src/HOL/Predicate_Compile_Examples/IMP_4.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Predicate_Compile_Examples/IMP_4.thy	Tue Sep 07 11:51:53 2010 +0200
@@ -0,0 +1,37 @@
+theory IMP_4
+imports Predicate_Compile_Quickcheck
+begin
+
+subsection {* IMP *}
+
+text {*
+  In this example, the state is a list of integers and the commands are Skip, Ass, Seq, IF and While.
+*}
+
+types
+  var = nat
+  state = "int list"
+
+datatype com =
+  Skip |
+  Ass var "int" |
+  Seq com com |
+  IF "state list" com com |
+  While "state list" com
+
+inductive exec :: "com => state => state => bool" where
+  "exec Skip s s" |
+  "exec (Ass x e) s (s[x := e])" |
+  "exec c1 s1 s2 ==> exec c2 s2 s3 ==> exec (Seq c1 c2) s1 s3" |
+  "s \<in> set b ==> exec c1 s t ==> exec (IF b c1 c2) s t" |
+  "s \<notin> set b ==> exec c2 s t ==> exec (IF b c1 c2) s t" |
+  "s \<notin> set b ==> exec (While b c) s s" |
+  "s1 \<in> set b ==> exec c s1 s2 ==> exec (While b c) s2 s3 ==> exec (While b c) s1 s3"
+
+lemma
+  "exec c s s' ==> exec (Seq c c) s s'"
+  nitpick (* nitpick fails here! *)
+  quickcheck[generator = predicate_compile_wo_ff, size=2, iterations=10, expect=counterexample]
+oops
+
+end
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