[Haskell-beginners] A little explanation!

[Michael Orlitzky]

On 04/30/2014 11:29 AM, Gilberto Melfe wrote:
> Hello everybody !
> 
> Could someone explain me exactly how this function works?
> 
> elementAt_w'pf = (last .) . take . (+ 1)
> 
> It's a posted solution to: 99 Haskell problems, problem 3.
> 
> I'm having trouble with the "(last .) ." thing!
> 

It's not your fault, that solution is retarded. Once you remove all of
the intentional obfuscation, it looks like,

  elementAt_w'pf n xs = last (take (n + 1) xs)

which is easy to understand. You can un-retard it step-by-step:

    elementAt_w'pf = (last .) . take . (+ 1)

<=> elementAt_w'pf n = ((last .) . take . (+ 1)) n

                     = (last .) ((take . (+ 1)) n)

                     = (last .) (take (n + 1))

                     = last . (take (n + 1))

<=> elementAt_w'pf n xs = (last . (take (n + 1))) xs

                        = last (take (n + 1) xs)

All I've used above is the precedence of the function composition
operator, and the fact that (f . g) x = f (g x).