Who can explain this Haskell function?

Question

The Haskell function

foo = zipWith ($) . repeat

does exactly the same as

map

but I cannot see why :-( Who can give an explanation? Thx a lot!

Answer 1

OK, so we have

foo = zipWith ($) . repeat

which is the same as

foo f = zipWith ($) (repeat f)

The repeat f generates an infinite list of copies of f . Then zipWith uses the ($) operator to apply each element of the [infinite copies of f ] list to each element of the incoming list. Which is what map does.

Yes?