sam lee skynare at gmail.com
Fri Mar 6 23:43:39 EST 2009

```map :: (a -> b) -> [a] -> [b]

map takes a function and transforms a list of a's to b's.

map succ [1,2,3]
==> [succ 1, succ 2, succ 3]
==> [2, 3, 4]

In general,
map f :: [a] -> [b]
where a is domain-type of f and b is image-type of f (f :: a -> b).

map map [x, y, z]
==> [map x, map y, map z]

so, x,y,z should functions of type (a -> b).
and the result list, [map x, map y, map z], should have type [([a] -> [b])]
because
map x :: [a] -> [b]    where x :: a -> b

On 3/6/09, R J <rj248842 at hotmail.com> wrote:
>
>
> Given the following (usual) definition of "map":
>
> map                    :: (a -> b) -> [a] -> [b]
> map f []               =  []
> map f (x : xs)         =  f x : map f xs
>
> What's the type of "map map"?
>
> GHCi's :t command reveals:
>
> *Main> :t map map
> map map :: [a -> b] -> [[a] -> [b]]
>
> I'd be grateful if anyone could provide a systematic type calculation so
> that I can reason through more complicated examples myself.
>
> Thanks.
>
> _________________________________________________________________
> Windows Live™: Life without walls.
> http://windowslive.com/explore?ocid=TXT_TAGLM_WL_allup_1a_explore_032009
```