[Haskell-cafe] MultiParamTypeClasses, FunctionalDependencies and FlexibleInstances using GHCi

[Jochem Berndsen]

Julian Fleischer wrote:
> Hello,
> 
> i'm playin' around with GHCs Haskell and some extensions. I'm already aware of that functional dependencies are "very very tricky", but there is something I don't understand about there implementation in GHC. I've constructed my own TypeClass "Num" providing a signature for (+), having multiple params a, b and c. I'm than declaring a (flexible) Instance for Prelude.Num, simply using (Prelude.+) for the definition of my (+) - and it does not work as I expect it to.
> 
> First, this is the code:
>> {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, TypeSynonymInstances, FlexibleInstances #-}
>> import qualified Prelude
>>
>> class Num a b c | a b -> c where
>> 	(+) :: a -> b -> c
>>
>> instance (Prelude.Num x) => Num x x x where
>> 	(+) = (Prelude.+)
> 
> now if I load it into GHCi and type "3 + 4" i get a whole bunch of error-messages.
> 
> I do understand that
>> (3::Prelude.Int) + (4::Prelude.Int)
> works, since I've explicitly declared 3 and 4 to be Prelude.Int and there is a functional dependency stating that (+) :: a b determines the results type c, by the Instance declaration cleary c will be the same as a and b.
> 
> Now, if I type
>> 3 + 4
> it does not work, and i really don't understand why. If i ask GHCi for 3's type ($ :t 3) it will answer "3 :: (Prelude.Num t) => t". But, if 3 and 4 are Prelude.Nums and there is an instanfe Num x x x for x of Prelude.Num - than why can't GHC deduce from the definitions that 3 and 4, both Prelude.Nums, can be used with (+) since there is an instance for Prelude.Num and my class Num - and the result will of course be something of Prelude.Num?

My guess would be, that while 3 and 4 are both of a type instantiating 
Prelude.Num (your terminology "are Prelude.Nums" is quite confusing -- 
Prelude.Num is not a type but a type class), they need not be of the 
same type (e.g., 3 could be of type Integer, and 4 of type Double).

Jochem

-- 
Jochem Berndsen | jochem at functor.nl