--- a/src/HOL/Bali/Example.thy Fri May 15 15:13:09 2009 -0700
+++ b/src/HOL/Bali/Example.thy Sat May 16 11:28:23 2009 +0200
@@ -1075,10 +1075,7 @@
lemma max_spec_Base_foo: "max_spec tprg S (ClassT Base) \<lparr>name=foo,parTs=[NT]\<rparr> =
{((ClassT Base, \<lparr>access=Public,static=False,pars=[z],resT=Class Base\<rparr>)
, [Class Base])}"
-apply (unfold max_spec_def)
-apply (simp (no_asm) add: appl_methds_Base_foo)
-apply auto
-done
+by (simp (no_asm) add: max_spec_def appl_methds_Base_foo)
section "well-typedness"
--- a/src/HOL/HOL.thy Fri May 15 15:13:09 2009 -0700
+++ b/src/HOL/HOL.thy Sat May 16 11:28:23 2009 +0200
@@ -1050,8 +1050,7 @@
"(P | False) = P" "(False | P) = P"
"(P | P) = P" "(P | (P | Q)) = (P | Q)" and
"(ALL x. P) = P" "(EX x. P) = P" "EX x. x=t" "EX x. t=x"
- -- {* needed for the one-point-rule quantifier simplification procs *}
- -- {* essential for termination!! *} and
+ and
"!!P. (EX x. x=t & P(x)) = P(t)"
"!!P. (EX x. t=x & P(x)) = P(t)"
"!!P. (ALL x. x=t --> P(x)) = P(t)"
--- a/src/HOL/Library/Binomial.thy Fri May 15 15:13:09 2009 -0700
+++ b/src/HOL/Library/Binomial.thy Sat May 16 11:28:23 2009 +0200
@@ -88,9 +88,7 @@
lemma card_s_0_eq_empty:
"finite A ==> card {B. B \<subseteq> A & card B = 0} = 1"
- apply (simp cong add: conj_cong add: finite_subset [THEN card_0_eq])
- apply (simp cong add: rev_conj_cong)
- done
+by (simp cong add: conj_cong add: finite_subset [THEN card_0_eq])
lemma choose_deconstruct: "finite M ==> x \<notin> M
==> {s. s <= insert x M & card(s) = Suc k}
--- a/src/HOL/MicroJava/BV/BVExample.thy Fri May 15 15:13:09 2009 -0700
+++ b/src/HOL/MicroJava/BV/BVExample.thy Sat May 16 11:28:23 2009 +0200
@@ -69,10 +69,11 @@
lemma subcls1:
"subcls1 E = (\<lambda>C D. (C, D) \<in> {(list_name,Object), (test_name,Object), (Xcpt NullPointer, Object),
(Xcpt ClassCast, Object), (Xcpt OutOfMemory, Object)})"
- apply (simp add: subcls1_def2)
- apply (simp add: name_defs class_defs system_defs E_def class_def)
- apply (auto simp: expand_fun_eq split: split_if_asm)
- done
+apply (simp add: subcls1_def2)
+apply (simp add: name_defs class_defs system_defs E_def class_def)
+apply (auto simp: expand_fun_eq name_defs[symmetric] class_defs split:split_if_asm)
+apply(simp add:name_defs)+
+done
text {* The subclass relation is acyclic; hence its converse is well founded: *}
lemma notin_rtrancl:
--- a/src/HOL/NanoJava/TypeRel.thy Fri May 15 15:13:09 2009 -0700
+++ b/src/HOL/NanoJava/TypeRel.thy Sat May 16 11:28:23 2009 +0200
@@ -56,7 +56,7 @@
"subcls1 =
(SIGMA C: {C. is_class C} . {D. C\<noteq>Object \<and> super (the (class C)) = D})"
apply (unfold subcls1_def is_class_def)
-apply auto
+apply (auto split:split_if_asm)
done
lemma finite_subcls1: "finite subcls1"
--- a/src/HOL/Set.thy Fri May 15 15:13:09 2009 -0700
+++ b/src/HOL/Set.thy Sat May 16 11:28:23 2009 +0200
@@ -1034,6 +1034,29 @@
subsubsection {* Set reasoning tools *}
+text{* Elimination of @{text"{x. \<dots> & x=t & \<dots>}"}. *}
+
+lemma singleton_conj_conv[simp]: "{x. x=a & P x} = (if P a then {a} else {})"
+by auto
+
+lemma singleton_conj_conv2[simp]: "{x. a=x & P x} = (if P a then {a} else {})"
+by auto
+
+ML{*
+ local
+ val Coll_perm_tac = rtac @{thm Collect_cong} 1 THEN rtac @{thm iffI} 1 THEN
+ ALLGOALS(EVERY'[REPEAT_DETERM o (etac @{thm conjE}),
+ DEPTH_SOLVE_1 o (ares_tac [@{thm conjI}])])
+ in
+ val defColl_regroup = Simplifier.simproc (the_context ())
+ "defined Collect" ["{x. P x & Q x}"]
+ (Quantifier1.rearrange_Coll Coll_perm_tac)
+ end;
+
+ Addsimprocs [defColl_regroup];
+
+*}
+
text {*
Rewrite rules for boolean case-splitting: faster than @{text
"split_if [split]"}.
--- a/src/Provers/quantifier1.ML Fri May 15 15:13:09 2009 -0700
+++ b/src/Provers/quantifier1.ML Sat May 16 11:28:23 2009 +0200
@@ -21,11 +21,21 @@
"!x. x=t --> P(x)" is covered by the congreunce rule for -->;
"!x. t=x --> P(x)" must be taken care of by an ordinary rewrite rule.
As must be "? x. t=x & P(x)".
-
And similarly for the bounded quantifiers.
Gries etc call this the "1 point rules"
+
+The above also works for !x1..xn. and ?x1..xn by moving the defined
+qunatifier inside first, but not for nested bounded quantifiers.
+
+For set comprehensions the basic permutations
+ ... & x = t & ... -> x = t & (... & ...)
+ ... & t = x & ... -> t = x & (... & ...)
+are also exported.
+
+To avoid looping, NONE is returned if the term cannot be rearranged,
+esp if x=t/t=x sits at the front already.
*)
signature QUANTIFIER1_DATA =
@@ -61,6 +71,7 @@
val rearrange_ex: theory -> simpset -> term -> thm option
val rearrange_ball: (simpset -> tactic) -> theory -> simpset -> term -> thm option
val rearrange_bex: (simpset -> tactic) -> theory -> simpset -> term -> thm option
+ val rearrange_Coll: tactic -> theory -> simpset -> term -> thm option
end;
functor Quantifier1Fun(Data: QUANTIFIER1_DATA): QUANTIFIER1 =
@@ -70,29 +81,28 @@
(* FIXME: only test! *)
fun def xs eq =
- let val n = length xs
- in case dest_eq eq of
- SOME(c,s,t) =>
- s = Bound n andalso not(loose_bvar1(t,n)) orelse
- t = Bound n andalso not(loose_bvar1(s,n))
- | NONE => false
- end;
+ (case dest_eq eq of
+ SOME(c,s,t) =>
+ let val n = length xs
+ in s = Bound n andalso not(loose_bvar1(t,n)) orelse
+ t = Bound n andalso not(loose_bvar1(s,n)) end
+ | NONE => false);
-fun extract_conj xs t = case dest_conj t of NONE => NONE
+fun extract_conj fst xs t = case dest_conj t of NONE => NONE
| SOME(conj,P,Q) =>
- (if def xs P then SOME(xs,P,Q) else
+ (if not fst andalso def xs P then SOME(xs,P,Q) else
if def xs Q then SOME(xs,Q,P) else
- (case extract_conj xs P of
+ (case extract_conj false xs P of
SOME(xs,eq,P') => SOME(xs,eq, conj $ P' $ Q)
- | NONE => (case extract_conj xs Q of
+ | NONE => (case extract_conj false xs Q of
SOME(xs,eq,Q') => SOME(xs,eq,conj $ P $ Q')
| NONE => NONE)));
-fun extract_imp xs t = case dest_imp t of NONE => NONE
- | SOME(imp,P,Q) => if def xs P then SOME(xs,P,Q)
- else (case extract_conj xs P of
+fun extract_imp fst xs t = case dest_imp t of NONE => NONE
+ | SOME(imp,P,Q) => if not fst andalso def xs P then SOME(xs,P,Q)
+ else (case extract_conj false xs P of
SOME(xs,eq,P') => SOME(xs, eq, imp $ P' $ Q)
- | NONE => (case extract_imp xs Q of
+ | NONE => (case extract_imp false xs Q of
NONE => NONE
| SOME(xs,eq,Q') =>
SOME(xs,eq,imp$P$Q')));
@@ -100,8 +110,8 @@
fun extract_quant extract q =
let fun exqu xs ((qC as Const(qa,_)) $ Abs(x,T,Q)) =
if qa = q then exqu ((qC,x,T)::xs) Q else NONE
- | exqu xs P = extract xs P
- in exqu end;
+ | exqu xs P = extract (null xs) xs P
+ in exqu [] end;
fun prove_conv tac thy tu =
Goal.prove (ProofContext.init thy) [] [] (Logic.mk_equals tu)
@@ -147,7 +157,7 @@
in quant xs (qC $ Abs(x,T,Q)) end;
fun rearrange_all thy _ (F as (all as Const(q,_)) $ Abs(x,T, P)) =
- (case extract_quant extract_imp q [] P of
+ (case extract_quant extract_imp q P of
NONE => NONE
| SOME(xs,eq,Q) =>
let val R = quantify all x T xs (imp $ eq $ Q)
@@ -155,7 +165,7 @@
| rearrange_all _ _ _ = NONE;
fun rearrange_ball tac thy ss (F as Ball $ A $ Abs(x,T,P)) =
- (case extract_imp [] P of
+ (case extract_imp true [] P of
NONE => NONE
| SOME(xs,eq,Q) => if not(null xs) then NONE else
let val R = imp $ eq $ Q
@@ -163,7 +173,7 @@
| rearrange_ball _ _ _ _ = NONE;
fun rearrange_ex thy _ (F as (ex as Const(q,_)) $ Abs(x,T,P)) =
- (case extract_quant extract_conj q [] P of
+ (case extract_quant extract_conj q P of
NONE => NONE
| SOME(xs,eq,Q) =>
let val R = quantify ex x T xs (conj $ eq $ Q)
@@ -171,10 +181,17 @@
| rearrange_ex _ _ _ = NONE;
fun rearrange_bex tac thy ss (F as Bex $ A $ Abs(x,T,P)) =
- (case extract_conj [] P of
+ (case extract_conj true [] P of
NONE => NONE
| SOME(xs,eq,Q) => if not(null xs) then NONE else
SOME(prove_conv (tac ss) thy (F,Bex $ A $ Abs(x,T,conj$eq$Q))))
| rearrange_bex _ _ _ _ = NONE;
+fun rearrange_Coll tac thy _ (F as Coll $ Abs(x,T,P)) =
+ (case extract_conj true [] P of
+ NONE => NONE
+ | SOME(_,eq,Q) =>
+ let val R = Coll $ Abs(x,T, conj $ eq $ Q)
+ in SOME(prove_conv tac thy (F,R)) end);
+
end;