src/HOL/Tools/inductive_package.ML
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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 inductive_cases: (((bstring * Args.src list) * xstring) * string list) * Comment.text
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    -> theory -> theory
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  val inductive_cases_i: (((bstring * theory attribute list) * string) * term list) * Comment.text
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    -> theory -> theory
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  val setup: (theory -> theory) list
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end;
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structure InductivePackage: INDUCTIVE_PACKAGE =
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struct
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(** 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 default_monos = basic_monos @ [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
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      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
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        (fn _ => [rtac monoI 1, REPEAT (ares_tac (default_monos @ monos) 1)])
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  in mono end;
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(** prove introduction rules **)
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fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
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  let
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    val _ = message "  Proving the introduction rules ...";
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    val unfold = standard (mono RS (fp_def RS
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      (if coind then def_gfp_Tarski else def_lfp_Tarski)));
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    fun select_disj 1 1 = []
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      | select_disj _ 1 = [rtac disjI1]
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      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
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    val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
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3d9fd50fcc43 Theory.sign_of;
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      (cterm_of (Theory.sign_of thy) intr) (fn prems =>
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       [(*insert prems and underlying sets*)
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       cut_facts_tac prems 1,
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       stac unfold 1,
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   357
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
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       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
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       EVERY1 (select_disj (length intr_ts) i),
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       (*Not ares_tac, since refl must be tried before any equality assumptions;
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         backtracking may occur if the premises have extra variables!*)
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   362
       DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
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       (*Now solve the equations like Inl 0 = Inl ?b2*)
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   364
       rewrite_goals_tac con_defs,
ddcc3c114a0e New inductive definition package
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   365
       REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
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   366
ddcc3c114a0e New inductive definition package
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  in (intrs, unfold) end;
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   368
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ceab9e663e08 tuned comments;
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parents: 6394
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   369
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
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   370
ceab9e663e08 tuned comments;
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parents: 6394
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(** prove elimination rules **)
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   372
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   373
fun prove_elims cs cTs params intr_ts unfold rec_sets_defs thy =
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   374
  let
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   375
    val _ = message "  Proving the elimination rules ...";
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   376
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   377
    val rules1 = [CollectE, disjE, make_elim vimageD];
ddcc3c114a0e New inductive definition package
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   378
    val rules2 = [exE, conjE, Inl_neq_Inr, Inr_neq_Inl] @
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   379
      map make_elim [Inl_inject, Inr_inject];
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   380
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   381
    val elims = map (fn t => prove_goalw_cterm rec_sets_defs
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3d9fd50fcc43 Theory.sign_of;
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   382
      (cterm_of (Theory.sign_of thy) t) (fn prems =>
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   383
        [cut_facts_tac [hd prems] 1,
ddcc3c114a0e New inductive definition package
berghofe
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   384
         dtac (unfold RS subst) 1,
ddcc3c114a0e New inductive definition package
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   385
         REPEAT (FIRSTGOAL (eresolve_tac rules1)),
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   386
         REPEAT (FIRSTGOAL (eresolve_tac rules2)),
ddcc3c114a0e New inductive definition package
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   387
         EVERY (map (fn prem =>
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   388
           DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))]))
5094
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   389
      (mk_elims cs cTs params intr_ts)
ddcc3c114a0e New inductive definition package
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   390
ddcc3c114a0e New inductive definition package
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   391
  in elims end;
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   392
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ceab9e663e08 tuned comments;
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parents: 6394
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   393
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   394
(** derivation of simplified elimination rules **)
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   395
ddcc3c114a0e New inductive definition package
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   396
(*Applies freeness of the given constructors, which *must* be unfolded by
ddcc3c114a0e New inductive definition package
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   397
  the given defs.  Cannot simply use the local con_defs because con_defs=[] 
ddcc3c114a0e New inductive definition package
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   398
  for inference systems.
ddcc3c114a0e New inductive definition package
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parents:
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   399
 *)
6141
a6922171b396 removal of the (thm list) argument of mk_cases
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parents: 6092
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   400
fun con_elim_tac ss =
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ddcc3c114a0e New inductive definition package
berghofe
parents:
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   401
  let val elim_tac = REPEAT o (eresolve_tac elim_rls)
ddcc3c114a0e New inductive definition package
berghofe
parents:
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   402
  in ALLGOALS(EVERY'[elim_tac,
6141
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 6092
diff changeset
   403
		     asm_full_simp_tac ss,
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 6092
diff changeset
   404
		     elim_tac,
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 6092
diff changeset
   405
		     REPEAT o bound_hyp_subst_tac])
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ddcc3c114a0e New inductive definition package
berghofe
parents:
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   406
     THEN prune_params_tac
ddcc3c114a0e New inductive definition package
berghofe
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   407
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   408
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   409
(*cprop should have the form t:Si where Si is an inductive set*)
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
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   410
fun mk_cases_i elims ss cprop =
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   411
  let
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   412
    val prem = Thm.assume cprop;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
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   413
    fun mk_elim rl = standard (rule_by_tactic (con_elim_tac ss) (prem RS rl));
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
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   414
  in
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   415
    (case get_first (try mk_elim) elims of
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   416
      Some r => r
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   417
    | None => error (Pretty.string_of (Pretty.block
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   418
        [Pretty.str "mk_cases: proposition not of form 't : S_i'", Pretty.fbrk,
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
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   419
          Display.pretty_cterm cprop])))
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   420
  end;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   421
6141
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 6092
diff changeset
   422
fun mk_cases elims s =
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   423
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.sign_of_thm (hd elims)) (s, propT));
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
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parents: 7020
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   424
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
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   425
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
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   426
(* inductive_cases(_i) *)
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
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   427
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
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diff changeset
   428
fun gen_inductive_cases prep_att prep_const prep_prop
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   429
    ((((name, raw_atts), raw_set), raw_props), comment) thy =
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   430
  let
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   431
    val sign = Theory.sign_of thy;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   432
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   433
    val atts = map (prep_att thy) raw_atts;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   434
    val (_, {elims, ...}) = get_inductive thy (prep_const sign raw_set);
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   435
    val cprops = map (Thm.cterm_of sign o prep_prop (ProofContext.init thy)) raw_props;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   436
    val thms = map (mk_cases_i elims (Simplifier.simpset_of thy)) cprops;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   437
  in
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   438
    thy
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   439
    |> IsarThy.have_theorems_i (((name, atts), map Thm.no_attributes thms), comment)
5094
ddcc3c114a0e New inductive definition package
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parents:
diff changeset
   440
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   441
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   442
val inductive_cases =
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   443
  gen_inductive_cases Attrib.global_attribute Sign.intern_const ProofContext.read_prop;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   444
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   445
val inductive_cases_i = gen_inductive_cases (K I) (K I) ProofContext.cert_prop;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   446
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   447
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   448
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   449
(** prove induction rule **)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   450
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   451
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   452
    fp_def rec_sets_defs thy =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   453
  let
6427
fd36b2e7d80e tuned messages;
wenzelm
parents: 6424
diff changeset
   454
    val _ = message "  Proving the induction rule ...";
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   455
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6141
diff changeset
   456
    val sign = Theory.sign_of thy;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   457
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   458
    val sum_case_rewrites = (case ThyInfo.lookup_theory "Datatype" of
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   459
        None => []
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   460
      | Some thy' => map mk_meta_eq (PureThy.get_thms thy' "sum.cases"));
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   461
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   462
    val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   463
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   464
    (* make predicate for instantiation of abstract induction rule *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   465
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   466
    fun mk_ind_pred _ [P] = P
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   467
      | mk_ind_pred T Ps =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   468
         let val n = (length Ps) div 2;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   469
             val Type (_, [T1, T2]) = T
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   470
         in Const ("Datatype.sum.sum_case",
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   471
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   472
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   473
         end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   474
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   475
    val ind_pred = mk_ind_pred sumT preds;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   476
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   477
    val ind_concl = HOLogic.mk_Trueprop
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   478
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   479
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   480
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   481
    (* simplification rules for vimage and Collect *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   482
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   483
    val vimage_simps = if length cs < 2 then [] else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   484
      map (fn c => prove_goalw_cterm [] (cterm_of sign
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   485
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   486
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   487
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   488
             nth_elem (find_index_eq c cs, preds)))))
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   489
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites,
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   490
          rtac refl 1])) cs;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   491
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   492
    val induct = prove_goalw_cterm [] (cterm_of sign
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   493
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   494
        [rtac (impI RS allI) 1,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   495
         DETERM (etac (mono RS (fp_def RS def_induct)) 1),
5553
ae42b36a50c2 renamed mk_meta_eq to mk_eq
oheimb
parents: 5303
diff changeset
   496
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::vimage_simps)),
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   497
         fold_goals_tac rec_sets_defs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   498
         (*This CollectE and disjE separates out the introduction rules*)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   499
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   500
         (*Now break down the individual cases.  No disjE here in case
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   501
           some premise involves disjunction.*)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   502
         REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE] 
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   503
                     ORELSE' hyp_subst_tac)),
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   504
         rewrite_goals_tac sum_case_rewrites,
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   505
         EVERY (map (fn prem =>
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   506
           DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   507
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   508
    val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   509
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   510
        [cut_facts_tac prems 1,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   511
         REPEAT (EVERY
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   512
           [REPEAT (resolve_tac [conjI, impI] 1),
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   513
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
7293
959e060f4a2f Moved sum_case stuff from Sum to Datatype.
berghofe
parents: 7257
diff changeset
   514
            rewrite_goals_tac sum_case_rewrites,
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   515
            atac 1])])
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   516
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   517
  in standard (split_rule (induct RS lemma))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   518
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   519
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   520
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   521
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   522
(*** specification of (co)inductive sets ****)
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   523
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   524
(** definitional introduction of (co)inductive sets **)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   525
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   526
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   527
    atts intros monos con_defs thy params paramTs cTs cnames =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   528
  let
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   529
    val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   530
      commas_quote cnames) else ();
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   531
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   532
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   533
    val setT = HOLogic.mk_setT sumT;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   534
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6141
diff changeset
   535
    val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6141
diff changeset
   536
      else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   537
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   538
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   539
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   540
    val used = foldr add_term_names (intr_ts, []);
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   541
    val [sname, xname] = variantlist (["S", "x"], used);
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   542
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   543
    (* transform an introduction rule into a conjunction  *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   544
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   545
    (* is transformed into                                *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   546
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   547
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   548
    fun transform_rule r =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   549
      let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   550
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   551
        val subst = subst_free
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   552
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   553
        val Const ("op :", _) $ t $ u =
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   554
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   555
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   556
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   557
        (frees, foldr1 (app HOLogic.conj)
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   558
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   559
            (map (subst o HOLogic.dest_Trueprop)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   560
              (Logic.strip_imp_prems r))))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   561
      end
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   562
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   563
    (* make a disjunction of all introduction rules *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   564
5149
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   565
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
10f0be29c0d1 Fixed bug in transform_rule.
berghofe
parents: 5120
diff changeset
   566
      absfree (xname, sumT, foldr1 (app HOLogic.disj) (map transform_rule intr_ts)));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   567
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   568
    (* add definiton of recursive sets to theory *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   569
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   570
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6141
diff changeset
   571
    val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   572
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   573
    val rec_const = list_comb
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   574
      (Const (full_rec_name, paramTs ---> setT), params);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   575
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   576
    val fp_def_term = Logic.mk_equals (rec_const,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   577
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   578
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   579
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   580
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   581
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   582
    val thy' = thy |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   583
      (if declare_consts then
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   584
        Theory.add_consts_i (map (fn (c, n) =>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   585
          (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   586
       else I) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   587
      (if length cs < 2 then I else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   588
       Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)]) |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   589
      Theory.add_path rec_name |>
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   590
      PureThy.add_defss_i [(("defs", def_terms), [])];
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   591
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   592
    (* get definitions from theory *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   593
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   594
    val fp_def::rec_sets_defs = PureThy.get_thms thy' "defs";
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   595
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   596
    (* prove and store theorems *)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   597
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   598
    val mono = prove_mono setT fp_fun monos thy';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   599
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   600
      rec_sets_defs thy';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   601
    val elims = if no_elim then [] else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   602
      prove_elims cs cTs params intr_ts unfold rec_sets_defs thy';
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   603
    val raw_induct = if no_ind then TrueI else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   604
      if coind then standard (rule_by_tactic
5553
ae42b36a50c2 renamed mk_meta_eq to mk_eq
oheimb
parents: 5303
diff changeset
   605
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   606
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   607
      else
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   608
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   609
          rec_sets_defs thy';
5108
4074c7d86d44 Fixed bug (improper handling of flag no_ind).
berghofe
parents: 5094
diff changeset
   610
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   611
      else standard (raw_induct RSN (2, rev_mp));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   612
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   613
    val thy'' = thy'
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   614
      |> PureThy.add_thmss [(("intrs", intrs), atts)]
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   615
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   616
      |> (if no_elim then I else PureThy.add_thmss [(("elims", elims), [])])
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   617
      |> (if no_ind then I else PureThy.add_thms
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   618
        [((coind_prefix coind ^ "induct", induct), [])])
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   619
      |> Theory.parent_path;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   620
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   621
  in (thy'',
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   622
    {defs = fp_def::rec_sets_defs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   623
     mono = mono,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   624
     unfold = unfold,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   625
     intrs = intrs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   626
     elims = elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   627
     mk_cases = mk_cases elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   628
     raw_induct = raw_induct,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   629
     induct = induct})
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   630
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   631
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   632
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   633
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   634
(** axiomatic introduction of (co)inductive sets **)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   635
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   636
fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   637
    atts intros monos con_defs thy params paramTs cTs cnames =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   638
  let
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   639
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   640
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   641
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   642
    val elim_ts = mk_elims cs cTs params intr_ts;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   643
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   644
    val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   645
    val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   646
    
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   647
    val thy' = thy
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   648
      |> (if declare_consts then
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   649
            Theory.add_consts_i
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   650
              (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   651
         else I)
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   652
      |> Theory.add_path rec_name
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   653
      |> PureThy.add_axiomss_i [(("intrs", intr_ts), atts), (("elims", elim_ts), [])]
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   654
      |> (if coind then I else PureThy.add_axioms_i [(("internal_induct", ind_t), [])]);
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   655
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   656
    val intrs = PureThy.get_thms thy' "intrs";
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   657
    val elims = PureThy.get_thms thy' "elims";
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   658
    val raw_induct = if coind then TrueI else
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   659
      standard (split_rule (PureThy.get_thm thy' "internal_induct"));
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   660
    val induct = if coind orelse length cs > 1 then raw_induct
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   661
      else standard (raw_induct RSN (2, rev_mp));
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   662
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   663
    val thy'' =
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   664
      thy'
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   665
      |> (if coind then I else PureThy.add_thms [(("induct", induct), [])])
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   666
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   667
      |> Theory.parent_path;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   668
  in (thy'',
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   669
    {defs = [],
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   670
     mono = TrueI,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   671
     unfold = TrueI,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   672
     intrs = intrs,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   673
     elims = elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   674
     mk_cases = mk_cases elims,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   675
     raw_induct = raw_induct,
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   676
     induct = induct})
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   677
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   678
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   679
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   680
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   681
(** introduction of (co)inductive sets **)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   682
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   683
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   684
    atts intros monos con_defs thy =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   685
  let
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   686
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6141
diff changeset
   687
    val sign = Theory.sign_of thy;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   688
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   689
    (*parameters should agree for all mutually recursive components*)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   690
    val (_, params) = strip_comb (hd cs);
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   691
    val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   692
      \ component is not a free variable: " sign) params;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   693
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   694
    val cTs = map (try' (HOLogic.dest_setT o fastype_of)
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   695
      "Recursive component not of type set: " sign) cs;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   696
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   697
    val full_cnames = map (try' (fst o dest_Const o head_of)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   698
      "Recursive set not previously declared as constant: " sign) cs;
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   699
    val cnames = map Sign.base_name full_cnames;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   700
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   701
    val _ = assert_all Syntax.is_identifier cnames	(* FIXME why? *)
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   702
       (fn a => "Base name of recursive set not an identifier: " ^ a);
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   703
    val _ = seq (check_rule sign cs o snd o fst) intros;
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   704
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   705
    val (thy1, result) =
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   706
      (if ! quick_and_dirty then add_ind_axm else add_ind_def)
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   707
        verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   708
        con_defs thy params paramTs cTs cnames;
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   709
    val thy2 = thy1 |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result);
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   710
  in (thy2, result) end;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   711
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   712
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   713
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   714
(** external interface **)
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   715
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   716
fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   717
  let
6394
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6141
diff changeset
   718
    val sign = Theory.sign_of thy;
3d9fd50fcc43 Theory.sign_of;
wenzelm
parents: 6141
diff changeset
   719
    val cs = map (readtm (Theory.sign_of thy) HOLogic.termTVar) c_strings;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   720
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   721
    val atts = map (Attrib.global_attribute thy) srcs;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   722
    val intr_names = map (fst o fst) intro_srcs;
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   723
    val intr_ts = map (readtm (Theory.sign_of thy) propT o snd o fst) intro_srcs;
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   724
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
7020
75ff179df7b7 Exported function unify_consts (workaround to avoid inconsistently
berghofe
parents: 6851
diff changeset
   725
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   726
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   727
    val ((thy', con_defs), monos) = thy
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   728
      |> IsarThy.apply_theorems raw_monos
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   729
      |> apfst (IsarThy.apply_theorems raw_con_defs);
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   730
  in
7020
75ff179df7b7 Exported function unify_consts (workaround to avoid inconsistently
berghofe
parents: 6851
diff changeset
   731
    add_inductive_i verbose false "" coind false false cs'
75ff179df7b7 Exported function unify_consts (workaround to avoid inconsistently
berghofe
parents: 6851
diff changeset
   732
      atts ((intr_names ~~ intr_ts') ~~ intr_atts) monos con_defs thy'
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   733
  end;
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   734
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   735
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   736
6437
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   737
(** package setup **)
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   738
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   739
(* setup theory *)
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   740
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   741
val setup = [InductiveData.init];
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   742
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   743
9bdfe07ba8e9 'HOL/inductive' theory data;
wenzelm
parents: 6430
diff changeset
   744
(* outer syntax *)
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   745
6723
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   746
local structure P = OuterParse and K = OuterSyntax.Keyword in
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   747
6521
16c425fc00cb intrs attributes;
wenzelm
parents: 6437
diff changeset
   748
fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
6723
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   749
  #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   750
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   751
fun ind_decl coind =
6729
b6e167580a32 formal comments (still dummy);
wenzelm
parents: 6723
diff changeset
   752
  (Scan.repeat1 P.term --| P.marg_comment) --
b6e167580a32 formal comments (still dummy);
wenzelm
parents: 6723
diff changeset
   753
  (P.$$$ "intrs" |--
7152
44d46a112127 tuned outer syntax;
wenzelm
parents: 7107
diff changeset
   754
    P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop --| P.marg_comment))) --
6729
b6e167580a32 formal comments (still dummy);
wenzelm
parents: 6723
diff changeset
   755
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
b6e167580a32 formal comments (still dummy);
wenzelm
parents: 6723
diff changeset
   756
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   757
  >> (Toplevel.theory o mk_ind coind);
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   758
6723
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   759
val inductiveP =
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   760
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   761
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   762
val coinductiveP =
f342449d73ca outer syntax keyword classification;
wenzelm
parents: 6556
diff changeset
   763
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   764
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   765
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   766
val ind_cases =
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   767
  P.opt_thm_name "=" -- P.xname --| P.$$$ ":" -- Scan.repeat1 P.prop -- P.marg_comment
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   768
  >> (Toplevel.theory o inductive_cases);
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   769
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   770
val inductive_casesP =
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   771
  OuterSyntax.command "inductive_cases" "create simplified instances of elimination rules"
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   772
    K.thy_decl ind_cases;
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   773
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   774
val _ = OuterSyntax.add_keywords ["intrs", "monos", "con_defs"];
7107
ce69de572bca inductive_cases(_i): Isar interface to mk_cases;
wenzelm
parents: 7020
diff changeset
   775
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   776
5094
ddcc3c114a0e New inductive definition package
berghofe
parents:
diff changeset
   777
end;
6424
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   778
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   779
ceab9e663e08 tuned comments;
wenzelm
parents: 6394
diff changeset
   780
end;