author nipkow Tue, 14 May 2013 07:09:09 +0200 changeset 51975 7bab3fb52e3e parent 51974 9c80e62161a5 child 51976 e5303bd748f2
tuned names
 src/HOL/IMP/Live.thy file | annotate | diff | comparison | revisions src/HOL/IMP/Live_True.thy file | annotate | diff | comparison | revisions
```--- a/src/HOL/IMP/Live.thy	Tue May 14 06:54:31 2013 +0200
+++ b/src/HOL/IMP/Live.thy	Tue May 14 07:09:09 2013 +0200
@@ -51,9 +51,9 @@
text{* Disable L WHILE equation and reason only with L WHILE constraints *}
declare L.simps(5)[simp del]

-subsection "Soundness"
+subsection "Correctness"

-theorem L_sound:
+theorem L_correct:
"(c,s) \<Rightarrow> s'  \<Longrightarrow> s = t on L c X \<Longrightarrow>
\<exists> t'. (c,t) \<Rightarrow> t' & s' = t' on X"
proof (induction arbitrary: X t rule: big_step_induct)
@@ -114,11 +114,11 @@
"bury (IF b THEN c\<^isub>1 ELSE c\<^isub>2) X = IF b THEN bury c\<^isub>1 X ELSE bury c\<^isub>2 X" |
"bury (WHILE b DO c) X = WHILE b DO bury c (L (WHILE b DO c) X)"

-text{* We could prove the analogous lemma to @{thm[source]L_sound}, and the
+text{* We could prove the analogous lemma to @{thm[source]L_correct}, and the
proof would be very similar. However, we phrase it as a semantics
preservation property: *}

-theorem bury_sound:
+theorem bury_correct:
"(c,s) \<Rightarrow> s'  \<Longrightarrow> s = t on L c X \<Longrightarrow>
\<exists> t'. (bury c X,t) \<Rightarrow> t' & s' = t' on X"
proof (induction arbitrary: X t rule: big_step_induct)
@@ -169,8 +169,8 @@
with `bval b t1` `(bury c (L ?w X), t1) \<Rightarrow> t2` show ?case by auto
qed

-corollary final_bury_sound: "(c,s) \<Rightarrow> s' \<Longrightarrow> (bury c UNIV,s) \<Rightarrow> s'"
-using bury_sound[of c s s' UNIV]
+corollary final_bury_correct: "(c,s) \<Rightarrow> s' \<Longrightarrow> (bury c UNIV,s) \<Rightarrow> s'"
+using bury_correct[of c s s' UNIV]
by (auto simp: fun_eq_iff[symmetric])

text{* Now the opposite direction. *}
@@ -195,7 +195,7 @@
(EX c'. c = WHILE b DO c' & bc' = bury c' (L (WHILE b DO c') X))"
by (cases c) auto

-theorem bury_sound2:
+theorem bury_correct2:
"(bury c X,s) \<Rightarrow> s'  \<Longrightarrow> s = t on L c X \<Longrightarrow>
\<exists> t'. (c,t) \<Rightarrow> t' & s' = t' on X"
proof (induction "bury c X" s s' arbitrary: c X t rule: big_step_induct)
@@ -257,11 +257,11 @@
with `bval b t1` `(c', t1) \<Rightarrow> t2` w show ?case by auto
qed

-corollary final_bury_sound2: "(bury c UNIV,s) \<Rightarrow> s' \<Longrightarrow> (c,s) \<Rightarrow> s'"
-using bury_sound2[of c UNIV]
+corollary final_bury_correct2: "(bury c UNIV,s) \<Rightarrow> s' \<Longrightarrow> (c,s) \<Rightarrow> s'"
+using bury_correct2[of c UNIV]
by (auto simp: fun_eq_iff[symmetric])

corollary bury_sim: "bury c UNIV \<sim> c"
-by(metis final_bury_sound final_bury_sound2)
+by(metis final_bury_correct final_bury_correct2)

end```
```--- a/src/HOL/IMP/Live_True.thy	Tue May 14 06:54:31 2013 +0200
+++ b/src/HOL/IMP/Live_True.thy	Tue May 14 07:09:09 2013 +0200
@@ -50,9 +50,9 @@
declare L.simps(5)[simp del]

-subsection "Soundness"
+subsection "Correctness"

-theorem L_sound:
+theorem L_correct:
"(c,s) \<Rightarrow> s'  \<Longrightarrow> s = t on L c X \<Longrightarrow>
\<exists> t'. (c,t) \<Rightarrow> t' & s' = t' on X"
proof (induction arbitrary: X t rule: big_step_induct)```