[Haskell-cafe] Comparing functions

[Vlatko Basic]

Thanks Roman. Tried it and implemented, but had troubles until I realized that 
for String, 10 test take quite long. :-)

However, I decided to solve this problem in a more "natural" way


-------- Original Message  --------
Subject: Re: [Haskell-cafe] Comparing functions
From: Roman Cheplyaka <roma at ro-che.info>
To: Vlatko Basic <vlatko.basic at gmail.com>
Cc: Haskell-Cafe <haskell-cafe at haskell.org>
Date: 11.07.2013 20:10

> * Vlatko Basic <vlatko.basic at gmail.com> [2013-07-11 19:33:38+0200]
>> Hello Cafe,
>>
>> I have
>>
>>      data CmpFunction a = CF (a -> a -> Bool)
>>
>> that contains comparing functions, like ==, <, > ..., and I'm trying
>> to declare the Show instance for it like this
>>
>>      instance Show (CmpFunction a) where
>>        show (CF (==)) = "== "                   -- no good
>>        show f = case f of                            -- no good also
>>                         CBF (==) -> "=="
>>                          _ -> "Other"
>>
>> but compiler complains for both with
>>
>> This binding for `==' shadows the existing binding
>>             imported from `Prelude' at src/Main.hs:6:8-11
>>             (and originally defined in `ghc-prim:GHC.Classes')
>>
>> Is it possible at all to compare two functions or how to solve this
>> problem, to show some string for a specific function?
>
> Depending on why you need that...
>
>    {-# LANGUAGE FlexibleContexts, UndecidableInstances, FlexibleInstances #-}
>    import Test.SmallCheck
>    import Test.SmallCheck.Series
>    import Test.SmallCheck.Drivers
>    import Control.Monad.Identity
>    import Data.Maybe
>
>    data CmpFunction a = CF (a -> a -> Bool)
>
>    feq :: (Show a, Serial Identity a) => CmpFunction a -> CmpFunction a -> Bool
>    feq (CF f1) (CF f2) =
>      isNothing $
>        runIdentity $
>          smallCheckM 10 (\x1 x2 -> f1 x1 x2 == f2 x1 x2)
>
>    instance Show (CmpFunction Integer) where
>      show f
>        | f `feq` CF (==) = "=="
>        | f `feq` CF (/=) = "/="
>        | f `feq` CF (<)  = "<"
>        | f `feq` CF (<=)  = "<="
>        | otherwise = "Unknown function"
>
> This uses SmallCheck to figure out, with some degree of certainty,
> whether two functions are equal.
>
> Of course, Rice's theorem still holds, and the above instance is easy
> to fool, but it still might be useful in some cases.
>
> Roman
>