src/HOL/Predicate_Compile_Examples/IMP_3.thy
 author hoelzl Fri Feb 19 13:40:50 2016 +0100 (2016-02-19) changeset 62378 85ed00c1fe7c parent 58310 91ea607a34d8 child 63167 0909deb8059b permissions -rw-r--r--
generalize more theorems to support enat and ennreal
```     1 theory IMP_3
```
```     2 imports "~~/src/HOL/Library/Predicate_Compile_Quickcheck"
```
```     3 begin
```
```     4
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```     5 subsection {* IMP *}
```
```     6
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```     7 text {*
```
```     8   In this example, the state is one integer variable and the commands are Skip, Ass, Seq, IF, and While.
```
```     9 *}
```
```    10
```
```    11 type_synonym var = unit
```
```    12 type_synonym state = int
```
```    13
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```    14 datatype com =
```
```    15   Skip |
```
```    16   Ass var "int" |
```
```    17   Seq com com |
```
```    18   IF "state list" com com |
```
```    19   While "state list" com
```
```    20
```
```    21 inductive exec :: "com => state => state => bool" where
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```    22   "exec Skip s s" |
```
```    23   "exec (Ass x e) s e" |
```
```    24   "exec c1 s1 s2 ==> exec c2 s2 s3 ==> exec (Seq c1 c2) s1 s3" |
```
```    25   "s \<in> set b ==> exec c1 s t ==> exec (IF b c1 c2) s t" |
```
```    26   "s \<notin> set b ==> exec c2 s t ==> exec (IF b c1 c2) s t" |
```
```    27   "s \<notin> set b ==> exec (While b c) s s" |
```
```    28   "s1 \<in> set b ==> exec c s1 s2 ==> exec (While b c) s2 s3 ==> exec (While b c) s1 s3"
```
```    29
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```    30 lemma
```
```    31   "exec c s s' ==> exec (Seq c c) s s'"
```
```    32   quickcheck[tester = smart_exhaustive, size=2, iterations=100, quiet = false, expect = counterexample]
```
```    33 oops
```
```    34
```
```    35
```
```    36 end
```