[Haskell-beginners] Simple function comparison

[Stephen Renehan]

Many thanks Franceso, I had thought as much as I was dealing with them
only abstractly. Appreciate the quick reply and thanks for the help.

On 25 November 2015 at 14:20, Francesco Ariis <fa-ml at ariis.it> wrote:
> On Wed, Nov 25, 2015 at 11:39:15AM +0000, Stephen Renehan wrote:
>> Hi,
>>
>> I'm looking to do a comparison between 2 simple functions to see if
>> they are equivalent but I appear to be running into some problems if
>> anyone can help.
>>
>> The two functions I want to compare are f (g a) and g (f a).
>>
>> I have f defined and g defined as
>>  f :: a -> a
>>  f = undefined
>>
>> g :: a -> a.
>> g =  undefined
>>
>> The compiler was complaining about the type signature lacking a
>> binding so added undefined to get around the error. I understand that
>> I must be missing something very basic as they look incomparable in
>> this form. Any suggestions of what changes I should make such a
>> comparison practical?
>
> Hello Stephen,
>     I don't think there is a way to /prove/ f (g a) == g (f a) if their
> domain is not finite inside Haskell (you could do it with pen and
> paper).
>
> If you have two functions and a finite domain you can do, say:
>
>     -- function function domain
>     compfun :: (Eq a) => (a -> a) -> (a -> a) -> [a] -> Bool
>     compfun f g d = and $ map (\x -> (f . g) x == (g . f) x) d
>
>     λ> compfun (+1) (+17) [1..10]
>     True
>     λ> compfun (*5) (+17) [1..10]
>     False
>
> Of course this is a toy example, use a proper library (quickcheck, etc.)
> if you are writing a real program.
>
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