[Haskell-cafe] How to understand the fmap here ?

[Thomas Davie]

On 5 May 2009, at 11:27, z_axis wrote:

> The following code snippets is from xmonad:
> -- Given a window, find the screen it is located on, and compute
> -- the geometry of that window wrt. that screen.
> floatLocation :: Window -> X (ScreenId, W.RationalRect)
> --.......
> rr <- snd `fmap` floatLocation w
>
> Prelude> :i fmap
> class Functor f where fmap :: (a -> b) -> f a -> f b
>
> It seems it is different from the definition of fmap ?
> sincerely!

As the type signature of fmap explains, it transforms a function.   
Specifically, it starts with a function (a -> b), and it transforms it  
to accept an 'a' inside a functor instead of just an a, and return a  
'b' inside the same functor instead of just a b.  In other words, fmap  
applies functions inside containers.

We can see from floatLocation that it returns a pair inside a  
container - specifically, an X container.  Fmap takes snd, and  
transforms it to work on values inside the X.

So, snd has type (a,b) -> b, thus fmap snd has type f (a,b) -> f b.   
In this case, the type it's being applied to is X (ScreenId,  
W.RationalRect), so f unifies with X, a with ScreenID and b with  
W.RationalRect.  Making snd `fmap` floatLocation w hav the type X  
W.RationalRect.

Finally, the bind into rr there takes it out of the X monad all  
together, getting you a W.RationalRect.

You may want to read this article which explains some of Haskell's  
abstraciton mechanisms:

http://noordering.wordpress.com/2009/03/31/how-you-shouldnt-use-monad/

Bob
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