Function is applied to too few arguments in haskell

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I just started learning haskell and i'm not able to solve this issue. Can someone tell me why i get error that g is applied to too few arguments in the code below.

f :: Int -> Int f first  = 5+first  g :: Int -> Int -> Int g  first second = first+second   compute :: (Int -> Int) -> (Int -> Int -> Int) -> Int -> Int -> Int compute f g x y = (f . g) x y 

 


First, look at the definition of f . g:

f . g = /x -> f (g x) 

Then we can expand the definition of compute as follows:

compute f g x y = (f . g) x y                 = (/z -> f (g z)) x y                 = (f (g x)) y                 = (5 + (g x)) y 

g x : Int -> Int, for which there is no Num instance, so you can't add it to 5.

The problem is that you want g applied to both x and y before its result is passed to f. To do that, you need something more than simple composition. The simplest way to write this is directly:

compute f g x y = f (g x y) 

If you are aiming for something more point-free, you need to get fancy with the composition:

compute f g = /x -> /y -> f (g x y)             -- application is left-associative             = /x -> /y -> f ((g x) y)             -- def'n of (.)             = /x -> f . (g x)             -- eta abstraction             = /x -> (/z -> f . z) (g x)             -- def'n of an operator section             = /x -> (f .) (g x)             -- def'n of (.)             = (f .) . g 

If you want to be completely point-free, you can write

compute = (.) . (.) 

You compose the composition operator with itself.

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