theory IMP_4
imports "~~/src/HOL/Library/Predicate_Compile_Quickcheck"
begin
subsection \<open>IMP\<close>
text \<open>
In this example, the state is a list of integers and the commands are Skip, Ass, Seq, IF and While.
\<close>
type_synonym var = nat
type_synonym 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[tester = smart_exhaustive, size=2, iterations=100, expect=counterexample]
oops
end