[Haskell-cafe] Simplifying a IsFunction type class using type equality constraints

[Manuel M T Chakravarty]

Corey O'Connor:
> I recently had a need to use the IsFunction typeclass described by  
> Oleg here:
> http://okmij.org/ftp/Haskell/isFunction.lhs
>
> and am wondering if the use of the TypeCast class can be correctly
> replaced by a type equality constraint.
>
> The IsFunction and TypeCast classes were defined as:
>> data HTrue
>> data HFalse
>>
>> class IsFunction a b | a -> b
>> instance TypeCast f HTrue => IsFunction (x->y) f
>> instance TypeCast f HFalse => IsFunction a f
>>
>> -- literally lifted from the HList library
>> class TypeCast   a b   | a -> b, b->a   where typeCast   :: a -> b
>> class TypeCast'  t a b | t a -> b, t b -> a where typeCast'  :: t- 
>> >a->b
>> class TypeCast'' t a b | t a -> b, t b -> a where typeCast'' :: t- 
>> >a->b
>> instance TypeCast'  () a b => TypeCast a b where typeCast x =  
>> typeCast' () x
>> instance TypeCast'' t a b => TypeCast' t a b where typeCast' =  
>> typeCast''
>> instance TypeCast'' () a a where typeCast'' _ x  = x
>
> I found the use of TypeCast in the IsFunction could be replaced by a
> type family:
>
>> class IsFunction a b | a -> b
>> instance (f ~ TTrue) => IsFunction (x->y) f
>> instance (f ~ TFalse) => IsFunction a f

Yes, that's a fine way of simplifying the definition.  In fact, you  
should also be able to drop the functional dependency in the  
IsFunction class.

Manuel