
wenzelm@9643
   883
val _ = OuterSyntax.add_keywords ["intros", "monos", "con_defs"];
wenzelm@7107
   884
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   885
berghofe@5094
   886
end;
wenzelm@6424
   887
wenzelm@6424
   888
wenzelm@6424
   889
end;