src/HOL/ex/IArray_Examples.thy
 author haftmann Wed Feb 13 13:38:52 2013 +0100 (2013-02-13) changeset 51094 84b03c49c223 parent 50138 ca989d793b34 child 51143 0a2371e7ced3 permissions -rw-r--r--
IArray ignorant of particular representation of nat
```     1 theory IArray_Examples
```
```     2 imports "~~/src/HOL/Library/IArray" "~~/src/HOL/Library/Efficient_Nat"
```
```     3 begin
```
```     4
```
```     5 lemma "IArray [True,False] !! 1 = False"
```
```     6 by eval
```
```     7
```
```     8 lemma "IArray.length (IArray [[],[]]) = 2"
```
```     9 by eval
```
```    10
```
```    11 lemma "IArray.list_of (IArray [1,3::int]) = [1,3]"
```
```    12 by eval
```
```    13
```
```    14 lemma "IArray.list_of (IArray.of_fun (%n. n*n) 5) = [0,1,4,9,16]"
```
```    15 by eval
```
```    16
```
```    17 fun sum2 :: "'a::monoid_add iarray \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a" where
```
```    18 "sum2 A n s = (if n=0 then s else sum2 A (n - 1) (s + A!!(n - 1)))"
```
```    19
```
```    20 definition sum :: "'a::monoid_add iarray \<Rightarrow> 'a" where
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```    21 "sum A = sum2 A (IArray.length A) 0"
```
```    22
```
```    23 lemma "sum (IArray [1,2,3,4,5,6,7,8,9::int]) = 45"
```
```    24 by eval
```
```    25
```
```    26 end
```
```    27
```