src/HOL/Tools/inductive_package.ML
author skalberg
Sun Feb 13 17:15:14 2005 +0100 (2005-02-13)
changeset 15531 08c8dad8e399
parent 15525 396268ad58b3
child 15570 8d8c70b41bab
permissions -rw-r--r--
Deleted Library.option type.
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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: Sign.sg -> 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 * Args.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) * Args.src list) list -> (thmref * Args.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 = "Gfp.gfp";
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val lfp_name = "Lfp.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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(* data kind 'HOL/inductive' *)
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type inductive_info =
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  {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
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    induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
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structure InductiveArgs =
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struct
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  val name = "HOL/inductive";
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  type T = inductive_info Symtab.table * thm list;
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  val empty = (Symtab.empty, []);
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  val copy = I;
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  val prep_ext = I;
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  fun merge ((tab1, monos1), (tab2, monos2)) =
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    (Symtab.merge (K true) (tab1, tab2), Drule.merge_rules (monos1, monos2));
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  fun print sg (tab, monos) =
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    [Pretty.strs ("(co)inductives:" :: map #1 (Sign.cond_extern_table sg Sign.constK tab)),
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     Pretty.big_list "monotonicity rules:" (map (Display.pretty_thm_sg sg) monos)]
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    |> Pretty.chunks |> Pretty.writeln;
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end;
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structure InductiveData = TheoryDataFun(InductiveArgs);
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val print_inductives = InductiveData.print;
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(* get and put data *)
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fun get_inductive thy name = Symtab.lookup (fst (InductiveData.get thy), name);
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fun the_inductive thy name =
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  (case get_inductive thy name of
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    NONE => error ("Unknown (co)inductive set " ^ quote name)
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  | SOME info => info);
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val the_mk_cases = (#mk_cases o #2) oo the_inductive;
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fun put_inductives names info thy =
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  let
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    fun upd ((tab, monos), name) = (Symtab.update_new ((name, info), tab), monos);
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    val tab_monos = foldl upd (InductiveData.get thy, names)
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      handle Symtab.DUP name => error ("Duplicate definition of (co)inductive set " ^ quote name);
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  in InductiveData.put tab_monos thy end;
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(** monotonicity rules **)
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val get_monos = #2 o InductiveData.get;
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fun map_monos f = InductiveData.map (Library.apsnd f);
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fun mk_mono thm =
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  let
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    fun eq2mono thm' = [standard (thm' RS (thm' RS eq_to_mono))] @
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      (case concl_of thm of
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          (_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
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        | _ => [standard (thm' RS (thm' RS eq_to_mono2))]);
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    val concl = concl_of thm
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  in
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    if Logic.is_equals concl then
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      eq2mono (thm RS meta_eq_to_obj_eq)
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    else if can (HOLogic.dest_eq o HOLogic.dest_Trueprop) concl then
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      eq2mono thm
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    else [thm]
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  end;
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(* attributes *)
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fun mono_add_global (thy, thm) = (map_monos (Drule.add_rules (mk_mono thm)) thy, thm);
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fun mono_del_global (thy, thm) = (map_monos (Drule.del_rules (mk_mono thm)) thy, thm);
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val mono_attr =
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 (Attrib.add_del_args mono_add_global mono_del_global,
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  Attrib.add_del_args Attrib.undef_local_attribute Attrib.undef_local_attribute);
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(** 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 sign cs intr_ts =
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  (let
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    val tsig = Sign.tsig_of sign;
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    val add_term_consts_2 =
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      foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
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    fun varify (t, (i, ts)) =
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      let val t' = map_term_types (incr_tvar (i + 1)) (#1 (Type.varify (t, [])))
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      in (maxidx_of_term t', t'::ts) end;
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    val (i, cs') = foldr varify (cs, (~1, []));
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    val (i', intr_ts') = foldr varify (intr_ts, (i, []));
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    val rec_consts = foldl add_term_consts_2 ([], cs');
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    val intr_consts = foldl add_term_consts_2 ([], intr_ts');
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    fun unify (env, (cname, cT)) =
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      let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
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      in foldl (fn ((env', j'), Tp) => (Type.unify tsig (env', j') Tp))
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          (env, (replicate (length consts) cT) ~~ consts)
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      end;
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    val (env, _) = foldl unify ((Vartab.empty, i'), rec_consts);
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    fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars_Vartab env T
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      in if T = T' then T else typ_subst_TVars_2 env T' end;
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    val subst = fst o Type.freeze_thaw o
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      (map_term_types (typ_subst_TVars_2 env))
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  in (map subst cs', map subst intr_ts')
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  end) handle Type.TUNIFY =>
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    (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
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(*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 (fs, t $ u) = if t mem ts then
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        let val f = prod_factors [] u
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        in overwrite (fs, (t, f inter if_none (assoc (fs, t)) f)) end
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      else mg_prod_factors ts (mg_prod_factors ts (fs, t), u)
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  | mg_prod_factors ts (fs, Abs (_, _, t)) = mg_prod_factors ts (fs, t)
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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 (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.sign_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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  (mg_prod_factors vs ([], Thm.prop_of rl), rl)));
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fun split_rule vs rl = standard (remove_split (foldr split_rule_var'
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  (mapfilter (fn (t as Var ((a, _), _)) =>
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    apsome (pair t) (assoc (vs, a))) (term_vars (Thm.prop_of rl)), rl)));
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(** process rules **)
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local
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fun err_in_rule sg name t msg =
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  error (cat_lines ["Ill-formed introduction rule " ^ quote name, Sign.string_of_term sg t, msg]);
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fun err_in_prem sg name t p msg =
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  error (cat_lines ["Ill-formed premise", Sign.string_of_term sg p,
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    "in introduction rule " ^ quote name, Sign.string_of_term sg t, msg]);
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val bad_concl = "Conclusion of introduction rule must have form \"t : S_i\"";
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val all_not_allowed = 
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    "Introduction rule must not have a leading \"!!\" quantifier";
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fun atomize_term sg = MetaSimplifier.rewrite_term sg inductive_atomize [];
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in
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fun check_rule sg cs ((name, rule), att) =
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  let
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    val concl = Logic.strip_imp_concl rule;
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    val prems = Logic.strip_imp_prems rule;
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    val aprems = map (atomize_term sg) 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 sg 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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   316
          if exists (Logic.occs o rpair t) cs then
wenzelm@10729
   317
            err_in_rule sg name rule "Recursion term on left of member symbol"
wenzelm@10729
   318
          else seq check_prem (prems ~~ aprems)
wenzelm@10729
   319
        else err_in_rule sg name rule bad_concl
paulson@11358
   320
      | Const ("all", _) $ _ => err_in_rule sg name rule all_not_allowed
wenzelm@10729
   321
      | _ => err_in_rule sg name rule bad_concl);
wenzelm@10729
   322
    ((name, arule), att)
wenzelm@10729
   323
  end;
berghofe@5094
   324
wenzelm@10729
   325
val rulify =
berghofe@13709
   326
  standard o
wenzelm@11036
   327
  hol_simplify inductive_rulify2 o hol_simplify inductive_rulify1 o
wenzelm@11036
   328
  hol_simplify inductive_conj;
wenzelm@10729
   329
wenzelm@10729
   330
end;
wenzelm@10729
   331
berghofe@5094
   332
wenzelm@6424
   333
wenzelm@10735
   334
(** properties of (co)inductive sets **)
berghofe@5094
   335
wenzelm@10735
   336
(* elimination rules *)
berghofe@5094
   337
wenzelm@8375
   338
fun mk_elims cs cTs params intr_ts intr_names =
berghofe@5094
   339
  let
berghofe@5094
   340
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   341
    val [aname, pname] = variantlist (["a", "P"], used);
berghofe@5094
   342
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@5094
   343
berghofe@5094
   344
    fun dest_intr r =
berghofe@5094
   345
      let val Const ("op :", _) $ t $ u =
berghofe@5094
   346
        HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   347
      in (u, t, Logic.strip_imp_prems r) end;
berghofe@5094
   348
wenzelm@8380
   349
    val intrs = map dest_intr intr_ts ~~ intr_names;
berghofe@5094
   350
berghofe@5094
   351
    fun mk_elim (c, T) =
berghofe@5094
   352
      let
berghofe@5094
   353
        val a = Free (aname, T);
berghofe@5094
   354
berghofe@5094
   355
        fun mk_elim_prem (_, t, ts) =
berghofe@5094
   356
          list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
berghofe@5094
   357
            Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
wenzelm@8375
   358
        val c_intrs = (filter (equal c o #1 o #1) intrs);
berghofe@5094
   359
      in
wenzelm@8375
   360
        (Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
wenzelm@8375
   361
          map mk_elim_prem (map #1 c_intrs), P), map #2 c_intrs)
berghofe@5094
   362
      end
berghofe@5094
   363
  in
berghofe@5094
   364
    map mk_elim (cs ~~ cTs)
berghofe@5094
   365
  end;
wenzelm@9598
   366
wenzelm@6424
   367
wenzelm@10735
   368
(* premises and conclusions of induction rules *)
berghofe@5094
   369
berghofe@5094
   370
fun mk_indrule cs cTs params intr_ts =
berghofe@5094
   371
  let
berghofe@5094
   372
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   373
berghofe@5094
   374
    (* predicates for induction rule *)
berghofe@5094
   375
berghofe@5094
   376
    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
berghofe@5094
   377
      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
berghofe@5094
   378
        map (fn T => T --> HOLogic.boolT) cTs);
berghofe@5094
   379
berghofe@5094
   380
    (* transform an introduction rule into a premise for induction rule *)
berghofe@5094
   381
berghofe@5094
   382
    fun mk_ind_prem r =
berghofe@5094
   383
      let
berghofe@5094
   384
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5094
   385
berghofe@7710
   386
        val pred_of = curry (Library.gen_assoc (op aconv)) (cs ~~ preds);
berghofe@5094
   387
berghofe@7710
   388
        fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
berghofe@7710
   389
              (case pred_of u of
skalberg@15531
   390
                  NONE => (m $ fst (subst t) $ fst (subst u), NONE)
skalberg@15531
   391
                | SOME P => (HOLogic.mk_binop inductive_conj_name (s, P $ t), SOME (s, P $ t)))
berghofe@7710
   392
          | subst s =
berghofe@7710
   393
              (case pred_of s of
skalberg@15531
   394
                  SOME P => (HOLogic.mk_binop "op Int"
berghofe@7710
   395
                    (s, HOLogic.Collect_const (HOLogic.dest_setT
skalberg@15531
   396
                      (fastype_of s)) $ P), NONE)
skalberg@15531
   397
                | NONE => (case s of
skalberg@15531
   398
                     (t $ u) => (fst (subst t) $ fst (subst u), NONE)
skalberg@15531
   399
                   | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
skalberg@15531
   400
                   | _ => (s, NONE)));
berghofe@7710
   401
berghofe@7710
   402
        fun mk_prem (s, prems) = (case subst s of
skalberg@15531
   403
              (_, SOME (t, u)) => t :: u :: prems
berghofe@7710
   404
            | (t, _) => t :: prems);
wenzelm@9598
   405
berghofe@5094
   406
        val Const ("op :", _) $ t $ u =
berghofe@5094
   407
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   408
berghofe@5094
   409
      in list_all_free (frees,
berghofe@7710
   410
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
berghofe@5094
   411
             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
berghofe@7710
   412
               HOLogic.mk_Trueprop (the (pred_of u) $ t)))
berghofe@5094
   413
      end;
berghofe@5094
   414
berghofe@5094
   415
    val ind_prems = map mk_ind_prem intr_ts;
paulson@13626
   416
berghofe@10988
   417
    val factors = foldl (mg_prod_factors preds) ([], ind_prems);
berghofe@5094
   418
berghofe@5094
   419
    (* make conclusions for induction rules *)
berghofe@5094
   420
berghofe@5094
   421
    fun mk_ind_concl ((c, P), (ts, x)) =
berghofe@5094
   422
      let val T = HOLogic.dest_setT (fastype_of c);
berghofe@10988
   423
          val ps = if_none (assoc (factors, P)) [];
berghofe@10988
   424
          val Ts = prodT_factors [] ps T;
berghofe@5094
   425
          val (frees, x') = foldr (fn (T', (fs, s)) =>
wenzelm@12902
   426
            ((Free (s, T'))::fs, Symbol.bump_string s)) (Ts, ([], x));
berghofe@10988
   427
          val tuple = mk_tuple [] ps T frees;
berghofe@5094
   428
      in ((HOLogic.mk_binop "op -->"
berghofe@5094
   429
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
berghofe@5094
   430
      end;
berghofe@5094
   431
berghofe@7710
   432
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@5094
   433
        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
berghofe@5094
   434
berghofe@10988
   435
  in (preds, ind_prems, mutual_ind_concl,
berghofe@10988
   436
    map (apfst (fst o dest_Free)) factors)
berghofe@5094
   437
  end;
berghofe@5094
   438
wenzelm@6424
   439
wenzelm@10735
   440
(* prepare cases and induct rules *)
wenzelm@8316
   441
wenzelm@8316
   442
(*
wenzelm@8316
   443
  transform mutual rule:
wenzelm@8316
   444
    HH ==> (x1:A1 --> P1 x1) & ... & (xn:An --> Pn xn)
wenzelm@8316
   445
  into i-th projection:
wenzelm@8316
   446
    xi:Ai ==> HH ==> Pi xi
wenzelm@8316
   447
*)
wenzelm@8316
   448
wenzelm@8316
   449
fun project_rules [name] rule = [(name, rule)]
wenzelm@8316
   450
  | project_rules names mutual_rule =
wenzelm@8316
   451
      let
wenzelm@8316
   452
        val n = length names;
wenzelm@8316
   453
        fun proj i =
wenzelm@8316
   454
          (if i < n then (fn th => th RS conjunct1) else I)
wenzelm@8316
   455
            (Library.funpow (i - 1) (fn th => th RS conjunct2) mutual_rule)
wenzelm@8316
   456
            RS mp |> Thm.permute_prems 0 ~1 |> Drule.standard;
wenzelm@8316
   457
      in names ~~ map proj (1 upto n) end;
wenzelm@8316
   458
wenzelm@12172
   459
fun add_cases_induct no_elim no_induct names elims induct =
wenzelm@8316
   460
  let
wenzelm@9405
   461
    fun cases_spec (name, elim) thy =
wenzelm@9405
   462
      thy
wenzelm@9405
   463
      |> Theory.add_path (Sign.base_name name)
wenzelm@10279
   464
      |> (#1 o PureThy.add_thms [(("cases", elim), [InductAttrib.cases_set_global name])])
wenzelm@9405
   465
      |> Theory.parent_path;
wenzelm@8375
   466
    val cases_specs = if no_elim then [] else map2 cases_spec (names, elims);
wenzelm@8316
   467
wenzelm@11005
   468
    fun induct_spec (name, th) = #1 o PureThy.add_thms
wenzelm@11005
   469
      [(("", RuleCases.save induct th), [InductAttrib.induct_set_global name])];
wenzelm@12172
   470
    val induct_specs = if no_induct then [] else map induct_spec (project_rules names induct);
wenzelm@9405
   471
  in Library.apply (cases_specs @ induct_specs) end;
wenzelm@8316
   472
wenzelm@8316
   473
wenzelm@8316
   474
wenzelm@10735
   475
(** proofs for (co)inductive sets **)
wenzelm@6424
   476
wenzelm@10735
   477
(* prove monotonicity -- NOT subject to quick_and_dirty! *)
berghofe@5094
   478
berghofe@5094
   479
fun prove_mono setT fp_fun monos thy =
wenzelm@10735
   480
 (message "  Proving monotonicity ...";
wenzelm@11880
   481
  Goals.prove_goalw_cterm []      (*NO quick_and_dirty_prove_goalw_cterm here!*)
wenzelm@10735
   482
    (Thm.cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
berghofe@5094
   483
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
wenzelm@11502
   484
    (fn _ => [rtac monoI 1, REPEAT (ares_tac (flat (map mk_mono monos) @ get_monos thy) 1)]));
berghofe@5094
   485
wenzelm@6424
   486
wenzelm@10735
   487
(* prove introduction rules *)
berghofe@5094
   488
wenzelm@12180
   489
fun prove_intrs coind mono fp_def intr_ts rec_sets_defs thy =
berghofe@5094
   490
  let
wenzelm@10735
   491
    val _ = clean_message "  Proving the introduction rules ...";
berghofe@5094
   492
berghofe@13657
   493
    val unfold = standard' (mono RS (fp_def RS
nipkow@10186
   494
      (if coind then def_gfp_unfold else def_lfp_unfold)));
berghofe@5094
   495
berghofe@5094
   496
    fun select_disj 1 1 = []
berghofe@5094
   497
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   498
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   499
wenzelm@11880
   500
    val intrs = map (fn (i, intr) => quick_and_dirty_prove_goalw_cterm thy rec_sets_defs
wenzelm@10735
   501
      (Thm.cterm_of (Theory.sign_of thy) intr) (fn prems =>
berghofe@5094
   502
       [(*insert prems and underlying sets*)
berghofe@5094
   503
       cut_facts_tac prems 1,
berghofe@5094
   504
       stac unfold 1,
berghofe@5094
   505
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
berghofe@5094
   506
       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
berghofe@5094
   507
       EVERY1 (select_disj (length intr_ts) i),
berghofe@5094
   508
       (*Not ares_tac, since refl must be tried before any equality assumptions;
berghofe@5094
   509
         backtracking may occur if the premises have extra variables!*)
wenzelm@10735
   510
       DEPTH_SOLVE_1 (resolve_tac [refl, exI, conjI] 1 APPEND assume_tac 1),
berghofe@5094
   511
       (*Now solve the equations like Inl 0 = Inl ?b2*)
wenzelm@10729
   512
       REPEAT (rtac refl 1)])
wenzelm@10729
   513
      |> rulify) (1 upto (length intr_ts) ~~ intr_ts)
berghofe@5094
   514
berghofe@5094
   515
  in (intrs, unfold) end;
berghofe@5094
   516
wenzelm@6424
   517
wenzelm@10735
   518
(* prove elimination rules *)
berghofe@5094
   519
wenzelm@8375
   520
fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy =
berghofe@5094
   521
  let
wenzelm@10735
   522
    val _ = clean_message "  Proving the elimination rules ...";
berghofe@5094
   523
berghofe@7710
   524
    val rules1 = [CollectE, disjE, make_elim vimageD, exE];
wenzelm@10735
   525
    val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @ map make_elim [Inl_inject, Inr_inject];
wenzelm@8375
   526
  in
wenzelm@11005
   527
    mk_elims cs cTs params intr_ts intr_names |> map (fn (t, cases) =>
wenzelm@11880
   528
      quick_and_dirty_prove_goalw_cterm thy rec_sets_defs
wenzelm@11005
   529
        (Thm.cterm_of (Theory.sign_of thy) t) (fn prems =>
wenzelm@11005
   530
          [cut_facts_tac [hd prems] 1,
wenzelm@11005
   531
           dtac (unfold RS subst) 1,
wenzelm@11005
   532
           REPEAT (FIRSTGOAL (eresolve_tac rules1)),
wenzelm@11005
   533
           REPEAT (FIRSTGOAL (eresolve_tac rules2)),
wenzelm@11005
   534
           EVERY (map (fn prem => DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))])
wenzelm@11005
   535
        |> rulify
wenzelm@11005
   536
        |> RuleCases.name cases)
wenzelm@8375
   537
  end;
berghofe@5094
   538
wenzelm@6424
   539
wenzelm@10735
   540
(* derivation of simplified elimination rules *)
berghofe@5094
   541
wenzelm@11682
   542
local
wenzelm@11682
   543
wenzelm@7107
   544
(*cprop should have the form t:Si where Si is an inductive set*)
wenzelm@11682
   545
val mk_cases_err = "mk_cases: proposition not of form \"t : S_i\"";
wenzelm@9598
   546
wenzelm@11682
   547
(*delete needless equality assumptions*)
wenzelm@11682
   548
val refl_thin = prove_goal HOL.thy "!!P. a = a ==> P ==> P" (fn _ => [assume_tac 1]);
wenzelm@11682
   549
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
wenzelm@11682
   550
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
wenzelm@11682
   551
wenzelm@11682
   552
fun simp_case_tac solved ss i =
wenzelm@11682
   553
  EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i
wenzelm@11682
   554
  THEN_MAYBE (if solved then no_tac else all_tac);
wenzelm@11682
   555
wenzelm@11682
   556
in
wenzelm@9598
   557
wenzelm@9598
   558
fun mk_cases_i elims ss cprop =
wenzelm@7107
   559
  let
wenzelm@7107
   560
    val prem = Thm.assume cprop;
wenzelm@11682
   561
    val tac = ALLGOALS (simp_case_tac false ss) THEN prune_params_tac;
wenzelm@9298
   562
    fun mk_elim rl = Drule.standard (Tactic.rule_by_tactic tac (prem RS rl));
wenzelm@7107
   563
  in
wenzelm@7107
   564
    (case get_first (try mk_elim) elims of
skalberg@15531
   565
      SOME r => r
skalberg@15531
   566
    | NONE => error (Pretty.string_of (Pretty.block
wenzelm@9598
   567
        [Pretty.str mk_cases_err, Pretty.fbrk, Display.pretty_cterm cprop])))
wenzelm@7107
   568
  end;
wenzelm@7107
   569
paulson@6141
   570
fun mk_cases elims s =
wenzelm@9598
   571
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.sign_of_thm (hd elims)) (s, propT));
wenzelm@9598
   572
wenzelm@9598
   573
fun smart_mk_cases thy ss cprop =
wenzelm@9598
   574
  let
wenzelm@9598
   575
    val c = #1 (Term.dest_Const (Term.head_of (#2 (HOLogic.dest_mem (HOLogic.dest_Trueprop
wenzelm@9598
   576
      (Logic.strip_imp_concl (Thm.term_of cprop))))))) handle TERM _ => error mk_cases_err;
wenzelm@9598
   577
    val (_, {elims, ...}) = the_inductive thy c;
wenzelm@9598
   578
  in mk_cases_i elims ss cprop end;
wenzelm@7107
   579
wenzelm@11682
   580
end;
wenzelm@11682
   581
wenzelm@7107
   582
wenzelm@7107
   583
(* inductive_cases(_i) *)
wenzelm@7107
   584
wenzelm@12609
   585
fun gen_inductive_cases prep_att prep_prop args thy =
wenzelm@9598
   586
  let
wenzelm@12609
   587
    val cert_prop = Thm.cterm_of (Theory.sign_of thy) o prep_prop (ProofContext.init thy);
wenzelm@12609
   588
    val mk_cases = smart_mk_cases thy (Simplifier.simpset_of thy) o cert_prop;
wenzelm@12609
   589
wenzelm@12876
   590
    val facts = args |> map (fn ((a, atts), props) =>
wenzelm@12876
   591
     ((a, map (prep_att thy) atts), map (Thm.no_attributes o single o mk_cases) props));
wenzelm@12709
   592
  in thy |> IsarThy.theorems_i Drule.lemmaK facts |> #1 end;
berghofe@5094
   593
wenzelm@12172
   594
val inductive_cases = gen_inductive_cases Attrib.global_attribute ProofContext.read_prop;
wenzelm@12172
   595
val inductive_cases_i = gen_inductive_cases (K I) ProofContext.cert_prop;
wenzelm@7107
   596
wenzelm@6424
   597
wenzelm@9598
   598
(* mk_cases_meth *)
wenzelm@9598
   599
wenzelm@9598
   600
fun mk_cases_meth (ctxt, raw_props) =
wenzelm@9598
   601
  let
wenzelm@9598
   602
    val thy = ProofContext.theory_of ctxt;
wenzelm@15032
   603
    val ss = local_simpset_of ctxt;
wenzelm@9598
   604
    val cprops = map (Thm.cterm_of (Theory.sign_of thy) o ProofContext.read_prop ctxt) raw_props;
wenzelm@10743
   605
  in Method.erule 0 (map (smart_mk_cases thy ss) cprops) end;
wenzelm@9598
   606
wenzelm@9598
   607
val mk_cases_args = Method.syntax (Scan.lift (Scan.repeat1 Args.name));
wenzelm@9598
   608
wenzelm@9598
   609
wenzelm@10735
   610
(* prove induction rule *)
berghofe@5094
   611
berghofe@5094
   612
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   613
    fp_def rec_sets_defs thy =
berghofe@5094
   614
  let
wenzelm@10735
   615
    val _ = clean_message "  Proving the induction rule ...";
berghofe@5094
   616
wenzelm@6394
   617
    val sign = Theory.sign_of thy;
berghofe@5094
   618
wenzelm@12922
   619
    val sum_case_rewrites =
skalberg@15531
   620
      (if PureThy.get_name thy = "Datatype" then PureThy.get_thms thy ("sum.cases", NONE)
wenzelm@12922
   621
        else
wenzelm@12922
   622
          (case ThyInfo.lookup_theory "Datatype" of
skalberg@15531
   623
            NONE => []
skalberg@15531
   624
          | SOME thy' => PureThy.get_thms thy' ("sum.cases", NONE))) |> map mk_meta_eq;
berghofe@7293
   625
berghofe@10988
   626
    val (preds, ind_prems, mutual_ind_concl, factors) =
berghofe@10988
   627
      mk_indrule cs cTs params intr_ts;
berghofe@5094
   628
paulson@13626
   629
    val dummy = if !trace then
paulson@13626
   630
		(writeln "ind_prems = ";
paulson@13626
   631
		 seq (writeln o Sign.string_of_term sign) ind_prems)
paulson@13626
   632
	    else ();
paulson@13626
   633
berghofe@5094
   634
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   635
berghofe@5094
   636
    fun mk_ind_pred _ [P] = P
berghofe@5094
   637
      | mk_ind_pred T Ps =
berghofe@5094
   638
         let val n = (length Ps) div 2;
berghofe@5094
   639
             val Type (_, [T1, T2]) = T
berghofe@7293
   640
         in Const ("Datatype.sum.sum_case",
berghofe@5094
   641
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
berghofe@5094
   642
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
berghofe@5094
   643
         end;
berghofe@5094
   644
berghofe@5094
   645
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   646
berghofe@5094
   647
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   648
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   649
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   650
berghofe@5094
   651
    (* simplification rules for vimage and Collect *)
berghofe@5094
   652
berghofe@5094
   653
    val vimage_simps = if length cs < 2 then [] else
wenzelm@11880
   654
      map (fn c => quick_and_dirty_prove_goalw_cterm thy [] (Thm.cterm_of sign
berghofe@5094
   655
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   656
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   657
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
berghofe@5094
   658
             nth_elem (find_index_eq c cs, preds)))))
wenzelm@10735
   659
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites, rtac refl 1])) cs;
berghofe@5094
   660
paulson@13626
   661
    val raw_fp_induct = (mono RS (fp_def RS def_lfp_induct));
paulson@13626
   662
paulson@13626
   663
    val dummy = if !trace then
paulson@13626
   664
		(writeln "raw_fp_induct = "; print_thm raw_fp_induct)
paulson@13626
   665
	    else ();
paulson@13626
   666
wenzelm@11880
   667
    val induct = quick_and_dirty_prove_goalw_cterm thy [inductive_conj_def] (Thm.cterm_of sign
berghofe@5094
   668
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
berghofe@5094
   669
        [rtac (impI RS allI) 1,
paulson@13626
   670
         DETERM (etac raw_fp_induct 1),
berghofe@7710
   671
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
berghofe@5094
   672
         fold_goals_tac rec_sets_defs,
berghofe@5094
   673
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@7710
   674
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE])),
berghofe@5094
   675
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   676
           some premise involves disjunction.*)
paulson@13747
   677
         REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
paulson@15416
   678
         ALLGOALS (simp_tac (HOL_basic_ss addsimps sum_case_rewrites)),
berghofe@5094
   679
         EVERY (map (fn prem =>
paulson@13747
   680
   	             DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
berghofe@5094
   681
wenzelm@11880
   682
    val lemma = quick_and_dirty_prove_goalw_cterm thy rec_sets_defs (Thm.cterm_of sign
berghofe@5094
   683
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
berghofe@5094
   684
        [cut_facts_tac prems 1,
berghofe@5094
   685
         REPEAT (EVERY
berghofe@5094
   686
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   687
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
berghofe@7293
   688
            rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   689
            atac 1])])
berghofe@5094
   690
berghofe@10988
   691
  in standard (split_rule factors (induct RS lemma)) end;
berghofe@5094
   692
wenzelm@6424
   693
wenzelm@6424
   694
wenzelm@10735
   695
(** specification of (co)inductive sets **)
berghofe@5094
   696
wenzelm@10729
   697
fun cond_declare_consts declare_consts cs paramTs cnames =
wenzelm@10729
   698
  if declare_consts then
berghofe@14235
   699
    Theory.add_consts_i (map (fn (c, n) => (Sign.base_name n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@10729
   700
  else I;
wenzelm@10729
   701
wenzelm@12180
   702
fun mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
berghofe@9072
   703
      params paramTs cTs cnames =
berghofe@5094
   704
  let
berghofe@5094
   705
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   706
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   707
wenzelm@10735
   708
    val fp_name = if coind then gfp_name else lfp_name;
berghofe@5094
   709
berghofe@5149
   710
    val used = foldr add_term_names (intr_ts, []);
berghofe@5149
   711
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   712
berghofe@5094
   713
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   714
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   715
    (* is transformed into                                *)
berghofe@5094
   716
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   717
berghofe@5094
   718
    fun transform_rule r =
berghofe@5094
   719
      let
berghofe@5094
   720
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   721
        val subst = subst_free
berghofe@5149
   722
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   723
        val Const ("op :", _) $ t $ u =
berghofe@5094
   724
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   725
berghofe@5094
   726
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
berghofe@7710
   727
        (frees, foldr1 HOLogic.mk_conj
berghofe@5149
   728
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   729
            (map (subst o HOLogic.dest_Trueprop)
berghofe@5094
   730
              (Logic.strip_imp_prems r))))
berghofe@5094
   731
      end
berghofe@5094
   732
berghofe@5094
   733
    (* make a disjunction of all introduction rules *)
berghofe@5094
   734
berghofe@5149
   735
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@7710
   736
      absfree (xname, sumT, foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
berghofe@5094
   737
berghofe@5094
   738
    (* add definiton of recursive sets to theory *)
berghofe@5094
   739
berghofe@14235
   740
    val rec_name = if alt_name = "" then
berghofe@14235
   741
      space_implode "_" (map Sign.base_name cnames) else alt_name;
berghofe@14235
   742
    val full_rec_name = if length cs < 2 then hd cnames
berghofe@14235
   743
      else Sign.full_name (Theory.sign_of thy) rec_name;
berghofe@5094
   744
berghofe@5094
   745
    val rec_const = list_comb
berghofe@5094
   746
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   747
berghofe@5094
   748
    val fp_def_term = Logic.mk_equals (rec_const,
wenzelm@10735
   749
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun);
berghofe@5094
   750
berghofe@5094
   751
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   752
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   753
wenzelm@8433
   754
    val (thy', [fp_def :: rec_sets_defs]) =
wenzelm@8433
   755
      thy
wenzelm@10729
   756
      |> cond_declare_consts declare_consts cs paramTs cnames
wenzelm@8433
   757
      |> (if length cs < 2 then I
wenzelm@8433
   758
          else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
wenzelm@8433
   759
      |> Theory.add_path rec_name
wenzelm@9315
   760
      |> PureThy.add_defss_i false [(("defs", def_terms), [])];
berghofe@5094
   761
berghofe@9072
   762
    val mono = prove_mono setT fp_fun monos thy'
berghofe@5094
   763
wenzelm@10735
   764
  in (thy', mono, fp_def, rec_sets_defs, rec_const, sumT) end;
berghofe@5094
   765
berghofe@9072
   766
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@12180
   767
    intros monos thy params paramTs cTs cnames induct_cases =
berghofe@9072
   768
  let
wenzelm@10735
   769
    val _ =
wenzelm@10735
   770
      if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
berghofe@14235
   771
        commas_quote (map Sign.base_name cnames)) else ();
berghofe@9072
   772
berghofe@9072
   773
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
berghofe@9072
   774
wenzelm@9939
   775
    val (thy1, mono, fp_def, rec_sets_defs, rec_const, sumT) =
wenzelm@12180
   776
      mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
berghofe@9072
   777
        params paramTs cTs cnames;
berghofe@9072
   778
wenzelm@12180
   779
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts rec_sets_defs thy1;
berghofe@5094
   780
    val elims = if no_elim then [] else
wenzelm@9939
   781
      prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy1;
wenzelm@8312
   782
    val raw_induct = if no_ind then Drule.asm_rl else
berghofe@5094
   783
      if coind then standard (rule_by_tactic
oheimb@5553
   784
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   785
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   786
      else
berghofe@5094
   787
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
wenzelm@9939
   788
          rec_sets_defs thy1;
wenzelm@12165
   789
    val induct =
wenzelm@12165
   790
      if coind orelse no_ind orelse length cs > 1 then (raw_induct, [RuleCases.consumes 0])
wenzelm@12165
   791
      else (raw_induct RSN (2, rev_mp), [RuleCases.consumes 1]);
berghofe@5094
   792
wenzelm@9939
   793
    val (thy2, intrs') =
wenzelm@9939
   794
      thy1 |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts);
wenzelm@10735
   795
    val (thy3, ([intrs'', elims'], [induct'])) =
wenzelm@10735
   796
      thy2
wenzelm@11005
   797
      |> PureThy.add_thmss
wenzelm@11628
   798
        [(("intros", intrs'), []),
wenzelm@11005
   799
          (("elims", elims), [RuleCases.consumes 1])]
wenzelm@10735
   800
      |>>> PureThy.add_thms
wenzelm@12165
   801
        [((coind_prefix coind ^ "induct", rulify (#1 induct)),
wenzelm@12165
   802
         (RuleCases.case_names induct_cases :: #2 induct))]
wenzelm@8433
   803
      |>> Theory.parent_path;
wenzelm@9939
   804
  in (thy3,
wenzelm@10735
   805
    {defs = fp_def :: rec_sets_defs,
berghofe@5094
   806
     mono = mono,
berghofe@5094
   807
     unfold = unfold,
berghofe@13709
   808
     intrs = intrs',
wenzelm@7798
   809
     elims = elims',
wenzelm@7798
   810
     mk_cases = mk_cases elims',
wenzelm@10729
   811
     raw_induct = rulify raw_induct,
wenzelm@7798
   812
     induct = induct'})
berghofe@5094
   813
  end;
berghofe@5094
   814
wenzelm@6424
   815
wenzelm@10735
   816
(* external interfaces *)
berghofe@5094
   817
wenzelm@10735
   818
fun try_term f msg sign t =
wenzelm@10735
   819
  (case Library.try f t of
skalberg@15531
   820
    SOME x => x
skalberg@15531
   821
  | NONE => error (msg ^ Sign.string_of_term sign t));
berghofe@5094
   822
wenzelm@12180
   823
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs pre_intros monos thy =
berghofe@5094
   824
  let
wenzelm@6424
   825
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
wenzelm@6394
   826
    val sign = Theory.sign_of thy;
berghofe@5094
   827
berghofe@5094
   828
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   829
    val (_, params) = strip_comb (hd cs);
wenzelm@10735
   830
    val paramTs = map (try_term (snd o dest_Free) "Parameter in recursive\
berghofe@5094
   831
      \ component is not a free variable: " sign) params;
berghofe@5094
   832
wenzelm@10735
   833
    val cTs = map (try_term (HOLogic.dest_setT o fastype_of)
berghofe@5094
   834
      "Recursive component not of type set: " sign) cs;
berghofe@5094
   835
berghofe@14235
   836
    val cnames = map (try_term (fst o dest_Const o head_of)
berghofe@5094
   837
      "Recursive set not previously declared as constant: " sign) cs;
berghofe@5094
   838
wenzelm@10729
   839
    val save_sign =
wenzelm@10729
   840
      thy |> Theory.copy |> cond_declare_consts declare_consts cs paramTs cnames |> Theory.sign_of;
wenzelm@10729
   841
    val intros = map (check_rule save_sign cs) pre_intros;
wenzelm@8401
   842
    val induct_cases = map (#1 o #1) intros;
wenzelm@6437
   843
wenzelm@9405
   844
    val (thy1, result as {elims, induct, ...}) =
wenzelm@11628
   845
      add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs intros monos
wenzelm@12180
   846
        thy params paramTs cTs cnames induct_cases;
wenzelm@8307
   847
    val thy2 = thy1
berghofe@14235
   848
      |> put_inductives cnames ({names = cnames, coind = coind}, result)
wenzelm@12172
   849
      |> add_cases_induct no_elim (no_ind orelse coind orelse length cs > 1)
berghofe@14235
   850
          cnames elims induct;
wenzelm@6437
   851
  in (thy2, result) end;
berghofe@5094
   852
wenzelm@12180
   853
fun add_inductive verbose coind c_strings intro_srcs raw_monos thy =
berghofe@5094
   854
  let
wenzelm@6394
   855
    val sign = Theory.sign_of thy;
wenzelm@12338
   856
    val cs = map (term_of o HOLogic.read_cterm sign) c_strings;
wenzelm@6424
   857
wenzelm@6424
   858
    val intr_names = map (fst o fst) intro_srcs;
wenzelm@9405
   859
    fun read_rule s = Thm.read_cterm sign (s, propT)
wenzelm@9405
   860
      handle ERROR => error ("The error(s) above occurred for " ^ s);
wenzelm@9405
   861
    val intr_ts = map (Thm.term_of o read_rule o snd o fst) intro_srcs;
wenzelm@6424
   862
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
berghofe@7020
   863
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
berghofe@5094
   864
wenzelm@12180
   865
    val (thy', monos) = thy |> IsarThy.apply_theorems raw_monos;
wenzelm@6424
   866
  in
berghofe@7020
   867
    add_inductive_i verbose false "" coind false false cs'
wenzelm@12180
   868
      ((intr_names ~~ intr_ts') ~~ intr_atts) monos thy'
berghofe@5094
   869
  end;
berghofe@5094
   870
wenzelm@6424
   871
wenzelm@6424
   872
wenzelm@6437
   873
(** package setup **)
wenzelm@6437
   874
wenzelm@6437
   875
(* setup theory *)
wenzelm@6437
   876
wenzelm@8634
   877
val setup =
wenzelm@8634
   878
 [InductiveData.init,
wenzelm@9625
   879
  Method.add_methods [("ind_cases", mk_cases_meth oo mk_cases_args,
wenzelm@9598
   880
    "dynamic case analysis on sets")],
wenzelm@9893
   881
  Attrib.add_attributes [("mono", mono_attr, "declaration of monotonicity rule")]];
wenzelm@6437
   882
wenzelm@6437
   883
wenzelm@6437
   884
(* outer syntax *)
wenzelm@6424
   885
wenzelm@6723
   886
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6424
   887
wenzelm@12180
   888
fun mk_ind coind ((sets, intrs), monos) =
wenzelm@12180
   889
  #1 o add_inductive true coind sets (map P.triple_swap intrs) monos;
wenzelm@6424
   890
wenzelm@6424
   891
fun ind_decl coind =
wenzelm@12876
   892
  Scan.repeat1 P.term --
wenzelm@9598
   893
  (P.$$$ "intros" |--
wenzelm@12876
   894
    P.!!! (Scan.repeat1 (P.opt_thm_name ":" -- P.prop))) --
wenzelm@12876
   895
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1) []
wenzelm@6424
   896
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   897
wenzelm@6723
   898
val inductiveP =
wenzelm@6723
   899
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   900
wenzelm@6723
   901
val coinductiveP =
wenzelm@6723
   902
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   903
wenzelm@7107
   904
wenzelm@7107
   905
val ind_cases =
wenzelm@12876
   906
  P.and_list1 (P.opt_thm_name ":" -- Scan.repeat1 P.prop)
wenzelm@7107
   907
  >> (Toplevel.theory o inductive_cases);
wenzelm@7107
   908
wenzelm@7107
   909
val inductive_casesP =
wenzelm@9804
   910
  OuterSyntax.command "inductive_cases"
wenzelm@9598
   911
    "create simplified instances of elimination rules (improper)" K.thy_script ind_cases;
wenzelm@7107
   912
wenzelm@12180
   913
val _ = OuterSyntax.add_keywords ["intros", "monos"];
wenzelm@7107
   914
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   915
berghofe@5094
   916
end;
wenzelm@6424
   917
wenzelm@6424
   918
end;