src/HOL/Predicate_Compile_Examples/IMP_3.thy
 author bulwahn Fri Dec 03 08:40:47 2010 +0100 (2010-12-03) changeset 40924 a9be7f26b4e6 parent 39249 9c866b248cb1 child 41413 64cd30d6b0b8 permissions -rw-r--r--
```     1 theory IMP_3
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```     2 imports "Predicate_Compile_Quickcheck"
```
```     3 begin
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```     4
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```     5 subsection {* IMP *}
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```     6
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```     7 text {*
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```     8   In this example, the state is one integer variable and the commands are Skip, Ass, Seq, IF, and While.
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```     9 *}
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```    10
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```    11 types
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```    12   var = unit
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```    13   state = int
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```    14
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```    15 datatype com =
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```    16   Skip |
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```    17   Ass var "int" |
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```    18   Seq com com |
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```    19   IF "state list" com com |
```
```    20   While "state list" com
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```    21
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```    22 inductive exec :: "com => state => state => bool" where
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```    23   "exec Skip s s" |
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```    24   "exec (Ass x e) s e" |
```
```    25   "exec c1 s1 s2 ==> exec c2 s2 s3 ==> exec (Seq c1 c2) s1 s3" |
```
```    26   "s \<in> set b ==> exec c1 s t ==> exec (IF b c1 c2) s t" |
```
```    27   "s \<notin> set b ==> exec c2 s t ==> exec (IF b c1 c2) s t" |
```
```    28   "s \<notin> set b ==> exec (While b c) s s" |
```
```    29   "s1 \<in> set b ==> exec c s1 s2 ==> exec (While b c) s2 s3 ==> exec (While b c) s1 s3"
```
```    30
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```    31 lemma
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```    32   "exec c s s' ==> exec (Seq c c) s s'"
```
```    33   quickcheck[tester = predicate_compile_ff_nofs, size=2, iterations=10, quiet = false, expect = counterexample]
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```    34 oops
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```    35
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```    36
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`    37 end`