src/HOL/Tools/inductive_package.ML
author haftmann
Fri, 16 Dec 2005 09:00:11 +0100
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re-arranged tuples (theory * 'a) to ('a * theory) in Pure
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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_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 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 * theory 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) * theory 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) list
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end;
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structure InductivePackage: INDUCTIVE_PACKAGE =
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struct
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(** theory context references **)
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val 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_rulify1 = thms "induct_rulify1";
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val inductive_rulify2 = thms "induct_rulify2";
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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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fun map_monos f = InductiveData.map (Library.apsnd f);
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fun mk_mono thm =
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  let
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    fun eq2mono thm' = [standard (thm' RS (thm' RS eq_to_mono))] @
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      (case concl_of thm of
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          (_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
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        | _ => [standard (thm' RS (thm' RS eq_to_mono2))]);
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    val concl = concl_of thm
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  in
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    if Logic.is_equals concl then
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      eq2mono (thm RS meta_eq_to_obj_eq)
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    else if can (HOLogic.dest_eq o HOLogic.dest_Trueprop) concl then
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      eq2mono thm
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    else [thm]
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  end;
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(* attributes *)
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fun mono_add_global (thy, thm) = (map_monos (Drule.add_rules (mk_mono thm)) thy, thm);
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fun mono_del_global (thy, thm) = (map_monos (Drule.del_rules (mk_mono thm)) thy, thm);
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val mono_attr =
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 (Attrib.add_del_args mono_add_global mono_del_global,
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  Attrib.add_del_args Attrib.undef_local_attribute Attrib.undef_local_attribute);
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(** 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_rulify1
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  #> hol_simplify inductive_rulify2
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  #> standard;
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end;
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(** properties of (co)inductive sets **)
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(* elimination rules *)
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8375
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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 = (List.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)) ::
0544749a5e8f mk_elims, add_cases_induct: name rule cases;
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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
ddcc3c114a0e New inductive definition package
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    map mk_elim (cs ~~ cTs)
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  end;
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6424
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10735
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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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   365
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    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
ddcc3c114a0e New inductive definition package
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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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17485
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        val pred_of = AList.lookup (op aconv) (cs ~~ preds);
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7710
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        fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
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              (case pred_of u of
15531
08c8dad8e399 Deleted Library.option type.
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                  NONE => (m $ fst (subst t) $ fst (subst u), NONE)
08c8dad8e399 Deleted Library.option type.
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                | SOME P => (HOLogic.mk_binop inductive_conj_name (s, P $ t), SOME (s, P $ t)))
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          | subst s =
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   383
              (case pred_of s of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15525
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   384
                  SOME P => (HOLogic.mk_binop "op Int"
7710
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   385
                    (s, HOLogic.Collect_const (HOLogic.dest_setT
15531
08c8dad8e399 Deleted Library.option type.
skalberg
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diff changeset
   386
                      (fastype_of s)) $ P), NONE)
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15525
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   387
                | NONE => (case s of
08c8dad8e399 Deleted Library.option type.
skalberg
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   388
                     (t $ u) => (fst (subst t) $ fst (subst u), NONE)
08c8dad8e399 Deleted Library.option type.
skalberg
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   389
                   | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15525
diff changeset
   390
                   | _ => (s, NONE)));
7710
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   391
bf8cb3fc5d64 Monotonicity rules for inductive definitions can now be added to a theory via
berghofe
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diff changeset
   392
        fun mk_prem (s, prems) = (case subst s of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15525
diff changeset
   393
              (_, SOME (t, u)) => t :: u :: prems
7710
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   394
            | (t, _) => t :: prems);
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   395
5094
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   396
        val Const ("op :", _) $ t $ u =
ddcc3c114a0e New inductive definition package
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parents:
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   397
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   398
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   399
      in list_all_free (frees,
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   400
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   401
             [] (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r))),
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   402
               HOLogic.mk_Trueprop (valOf (pred_of u) $ t)))
5094
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berghofe
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diff changeset
   403
      end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   404
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   405
    val ind_prems = map mk_ind_prem intr_ts;
13626
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   406
17485
c39871c52977 introduced AList module
haftmann
parents: 17412
diff changeset
   407
    val factors = Library.fold (mg_prod_factors preds) ind_prems [];
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   408
ddcc3c114a0e New inductive definition package
berghofe
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diff changeset
   409
    (* make conclusions for induction rules *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   410
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   411
    fun mk_ind_concl ((c, P), (ts, x)) =
ddcc3c114a0e New inductive definition package
berghofe
parents:
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   412
      let val T = HOLogic.dest_setT (fastype_of c);
17485
c39871c52977 introduced AList module
haftmann
parents: 17412
diff changeset
   413
          val ps = AList.lookup (op =) factors P |> the_default [];
10988
e0016a009c17 Splitting of arguments of product types in induction rules is now less
berghofe
parents: 10910
diff changeset
   414
          val Ts = prodT_factors [] ps T;
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   415
          val (frees, x') = foldr (fn (T', (fs, s)) =>
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   416
            ((Free (s, T'))::fs, Symbol.bump_string s)) ([], x) Ts;
10988
e0016a009c17 Splitting of arguments of product types in induction rules is now less
berghofe
parents: 10910
diff changeset
   417
          val tuple = mk_tuple [] ps T frees;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   418
      in ((HOLogic.mk_binop "op -->"
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   419
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   420
      end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   421
7710
bf8cb3fc5d64 Monotonicity rules for inductive definitions can now be added to a theory via
berghofe
parents: 7349
diff changeset
   422
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   423
        (fst (foldr mk_ind_concl ([], "xa") (cs ~~ preds))))
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   424
10988
e0016a009c17 Splitting of arguments of product types in induction rules is now less
berghofe
parents: 10910
diff changeset
   425
  in (preds, ind_prems, mutual_ind_concl,
e0016a009c17 Splitting of arguments of product types in induction rules is now less
berghofe
parents: 10910
diff changeset
   426
    map (apfst (fst o dest_Free)) factors)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   427
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   428
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   429
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   430
(* prepare cases and induct rules *)
8316
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   431
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   432
(*
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   433
  transform mutual rule:
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   434
    HH ==> (x1:A1 --> P1 x1) & ... & (xn:An --> Pn xn)
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   435
  into i-th projection:
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   436
    xi:Ai ==> HH ==> Pi xi
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   437
*)
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   438
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   439
fun project_rules [name] rule = [(name, rule)]
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   440
  | project_rules names mutual_rule =
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   441
      let
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   442
        val n = length names;
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   443
        fun proj i =
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   444
          (if i < n then (fn th => th RS conjunct1) else I)
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   445
            (Library.funpow (i - 1) (fn th => th RS conjunct2) mutual_rule)
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   446
            RS mp |> Thm.permute_prems 0 ~1 |> Drule.standard;
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   447
      in names ~~ map proj (1 upto n) end;
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   448
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   449
fun add_cases_induct no_elim no_induct coind names elims induct =
8316
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   450
  let
18330
444f16d232a2 introduced new map2, fold
haftmann
parents: 18234
diff changeset
   451
    fun cases_spec name elim thy =
9405
3235873fdd90 improved error msg;
wenzelm
parents: 9315
diff changeset
   452
      thy
3235873fdd90 improved error msg;
wenzelm
parents: 9315
diff changeset
   453
      |> Theory.add_path (Sign.base_name name)
18377
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   454
      |> (snd o PureThy.add_thms [(("cases", elim), [InductAttrib.cases_set_global name])])
9405
3235873fdd90 improved error msg;
wenzelm
parents: 9315
diff changeset
   455
      |> Theory.parent_path;
18330
444f16d232a2 introduced new map2, fold
haftmann
parents: 18234
diff changeset
   456
    val cases_specs = if no_elim then [] else map2 cases_spec names elims;
8316
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   457
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   458
    val induct_att =
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   459
      if coind then InductAttrib.coinduct_set_global else InductAttrib.induct_set_global;
18377
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   460
    fun induct_spec (name, th) = snd o PureThy.add_thms
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   461
      [(("", RuleCases.save induct th), [induct_att name])];
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   462
    val induct_specs =
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   463
      if no_induct then [] else map induct_spec (project_rules names induct);
9405
3235873fdd90 improved error msg;
wenzelm
parents: 9315
diff changeset
   464
  in Library.apply (cases_specs @ induct_specs) end;
8316
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   465
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   466
74639e19eca0 add_cases_induct: project_rules accomodates mutual induction;
wenzelm
parents: 8312
diff changeset
   467
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   468
(** proofs for (co)inductive sets **)
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   469
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   470
(* prove monotonicity -- NOT subject to quick_and_dirty! *)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   471
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   472
fun prove_mono setT fp_fun monos thy =
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   473
 (message "  Proving monotonicity ...";
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   474
  standard (Goal.prove thy [] []   (*NO quick_and_dirty here!*)
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   475
    (HOLogic.mk_Trueprop
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   476
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun))
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   477
    (fn _ => EVERY [rtac monoI 1,
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   478
      REPEAT (ares_tac (List.concat (map mk_mono monos) @ get_monos thy) 1)])));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   479
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   480
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   481
(* prove introduction rules *)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   482
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   483
fun prove_intrs coind mono fp_def intr_ts rec_sets_defs thy =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   484
  let
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   485
    val _ = clean_message "  Proving the introduction rules ...";
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   486
13657
c1637d60a846 Now applies standard' to "unfold" theorem (due to flex-flex constraints).
berghofe
parents: 13626
diff changeset
   487
    val unfold = standard' (mono RS (fp_def RS
10186
499637e8f2c6 *** empty log message ***
nipkow
parents: 10065
diff changeset
   488
      (if coind then def_gfp_unfold else def_lfp_unfold)));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   489
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   490
    fun select_disj 1 1 = []
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   491
      | select_disj _ 1 = [rtac disjI1]
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   492
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   493
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   494
    val intrs = (1 upto (length intr_ts) ~~ intr_ts) |> map (fn (i, intr) =>
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   495
      rulify (SkipProof.prove thy [] [] intr (fn _ => EVERY
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   496
       [rewrite_goals_tac rec_sets_defs,
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   497
        stac unfold 1,
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   498
        REPEAT (resolve_tac [vimageI2, CollectI] 1),
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   499
        (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   500
        EVERY1 (select_disj (length intr_ts) i),
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   501
        (*Not ares_tac, since refl must be tried before any equality assumptions;
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   502
          backtracking may occur if the premises have extra variables!*)
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   503
        DEPTH_SOLVE_1 (resolve_tac [refl, exI, conjI] 1 APPEND assume_tac 1),
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   504
        (*Now solve the equations like Inl 0 = Inl ?b2*)
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   505
        REPEAT (rtac refl 1)])))
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   506
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   507
  in (intrs, unfold) end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   508
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   509
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   510
(* prove elimination rules *)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   511
8375
0544749a5e8f mk_elims, add_cases_induct: name rule cases;
wenzelm
parents: 8336
diff changeset
   512
fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   513
  let
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   514
    val _ = clean_message "  Proving the elimination rules ...";
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   515
7710
bf8cb3fc5d64 Monotonicity rules for inductive definitions can now be added to a theory via
berghofe
parents: 7349
diff changeset
   516
    val rules1 = [CollectE, disjE, make_elim vimageD, exE];
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   517
    val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @ map make_elim [Inl_inject, Inr_inject];
8375
0544749a5e8f mk_elims, add_cases_induct: name rule cases;
wenzelm
parents: 8336
diff changeset
   518
  in
11005
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   519
    mk_elims cs cTs params intr_ts intr_names |> map (fn (t, cases) =>
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   520
      SkipProof.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   521
        (fn prems => EVERY
11005
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   522
          [cut_facts_tac [hd prems] 1,
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   523
           rewrite_goals_tac rec_sets_defs,
11005
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   524
           dtac (unfold RS subst) 1,
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   525
           REPEAT (FIRSTGOAL (eresolve_tac rules1)),
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   526
           REPEAT (FIRSTGOAL (eresolve_tac rules2)),
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   527
           EVERY (map (fn prem =>
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   528
             DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_sets_defs prem, conjI] 1)) (tl prems))])
11005
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   529
        |> rulify
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   530
        |> RuleCases.name cases)
8375
0544749a5e8f mk_elims, add_cases_induct: name rule cases;
wenzelm
parents: 8336
diff changeset
   531
  end;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   532
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   533
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   534
(* derivation of simplified elimination rules *)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   535
11682
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   536
local
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   537
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   538
(*cprop should have the form t:Si where Si is an inductive set*)
11682
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   539
val mk_cases_err = "mk_cases: proposition not of form \"t : S_i\"";
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   540
11682
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   541
(*delete needless equality assumptions*)
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   542
val refl_thin = prove_goal HOL.thy "!!P. a = a ==> P ==> P" (fn _ => [assume_tac 1]);
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   543
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   544
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   545
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   546
fun simp_case_tac solved ss i =
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   547
  EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   548
  THEN_MAYBE (if solved then no_tac else all_tac);
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   549
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   550
in
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   551
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   552
fun mk_cases_i elims ss cprop =
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   553
  let
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   554
    val prem = Thm.assume cprop;
11682
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   555
    val tac = ALLGOALS (simp_case_tac false ss) THEN prune_params_tac;
9298
7d9b562a750b use InductMethod.simp_case_tac;
wenzelm
parents: 9235
diff changeset
   556
    fun mk_elim rl = Drule.standard (Tactic.rule_by_tactic tac (prem RS rl));
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   557
  in
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   558
    (case get_first (try mk_elim) elims of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15525
diff changeset
   559
      SOME r => r
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15525
diff changeset
   560
    | NONE => error (Pretty.string_of (Pretty.block
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   561
        [Pretty.str mk_cases_err, Pretty.fbrk, Display.pretty_cterm cprop])))
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   562
  end;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   563
6141
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 6092
diff changeset
   564
fun mk_cases elims s =
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   565
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.theory_of_thm (hd elims)) (s, propT));
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   566
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   567
fun smart_mk_cases thy ss cprop =
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   568
  let
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   569
    val c = #1 (Term.dest_Const (Term.head_of (#2 (HOLogic.dest_mem (HOLogic.dest_Trueprop
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   570
      (Logic.strip_imp_concl (Thm.term_of cprop))))))) handle TERM _ => error mk_cases_err;
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   571
    val (_, {elims, ...}) = the_inductive thy c;
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   572
  in mk_cases_i elims ss cprop end;
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   573
11682
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   574
end;
d9063229b4a1 simp_case_tac is back again from induct_method.ML;
wenzelm
parents: 11628
diff changeset
   575
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   576
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   577
(* inductive_cases(_i) *)
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   578
12609
fb073a34b537 'inductive_cases': support 'and' form;
wenzelm
parents: 12527
diff changeset
   579
fun gen_inductive_cases prep_att prep_prop args thy =
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   580
  let
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   581
    val cert_prop = Thm.cterm_of thy o prep_prop (ProofContext.init thy);
12609
fb073a34b537 'inductive_cases': support 'and' form;
wenzelm
parents: 12527
diff changeset
   582
    val mk_cases = smart_mk_cases thy (Simplifier.simpset_of thy) o cert_prop;
fb073a34b537 'inductive_cases': support 'and' form;
wenzelm
parents: 12527
diff changeset
   583
12876
a70df1e5bf10 got rid of explicit marginal comments (now stripped earlier from input);
wenzelm
parents: 12798
diff changeset
   584
    val facts = args |> map (fn ((a, atts), props) =>
a70df1e5bf10 got rid of explicit marginal comments (now stripped earlier from input);
wenzelm
parents: 12798
diff changeset
   585
     ((a, map (prep_att thy) atts), map (Thm.no_attributes o single o mk_cases) props));
18418
bf448d999b7e re-arranged tuples (theory * 'a) to ('a * theory) in Pure
haftmann
parents: 18377
diff changeset
   586
  in thy |> IsarThy.theorems_i Drule.lemmaK facts |> snd end;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   587
12172
wenzelm
parents: 12165
diff changeset
   588
val inductive_cases = gen_inductive_cases Attrib.global_attribute ProofContext.read_prop;
wenzelm
parents: 12165
diff changeset
   589
val inductive_cases_i = gen_inductive_cases (K I) ProofContext.cert_prop;
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   590
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   591
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   592
(* mk_cases_meth *)
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   593
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   594
fun mk_cases_meth (ctxt, raw_props) =
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   595
  let
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   596
    val thy = ProofContext.theory_of ctxt;
15032
02aed07e01bf local_cla/simpset_of;
wenzelm
parents: 14981
diff changeset
   597
    val ss = local_simpset_of ctxt;
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   598
    val cprops = map (Thm.cterm_of thy o ProofContext.read_prop ctxt) raw_props;
10743
8ea821d1e3a4 Method.erule 0;
wenzelm
parents: 10735
diff changeset
   599
  in Method.erule 0 (map (smart_mk_cases thy ss) cprops) end;
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   600
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   601
val mk_cases_args = Method.syntax (Scan.lift (Scan.repeat1 Args.name));
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   602
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   603
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   604
(* prove induction rule *)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   605
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   606
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   607
    fp_def rec_sets_defs thy =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   608
  let
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   609
    val _ = clean_message "  Proving the induction rule ...";
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   610
12922
ed70a600f0ea clarified internal theory dependencies;
wenzelm
parents: 12902
diff changeset
   611
    val sum_case_rewrites =
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   612
      (if Context.theory_name thy = "Datatype" then
16486
1a12cdb6ee6b get_thm(s): Name;
wenzelm
parents: 16432
diff changeset
   613
        PureThy.get_thms thy (Name "sum.cases")
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   614
      else
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   615
        (case ThyInfo.lookup_theory "Datatype" of
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   616
          NONE => []
16975
34ed8d5d4f16 Sign.read_term;
wenzelm
parents: 16934
diff changeset
   617
        | SOME thy' =>
34ed8d5d4f16 Sign.read_term;
wenzelm
parents: 16934
diff changeset
   618
            if Theory.subthy (thy', thy) then
34ed8d5d4f16 Sign.read_term;
wenzelm
parents: 16934
diff changeset
   619
              PureThy.get_thms thy' (Name "sum.cases")
34ed8d5d4f16 Sign.read_term;
wenzelm
parents: 16934
diff changeset
   620
            else []))
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   621
      |> map mk_meta_eq;
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   622
10988
e0016a009c17 Splitting of arguments of product types in induction rules is now less
berghofe
parents: 10910
diff changeset
   623
    val (preds, ind_prems, mutual_ind_concl, factors) =
e0016a009c17 Splitting of arguments of product types in induction rules is now less
berghofe
parents: 10910
diff changeset
   624
      mk_indrule cs cTs params intr_ts;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   625
13626
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   626
    val dummy = if !trace then
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   627
                (writeln "ind_prems = ";
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   628
                 List.app (writeln o Sign.string_of_term thy) ind_prems)
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   629
            else ();
13626
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   630
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   631
    (* make predicate for instantiation of abstract induction rule *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   632
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   633
    fun mk_ind_pred _ [P] = P
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   634
      | mk_ind_pred T Ps =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   635
         let val n = (length Ps) div 2;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   636
             val Type (_, [T1, T2]) = T
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   637
         in Const ("Datatype.sum.sum_case",
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   638
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
15570
8d8c70b41bab Move towards standard functions.
skalberg
parents: 15531
diff changeset
   639
             mk_ind_pred T1 (Library.take (n, Ps)) $ mk_ind_pred T2 (Library.drop (n, Ps))
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   640
         end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   641
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   642
    val ind_pred = mk_ind_pred sumT preds;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   643
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   644
    val ind_concl = HOLogic.mk_Trueprop
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   645
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   646
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   647
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   648
    (* simplification rules for vimage and Collect *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   649
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   650
    val vimage_simps = if length cs < 2 then [] else
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   651
      map (fn c => standard (SkipProof.prove thy [] []
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   652
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   653
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   654
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   655
             List.nth (preds, find_index_eq c cs))))
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   656
        (fn _ => EVERY
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   657
          [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites, rtac refl 1]))) cs;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   658
13626
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   659
    val raw_fp_induct = (mono RS (fp_def RS def_lfp_induct));
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   660
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   661
    val dummy = if !trace then
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   662
                (writeln "raw_fp_induct = "; print_thm raw_fp_induct)
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   663
            else ();
13626
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   664
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   665
    val induct = standard (SkipProof.prove thy [] ind_prems ind_concl
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   666
      (fn prems => EVERY
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   667
        [rewrite_goals_tac [inductive_conj_def],
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   668
         rtac (impI RS allI) 1,
13626
282fbabec862 Fixed bug involving inductive definitions having equalities in the premises,
paulson
parents: 13197
diff changeset
   669
         DETERM (etac raw_fp_induct 1),
7710
bf8cb3fc5d64 Monotonicity rules for inductive definitions can now be added to a theory via
berghofe
parents: 7349
diff changeset
   670
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   671
         fold_goals_tac rec_sets_defs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   672
         (*This CollectE and disjE separates out the introduction rules*)
7710
bf8cb3fc5d64 Monotonicity rules for inductive definitions can now be added to a theory via
berghofe
parents: 7349
diff changeset
   673
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE])),
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   674
         (*Now break down the individual cases.  No disjE here in case
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   675
           some premise involves disjunction.*)
13747
bf308fcfd08e Better treatment of equality in premises of inductive definitions. Less
paulson
parents: 13709
diff changeset
   676
         REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
15416
db69af736ebb Further fix to a bug (involving equational premises) in inductive definitions
paulson
parents: 15391
diff changeset
   677
         ALLGOALS (simp_tac (HOL_basic_ss addsimps sum_case_rewrites)),
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   678
         EVERY (map (fn prem =>
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   679
           DEPTH_SOLVE_1 (ares_tac [rewrite_rule [inductive_conj_def] prem, conjI, refl] 1)) prems)]));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   680
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   681
    val lemma = standard (SkipProof.prove thy [] []
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   682
      (Logic.mk_implies (ind_concl, mutual_ind_concl)) (fn _ => EVERY
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   683
        [rewrite_goals_tac rec_sets_defs,
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   684
         REPEAT (EVERY
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   685
           [REPEAT (resolve_tac [conjI, impI] 1),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   686
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   687
            rewrite_goals_tac sum_case_rewrites,
17985
d5d576b72371 avoid legacy goals;
wenzelm
parents: 17959
diff changeset
   688
            atac 1])]))
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   689
10988
e0016a009c17 Splitting of arguments of product types in induction rules is now less
berghofe
parents: 10910
diff changeset
   690
  in standard (split_rule factors (induct RS lemma)) end;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   691
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   692
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   693
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   694
(** specification of (co)inductive sets **)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   695
10729
1b3350c4ee92 handle proper rules;
wenzelm
parents: 10569
diff changeset
   696
fun cond_declare_consts declare_consts cs paramTs cnames =
1b3350c4ee92 handle proper rules;
wenzelm
parents: 10569
diff changeset
   697
  if declare_consts then
14235
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   698
    Theory.add_consts_i (map (fn (c, n) => (Sign.base_name n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
10729
1b3350c4ee92 handle proper rules;
wenzelm
parents: 10569
diff changeset
   699
  else I;
1b3350c4ee92 handle proper rules;
wenzelm
parents: 10569
diff changeset
   700
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   701
fun mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
9072
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   702
      params paramTs cTs cnames =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   703
  let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   704
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   705
    val setT = HOLogic.mk_setT sumT;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   706
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   707
    val fp_name = if coind then gfp_name else lfp_name;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   708
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   709
    val used = foldr add_term_names [] intr_ts;
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   710
    val [sname, xname] = variantlist (["S", "x"], used);
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   711
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   712
    (* transform an introduction rule into a conjunction  *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   713
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   714
    (* is transformed into                                *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   715
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   716
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   717
    fun transform_rule r =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   718
      let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   719
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   720
        val subst = subst_free
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   721
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   722
        val Const ("op :", _) $ t $ u =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   723
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   724
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   725
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   726
        (foldr1 HOLogic.mk_conj
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   727
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   728
            (map (subst o HOLogic.dest_Trueprop)
15574
b1d1b5bfc464 Removed practically all references to Library.foldr.
skalberg
parents: 15570
diff changeset
   729
              (Logic.strip_imp_prems r)))) frees
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   730
      end
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   731
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   732
    (* make a disjunction of all introduction rules *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   733
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   734
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
7710
bf8cb3fc5d64 Monotonicity rules for inductive definitions can now be added to a theory via
berghofe
parents: 7349
diff changeset
   735
      absfree (xname, sumT, foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   736
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   737
    (* add definiton of recursive sets to theory *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   738
14235
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   739
    val rec_name = if alt_name = "" then
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   740
      space_implode "_" (map Sign.base_name cnames) else alt_name;
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   741
    val full_rec_name = if length cs < 2 then hd cnames
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   742
      else Sign.full_name thy rec_name;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   743
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   744
    val rec_const = list_comb
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   745
      (Const (full_rec_name, paramTs ---> setT), params);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   746
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   747
    val fp_def_term = Logic.mk_equals (rec_const,
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   748
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun);
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   749
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   750
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   751
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   752
18358
0a733e11021a re-oriented some result tuples in PureThy
haftmann
parents: 18330
diff changeset
   753
    val ([fp_def :: rec_sets_defs], thy') =
8433
8ae16c770fc8 adapted to new PureThy.add_thms etc.;
wenzelm
parents: 8410
diff changeset
   754
      thy
10729
1b3350c4ee92 handle proper rules;
wenzelm
parents: 10569
diff changeset
   755
      |> cond_declare_consts declare_consts cs paramTs cnames
8433
8ae16c770fc8 adapted to new PureThy.add_thms etc.;
wenzelm
parents: 8410
diff changeset
   756
      |> (if length cs < 2 then I
8ae16c770fc8 adapted to new PureThy.add_thms etc.;
wenzelm
parents: 8410
diff changeset
   757
          else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
8ae16c770fc8 adapted to new PureThy.add_thms etc.;
wenzelm
parents: 8410
diff changeset
   758
      |> Theory.add_path rec_name
9315
f793f05024f6 adapted PureThy.add_defs_i;
wenzelm
parents: 9298
diff changeset
   759
      |> PureThy.add_defss_i false [(("defs", def_terms), [])];
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   760
9072
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   761
    val mono = prove_mono setT fp_fun monos thy'
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   762
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   763
  in (thy', rec_name, mono, fp_def, rec_sets_defs, rec_const, sumT) end;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   764
9072
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   765
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   766
    intros monos thy params paramTs cTs cnames induct_cases =
9072
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   767
  let
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   768
    val _ =
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   769
      if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
14235
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   770
        commas_quote (map Sign.base_name cnames)) else ();
9072
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   771
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   772
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   773
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   774
    val (thy1, rec_name, mono, fp_def, rec_sets_defs, rec_const, sumT) =
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   775
      mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
9072
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   776
        params paramTs cTs cnames;
a4896cf23638 Now also proves monotonicity when in quick_and_dirty mode.
berghofe
parents: 8720
diff changeset
   777
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   778
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts rec_sets_defs thy1;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   779
    val elims = if no_elim then [] else
9939
44af7faa677e tuned handling of "intros";
wenzelm
parents: 9893
diff changeset
   780
      prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy1;
8312
b470bc28b59d add_cases_induct: accomodate no_elim and no_ind flags;
wenzelm
parents: 8307
diff changeset
   781
    val raw_induct = if no_ind then Drule.asm_rl else
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   782
      if coind then standard (rule_by_tactic
5553
ae42b36a50c2 renamed mk_meta_eq to mk_eq
oheimb
parents: 5303
diff changeset
   783
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   784
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   785
      else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   786
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
9939
44af7faa677e tuned handling of "intros";
wenzelm
parents: 9893
diff changeset
   787
          rec_sets_defs thy1;
12165
14e94ad99861 mutual rules declared as ``consumes 0'';
wenzelm
parents: 12128
diff changeset
   788
    val induct =
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   789
      if coind then
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   790
        (raw_induct, [RuleCases.case_names [rec_name],
18234
0183318232f2 RuleCases.case_conclusion;
wenzelm
parents: 18222
diff changeset
   791
          RuleCases.case_conclusion (rec_name, induct_cases),
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   792
          RuleCases.consumes 1])
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   793
      else if no_ind orelse length cs > 1 then
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   794
        (raw_induct, [RuleCases.case_names induct_cases, RuleCases.consumes 0])
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   795
      else (raw_induct RSN (2, rev_mp), [RuleCases.case_names induct_cases, RuleCases.consumes 1]);
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   796
18377
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   797
    val (intrs', thy2) =
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   798
      thy1
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   799
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts);
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   800
    val (([_, elims'], [induct']), thy3) =
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   801
      thy2
11005
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   802
      |> PureThy.add_thmss
11628
e57a6e51715e inductive: no collective atts;
wenzelm
parents: 11502
diff changeset
   803
        [(("intros", intrs'), []),
11005
86f662ba3c3f more robust handling of rule cases hints;
wenzelm
parents: 10988
diff changeset
   804
          (("elims", elims), [RuleCases.consumes 1])]
18377
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   805
      ||>> PureThy.add_thms
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   806
        [((coind_prefix coind ^ "induct", rulify (#1 induct)), #2 induct)]
18377
0e1d025d57b3 oriented result pairs in PureThy
haftmann
parents: 18358
diff changeset
   807
      ||> Theory.parent_path;
9939
44af7faa677e tuned handling of "intros";
wenzelm
parents: 9893
diff changeset
   808
  in (thy3,
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   809
    {defs = fp_def :: rec_sets_defs,
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   810
     mono = mono,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   811
     unfold = unfold,
13709
ec00ba43aee8 - No longer applies norm_hhf_rule
berghofe
parents: 13657
diff changeset
   812
     intrs = intrs',
7798
42e94b618f34 return stored thms with proper naming in derivation;
wenzelm
parents: 7710
diff changeset
   813
     elims = elims',
42e94b618f34 return stored thms with proper naming in derivation;
wenzelm
parents: 7710
diff changeset
   814
     mk_cases = mk_cases elims',
10729
1b3350c4ee92 handle proper rules;
wenzelm
parents: 10569
diff changeset
   815
     raw_induct = rulify raw_induct,
7798
42e94b618f34 return stored thms with proper naming in derivation;
wenzelm
parents: 7710
diff changeset
   816
     induct = induct'})
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   817
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   818
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   819
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   820
(* external interfaces *)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   821
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   822
fun try_term f msg thy t =
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   823
  (case Library.try f t of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15525
diff changeset
   824
    SOME x => x
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   825
  | NONE => error (msg ^ Sign.string_of_term thy t));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   826
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   827
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs pre_intros monos thy =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   828
  let
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   829
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   830
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   831
    (*parameters should agree for all mutually recursive components*)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   832
    val (_, params) = strip_comb (hd cs);
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   833
    val paramTs = map (try_term (snd o dest_Free) "Parameter in recursive\
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   834
      \ component is not a free variable: " thy) params;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   835
10735
dfaf75f0076f simplified quick_and_dirty stuff;
wenzelm
parents: 10729
diff changeset
   836
    val cTs = map (try_term (HOLogic.dest_setT o fastype_of)
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   837
      "Recursive component not of type set: " thy) cs;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   838
14235
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   839
    val cnames = map (try_term (fst o dest_Const o head_of)
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   840
      "Recursive set not previously declared as constant: " thy) cs;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   841
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   842
    val save_thy = thy
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   843
      |> Theory.copy |> cond_declare_consts declare_consts cs paramTs cnames;
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   844
    val intros = map (check_rule save_thy cs) pre_intros;
8401
50d5f4402305 more robust case names of induct;
wenzelm
parents: 8380
diff changeset
   845
    val induct_cases = map (#1 o #1) intros;
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   846
9405
3235873fdd90 improved error msg;
wenzelm
parents: 9315
diff changeset
   847
    val (thy1, result as {elims, induct, ...}) =
11628
e57a6e51715e inductive: no collective atts;
wenzelm
parents: 11502
diff changeset
   848
      add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs intros monos
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   849
        thy params paramTs cTs cnames induct_cases;
8307
6600c6e53111 add_cases_induct: induct_method setup;
wenzelm
parents: 8293
diff changeset
   850
    val thy2 = thy1
14235
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   851
      |> put_inductives cnames ({names = cnames, coind = coind}, result)
18222
a8ccacce3b52 declare coinduct rule;
wenzelm
parents: 17985
diff changeset
   852
      |> add_cases_induct no_elim (no_ind orelse length cs > 1) coind
14235
281295a1bbaa Fixed bug in mk_ind_def that caused the inductive definition package to
berghofe
parents: 13747
diff changeset
   853
          cnames elims induct;
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   854
  in (thy2, result) end;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   855
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   856
fun add_inductive verbose coind c_strings intro_srcs raw_monos thy =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   857
  let
16975
34ed8d5d4f16 Sign.read_term;
wenzelm
parents: 16934
diff changeset
   858
    val cs = map (Sign.read_term thy) c_strings;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   859
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   860
    val intr_names = map (fst o fst) intro_srcs;
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   861
    fun read_rule s = Thm.read_cterm thy (s, propT)
9405
3235873fdd90 improved error msg;
wenzelm
parents: 9315
diff changeset
   862
      handle ERROR => error ("The error(s) above occurred for " ^ s);
3235873fdd90 improved error msg;
wenzelm
parents: 9315
diff changeset
   863
    val intr_ts = map (Thm.term_of o read_rule o snd o fst) intro_srcs;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   864
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
16432
a6e8fb94a8ca accomodate change of TheoryDataFun;
wenzelm
parents: 16364
diff changeset
   865
    val (cs', intr_ts') = unify_consts thy cs intr_ts;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   866
18418
bf448d999b7e re-arranged tuples (theory * 'a) to ('a * theory) in Pure
haftmann
parents: 18377
diff changeset
   867
    val (monos, thy') = thy |> IsarThy.apply_theorems raw_monos;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   868
  in
7020
75ff179df7b7 Exported function unify_consts (workaround to avoid inconsistently
berghofe
parents: 6851
diff changeset
   869
    add_inductive_i verbose false "" coind false false cs'
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   870
      ((intr_names ~~ intr_ts') ~~ intr_atts) monos thy'
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   871
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   872
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   873
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   874
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   875
(** package setup **)
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   876
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   877
(* setup theory *)
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   878
8634
3f34637cb9c0 use Attrib.add_del_args;
wenzelm
parents: 8433
diff changeset
   879
val setup =
3f34637cb9c0 use Attrib.add_del_args;
wenzelm
parents: 8433
diff changeset
   880
 [InductiveData.init,
9625
77506775481e renamed 'mk_cases_tac' to 'ind_cases';
wenzelm
parents: 9598
diff changeset
   881
  Method.add_methods [("ind_cases", mk_cases_meth oo mk_cases_args,
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   882
    "dynamic case analysis on sets")],
9893
93d2fde0306c tuned msg;
wenzelm
parents: 9831
diff changeset
   883
  Attrib.add_attributes [("mono", mono_attr, "declaration of monotonicity rule")]];
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   884
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   885
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   886
(* outer syntax *)
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   887
17057
0934ac31985f OuterKeyword;
wenzelm
parents: 17010
diff changeset
   888
local structure P = OuterParse and K = OuterKeyword in
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   889
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   890
fun mk_ind coind ((sets, intrs), monos) =
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   891
  #1 o add_inductive true coind sets (map P.triple_swap intrs) monos;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   892
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   893
fun ind_decl coind =
12876
a70df1e5bf10 got rid of explicit marginal comments (now stripped earlier from input);
wenzelm
parents: 12798
diff changeset
   894
  Scan.repeat1 P.term --
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   895
  (P.$$$ "intros" |--
12876
a70df1e5bf10 got rid of explicit marginal comments (now stripped earlier from input);
wenzelm
parents: 12798
diff changeset
   896
    P.!!! (Scan.repeat1 (P.opt_thm_name ":" -- P.prop))) --
a70df1e5bf10 got rid of explicit marginal comments (now stripped earlier from input);
wenzelm
parents: 12798
diff changeset
   897
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1) []
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   898
  >> (Toplevel.theory o mk_ind coind);
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   899
6723
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   900
val inductiveP =
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   901
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   902
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   903
val coinductiveP =
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   904
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   905
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   906
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   907
val ind_cases =
12876
a70df1e5bf10 got rid of explicit marginal comments (now stripped earlier from input);
wenzelm
parents: 12798
diff changeset
   908
  P.and_list1 (P.opt_thm_name ":" -- Scan.repeat1 P.prop)
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   909
  >> (Toplevel.theory o inductive_cases);
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   910
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   911
val inductive_casesP =
9804
ee0c337327cf "inductive_cases": proper command;
wenzelm
parents: 9643
diff changeset
   912
  OuterSyntax.command "inductive_cases"
9598
65ee72db0236 raplaced "intrs" by "intrs" (new-style only);
wenzelm
parents: 9562
diff changeset
   913
    "create simplified instances of elimination rules (improper)" K.thy_script ind_cases;
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   914
12180
91c9f661b183 inductive: removed con_defs;
wenzelm
parents: 12172
diff changeset
   915
val _ = OuterSyntax.add_keywords ["intros", "monos"];
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   916
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   917
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   918
end;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   919
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   920
end;
15705
b5edb9dcec9a *** MESSAGE REFERS TO PREVIOUS VERSION ***
wenzelm
parents: 15703
diff changeset
   921