Re: [Haskell-cafe] Re: Composition of Type Constructors

On Wednesday 25 May 2005 17:20, Chung-chieh Shan wrote:

Jan Christiansen wrote in article in gmane.comp.lang.haskell.cafe:

...

The problem is that I don't know how to express the composition of type constructors like the function (.) for ordinary functions. I know that (map1 . map2) is wrong but it states what I want to express, namely the composition of two type constructors. With this I would like to define an instance definition like the following.

instance (Mapping map1 key1, Mapping map2 key2) => Mapping (map1 . map2) (key1, key2) where lookup (key1, key2) = lookup key2 . lookup key1 update (key1, key2) f = update key1 (update key2 f)

You can define the type-level composition yourself. Something like (untested):

newtype Comp map1 map2 v = Comp (map1 (map2 v)) instance (Mapping map1 key1, Mapping map2 key2) => Mapping (Comp map1 map2) (key1, key2) where lookup (key1, key2) (Comp map) = lookup key2 (lookup key1 map) update (key1, key2) f (Comp map) = Comp (update key1 (update key2 f) map)

Thanks. That's a solution. There is no prettier way of doing this, is there. It's not allowed to make an instance of a type synonym and partially applied type synonyms are not allowed anyway. Is there a reason why partial application of type synonyms are forbidden?