Applying multiple functions to the same value point-free style in Haskell

Question

I was bored one day and wanted to exercise my brain, so I decided to do the 99 Haskell Problems but restricted myself to doing them in point-free style. A problem that seems to

Answer 1

You will be interested in the Applicative instance of the reader monad:

instance Applicative (e ->)

Using it you can easily distribute an argument:

liftA2 (+) sin cos 3

Here sin and cos are functions, which both receive the value 3. The individual results are then combined using (+). You can further combine this with the Category instance of (->), but of cource specialized versions of (.) and id are already defined in the Prelude.

Background: The Applicative instance for (e ->) really represents the SKI calculus, where (<*>) is the S combinator and pure is the K combinator. S is precisely used to distribute an argument to two functions:

S f g x = f x (g x)

It takes a function application (f g) and makes both dependent on the value x ((f x) (g x)).