Haskell- composing three functions in weird way

Question

I have three functions x y z and a function called functionComposer.

I want functionComposer to have as arguments the functions x y z and to return me a function that uses the result of y and z as arguments into x and applies x.

In mathematical notation: x(y(a),z(b))

Im NOT asking for this : functionComposer x y z = x.y.z

For example:

double x = x + x

summer x y = x + y

functionComposer summer double double = summer (double) (double) 

if x = 2 the result should be 8 (2+2)+(2+2)

Answer 1

You can also use the applicative instance for (->) a like so

import Control.Applicative


funcComp summer double1 double2 = summer <$> double1 <*> double2

Or the monad instance

funcComp summer double1 double2 = liftM2 summer double1 double2

The way to understand this is that for (->) a, both the applicative and the monad instance are meant to "parametrize" over the function value that double1 and double2 both accept.

Answer 2

Using your notation:

functionComposer summer double1 double2 = \x -> summer (double1 x) (double2 x) 

The \x -> ... represents the function mapping x to the ....

Note I had to give different names to the double function argument, since in general you want to compose different functions.