Jon Fairbairn wrote:

Andrew Coppin writes:

...

As I lay in bed last night, a curios fact occurred to me. (Yes, I don't get out very much...)

You probably ought to get out of bed from time to time, you know.

LOL! Thanks for the tip. :-P

...

Consider the map function:

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

There are two ways you can think about this function. First, you can see it as meaning

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

Which is beautifully symmetric. Alternatively, you can think about how you actually use it:

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

No, if you think like that, you're wrong! That would be a function that takes an object of type ((a->b) -> [a]) and returns a [b] (which if you think about it, would be an odd sort of function). (->) associates to the right.

Hmm... I see the error of my ways. (Someone was asking my why map takes a function from a to b and returns a function from [a] to [b], rather than taking a function and a [a] and returning a [b]. And I pointed out that it's *both* of those things. And it seems that shortly after this point I confused myself! LOL.)

On Sun, May 27, 2007 at 02:10:40PM +0200, Stefan Holdermans wrote:

Andrew,

...

Which is beautifully symmetric. Alternatively, you can think about how you actually use it:

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

I am not following here: what do you mean? Clearly, this is not a valid typing for map. Moreover, modulo undefinedness, there are no functions with this typing.

map _ = [] Stefan

After a little too long trying, I managed to get code from which the type system will infer that type, without using 'undefined': *Main> :t map map :: ((a -> a1) -> [a]) -> [a1] import System.IO.Unsafe import Data.IORef import Prelude hiding (map) import qualified Prelude as P coerce a = unsafePerformIO (coerce' a) where ref = unsafePerformIO $ newIORef [] coerce' a = do writeIORef ref [a] b <- readIORef ref return (head b) map' a2b f = P.map a2b (f a2b) map = map' coerce On 27/05/07, Stefan Holdermans wrote:

...

...

...

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

I am not following here: what do you mean? Clearly, this is not a valid typing for map. Moreover, modulo undefinedness, there are no functions with this typing.

map _ = []

Ah, well, and that one, of course... :-)

Cheers,

Stefan _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe