src/HOL/Tools/inductive_package.ML
author wenzelm
Sat Jan 21 23:02:14 2006 +0100 (2006-01-21)
changeset 18728 6790126ab5f6
parent 18708 4b3dadb4fe33
child 18787 5784fe1b5657
permissions -rw-r--r--
simplified type attribute;
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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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    Author:     Stefan Berghofer, TU Muenchen
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    Author:     Markus Wenzel, 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 trace: bool ref
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  val unify_consts: theory -> term list -> term list -> term list * term list
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  val split_rule_vars: term list -> thm -> thm
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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 the_mk_cases: theory -> string -> string -> thm
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  val print_inductives: theory -> unit
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  val mono_add: attribute
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  val mono_del: attribute
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  val get_monos: theory -> thm list
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  val inductive_forall_name: string
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  val inductive_forall_def: thm
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  val rulify: thm -> thm
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  val inductive_cases: ((bstring * Attrib.src list) * string list) list -> theory -> theory
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  val inductive_cases_i: ((bstring * attribute list) * term list) list -> theory -> theory
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  val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
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    ((bstring * term) * attribute list) 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 ->
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    ((bstring * string) * Attrib.src list) list -> (thmref * Attrib.src list) list ->
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    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 setup: theory -> theory
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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 mono_name = "Orderings.mono";
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val gfp_name = "FixedPoint.gfp";
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val lfp_name = "FixedPoint.lfp";
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val vimage_name = "Set.vimage";
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val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (Thm.concl_of vimageD);
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val inductive_forall_name = "HOL.induct_forall";
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val inductive_forall_def = thm "induct_forall_def";
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val inductive_conj_name = "HOL.induct_conj";
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val inductive_conj_def = thm "induct_conj_def";
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val inductive_conj = thms "induct_conj";
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val inductive_atomize = thms "induct_atomize";
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val inductive_rulify = thms "induct_rulify";
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val inductive_rulify_fallback = thms "induct_rulify_fallback";
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(** theory data **)
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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 InductiveData = TheoryDataFun
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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 extend = I;
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  fun merge _ ((tab1, monos1), (tab2, monos2)) =
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    (Symtab.merge (K true) (tab1, tab2), Drule.merge_rules (monos1, monos2));
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  fun print thy (tab, monos) =
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    [Pretty.strs ("(co)inductives:" ::
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      map #1 (NameSpace.extern_table (Sign.const_space thy, tab))),
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     Pretty.big_list "monotonicity rules:" (map (Display.pretty_thm_sg thy) monos)]
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    |> Pretty.chunks |> Pretty.writeln;
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end);
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val print_inductives = InductiveData.print;
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(* get and put data *)
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val get_inductive = Symtab.lookup o #1 o InductiveData.get;
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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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val the_mk_cases = (#mk_cases o #2) oo the_inductive;
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fun put_inductives names info = InductiveData.map (apfst (fn tab =>
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  fold (fn name => Symtab.update_new (name, info)) names tab
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    handle Symtab.DUP dup => error ("Duplicate definition of (co)inductive set " ^ quote dup)));
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(** monotonicity rules **)
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val get_monos = #2 o InductiveData.get;
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val map_monos = Context.map_theory o InductiveData.map o Library.apsnd;
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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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val mono_add = Thm.declaration_attribute (map_monos o Drule.add_rules o mk_mono);
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val mono_del = Thm.declaration_attribute (map_monos o Drule.del_rules o mk_mono);
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(** misc utilities **)
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val quiet_mode = ref false;
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val trace = ref false;  (*for debugging*)
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fun message s = if ! quiet_mode then () else writeln s;
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fun clean_message s = if ! quick_and_dirty then () else message 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 always has the
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  same type in all introduction rules*)
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fun unify_consts thy cs intr_ts =
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  (let
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    val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
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    fun varify (t, (i, ts)) =
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      let val t' = map_term_types (Logic.incr_tvar (i + 1)) (#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 (~1, []) cs;
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    val (i', intr_ts') = foldr varify (i, []) intr_ts;
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    val rec_consts = fold add_term_consts_2 cs' [];
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    val intr_consts = fold add_term_consts_2 intr_ts' [];
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    fun unify (cname, cT) =
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      let val consts = map snd (List.filter (fn c => fst c = cname) intr_consts)
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      in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
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    val (env, _) = fold unify rec_consts (Vartab.empty, i');
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    val subst = Type.freeze o map_term_types (Envir.norm_type 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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(*make injections used 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 ("Sum_Type.Inl", T1 --> T) $ (mk_inj' T1 n2 i)
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        else
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          Const ("Sum_Type.Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
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      end
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  in mk_inj' sumT (length 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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(** proper splitting **)
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fun prod_factors p (Const ("Pair", _) $ t $ u) =
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      p :: prod_factors (1::p) t @ prod_factors (2::p) u
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  | prod_factors p _ = [];
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fun mg_prod_factors ts (t $ u) fs = if t mem ts then
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        let val f = prod_factors [] u
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        in AList.update (op =) (t, f inter (AList.lookup (op =) fs t) |> the_default f) fs end
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      else mg_prod_factors ts u (mg_prod_factors ts t fs)
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  | mg_prod_factors ts (Abs (_, _, t)) fs = mg_prod_factors ts t fs
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  | mg_prod_factors ts _ fs = fs;
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fun prodT_factors p ps (T as Type ("*", [T1, T2])) =
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      if p mem ps then prodT_factors (1::p) ps T1 @ prodT_factors (2::p) ps T2
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      else [T]
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  | prodT_factors _ _ T = [T];
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fun ap_split p ps (Type ("*", [T1, T2])) T3 u =
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      if p mem ps then HOLogic.split_const (T1, T2, T3) $
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        Abs ("v", T1, ap_split (2::p) ps T2 T3 (ap_split (1::p) ps T1
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          (prodT_factors (2::p) ps T2 ---> T3) (incr_boundvars 1 u) $ Bound 0))
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      else u
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  | ap_split _ _ _ _ u =  u;
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fun mk_tuple p ps (Type ("*", [T1, T2])) (tms as t::_) =
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      if p mem ps then HOLogic.mk_prod (mk_tuple (1::p) ps T1 tms,
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        mk_tuple (2::p) ps T2 (Library.drop (length (prodT_factors (1::p) ps T1), tms)))
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      else t
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  | mk_tuple _ _ _ (t::_) = t;
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fun split_rule_var' ((t as Var (v, Type ("fun", [T1, T2])), ps), rl) =
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      let val T' = prodT_factors [] ps T1 ---> T2
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          val newt = ap_split [] ps T1 T2 (Var (v, T'))
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          val cterm = Thm.cterm_of (Thm.theory_of_thm rl)
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      in
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          instantiate ([], [(cterm t, cterm newt)]) rl
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      end
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  | split_rule_var' (_, rl) = rl;
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val remove_split = rewrite_rule [split_conv RS eq_reflection];
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fun split_rule_vars vs rl = standard (remove_split (foldr split_rule_var'
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  rl (mg_prod_factors vs (Thm.prop_of rl) [])));
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fun split_rule vs rl = standard (remove_split (foldr split_rule_var'
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  rl (List.mapPartial (fn (t as Var ((a, _), _)) =>
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      Option.map (pair t) (AList.lookup (op =) vs a)) (term_vars (Thm.prop_of rl)))));
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(** process rules **)
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local
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fun err_in_rule thy name t msg =
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  error (cat_lines ["Ill-formed introduction rule " ^ quote name,
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    Sign.string_of_term thy t, msg]);
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fun err_in_prem thy name t p msg =
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  error (cat_lines ["Ill-formed premise", Sign.string_of_term thy p,
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    "in introduction rule " ^ quote name, Sign.string_of_term thy t, msg]);
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val bad_concl = "Conclusion of introduction rule must have form \"t : S_i\"";
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val all_not_allowed =
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    "Introduction rule must not have a leading \"!!\" quantifier";
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fun atomize_term thy = MetaSimplifier.rewrite_term thy inductive_atomize [];
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in
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fun check_rule thy 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 = map (atomize_term thy) prems;
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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 thy name rule prem "Non-atomic premise";
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  in
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    (case concl of
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      Const ("Trueprop", _) $ (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 thy name rule "Recursion term on left of member symbol"
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          else List.app check_prem (prems ~~ aprems)
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        else err_in_rule thy name rule bad_concl
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      | Const ("all", _) $ _ => err_in_rule thy name rule all_not_allowed
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      | _ => err_in_rule thy name rule bad_concl);
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    ((name, arule), att)
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  end;
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val rulify =  (* FIXME norm_hhf *)
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  hol_simplify inductive_conj
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  #> hol_simplify inductive_rulify
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  #> hol_simplify inductive_rulify_fallback
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  #> standard;
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end;
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(** properties of (co)inductive sets **)
berghofe@5094
   321
wenzelm@10735
   322
(* elimination rules *)
berghofe@5094
   323
wenzelm@8375
   324
fun mk_elims cs cTs params intr_ts intr_names =
berghofe@5094
   325
  let
skalberg@15574
   326
    val used = foldr add_term_names [] intr_ts;
berghofe@5094
   327
    val [aname, pname] = variantlist (["a", "P"], used);
berghofe@5094
   328
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@5094
   329
berghofe@5094
   330
    fun dest_intr r =
berghofe@5094
   331
      let val Const ("op :", _) $ t $ u =
berghofe@5094
   332
        HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   333
      in (u, t, Logic.strip_imp_prems r) end;
berghofe@5094
   334
wenzelm@8380
   335
    val intrs = map dest_intr intr_ts ~~ intr_names;
berghofe@5094
   336
berghofe@5094
   337
    fun mk_elim (c, T) =
berghofe@5094
   338
      let
berghofe@5094
   339
        val a = Free (aname, T);
berghofe@5094
   340
berghofe@5094
   341
        fun mk_elim_prem (_, t, ts) =
skalberg@15574
   342
          list_all_free (map dest_Free ((foldr add_term_frees [] (t::ts)) \\ params),
berghofe@5094
   343
            Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
skalberg@15570
   344
        val c_intrs = (List.filter (equal c o #1 o #1) intrs);
berghofe@5094
   345
      in
wenzelm@8375
   346
        (Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
wenzelm@8375
   347
          map mk_elim_prem (map #1 c_intrs), P), map #2 c_intrs)
berghofe@5094
   348
      end
berghofe@5094
   349
  in
berghofe@5094
   350
    map mk_elim (cs ~~ cTs)
berghofe@5094
   351
  end;
wenzelm@9598
   352
wenzelm@6424
   353
wenzelm@10735
   354
(* premises and conclusions of induction rules *)
berghofe@5094
   355
berghofe@5094
   356
fun mk_indrule cs cTs params intr_ts =
berghofe@5094
   357
  let
skalberg@15574
   358
    val used = foldr add_term_names [] intr_ts;
berghofe@5094
   359
berghofe@5094
   360
    (* predicates for induction rule *)
berghofe@5094
   361
berghofe@5094
   362
    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
berghofe@5094
   363
      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
berghofe@5094
   364
        map (fn T => T --> HOLogic.boolT) cTs);
berghofe@5094
   365
berghofe@5094
   366
    (* transform an introduction rule into a premise for induction rule *)
berghofe@5094
   367
berghofe@5094
   368
    fun mk_ind_prem r =
berghofe@5094
   369
      let
berghofe@5094
   370
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5094
   371
haftmann@17485
   372
        val pred_of = AList.lookup (op aconv) (cs ~~ preds);
berghofe@5094
   373
berghofe@7710
   374
        fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
berghofe@7710
   375
              (case pred_of u of
skalberg@15531
   376
                  NONE => (m $ fst (subst t) $ fst (subst u), NONE)
skalberg@15531
   377
                | SOME P => (HOLogic.mk_binop inductive_conj_name (s, P $ t), SOME (s, P $ t)))
berghofe@7710
   378
          | subst s =
berghofe@7710
   379
              (case pred_of s of
skalberg@15531
   380
                  SOME P => (HOLogic.mk_binop "op Int"
berghofe@7710
   381
                    (s, HOLogic.Collect_const (HOLogic.dest_setT
skalberg@15531
   382
                      (fastype_of s)) $ P), NONE)
skalberg@15531
   383
                | NONE => (case s of
skalberg@15531
   384
                     (t $ u) => (fst (subst t) $ fst (subst u), NONE)
skalberg@15531
   385
                   | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
skalberg@15531
   386
                   | _ => (s, NONE)));
berghofe@7710
   387
berghofe@7710
   388
        fun mk_prem (s, prems) = (case subst s of
skalberg@15531
   389
              (_, SOME (t, u)) => t :: u :: prems
berghofe@7710
   390
            | (t, _) => t :: prems);
wenzelm@9598
   391
berghofe@5094
   392
        val Const ("op :", _) $ t $ u =
berghofe@5094
   393
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   394
berghofe@5094
   395
      in list_all_free (frees,
skalberg@15574
   396
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
skalberg@15574
   397
             [] (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r))),
skalberg@15570
   398
               HOLogic.mk_Trueprop (valOf (pred_of u) $ t)))
berghofe@5094
   399
      end;
berghofe@5094
   400
berghofe@5094
   401
    val ind_prems = map mk_ind_prem intr_ts;
paulson@13626
   402
haftmann@17485
   403
    val factors = Library.fold (mg_prod_factors preds) ind_prems [];
berghofe@5094
   404
berghofe@5094
   405
    (* make conclusions for induction rules *)
berghofe@5094
   406
berghofe@5094
   407
    fun mk_ind_concl ((c, P), (ts, x)) =
berghofe@5094
   408
      let val T = HOLogic.dest_setT (fastype_of c);
haftmann@17485
   409
          val ps = AList.lookup (op =) factors P |> the_default [];
berghofe@10988
   410
          val Ts = prodT_factors [] ps T;
skalberg@15574
   411
          val (frees, x') = foldr (fn (T', (fs, s)) =>
skalberg@15574
   412
            ((Free (s, T'))::fs, Symbol.bump_string s)) ([], x) Ts;
berghofe@10988
   413
          val tuple = mk_tuple [] ps T frees;
berghofe@5094
   414
      in ((HOLogic.mk_binop "op -->"
berghofe@5094
   415
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
berghofe@5094
   416
      end;
berghofe@5094
   417
berghofe@7710
   418
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
skalberg@15574
   419
        (fst (foldr mk_ind_concl ([], "xa") (cs ~~ preds))))
berghofe@5094
   420
berghofe@10988
   421
  in (preds, ind_prems, mutual_ind_concl,
berghofe@10988
   422
    map (apfst (fst o dest_Free)) factors)
berghofe@5094
   423
  end;
berghofe@5094
   424
wenzelm@6424
   425
wenzelm@10735
   426
(* prepare cases and induct rules *)
wenzelm@8316
   427
wenzelm@18222
   428
fun add_cases_induct no_elim no_induct coind names elims induct =
wenzelm@8316
   429
  let
haftmann@18330
   430
    fun cases_spec name elim thy =
wenzelm@9405
   431
      thy
wenzelm@18463
   432
      |> Theory.parent_path
wenzelm@9405
   433
      |> Theory.add_path (Sign.base_name name)
wenzelm@18728
   434
      |> PureThy.add_thms [(("cases", elim), [InductAttrib.cases_set name])] |> snd
wenzelm@18463
   435
      |> Theory.restore_naming thy;
haftmann@18330
   436
    val cases_specs = if no_elim then [] else map2 cases_spec names elims;
wenzelm@8316
   437
wenzelm@18728
   438
    val induct_att = if coind then InductAttrib.coinduct_set else InductAttrib.induct_set;
wenzelm@18222
   439
    val induct_specs =
wenzelm@18463
   440
      if no_induct then I
wenzelm@18463
   441
      else
wenzelm@18463
   442
        let
wenzelm@18463
   443
          val rules = names ~~ map (ProjectRule.project induct) (1 upto length names);
wenzelm@18463
   444
          val inducts = map (RuleCases.save induct o standard o #2) rules;
wenzelm@18463
   445
        in
wenzelm@18463
   446
          PureThy.add_thms (rules |> map (fn (name, th) =>
wenzelm@18463
   447
            (("", th), [RuleCases.consumes 1, induct_att name]))) #> snd #>
wenzelm@18463
   448
          PureThy.add_thmss
wenzelm@18463
   449
            [((coind_prefix coind ^ "inducts", inducts), [RuleCases.consumes 1])] #> snd
wenzelm@18463
   450
        end;
wenzelm@18463
   451
  in Library.apply cases_specs #> induct_specs end;
wenzelm@8316
   452
wenzelm@8316
   453
wenzelm@8316
   454
wenzelm@10735
   455
(** proofs for (co)inductive sets **)
wenzelm@6424
   456
wenzelm@10735
   457
(* prove monotonicity -- NOT subject to quick_and_dirty! *)
berghofe@5094
   458
berghofe@5094
   459
fun prove_mono setT fp_fun monos thy =
wenzelm@10735
   460
 (message "  Proving monotonicity ...";
wenzelm@17985
   461
  standard (Goal.prove thy [] []   (*NO quick_and_dirty here!*)
wenzelm@17985
   462
    (HOLogic.mk_Trueprop
wenzelm@17985
   463
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun))
wenzelm@17985
   464
    (fn _ => EVERY [rtac monoI 1,
wenzelm@17985
   465
      REPEAT (ares_tac (List.concat (map mk_mono monos) @ get_monos thy) 1)])));
berghofe@5094
   466
wenzelm@6424
   467
wenzelm@10735
   468
(* prove introduction rules *)
berghofe@5094
   469
wenzelm@12180
   470
fun prove_intrs coind mono fp_def intr_ts rec_sets_defs thy =
berghofe@5094
   471
  let
wenzelm@10735
   472
    val _ = clean_message "  Proving the introduction rules ...";
berghofe@5094
   473
berghofe@13657
   474
    val unfold = standard' (mono RS (fp_def RS
nipkow@10186
   475
      (if coind then def_gfp_unfold else def_lfp_unfold)));
berghofe@5094
   476
berghofe@5094
   477
    fun select_disj 1 1 = []
berghofe@5094
   478
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   479
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   480
wenzelm@17985
   481
    val intrs = (1 upto (length intr_ts) ~~ intr_ts) |> map (fn (i, intr) =>
wenzelm@18222
   482
      rulify (SkipProof.prove thy [] [] intr (fn _ => EVERY
wenzelm@17985
   483
       [rewrite_goals_tac rec_sets_defs,
wenzelm@17985
   484
        stac unfold 1,
wenzelm@17985
   485
        REPEAT (resolve_tac [vimageI2, CollectI] 1),
wenzelm@17985
   486
        (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
wenzelm@17985
   487
        EVERY1 (select_disj (length intr_ts) i),
wenzelm@17985
   488
        (*Not ares_tac, since refl must be tried before any equality assumptions;
wenzelm@17985
   489
          backtracking may occur if the premises have extra variables!*)
wenzelm@17985
   490
        DEPTH_SOLVE_1 (resolve_tac [refl, exI, conjI] 1 APPEND assume_tac 1),
wenzelm@17985
   491
        (*Now solve the equations like Inl 0 = Inl ?b2*)
wenzelm@18222
   492
        REPEAT (rtac refl 1)])))
berghofe@5094
   493
berghofe@5094
   494
  in (intrs, unfold) end;
berghofe@5094
   495
wenzelm@6424
   496
wenzelm@10735
   497
(* prove elimination rules *)
berghofe@5094
   498
wenzelm@8375
   499
fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy =
berghofe@5094
   500
  let
wenzelm@10735
   501
    val _ = clean_message "  Proving the elimination rules ...";
berghofe@5094
   502
berghofe@7710
   503
    val rules1 = [CollectE, disjE, make_elim vimageD, exE];
wenzelm@10735
   504
    val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @ map make_elim [Inl_inject, Inr_inject];
wenzelm@8375
   505
  in
wenzelm@11005
   506
    mk_elims cs cTs params intr_ts intr_names |> map (fn (t, cases) =>
wenzelm@17985
   507
      SkipProof.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@17985
   508
        (fn prems => EVERY
wenzelm@11005
   509
          [cut_facts_tac [hd prems] 1,
wenzelm@17985
   510
           rewrite_goals_tac rec_sets_defs,
wenzelm@11005
   511
           dtac (unfold RS subst) 1,
wenzelm@11005
   512
           REPEAT (FIRSTGOAL (eresolve_tac rules1)),
wenzelm@11005
   513
           REPEAT (FIRSTGOAL (eresolve_tac rules2)),
wenzelm@17985
   514
           EVERY (map (fn prem =>
wenzelm@17985
   515
             DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_sets_defs prem, conjI] 1)) (tl prems))])
wenzelm@11005
   516
        |> rulify
wenzelm@11005
   517
        |> RuleCases.name cases)
wenzelm@8375
   518
  end;
berghofe@5094
   519
wenzelm@6424
   520
wenzelm@10735
   521
(* derivation of simplified elimination rules *)
berghofe@5094
   522
wenzelm@11682
   523
local
wenzelm@11682
   524
wenzelm@7107
   525
(*cprop should have the form t:Si where Si is an inductive set*)
wenzelm@11682
   526
val mk_cases_err = "mk_cases: proposition not of form \"t : S_i\"";
wenzelm@9598
   527
wenzelm@11682
   528
(*delete needless equality assumptions*)
wenzelm@11682
   529
val refl_thin = prove_goal HOL.thy "!!P. a = a ==> P ==> P" (fn _ => [assume_tac 1]);
wenzelm@11682
   530
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
wenzelm@11682
   531
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
wenzelm@11682
   532
wenzelm@11682
   533
fun simp_case_tac solved ss i =
wenzelm@11682
   534
  EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i
wenzelm@11682
   535
  THEN_MAYBE (if solved then no_tac else all_tac);
wenzelm@11682
   536
wenzelm@11682
   537
in
wenzelm@9598
   538
wenzelm@9598
   539
fun mk_cases_i elims ss cprop =
wenzelm@7107
   540
  let
wenzelm@7107
   541
    val prem = Thm.assume cprop;
wenzelm@11682
   542
    val tac = ALLGOALS (simp_case_tac false ss) THEN prune_params_tac;
wenzelm@9298
   543
    fun mk_elim rl = Drule.standard (Tactic.rule_by_tactic tac (prem RS rl));
wenzelm@7107
   544
  in
wenzelm@7107
   545
    (case get_first (try mk_elim) elims of
skalberg@15531
   546
      SOME r => r
skalberg@15531
   547
    | NONE => error (Pretty.string_of (Pretty.block
wenzelm@9598
   548
        [Pretty.str mk_cases_err, Pretty.fbrk, Display.pretty_cterm cprop])))
wenzelm@7107
   549
  end;
wenzelm@7107
   550
paulson@6141
   551
fun mk_cases elims s =
wenzelm@16432
   552
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.theory_of_thm (hd elims)) (s, propT));
wenzelm@9598
   553
wenzelm@9598
   554
fun smart_mk_cases thy ss cprop =
wenzelm@9598
   555
  let
wenzelm@9598
   556
    val c = #1 (Term.dest_Const (Term.head_of (#2 (HOLogic.dest_mem (HOLogic.dest_Trueprop
wenzelm@9598
   557
      (Logic.strip_imp_concl (Thm.term_of cprop))))))) handle TERM _ => error mk_cases_err;
wenzelm@9598
   558
    val (_, {elims, ...}) = the_inductive thy c;
wenzelm@9598
   559
  in mk_cases_i elims ss cprop end;
wenzelm@7107
   560
wenzelm@11682
   561
end;
wenzelm@11682
   562
wenzelm@7107
   563
wenzelm@7107
   564
(* inductive_cases(_i) *)
wenzelm@7107
   565
wenzelm@12609
   566
fun gen_inductive_cases prep_att prep_prop args thy =
wenzelm@9598
   567
  let
wenzelm@16432
   568
    val cert_prop = Thm.cterm_of thy o prep_prop (ProofContext.init thy);
wenzelm@12609
   569
    val mk_cases = smart_mk_cases thy (Simplifier.simpset_of thy) o cert_prop;
wenzelm@12609
   570
wenzelm@12876
   571
    val facts = args |> map (fn ((a, atts), props) =>
wenzelm@12876
   572
     ((a, map (prep_att thy) atts), map (Thm.no_attributes o single o mk_cases) props));
haftmann@18418
   573
  in thy |> IsarThy.theorems_i Drule.lemmaK facts |> snd end;
berghofe@5094
   574
wenzelm@18728
   575
val inductive_cases = gen_inductive_cases Attrib.attribute ProofContext.read_prop;
wenzelm@12172
   576
val inductive_cases_i = gen_inductive_cases (K I) ProofContext.cert_prop;
wenzelm@7107
   577
wenzelm@6424
   578
wenzelm@9598
   579
(* mk_cases_meth *)
wenzelm@9598
   580
wenzelm@9598
   581
fun mk_cases_meth (ctxt, raw_props) =
wenzelm@9598
   582
  let
wenzelm@9598
   583
    val thy = ProofContext.theory_of ctxt;
wenzelm@15032
   584
    val ss = local_simpset_of ctxt;
wenzelm@16432
   585
    val cprops = map (Thm.cterm_of thy o ProofContext.read_prop ctxt) raw_props;
wenzelm@10743
   586
  in Method.erule 0 (map (smart_mk_cases thy ss) cprops) end;
wenzelm@9598
   587
wenzelm@9598
   588
val mk_cases_args = Method.syntax (Scan.lift (Scan.repeat1 Args.name));
wenzelm@9598
   589
wenzelm@9598
   590
wenzelm@10735
   591
(* prove induction rule *)
berghofe@5094
   592
berghofe@5094
   593
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   594
    fp_def rec_sets_defs thy =
berghofe@5094
   595
  let
wenzelm@10735
   596
    val _ = clean_message "  Proving the induction rule ...";
berghofe@5094
   597
wenzelm@12922
   598
    val sum_case_rewrites =
wenzelm@16432
   599
      (if Context.theory_name thy = "Datatype" then
wenzelm@16486
   600
        PureThy.get_thms thy (Name "sum.cases")
wenzelm@16432
   601
      else
wenzelm@16432
   602
        (case ThyInfo.lookup_theory "Datatype" of
wenzelm@16432
   603
          NONE => []
wenzelm@16975
   604
        | SOME thy' =>
wenzelm@16975
   605
            if Theory.subthy (thy', thy) then
wenzelm@16975
   606
              PureThy.get_thms thy' (Name "sum.cases")
wenzelm@16975
   607
            else []))
wenzelm@16432
   608
      |> map mk_meta_eq;
berghofe@7293
   609
berghofe@10988
   610
    val (preds, ind_prems, mutual_ind_concl, factors) =
berghofe@10988
   611
      mk_indrule cs cTs params intr_ts;
berghofe@5094
   612
paulson@13626
   613
    val dummy = if !trace then
wenzelm@17985
   614
                (writeln "ind_prems = ";
wenzelm@17985
   615
                 List.app (writeln o Sign.string_of_term thy) ind_prems)
wenzelm@17985
   616
            else ();
paulson@13626
   617
berghofe@5094
   618
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   619
berghofe@5094
   620
    fun mk_ind_pred _ [P] = P
berghofe@5094
   621
      | mk_ind_pred T Ps =
berghofe@5094
   622
         let val n = (length Ps) div 2;
berghofe@5094
   623
             val Type (_, [T1, T2]) = T
berghofe@7293
   624
         in Const ("Datatype.sum.sum_case",
berghofe@5094
   625
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
skalberg@15570
   626
             mk_ind_pred T1 (Library.take (n, Ps)) $ mk_ind_pred T2 (Library.drop (n, Ps))
berghofe@5094
   627
         end;
berghofe@5094
   628
berghofe@5094
   629
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   630
berghofe@5094
   631
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   632
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   633
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   634
berghofe@5094
   635
    (* simplification rules for vimage and Collect *)
berghofe@5094
   636
berghofe@5094
   637
    val vimage_simps = if length cs < 2 then [] else
wenzelm@17985
   638
      map (fn c => standard (SkipProof.prove thy [] []
berghofe@5094
   639
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   640
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   641
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
wenzelm@17985
   642
             List.nth (preds, find_index_eq c cs))))
wenzelm@17985
   643
        (fn _ => EVERY
wenzelm@17985
   644
          [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites, rtac refl 1]))) cs;
berghofe@5094
   645
paulson@13626
   646
    val raw_fp_induct = (mono RS (fp_def RS def_lfp_induct));
paulson@13626
   647
paulson@13626
   648
    val dummy = if !trace then
wenzelm@17985
   649
                (writeln "raw_fp_induct = "; print_thm raw_fp_induct)
wenzelm@17985
   650
            else ();
paulson@13626
   651
wenzelm@17985
   652
    val induct = standard (SkipProof.prove thy [] ind_prems ind_concl
wenzelm@17985
   653
      (fn prems => EVERY
wenzelm@17985
   654
        [rewrite_goals_tac [inductive_conj_def],
wenzelm@17985
   655
         rtac (impI RS allI) 1,
paulson@13626
   656
         DETERM (etac raw_fp_induct 1),
berghofe@7710
   657
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
berghofe@5094
   658
         fold_goals_tac rec_sets_defs,
berghofe@5094
   659
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@7710
   660
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE])),
berghofe@5094
   661
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   662
           some premise involves disjunction.*)
paulson@13747
   663
         REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
paulson@15416
   664
         ALLGOALS (simp_tac (HOL_basic_ss addsimps sum_case_rewrites)),
berghofe@5094
   665
         EVERY (map (fn prem =>
wenzelm@17985
   666
           DEPTH_SOLVE_1 (ares_tac [rewrite_rule [inductive_conj_def] prem, conjI, refl] 1)) prems)]));
berghofe@5094
   667
wenzelm@17985
   668
    val lemma = standard (SkipProof.prove thy [] []
wenzelm@17985
   669
      (Logic.mk_implies (ind_concl, mutual_ind_concl)) (fn _ => EVERY
wenzelm@17985
   670
        [rewrite_goals_tac rec_sets_defs,
berghofe@5094
   671
         REPEAT (EVERY
berghofe@5094
   672
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   673
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
berghofe@7293
   674
            rewrite_goals_tac sum_case_rewrites,
wenzelm@17985
   675
            atac 1])]))
berghofe@5094
   676
berghofe@10988
   677
  in standard (split_rule factors (induct RS lemma)) end;
berghofe@5094
   678
wenzelm@6424
   679
wenzelm@6424
   680
wenzelm@10735
   681
(** specification of (co)inductive sets **)
berghofe@5094
   682
wenzelm@10729
   683
fun cond_declare_consts declare_consts cs paramTs cnames =
wenzelm@10729
   684
  if declare_consts then
berghofe@14235
   685
    Theory.add_consts_i (map (fn (c, n) => (Sign.base_name n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@10729
   686
  else I;
wenzelm@10729
   687
wenzelm@12180
   688
fun mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
berghofe@9072
   689
      params paramTs cTs cnames =
berghofe@5094
   690
  let
berghofe@5094
   691
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   692
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   693
wenzelm@10735
   694
    val fp_name = if coind then gfp_name else lfp_name;
berghofe@5094
   695
skalberg@15574
   696
    val used = foldr add_term_names [] intr_ts;
berghofe@5149
   697
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   698
berghofe@5094
   699
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   700
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   701
    (* is transformed into                                *)
berghofe@5094
   702
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   703
berghofe@5094
   704
    fun transform_rule r =
berghofe@5094
   705
      let
berghofe@5094
   706
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   707
        val subst = subst_free
berghofe@5149
   708
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   709
        val Const ("op :", _) $ t $ u =
berghofe@5094
   710
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   711
skalberg@15574
   712
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
skalberg@15574
   713
        (foldr1 HOLogic.mk_conj
berghofe@5149
   714
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   715
            (map (subst o HOLogic.dest_Trueprop)
skalberg@15574
   716
              (Logic.strip_imp_prems r)))) frees
berghofe@5094
   717
      end
berghofe@5094
   718
berghofe@5094
   719
    (* make a disjunction of all introduction rules *)
berghofe@5094
   720
berghofe@5149
   721
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@7710
   722
      absfree (xname, sumT, foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
berghofe@5094
   723
berghofe@5094
   724
    (* add definiton of recursive sets to theory *)
berghofe@5094
   725
berghofe@14235
   726
    val rec_name = if alt_name = "" then
berghofe@14235
   727
      space_implode "_" (map Sign.base_name cnames) else alt_name;
berghofe@14235
   728
    val full_rec_name = if length cs < 2 then hd cnames
wenzelm@16432
   729
      else Sign.full_name thy rec_name;
berghofe@5094
   730
berghofe@5094
   731
    val rec_const = list_comb
berghofe@5094
   732
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   733
berghofe@5094
   734
    val fp_def_term = Logic.mk_equals (rec_const,
wenzelm@10735
   735
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun);
berghofe@5094
   736
berghofe@5094
   737
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   738
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   739
haftmann@18358
   740
    val ([fp_def :: rec_sets_defs], thy') =
wenzelm@8433
   741
      thy
wenzelm@10729
   742
      |> cond_declare_consts declare_consts cs paramTs cnames
wenzelm@8433
   743
      |> (if length cs < 2 then I
wenzelm@8433
   744
          else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
wenzelm@8433
   745
      |> Theory.add_path rec_name
wenzelm@9315
   746
      |> PureThy.add_defss_i false [(("defs", def_terms), [])];
berghofe@5094
   747
berghofe@9072
   748
    val mono = prove_mono setT fp_fun monos thy'
berghofe@5094
   749
wenzelm@18222
   750
  in (thy', rec_name, mono, fp_def, rec_sets_defs, rec_const, sumT) end;
berghofe@5094
   751
berghofe@9072
   752
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@12180
   753
    intros monos thy params paramTs cTs cnames induct_cases =
berghofe@9072
   754
  let
wenzelm@10735
   755
    val _ =
wenzelm@10735
   756
      if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
berghofe@14235
   757
        commas_quote (map Sign.base_name cnames)) else ();
berghofe@9072
   758
berghofe@9072
   759
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
berghofe@9072
   760
wenzelm@18222
   761
    val (thy1, rec_name, mono, fp_def, rec_sets_defs, rec_const, sumT) =
wenzelm@12180
   762
      mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
berghofe@9072
   763
        params paramTs cTs cnames;
berghofe@9072
   764
wenzelm@12180
   765
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts rec_sets_defs thy1;
berghofe@5094
   766
    val elims = if no_elim then [] else
wenzelm@9939
   767
      prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy1;
wenzelm@8312
   768
    val raw_induct = if no_ind then Drule.asm_rl else
berghofe@5094
   769
      if coind then standard (rule_by_tactic
oheimb@5553
   770
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   771
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   772
      else
berghofe@5094
   773
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
wenzelm@9939
   774
          rec_sets_defs thy1;
wenzelm@12165
   775
    val induct =
wenzelm@18222
   776
      if coind then
wenzelm@18222
   777
        (raw_induct, [RuleCases.case_names [rec_name],
wenzelm@18234
   778
          RuleCases.case_conclusion (rec_name, induct_cases),
wenzelm@18222
   779
          RuleCases.consumes 1])
wenzelm@18222
   780
      else if no_ind orelse length cs > 1 then
wenzelm@18222
   781
        (raw_induct, [RuleCases.case_names induct_cases, RuleCases.consumes 0])
wenzelm@18222
   782
      else (raw_induct RSN (2, rev_mp), [RuleCases.case_names induct_cases, RuleCases.consumes 1]);
berghofe@5094
   783
haftmann@18377
   784
    val (intrs', thy2) =
haftmann@18377
   785
      thy1
haftmann@18377
   786
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts);
haftmann@18377
   787
    val (([_, elims'], [induct']), thy3) =
wenzelm@10735
   788
      thy2
wenzelm@11005
   789
      |> PureThy.add_thmss
wenzelm@11628
   790
        [(("intros", intrs'), []),
wenzelm@11005
   791
          (("elims", elims), [RuleCases.consumes 1])]
haftmann@18377
   792
      ||>> PureThy.add_thms
wenzelm@18463
   793
        [((coind_prefix coind ^ "induct", rulify (#1 induct)), #2 induct)];
wenzelm@9939
   794
  in (thy3,
wenzelm@10735
   795
    {defs = fp_def :: rec_sets_defs,
berghofe@5094
   796
     mono = mono,
berghofe@5094
   797
     unfold = unfold,
berghofe@13709
   798
     intrs = intrs',
wenzelm@7798
   799
     elims = elims',
wenzelm@7798
   800
     mk_cases = mk_cases elims',
wenzelm@10729
   801
     raw_induct = rulify raw_induct,
wenzelm@7798
   802
     induct = induct'})
berghofe@5094
   803
  end;
berghofe@5094
   804
wenzelm@6424
   805
wenzelm@10735
   806
(* external interfaces *)
berghofe@5094
   807
wenzelm@16432
   808
fun try_term f msg thy t =
wenzelm@10735
   809
  (case Library.try f t of
skalberg@15531
   810
    SOME x => x
wenzelm@16432
   811
  | NONE => error (msg ^ Sign.string_of_term thy t));
berghofe@5094
   812
wenzelm@12180
   813
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs pre_intros monos thy =
berghofe@5094
   814
  let
wenzelm@6424
   815
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
berghofe@5094
   816
berghofe@5094
   817
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   818
    val (_, params) = strip_comb (hd cs);
wenzelm@10735
   819
    val paramTs = map (try_term (snd o dest_Free) "Parameter in recursive\
wenzelm@16432
   820
      \ component is not a free variable: " thy) params;
berghofe@5094
   821
wenzelm@10735
   822
    val cTs = map (try_term (HOLogic.dest_setT o fastype_of)
wenzelm@16432
   823
      "Recursive component not of type set: " thy) cs;
berghofe@5094
   824
berghofe@14235
   825
    val cnames = map (try_term (fst o dest_Const o head_of)
wenzelm@16432
   826
      "Recursive set not previously declared as constant: " thy) cs;
berghofe@5094
   827
wenzelm@16432
   828
    val save_thy = thy
wenzelm@16432
   829
      |> Theory.copy |> cond_declare_consts declare_consts cs paramTs cnames;
wenzelm@16432
   830
    val intros = map (check_rule save_thy cs) pre_intros;
wenzelm@8401
   831
    val induct_cases = map (#1 o #1) intros;
wenzelm@6437
   832
wenzelm@9405
   833
    val (thy1, result as {elims, induct, ...}) =
wenzelm@11628
   834
      add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs intros monos
wenzelm@12180
   835
        thy params paramTs cTs cnames induct_cases;
wenzelm@8307
   836
    val thy2 = thy1
berghofe@14235
   837
      |> put_inductives cnames ({names = cnames, coind = coind}, result)
wenzelm@18463
   838
      |> add_cases_induct no_elim no_ind coind cnames elims induct
wenzelm@18463
   839
      |> Theory.parent_path;
wenzelm@6437
   840
  in (thy2, result) end;
berghofe@5094
   841
wenzelm@12180
   842
fun add_inductive verbose coind c_strings intro_srcs raw_monos thy =
berghofe@5094
   843
  let
wenzelm@16975
   844
    val cs = map (Sign.read_term thy) c_strings;
wenzelm@6424
   845
wenzelm@6424
   846
    val intr_names = map (fst o fst) intro_srcs;
wenzelm@16432
   847
    fun read_rule s = Thm.read_cterm thy (s, propT)
wenzelm@18678
   848
      handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s);
wenzelm@9405
   849
    val intr_ts = map (Thm.term_of o read_rule o snd o fst) intro_srcs;
wenzelm@18728
   850
    val intr_atts = map (map (Attrib.attribute thy) o snd) intro_srcs;
wenzelm@16432
   851
    val (cs', intr_ts') = unify_consts thy cs intr_ts;
berghofe@5094
   852
haftmann@18418
   853
    val (monos, thy') = thy |> IsarThy.apply_theorems raw_monos;
wenzelm@6424
   854
  in
berghofe@7020
   855
    add_inductive_i verbose false "" coind false false cs'
wenzelm@12180
   856
      ((intr_names ~~ intr_ts') ~~ intr_atts) monos thy'
berghofe@5094
   857
  end;
berghofe@5094
   858
wenzelm@6424
   859
wenzelm@6424
   860
wenzelm@6437
   861
(** package setup **)
wenzelm@6437
   862
wenzelm@6437
   863
(* setup theory *)
wenzelm@6437
   864
wenzelm@8634
   865
val setup =
wenzelm@18708
   866
  InductiveData.init #>
wenzelm@9625
   867
  Method.add_methods [("ind_cases", mk_cases_meth oo mk_cases_args,
wenzelm@18708
   868
    "dynamic case analysis on sets")] #>
wenzelm@18728
   869
  Attrib.add_attributes [("mono", Attrib.add_del_args mono_add mono_del,
wenzelm@18728
   870
    "declaration of monotonicity rule")];
wenzelm@6437
   871
wenzelm@6437
   872
wenzelm@6437
   873
(* outer syntax *)
wenzelm@6424
   874
wenzelm@17057
   875
local structure P = OuterParse and K = OuterKeyword in
wenzelm@6424
   876
wenzelm@12180
   877
fun mk_ind coind ((sets, intrs), monos) =
wenzelm@12180
   878
  #1 o add_inductive true coind sets (map P.triple_swap intrs) monos;
wenzelm@6424
   879
wenzelm@6424
   880
fun ind_decl coind =
wenzelm@12876
   881
  Scan.repeat1 P.term --
wenzelm@9598
   882
  (P.$$$ "intros" |--
wenzelm@12876
   883
    P.!!! (Scan.repeat1 (P.opt_thm_name ":" -- P.prop))) --
wenzelm@12876
   884
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1) []
wenzelm@6424
   885
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   886
wenzelm@6723
   887
val inductiveP =
wenzelm@6723
   888
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   889
wenzelm@6723
   890
val coinductiveP =
wenzelm@6723
   891
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   892
wenzelm@7107
   893
wenzelm@7107
   894
val ind_cases =
wenzelm@12876
   895
  P.and_list1 (P.opt_thm_name ":" -- Scan.repeat1 P.prop)
wenzelm@7107
   896
  >> (Toplevel.theory o inductive_cases);
wenzelm@7107
   897
wenzelm@7107
   898
val inductive_casesP =
wenzelm@9804
   899
  OuterSyntax.command "inductive_cases"
wenzelm@9598
   900
    "create simplified instances of elimination rules (improper)" K.thy_script ind_cases;
wenzelm@7107
   901
wenzelm@12180
   902
val _ = OuterSyntax.add_keywords ["intros", "monos"];
wenzelm@7107
   903
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   904
berghofe@5094
   905
end;
wenzelm@6424
   906
wenzelm@6424
   907
end;
wenzelm@15705
   908