Theory IArray_Examples

theory IArray_Examples
imports "~~/src/HOL/Library/IArray" "~~/src/HOL/Library/Code_Target_Numeral"
begin

lemma "IArray [True,False] !! 1 = False"
by eval

lemma "IArray.length (IArray [[],[]]) = 2"
by eval

lemma "IArray.list_of (IArray [1,3::int]) = [1,3]"
by eval

lemma "IArray.list_of (IArray.of_fun (%n. n*n) 5) = [0,1,4,9,16]"
by eval

lemma "¬ IArray.all (λx. x > 2) (IArray [1,3::int])"
by eval

lemma "IArray.exists (λx. x > 2) (IArray [1,3::int])"
by eval

fun sum2 :: "'a::monoid_add iarray ⇒ nat ⇒ 'a ⇒ 'a" where
"sum2 A n s = (if n=0 then s else sum2 A (n - 1) (s + A!!(n - 1)))"

definition sum :: "'a::monoid_add iarray ⇒ 'a" where
"sum A = sum2 A (IArray.length A) 0"

lemma "sum (IArray [1,2,3,4,5,6,7,8,9::int]) = 45"
by eval

end