theory IMP_1 imports "HOL-Library.Predicate_Compile_Quickcheck" begin subsection ‹IMP› text ‹ In this example, the state is one boolean variable and the commands are Skip, Ass, Seq, and IF. › type_synonym var = unit type_synonym state = bool datatype com = Skip | Ass bool | Seq com com | IF com com inductive exec :: "com => state => state => bool" where "exec Skip s s" | "exec (Ass e) s e" | "exec c1 s1 s2 ==> exec c2 s2 s3 ==> exec (Seq c1 c2) s1 s3" | "s ==> exec c1 s t ==> exec (IF c1 c2) s t" | "¬ s ==> exec c2 s t ==> exec (IF c1 c2) s t" lemma "exec c s s' ==> exec (Seq c c) s s'" quickcheck[tester = smart_exhaustive, size = 2, iterations = 100, timeout = 600.0, expect = counterexample] oops end