# HG changeset patch
# User nipkow
# Date 1380116955 -7200
# Node ID b65b4e70a258bc53890258bc6bee37048c85b6a6
# Parent  87941795956c65e32c0c1e94080211cd785ee695# Parent  ac5b8687f1d9dffafae5bfff7e0a4ea797d1d491
merged

diff -r 87941795956c -r b65b4e70a258 src/HOL/IMP/Compiler.thy
--- a/src/HOL/IMP/Compiler.thy	Wed Sep 25 14:28:10 2013 +0200
+++ b/src/HOL/IMP/Compiler.thy	Wed Sep 25 15:49:15 2013 +0200
@@ -167,15 +167,15 @@
 by (induction a arbitrary: stk) fastforce+
 
 fun bcomp :: "bexp \<Rightarrow> bool \<Rightarrow> int \<Rightarrow> instr list" where
-"bcomp (Bc v) c n = (if v=c then [JMP n] else [])" |
-"bcomp (Not b) c n = bcomp b (\<not>c) n" |
-"bcomp (And b1 b2) c n =
- (let cb2 = bcomp b2 c n;
-        m = (if c then size cb2 else (size cb2::int)+n);
+"bcomp (Bc v) f n = (if v=f then [JMP n] else [])" |
+"bcomp (Not b) f n = bcomp b (\<not>f) n" |
+"bcomp (And b1 b2) f n =
+ (let cb2 = bcomp b2 f n;
+        m = (if f then size cb2 else (size cb2::int)+n);
       cb1 = bcomp b1 False m
   in cb1 @ cb2)" |
-"bcomp (Less a1 a2) c n =
- acomp a1 @ acomp a2 @ (if c then [JMPLESS n] else [JMPGE n])"
+"bcomp (Less a1 a2) f n =
+ acomp a1 @ acomp a2 @ (if f then [JMPLESS n] else [JMPGE n])"
 
 value
   "bcomp (And (Less (V ''x'') (V ''y'')) (Not(Less (V ''u'') (V ''v''))))
@@ -185,16 +185,16 @@
   fixes n :: int
   shows
   "0 \<le> n \<Longrightarrow>
-  bcomp b c n \<turnstile>
- (0,s,stk)  \<rightarrow>*  (size(bcomp b c n) + (if c = bval b s then n else 0),s,stk)"
-proof(induction b arbitrary: c n)
+  bcomp b f n \<turnstile>
+ (0,s,stk)  \<rightarrow>*  (size(bcomp b f n) + (if f = bval b s then n else 0),s,stk)"
+proof(induction b arbitrary: f n)
   case Not
-  from Not(1)[where c="~c"] Not(2) show ?case by fastforce
+  from Not(1)[where f="~f"] Not(2) show ?case by fastforce
 next
   case (And b1 b2)
-  from And(1)[of "if c then size(bcomp b2 c n) else size(bcomp b2 c n) + n" 
+  from And(1)[of "if f then size(bcomp b2 f n) else size(bcomp b2 f n) + n" 
                  "False"] 
-       And(2)[of n  "c"] And(3) 
+       And(2)[of n f] And(3) 
   show ?case by fastforce
 qed fastforce+
 
diff -r 87941795956c -r b65b4e70a258 src/HOL/IMP/Compiler2.thy
--- a/src/HOL/IMP/Compiler2.thy	Wed Sep 25 14:28:10 2013 +0200
+++ b/src/HOL/IMP/Compiler2.thy	Wed Sep 25 15:49:15 2013 +0200
@@ -199,13 +199,13 @@
 
 lemma bcomp_succs:
   "0 \<le> i \<Longrightarrow>
-  succs (bcomp b c i) n \<subseteq> {n .. n + size (bcomp b c i)}
-                           \<union> {n + i + size (bcomp b c i)}" 
-proof (induction b arbitrary: c i n)
+  succs (bcomp b f i) n \<subseteq> {n .. n + size (bcomp b f i)}
+                           \<union> {n + i + size (bcomp b f i)}" 
+proof (induction b arbitrary: f i n)
   case (And b1 b2)
   from And.prems
   show ?case 
-    by (cases c)
+    by (cases f)
        (auto dest: And.IH(1) [THEN subsetD, rotated] 
                    And.IH(2) [THEN subsetD, rotated])
 qed auto
@@ -216,12 +216,12 @@
   fixes i :: int
   shows
   "0 \<le> i \<Longrightarrow>
-  exits (bcomp b c i) \<subseteq> {size (bcomp b c i), i + size (bcomp b c i)}" 
+  exits (bcomp b f i) \<subseteq> {size (bcomp b f i), i + size (bcomp b f i)}" 
   by (auto simp: exits_def)
   
 lemma bcomp_exitsD [dest!]:
-  "p \<in> exits (bcomp b c i) \<Longrightarrow> 0 \<le> i \<Longrightarrow> 
-  p = size (bcomp b c i) \<or> p = i + size (bcomp b c i)"
+  "p \<in> exits (bcomp b f i) \<Longrightarrow> 0 \<le> i \<Longrightarrow> 
+  p = size (bcomp b f i) \<or> p = i + size (bcomp b f i)"
   using bcomp_exits by auto
 
 lemma ccomp_succs:
@@ -444,22 +444,22 @@
 
 lemma bcomp_split:
   fixes i j :: int
-  assumes "bcomp b c i @ P' \<turnstile> (0, s, stk) \<rightarrow>^n (j, s', stk')" 
-          "j \<notin> {0..<size (bcomp b c i)}" "0 \<le> i"
+  assumes "bcomp b f i @ P' \<turnstile> (0, s, stk) \<rightarrow>^n (j, s', stk')" 
+          "j \<notin> {0..<size (bcomp b f i)}" "0 \<le> i"
   shows "\<exists>s'' stk'' (i'::int) k m. 
-           bcomp b c i \<turnstile> (0, s, stk) \<rightarrow>^k (i', s'', stk'') \<and>
-           (i' = size (bcomp b c i) \<or> i' = i + size (bcomp b c i)) \<and>
-           bcomp b c i @ P' \<turnstile> (i', s'', stk'') \<rightarrow>^m (j, s', stk') \<and>
+           bcomp b f i \<turnstile> (0, s, stk) \<rightarrow>^k (i', s'', stk'') \<and>
+           (i' = size (bcomp b f i) \<or> i' = i + size (bcomp b f i)) \<and>
+           bcomp b f i @ P' \<turnstile> (i', s'', stk'') \<rightarrow>^m (j, s', stk') \<and>
            n = k + m"
-  using assms by (cases "bcomp b c i = []") (fastforce dest!: exec_n_drop_right)+
+  using assms by (cases "bcomp b f i = []") (fastforce dest!: exec_n_drop_right)+
 
 lemma bcomp_exec_n [dest]:
   fixes i j :: int
-  assumes "bcomp b c j \<turnstile> (0, s, stk) \<rightarrow>^n (i, s', stk')"
-          "size (bcomp b c j) \<le> i" "0 \<le> j"
-  shows "i = size(bcomp b c j) + (if c = bval b s then j else 0) \<and>
+  assumes "bcomp b f j \<turnstile> (0, s, stk) \<rightarrow>^n (i, s', stk')"
+          "size (bcomp b f j) \<le> i" "0 \<le> j"
+  shows "i = size(bcomp b f j) + (if f = bval b s then j else 0) \<and>
          s' = s \<and> stk' = stk"
-using assms proof (induction b arbitrary: c j i n s' stk')
+using assms proof (induction b arbitrary: f j i n s' stk')
   case Bc thus ?case 
     by (simp split: split_if_asm add: exec_n_simps exec1_def)
 next
@@ -469,11 +469,11 @@
 next
   case (And b1 b2)
   
-  let ?b2 = "bcomp b2 c j" 
-  let ?m  = "if c then size ?b2 else size ?b2 + j"
+  let ?b2 = "bcomp b2 f j" 
+  let ?m  = "if f then size ?b2 else size ?b2 + j"
   let ?b1 = "bcomp b1 False ?m" 
 
-  have j: "size (bcomp (And b1 b2) c j) \<le> i" "0 \<le> j" by fact+
+  have j: "size (bcomp (And b1 b2) f j) \<le> i" "0 \<le> j" by fact+
   
   from And.prems
   obtain s'' stk'' and i'::int and k m where 
@@ -563,8 +563,7 @@
       with "1.prems"
       have ?case
         by simp
-           (fastforce dest!: bcomp_exec_n bcomp_split 
-                     simp: exec_n_simps)
+           (fastforce dest!: bcomp_exec_n bcomp_split simp: exec_n_simps)
     } moreover {
       assume b: "bval b s"
       let ?c0 = "WHILE b DO c"