Functional Dependencies / Type Families

With functional dependencies I can constrain type of dependent parameter in a开发者_如何学编程 type class using multi-parameter type classes. Just like this:

{-# LANGUAGE FunctionalDependencies, MultiParamTypeClasses,TypeSynonymInstances  #-}

class (Num a, Integral b) => F a b | a -> b where
  f :: a -> b

instance F Int Int where
  f = id

instance F Float Integer where
  f = truncate

And everything'll work perfectly.

> f (1 :: Int)
1
> f (1.9 :: Float)
1

But if I try to write something like

instance F Double String where
  f = show

I'll get the following compilation error:

No instance for (Integral String)
arising from the superclasses of an instance declaration
Possible fix: add an instance declaration for (Integral String)
In the instance declaration for `F Double String'

Is there a way to approach this with type families instead of fundeps?

Basically not, and this actually has nothing to do with functional dependencies (or type families). Your class definition has

class (Num a, Integral b) => F a b

which declares that there must be an Integral instance for b. A String doesn't have an Integral instance, so you can't have anything of the form F a String unless you define

-- String is a type synonym for [Char]
instance Integral [Char] where

I don't know that this would be sensible in general. If it would make sense to create an Integral instance for Strings in your system, you would probably want to put a newtype wrapper around String and create the instance for that instead.

I guess you want to have something like this:

{-# LANGUAGE TypeFamilies, FlexibleContexts  #-}
class Num a => G a where
  type B a
  g :: (Integral (B a)) => a -> B a

instance G Int where
  type B Int = Int
  g = id

instance G Float where
  type B Float = Integer
  g = truncate

This example is not directly using a type family, but an associated type synonym, which is activated by the same flag. The idea is fairly easy. Instead of explicit giving a second parameter to the typeclass, we define a type synonym, that is filled in with the appropriate type.

This is also my first time to use associated type synonyms, but it seems to be a quite cool feature.