[Haskell-cafe] Re: Re-order type

[Alexander Solla]

On Oct 9, 2010, at 4:17 PM, André Batista Martins wrote:

> If i want compose   f  and f1, i need to do a correct input to f1  
> from the output of f.
> So i want one function to  convert the output of "f" to input off  
> "f!".
> In this case,  we do      f1 fst (snd (t,(t1,t2)))  snd (snd (t, 
> (t1,t2)))
> But i want do this automaticaly, for type of any two function. I  
> search for the "glue".


You have to write the glue.  There is no way to do it automatically,  
for all cases.  If there was a way to derive the glue, they wouldn't  
be separate cases.

Type classes are a common approach for writing glue functions.  The  
Functor and Monad type classes are good examples.  (And there is a  
nice algebra of functors in the small category of functors, too)   I  
wrote a weird little functorial type class yesterday, specifically to  
handle newtypes as functors over their underlying datatype/category.

class Transform obj functor where
	 transform :: (obj -> obj) -> functor -> functor

instance Functor f => Transform obj (f obj) where transform = fmap