[Haskell-cafe] Equality of functions

[Thomas Hallgren]

Adam Zachary Wyner wrote:

>Hi All,
>
>After some weeks of experimenting and digging around, I understand that
>functions cannot be compared for equality.  Thanks to Bjorn Lisper for
>pointing this out.  I basically understand (?) the underlying mathematical
>issue, which is that functions in general may have infinite domains...
>
>Other suggestions?
>  
>
You can define equality for functions with finite domains. See the 
enclosed Haskell module.

Loading package base ... linking ... done.
Compiling Finite           ( Finite.hs, interpreted )
Ok, modules loaded: Finite.
*Finite> not == not
True
*Finite> (&&) == (&&)
True
*Finite> (&&) == (||)
False

-- 
Thomas H

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module Finite where


instance (Finite a, Eq b) => Eq (a->b) where
  f == g = and [ f x == g x | x <- allValues ]


-- A class for finite types

class Finite a where
  allValues :: [a]

instance Finite () where allValues = [()]

instance Finite Bool where allValues = [False,True]

--instance Finite Ordering where ...
--instance Finite Char where ...
--instance Finite Int where ...

instance (Finite a,Finite b) => Finite (a,b) where
  allValues = [ (x,y) | x<-allValues, y<-allValues]

instance Finite a => Finite (Maybe a) where
  allValues = Nothing:[Just x|x<-allValues]

instance (Finite a,Finite b) => Finite (Either a b) where
   allValues = [Left x|x<-allValues]++[Right y|y<-allValues]

-- ...