--- a/src/HOL/Tools/Qelim/qelim.ML Mon Jun 25 00:36:37 2007 +0200
+++ b/src/HOL/Tools/Qelim/qelim.ML Mon Jun 25 00:36:38 2007 +0200
@@ -1,39 +1,41 @@
-(*
+(* Title: HOL/Tools/Qelim/qelim.ML
ID: $Id$
Author: Amine Chaieb and Tobias Nipkow, TU Muenchen
-File containing the implementation of the proof protocoling
-and proof generation for multiple quantified formulae.
+Proof protocoling and proof generation for multiple quantified
+formulae.
*)
signature QELIM =
sig
+ val gen_qelim_conv: Proof.context -> conv -> conv -> conv ->
+ (cterm -> 'a -> 'a) -> 'a -> ('a -> cterm -> thm) ->
+ ('a -> conv) -> ('a -> cterm -> thm) -> conv
val standard_qelim_conv: Proof.context -> (cterm list -> cterm -> thm) ->
- (cterm list -> Conv.conv) -> (cterm list -> cterm -> thm) -> cterm -> thm
- val gen_qelim_conv: Proof.context -> Conv.conv -> Conv.conv -> Conv.conv ->
- (cterm -> 'a -> 'a) -> 'a -> ('a -> cterm -> thm) ->
- ('a -> Conv.conv) -> ('a -> cterm -> thm) -> Conv.conv
+ (cterm list -> conv) -> (cterm list -> cterm -> thm) -> cterm -> thm
end;
-structure Qelim : QELIM =
+structure Qelim: QELIM =
struct
open Conv;
-local
- val all_not_ex = mk_meta_eq @{thm "all_not_ex"}
-in
-fun gen_qelim_conv ctxt precv postcv simpex_conv ins env atcv ncv qcv =
- let
+
+(* gen_qelim_conv *)
+
+val all_not_ex = mk_meta_eq @{thm "all_not_ex"};
+
+fun gen_qelim_conv ctxt precv postcv simpex_conv ins env atcv ncv qcv =
+ let
val thy = ProofContext.theory_of ctxt
fun conv env p =
- case (term_of p) of
- Const(s,T)$_$_ => if domain_type T = HOLogic.boolT
+ case (term_of p) of
+ Const(s,T)$_$_ => if domain_type T = HOLogic.boolT
andalso s mem ["op &","op |","op -->","op ="]
then binop_conv (conv env) p else atcv env p
| Const("Not",_)$_ => arg_conv (conv env) p
- | Const("Ex",_)$Abs(s,_,_) =>
- let
+ | Const("Ex",_)$Abs(s,_,_) =>
+ let
val (e,p0) = Thm.dest_comb p
val (x,p') = Thm.dest_abs (SOME s) p0
val env' = ins x env
@@ -43,34 +45,25 @@
val (l,r) = Thm.dest_equals (cprop_of th')
in if is_refl th' then Thm.transitive th (qcv env (Thm.rhs_of th))
else Thm.transitive (Thm.transitive th th') (conv env r) end
- | Const("Ex",_)$ _ => (eta_conv thy then_conv conv env) p
- | Const("All",_)$_ =>
- let
+ | Const("Ex",_)$ _ => (Thm.eta_long_conversion then_conv conv env) p
+ | Const("All",_)$_ =>
+ let
val p = Thm.dest_arg p
val ([(_,T)],[]) = Thm.match (@{cpat "All"}, Thm.dest_fun p)
- val th = instantiate' [SOME T] [SOME p] all_not_ex
- in transitive th (conv env (Thm.rhs_of th))
+ val th = instantiate' [SOME T] [SOME p] all_not_ex
+ in transitive th (conv env (Thm.rhs_of th))
end
| _ => atcv env p
in precv then_conv (conv env) then_conv postcv end
-end;
+
+
+(* standard_qelim_conv *)
-fun cterm_frees ct =
- let fun h acc t =
- case (term_of t) of
- _$_ => h (h acc (Thm.dest_arg t)) (Thm.dest_fun t)
- | Abs(_,_,_) => Thm.dest_abs NONE t ||> h acc |> uncurry (remove (op aconvc))
- | Free _ => insert (op aconvc) t acc
- | _ => acc
- in h [] ct end;
+val pcv = Simplifier.rewrite
+ (HOL_basic_ss addsimps (simp_thms @ ex_simps @ all_simps)
+ @ [@{thm "all_not_ex"}, not_all, ex_disj_distrib]);
-local
-val pcv = Simplifier.rewrite
- (HOL_basic_ss addsimps (simp_thms @ ex_simps @ all_simps)
- @ [@{thm "all_not_ex"}, not_all,ex_disj_distrib])
-in
-fun standard_qelim_conv ctxt atcv ncv qcv p =
- gen_qelim_conv ctxt pcv pcv pcv cons (cterm_frees p) atcv ncv qcv p
-end;
+fun standard_qelim_conv ctxt atcv ncv qcv p =
+ gen_qelim_conv ctxt pcv pcv pcv cons (Thm.add_cterm_frees p []) atcv ncv qcv p;
end;