The map is provided as part of the Haskell's base prelude (i.e. "standard library") and is implemented as:

Among other uses, this allows defining element-wise operations for various kinds of collections.

The mathematical basis of maps allow for a number of optimizations. The composition law ensures that both

Since reversing a singly linked list is also tail-recursive, reverse and reverse-map can be composed to perform normal map in a tail-recursive way, though it requires performing two passes over the list.