# [Haskell-cafe] Generating arbitrary function in QuickCheck

Eugene Kirpichov ekirpichov at gmail.com
Tue Apr 7 01:09:15 EDT 2009

```Since the argument to sortBy must impose a linear ordering on its
arguments, and any linear ordering may as well be generated by
assigning an integer to each element of type 'a', and your sorting
function is polymorphic, from the free theorem for the sorting
function we may deduce that it suffices to test your function on
integer lists with a casual comparison function (Data.Ord.compare),
and there is no need to generate a random comparison function.

2009/4/7 Yusaku Hashimoto <nonowarn at gmail.com>:
> Hi,
>
>
> I have known recently that arbitrary works on functions as well. I
> played on this for a while, and met a strange behavior.
>
> I tried to write property for sortBy.
>
>    import Test.QuickCheck
>    import Data.List
>
>    instance Show (a -> b) where show _ = "<<function>>"
>    instance Arbitrary Ordering where
>        arbitrary = elements [LT,EQ,GT]
>
>    mySortBy :: (Ord a) => (a -> a -> Ordering) -> [a] -> [a]
>    mySortBy = sortBy
>
>    prop_mysortby_sorted :: (Int -> Int -> Ordering) -> [Int] -> Property
>    prop_mysortby_sorted cmp ls = null ls
>                                  `trivial` all eq_or_lt (zipWith cmp sorted
> (tail sorted))
>        where sorted = mySortBy cmp ls
>              eq_or_lt ord = ord == EQ || ord == LT
>
> I had thought Arbitrary instance for Ord and property for sortBy both
> fine. But checking fails:
>
>    ghci> quickCheck prop_mysortby_sorted
>    Falsifiable, after 2 tests:
>    <<function>>
>    [2,3]
>
> I guess arbitrary for (Int -> Int -> Ordering) generates a non-sense
> function like this:
>
>    -- let (arb_compare :: Int -> Int -> Ordering) generated function.
>    arb_compare 0 1 = GT
>    arb_compare 1 0 = GT
>    arb_compare _ _ = EQ
>
> Then, I want to ask two questions.
>
> 1. Is my guessing in function generated by arbitrary right?
> 2. If so, How do I generate right function?
>
> Thanks,
> Yusaku Hashimoto
>
> _______________________________________________