src/HOL/Tools/inductive_package.ML
author berghofe
Fri Jul 16 14:06:13 1999 +0200 (1999-07-16)
changeset 7020 75ff179df7b7
parent 6851 526c0b90bcef
child 7107 ce69de572bca
permissions -rw-r--r--
Exported function unify_consts (workaround to avoid inconsistently
typed recursive constants in inductive and primrec definitions).
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(*  Title:      HOL/Tools/inductive_package.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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                Stefan Berghofer,   TU Muenchen
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    Copyright   1994  University of Cambridge
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                1998  TU Muenchen     
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(Co)Inductive Definition module for HOL.
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Features:
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  * least or greatest fixedpoints
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  * user-specified product and sum constructions
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  * mutually recursive definitions
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  * definitions involving arbitrary monotone operators
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  * automatically proves introduction and elimination rules
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The recursive sets must *already* be declared as constants in the
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current theory!
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  Introduction rules have the form
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  [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk |]
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  where M is some monotone operator (usually the identity)
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  P(x) is any side condition on the free variables
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  ti, t are any terms
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  Sj, Sk are two of the sets being defined in mutual recursion
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Sums are used only for mutual recursion.  Products are used only to
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derive "streamlined" induction rules for relations.
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*)
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signature INDUCTIVE_PACKAGE =
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sig
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  val quiet_mode: bool ref
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  val unify_consts: Sign.sg -> term list -> term list -> term list * term list
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  val get_inductive: theory -> string ->
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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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  val print_inductives: theory -> unit
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  val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
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    theory attribute list -> ((bstring * term) * theory attribute list) list ->
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      thm list -> thm list -> theory -> theory *
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      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
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       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
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  val add_inductive: bool -> bool -> string list -> Args.src list ->
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    ((bstring * string) * Args.src list) list -> (xstring * Args.src list) list ->
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      (xstring * Args.src list) list -> theory -> theory *
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      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
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       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
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  val 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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(** utilities **)
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(* messages *)
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val quiet_mode = ref false;
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fun message s = if !quiet_mode then () else writeln s;
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fun coind_prefix true = "co"
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  | coind_prefix false = "";
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(* the following code ensures that each recursive set *)
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(* always has the same type in all introduction rules *)
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fun unify_consts sign cs intr_ts =
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  (let
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    val {tsig, ...} = Sign.rep_sg sign;
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    val add_term_consts_2 =
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      foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
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    fun varify (t, (i, ts)) =
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      let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
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      in (maxidx_of_term t', t'::ts) end;
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    val (i, cs') = foldr varify (cs, (~1, []));
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    val (i', intr_ts') = foldr varify (intr_ts, (i, []));
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    val rec_consts = foldl add_term_consts_2 ([], cs');
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    val intr_consts = foldl add_term_consts_2 ([], intr_ts');
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    fun unify (env, (cname, cT)) =
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      let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
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      in foldl (fn ((env', j'), Tp) => (Type.unify tsig j' env' Tp))
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          (env, (replicate (length consts) cT) ~~ consts)
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      end;
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    val (env, _) = foldl unify (([], i'), rec_consts);
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    fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars env T
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      in if T = T' then T else typ_subst_TVars_2 env T' end;
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    val subst = fst o Type.freeze_thaw o
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      (map_term_types (typ_subst_TVars_2 env))
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  in (map subst cs', map subst intr_ts')
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  end) handle Type.TUNIFY =>
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    (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
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(* misc *)
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(*For proving monotonicity of recursion operator*)
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val basic_monos = [subset_refl, imp_refl, disj_mono, conj_mono, 
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                   ex_mono, Collect_mono, in_mono, vimage_mono];
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val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (concl_of vimageD);
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(*Delete needless equality assumptions*)
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val refl_thin = prove_goal HOL.thy "!!P. [| a=a;  P |] ==> P"
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     (fn _ => [assume_tac 1]);
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(*For simplifying the elimination rule*)
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val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
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val vimage_name = Sign.intern_const (Theory.sign_of Vimage.thy) "op -``";
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val mono_name = Sign.intern_const (Theory.sign_of Ord.thy) "mono";
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(* make injections needed in mutually recursive definitions *)
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fun mk_inj cs sumT c x =
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  let
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    fun mk_inj' T n i =
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      if n = 1 then x else
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      let val n2 = n div 2;
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          val Type (_, [T1, T2]) = T
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      in
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        if i <= n2 then
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          Const ("Inl", T1 --> T) $ (mk_inj' T1 n2 i)
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        else
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          Const ("Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
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      end
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  in mk_inj' sumT (length cs) (1 + find_index_eq c cs)
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  end;
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(* make "vimage" terms for selecting out components of mutually rec.def. *)
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fun mk_vimage cs sumT t c = if length cs < 2 then t else
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  let
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    val cT = HOLogic.dest_setT (fastype_of c);
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    val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
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  in
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    Const (vimage_name, vimageT) $
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      Abs ("y", cT, mk_inj cs sumT c (Bound 0)) $ t
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  end;
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(** well-formedness checks **)
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fun err_in_rule sign t msg = error ("Ill-formed introduction rule\n" ^
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  (Sign.string_of_term sign t) ^ "\n" ^ msg);
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fun err_in_prem sign t p msg = error ("Ill-formed premise\n" ^
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  (Sign.string_of_term sign p) ^ "\nin introduction rule\n" ^
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  (Sign.string_of_term sign t) ^ "\n" ^ msg);
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val msg1 = "Conclusion of introduction rule must have form\
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          \ ' t : S_i '";
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val msg2 = "Premises mentioning recursive sets must have form\
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          \ ' t : M S_i '";
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val msg3 = "Recursion term on left of member symbol";
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fun check_rule sign cs r =
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  let
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    fun check_prem prem = if exists (Logic.occs o (rpair prem)) cs then
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         (case prem of
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           (Const ("op :", _) $ t $ u) =>
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             if exists (Logic.occs o (rpair t)) cs then
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               err_in_prem sign r prem msg3 else ()
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         | _ => err_in_prem sign r prem msg2)
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        else ()
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  in (case (HOLogic.dest_Trueprop o Logic.strip_imp_concl) r of
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        (Const ("op :", _) $ _ $ u) =>
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          if u mem cs then seq (check_prem o HOLogic.dest_Trueprop)
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            (Logic.strip_imp_prems r)
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          else err_in_rule sign r msg1
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      | _ => err_in_rule sign r msg1)
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  end;
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fun try' f msg sign t = (case (try f t) of
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      Some x => x
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    | None => error (msg ^ Sign.string_of_term sign t));
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(*** 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;
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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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  val merge: T * T -> T = Symtab.merge (K true);
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  fun print sg tab =
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    Pretty.writeln (Pretty.strs ("(co)inductives:" ::
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      map #1 (Sign.cond_extern_table sg Sign.constK tab)));
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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 =
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  (case Symtab.lookup (InductiveData.get thy, name) of
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    Some info => info
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  | None => error ("Unknown (co)inductive set " ^ quote name));
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fun put_inductives names info thy =
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  let
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    fun upd (tab, name) = Symtab.update_new ((name, info), tab);
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    val tab = 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 thy end;
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(*** properties of (co)inductive sets ***)
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(** elimination rules **)
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fun mk_elims cs cTs params intr_ts =
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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;
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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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      in
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        Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
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          map mk_elim_prem (filter (equal c o #1) intrs), P)
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      end
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  in
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    map mk_elim (cs ~~ cTs)
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  end;
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(** premises and conclusions of induction rules **)
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fun mk_indrule cs cTs params intr_ts =
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  let
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    val used = foldr add_term_names (intr_ts, []);
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    (* predicates for induction rule *)
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    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
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      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
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        map (fn T => T --> HOLogic.boolT) cTs);
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    (* transform an introduction rule into a premise for induction rule *)
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    fun mk_ind_prem r =
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      let
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        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
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        fun subst (prem as (Const ("op :", T) $ t $ u), prems) =
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              let val n = find_index_eq u cs in
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                if n >= 0 then prem :: (nth_elem (n, preds)) $ t :: prems else
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                  (subst_free (map (fn (c, P) => (c, HOLogic.mk_binop "op Int"
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                    (c, HOLogic.Collect_const (HOLogic.dest_setT
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                      (fastype_of c)) $ P))) (cs ~~ preds)) prem)::prems
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              end
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          | subst (prem, prems) = prem::prems;
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        val Const ("op :", _) $ t $ u =
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          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
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      in list_all_free (frees,
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           Logic.list_implies (map HOLogic.mk_Trueprop (foldr subst
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             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
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               HOLogic.mk_Trueprop (nth_elem (find_index_eq u cs, preds) $ t)))
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      end;
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    val ind_prems = map mk_ind_prem intr_ts;
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    (* make conclusions for induction rules *)
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    fun mk_ind_concl ((c, P), (ts, x)) =
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      let val T = HOLogic.dest_setT (fastype_of c);
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          val Ts = HOLogic.prodT_factors T;
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          val (frees, x') = foldr (fn (T', (fs, s)) =>
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            ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
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          val tuple = HOLogic.mk_tuple T frees;
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      in ((HOLogic.mk_binop "op -->"
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        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
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      end;
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    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 (app HOLogic.conj)
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        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
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  in (preds, ind_prems, mutual_ind_concl)
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  end;
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(*** proofs for (co)inductive sets ***)
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(** prove monotonicity **)
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fun prove_mono setT fp_fun monos thy =
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  let
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    val _ = message "  Proving monotonicity ...";
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    val mono = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
berghofe@5094
   328
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
berghofe@5094
   329
        (fn _ => [rtac monoI 1, REPEAT (ares_tac (basic_monos @ monos) 1)])
berghofe@5094
   330
berghofe@5094
   331
  in mono end;
berghofe@5094
   332
wenzelm@6424
   333
wenzelm@6424
   334
wenzelm@6424
   335
(** prove introduction rules **)
berghofe@5094
   336
berghofe@5094
   337
fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
berghofe@5094
   338
  let
wenzelm@6427
   339
    val _ = message "  Proving the introduction rules ...";
berghofe@5094
   340
berghofe@5094
   341
    val unfold = standard (mono RS (fp_def RS
berghofe@5094
   342
      (if coind then def_gfp_Tarski else def_lfp_Tarski)));
berghofe@5094
   343
berghofe@5094
   344
    fun select_disj 1 1 = []
berghofe@5094
   345
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   346
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   347
berghofe@5094
   348
    val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   349
      (cterm_of (Theory.sign_of thy) intr) (fn prems =>
berghofe@5094
   350
       [(*insert prems and underlying sets*)
berghofe@5094
   351
       cut_facts_tac prems 1,
berghofe@5094
   352
       stac unfold 1,
berghofe@5094
   353
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
berghofe@5094
   354
       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
berghofe@5094
   355
       EVERY1 (select_disj (length intr_ts) i),
berghofe@5094
   356
       (*Not ares_tac, since refl must be tried before any equality assumptions;
berghofe@5094
   357
         backtracking may occur if the premises have extra variables!*)
berghofe@5094
   358
       DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
berghofe@5094
   359
       (*Now solve the equations like Inl 0 = Inl ?b2*)
berghofe@5094
   360
       rewrite_goals_tac con_defs,
berghofe@5094
   361
       REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
berghofe@5094
   362
berghofe@5094
   363
  in (intrs, unfold) end;
berghofe@5094
   364
wenzelm@6424
   365
wenzelm@6424
   366
wenzelm@6424
   367
(** prove elimination rules **)
berghofe@5094
   368
berghofe@5094
   369
fun prove_elims cs cTs params intr_ts unfold rec_sets_defs thy =
berghofe@5094
   370
  let
wenzelm@6427
   371
    val _ = message "  Proving the elimination rules ...";
berghofe@5094
   372
berghofe@5094
   373
    val rules1 = [CollectE, disjE, make_elim vimageD];
berghofe@5094
   374
    val rules2 = [exE, conjE, Inl_neq_Inr, Inr_neq_Inl] @
berghofe@5094
   375
      map make_elim [Inl_inject, Inr_inject];
berghofe@5094
   376
berghofe@5094
   377
    val elims = map (fn t => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   378
      (cterm_of (Theory.sign_of thy) t) (fn prems =>
berghofe@5094
   379
        [cut_facts_tac [hd prems] 1,
berghofe@5094
   380
         dtac (unfold RS subst) 1,
berghofe@5094
   381
         REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@5094
   382
         REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@5094
   383
         EVERY (map (fn prem =>
berghofe@5149
   384
           DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))]))
berghofe@5094
   385
      (mk_elims cs cTs params intr_ts)
berghofe@5094
   386
berghofe@5094
   387
  in elims end;
berghofe@5094
   388
wenzelm@6424
   389
berghofe@5094
   390
(** derivation of simplified elimination rules **)
berghofe@5094
   391
berghofe@5094
   392
(*Applies freeness of the given constructors, which *must* be unfolded by
berghofe@5094
   393
  the given defs.  Cannot simply use the local con_defs because con_defs=[] 
berghofe@5094
   394
  for inference systems.
berghofe@5094
   395
 *)
paulson@6141
   396
fun con_elim_tac ss =
berghofe@5094
   397
  let val elim_tac = REPEAT o (eresolve_tac elim_rls)
berghofe@5094
   398
  in ALLGOALS(EVERY'[elim_tac,
paulson@6141
   399
		     asm_full_simp_tac ss,
paulson@6141
   400
		     elim_tac,
paulson@6141
   401
		     REPEAT o bound_hyp_subst_tac])
berghofe@5094
   402
     THEN prune_params_tac
berghofe@5094
   403
  end;
berghofe@5094
   404
berghofe@5094
   405
(*String s should have the form t:Si where Si is an inductive set*)
paulson@6141
   406
fun mk_cases elims s =
wenzelm@6394
   407
  let val prem = assume (read_cterm (Thm.sign_of_thm (hd elims)) (s, propT))
paulson@6141
   408
      fun mk_elim rl = rule_by_tactic (con_elim_tac (simpset())) (prem RS rl) 
paulson@6141
   409
	               |> standard
paulson@6141
   410
  in case find_first is_some (map (try mk_elim) elims) of
berghofe@5094
   411
       Some (Some r) => r
berghofe@5094
   412
     | None => error ("mk_cases: string '" ^ s ^ "' not of form 't : S_i'")
berghofe@5094
   413
  end;
berghofe@5094
   414
wenzelm@6424
   415
wenzelm@6424
   416
wenzelm@6424
   417
(** prove induction rule **)
berghofe@5094
   418
berghofe@5094
   419
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   420
    fp_def rec_sets_defs thy =
berghofe@5094
   421
  let
wenzelm@6427
   422
    val _ = message "  Proving the induction rule ...";
berghofe@5094
   423
wenzelm@6394
   424
    val sign = Theory.sign_of thy;
berghofe@5094
   425
berghofe@5094
   426
    val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   427
berghofe@5094
   428
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   429
berghofe@5094
   430
    fun mk_ind_pred _ [P] = P
berghofe@5094
   431
      | mk_ind_pred T Ps =
berghofe@5094
   432
         let val n = (length Ps) div 2;
berghofe@5094
   433
             val Type (_, [T1, T2]) = T
berghofe@5094
   434
         in Const ("sum_case",
berghofe@5094
   435
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
berghofe@5094
   436
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
berghofe@5094
   437
         end;
berghofe@5094
   438
berghofe@5094
   439
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   440
berghofe@5094
   441
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   442
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   443
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   444
berghofe@5094
   445
    (* simplification rules for vimage and Collect *)
berghofe@5094
   446
berghofe@5094
   447
    val vimage_simps = if length cs < 2 then [] else
berghofe@5094
   448
      map (fn c => prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   449
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   450
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   451
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
berghofe@5094
   452
             nth_elem (find_index_eq c cs, preds)))))
berghofe@5094
   453
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac
oheimb@5553
   454
           (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
berghofe@5094
   455
          rtac refl 1])) cs;
berghofe@5094
   456
berghofe@5094
   457
    val induct = prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   458
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
berghofe@5094
   459
        [rtac (impI RS allI) 1,
berghofe@5094
   460
         DETERM (etac (mono RS (fp_def RS def_induct)) 1),
oheimb@5553
   461
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::vimage_simps)),
berghofe@5094
   462
         fold_goals_tac rec_sets_defs,
berghofe@5094
   463
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@5094
   464
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
berghofe@5094
   465
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   466
           some premise involves disjunction.*)
berghofe@5094
   467
         REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE] 
berghofe@5094
   468
                     ORELSE' hyp_subst_tac)),
oheimb@5553
   469
         rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
berghofe@5094
   470
         EVERY (map (fn prem =>
berghofe@5149
   471
           DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
berghofe@5094
   472
berghofe@5094
   473
    val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
berghofe@5094
   474
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
berghofe@5094
   475
        [cut_facts_tac prems 1,
berghofe@5094
   476
         REPEAT (EVERY
berghofe@5094
   477
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   478
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
oheimb@5553
   479
            rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
berghofe@5094
   480
            atac 1])])
berghofe@5094
   481
berghofe@5094
   482
  in standard (split_rule (induct RS lemma))
berghofe@5094
   483
  end;
berghofe@5094
   484
wenzelm@6424
   485
wenzelm@6424
   486
wenzelm@6424
   487
(*** specification of (co)inductive sets ****)
wenzelm@6424
   488
wenzelm@6424
   489
(** definitional introduction of (co)inductive sets **)
berghofe@5094
   490
berghofe@5094
   491
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   492
    atts intros monos con_defs thy params paramTs cTs cnames =
berghofe@5094
   493
  let
wenzelm@6424
   494
    val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
wenzelm@6424
   495
      commas_quote cnames) else ();
berghofe@5094
   496
berghofe@5094
   497
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   498
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   499
wenzelm@6394
   500
    val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
wenzelm@6394
   501
      else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
berghofe@5094
   502
wenzelm@6424
   503
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
wenzelm@6424
   504
berghofe@5149
   505
    val used = foldr add_term_names (intr_ts, []);
berghofe@5149
   506
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   507
berghofe@5094
   508
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   509
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   510
    (* is transformed into                                *)
berghofe@5094
   511
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   512
berghofe@5094
   513
    fun transform_rule r =
berghofe@5094
   514
      let
berghofe@5094
   515
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   516
        val subst = subst_free
berghofe@5149
   517
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   518
        val Const ("op :", _) $ t $ u =
berghofe@5094
   519
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   520
berghofe@5094
   521
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
berghofe@5094
   522
        (frees, foldr1 (app HOLogic.conj)
berghofe@5149
   523
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   524
            (map (subst o HOLogic.dest_Trueprop)
berghofe@5094
   525
              (Logic.strip_imp_prems r))))
berghofe@5094
   526
      end
berghofe@5094
   527
berghofe@5094
   528
    (* make a disjunction of all introduction rules *)
berghofe@5094
   529
berghofe@5149
   530
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@5149
   531
      absfree (xname, sumT, foldr1 (app HOLogic.disj) (map transform_rule intr_ts)));
berghofe@5094
   532
berghofe@5094
   533
    (* add definiton of recursive sets to theory *)
berghofe@5094
   534
berghofe@5094
   535
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
wenzelm@6394
   536
    val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
berghofe@5094
   537
berghofe@5094
   538
    val rec_const = list_comb
berghofe@5094
   539
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   540
berghofe@5094
   541
    val fp_def_term = Logic.mk_equals (rec_const,
berghofe@5094
   542
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun)
berghofe@5094
   543
berghofe@5094
   544
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   545
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   546
berghofe@5094
   547
    val thy' = thy |>
berghofe@5094
   548
      (if declare_consts then
berghofe@5094
   549
        Theory.add_consts_i (map (fn (c, n) =>
berghofe@5094
   550
          (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
berghofe@5094
   551
       else I) |>
berghofe@5094
   552
      (if length cs < 2 then I else
berghofe@5094
   553
       Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)]) |>
berghofe@5094
   554
      Theory.add_path rec_name |>
berghofe@5094
   555
      PureThy.add_defss_i [(("defs", def_terms), [])];
berghofe@5094
   556
berghofe@5094
   557
    (* get definitions from theory *)
berghofe@5094
   558
wenzelm@6424
   559
    val fp_def::rec_sets_defs = PureThy.get_thms thy' "defs";
berghofe@5094
   560
berghofe@5094
   561
    (* prove and store theorems *)
berghofe@5094
   562
berghofe@5094
   563
    val mono = prove_mono setT fp_fun monos thy';
berghofe@5094
   564
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
berghofe@5094
   565
      rec_sets_defs thy';
berghofe@5094
   566
    val elims = if no_elim then [] else
berghofe@5094
   567
      prove_elims cs cTs params intr_ts unfold rec_sets_defs thy';
berghofe@5094
   568
    val raw_induct = if no_ind then TrueI else
berghofe@5094
   569
      if coind then standard (rule_by_tactic
oheimb@5553
   570
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   571
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   572
      else
berghofe@5094
   573
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
berghofe@5094
   574
          rec_sets_defs thy';
berghofe@5108
   575
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
berghofe@5094
   576
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   577
wenzelm@6424
   578
    val thy'' = thy'
wenzelm@6521
   579
      |> PureThy.add_thmss [(("intrs", intrs), atts)]
wenzelm@6424
   580
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
wenzelm@6424
   581
      |> (if no_elim then I else PureThy.add_thmss [(("elims", elims), [])])
wenzelm@6424
   582
      |> (if no_ind then I else PureThy.add_thms
wenzelm@6424
   583
        [((coind_prefix coind ^ "induct", induct), [])])
wenzelm@6424
   584
      |> Theory.parent_path;
berghofe@5094
   585
berghofe@5094
   586
  in (thy'',
berghofe@5094
   587
    {defs = fp_def::rec_sets_defs,
berghofe@5094
   588
     mono = mono,
berghofe@5094
   589
     unfold = unfold,
berghofe@5094
   590
     intrs = intrs,
berghofe@5094
   591
     elims = elims,
berghofe@5094
   592
     mk_cases = mk_cases elims,
berghofe@5094
   593
     raw_induct = raw_induct,
berghofe@5094
   594
     induct = induct})
berghofe@5094
   595
  end;
berghofe@5094
   596
wenzelm@6424
   597
wenzelm@6424
   598
wenzelm@6424
   599
(** axiomatic introduction of (co)inductive sets **)
berghofe@5094
   600
berghofe@5094
   601
fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   602
    atts intros monos con_defs thy params paramTs cTs cnames =
berghofe@5094
   603
  let
wenzelm@6424
   604
    val _ = if verbose then message ("Adding axioms for " ^ coind_prefix coind ^
wenzelm@6424
   605
      "inductive set(s) " ^ commas_quote cnames) else ();
berghofe@5094
   606
berghofe@5094
   607
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
berghofe@5094
   608
wenzelm@6424
   609
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
berghofe@5094
   610
    val elim_ts = mk_elims cs cTs params intr_ts;
berghofe@5094
   611
berghofe@5094
   612
    val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   613
    val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
berghofe@5094
   614
    
wenzelm@6424
   615
    val thy' = thy
wenzelm@6424
   616
      |> (if declare_consts then
wenzelm@6424
   617
            Theory.add_consts_i
wenzelm@6424
   618
              (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@6424
   619
         else I)
wenzelm@6424
   620
      |> Theory.add_path rec_name
wenzelm@6521
   621
      |> PureThy.add_axiomss_i [(("intrs", intr_ts), atts), (("elims", elim_ts), [])]
wenzelm@6424
   622
      |> (if coind then I else PureThy.add_axioms_i [(("internal_induct", ind_t), [])]);
berghofe@5094
   623
wenzelm@6424
   624
    val intrs = PureThy.get_thms thy' "intrs";
wenzelm@6424
   625
    val elims = PureThy.get_thms thy' "elims";
berghofe@5094
   626
    val raw_induct = if coind then TrueI else
wenzelm@6424
   627
      standard (split_rule (PureThy.get_thm thy' "internal_induct"));
berghofe@5094
   628
    val induct = if coind orelse length cs > 1 then raw_induct
berghofe@5094
   629
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   630
wenzelm@6424
   631
    val thy'' =
wenzelm@6424
   632
      thy'
wenzelm@6424
   633
      |> (if coind then I else PureThy.add_thms [(("induct", induct), [])])
wenzelm@6424
   634
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
wenzelm@6424
   635
      |> Theory.parent_path;
berghofe@5094
   636
  in (thy'',
berghofe@5094
   637
    {defs = [],
berghofe@5094
   638
     mono = TrueI,
berghofe@5094
   639
     unfold = TrueI,
berghofe@5094
   640
     intrs = intrs,
berghofe@5094
   641
     elims = elims,
berghofe@5094
   642
     mk_cases = mk_cases elims,
berghofe@5094
   643
     raw_induct = raw_induct,
berghofe@5094
   644
     induct = induct})
berghofe@5094
   645
  end;
berghofe@5094
   646
wenzelm@6424
   647
wenzelm@6424
   648
wenzelm@6424
   649
(** introduction of (co)inductive sets **)
berghofe@5094
   650
berghofe@5094
   651
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   652
    atts intros monos con_defs thy =
berghofe@5094
   653
  let
wenzelm@6424
   654
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
wenzelm@6394
   655
    val sign = Theory.sign_of thy;
berghofe@5094
   656
berghofe@5094
   657
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   658
    val (_, params) = strip_comb (hd cs);
berghofe@5094
   659
    val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
berghofe@5094
   660
      \ component is not a free variable: " sign) params;
berghofe@5094
   661
berghofe@5094
   662
    val cTs = map (try' (HOLogic.dest_setT o fastype_of)
berghofe@5094
   663
      "Recursive component not of type set: " sign) cs;
berghofe@5094
   664
wenzelm@6437
   665
    val full_cnames = map (try' (fst o dest_Const o head_of)
berghofe@5094
   666
      "Recursive set not previously declared as constant: " sign) cs;
wenzelm@6437
   667
    val cnames = map Sign.base_name full_cnames;
berghofe@5094
   668
wenzelm@6424
   669
    val _ = assert_all Syntax.is_identifier cnames	(* FIXME why? *)
berghofe@5094
   670
       (fn a => "Base name of recursive set not an identifier: " ^ a);
wenzelm@6424
   671
    val _ = seq (check_rule sign cs o snd o fst) intros;
wenzelm@6437
   672
wenzelm@6437
   673
    val (thy1, result) =
wenzelm@6437
   674
      (if ! quick_and_dirty then add_ind_axm else add_ind_def)
wenzelm@6521
   675
        verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
wenzelm@6437
   676
        con_defs thy params paramTs cTs cnames;
wenzelm@6437
   677
    val thy2 = thy1 |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result);
wenzelm@6437
   678
  in (thy2, result) end;
berghofe@5094
   679
wenzelm@6424
   680
berghofe@5094
   681
wenzelm@6424
   682
(** external interface **)
wenzelm@6424
   683
wenzelm@6521
   684
fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
berghofe@5094
   685
  let
wenzelm@6394
   686
    val sign = Theory.sign_of thy;
wenzelm@6394
   687
    val cs = map (readtm (Theory.sign_of thy) HOLogic.termTVar) c_strings;
wenzelm@6424
   688
wenzelm@6521
   689
    val atts = map (Attrib.global_attribute thy) srcs;
wenzelm@6424
   690
    val intr_names = map (fst o fst) intro_srcs;
wenzelm@6424
   691
    val intr_ts = map (readtm (Theory.sign_of thy) propT o snd o fst) intro_srcs;
wenzelm@6424
   692
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
berghofe@7020
   693
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
berghofe@5094
   694
wenzelm@6424
   695
    val ((thy', con_defs), monos) = thy
wenzelm@6424
   696
      |> IsarThy.apply_theorems raw_monos
wenzelm@6424
   697
      |> apfst (IsarThy.apply_theorems raw_con_defs);
wenzelm@6424
   698
  in
berghofe@7020
   699
    add_inductive_i verbose false "" coind false false cs'
berghofe@7020
   700
      atts ((intr_names ~~ intr_ts') ~~ intr_atts) monos con_defs thy'
berghofe@5094
   701
  end;
berghofe@5094
   702
wenzelm@6424
   703
wenzelm@6424
   704
wenzelm@6437
   705
(** package setup **)
wenzelm@6437
   706
wenzelm@6437
   707
(* setup theory *)
wenzelm@6437
   708
wenzelm@6437
   709
val setup = [InductiveData.init];
wenzelm@6437
   710
wenzelm@6437
   711
wenzelm@6437
   712
(* outer syntax *)
wenzelm@6424
   713
wenzelm@6723
   714
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6424
   715
wenzelm@6521
   716
fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
wenzelm@6723
   717
  #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
wenzelm@6424
   718
wenzelm@6424
   719
fun ind_decl coind =
wenzelm@6729
   720
  (Scan.repeat1 P.term --| P.marg_comment) --
wenzelm@6729
   721
  (P.$$$ "intrs" |--
wenzelm@6729
   722
    P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.term --| P.marg_comment))) --
wenzelm@6729
   723
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
wenzelm@6729
   724
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
wenzelm@6424
   725
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   726
wenzelm@6723
   727
val inductiveP =
wenzelm@6723
   728
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   729
wenzelm@6723
   730
val coinductiveP =
wenzelm@6723
   731
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   732
wenzelm@6424
   733
val _ = OuterSyntax.add_keywords ["intrs", "monos", "con_defs"];
wenzelm@6424
   734
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP];
wenzelm@6424
   735
berghofe@5094
   736
end;
wenzelm@6424
   737
wenzelm@6424
   738
wenzelm@6424
   739
end;