Editing Function (section)

===<hask>map</hask> example===
As an example of the power of first-class functions, consider the function ''map'': 
<haskell>
map :: (a -> b) -> [a] -> [b]
map f xs = [f x | x <- xs]
</haskell>

(Note this is a  [[Higher order function]].)
This function takes two arguments: a function ''f'' which maps ''a''s to ''b''s, and a list ''xs'' of ''a''s. It returns a list of ''b''s which are the results of applying ''f'' to every member of ''xs''. So <hask>map square [1,1,2,3,5,8]</hask> would yield the list <hask>[1,1,4,9,25,64]</hask>. When you realize that the list of ''b''s that ''map'' returns can itself be a list of functions, things start to get interesting.

Suppose you have some data structure (e.g. ''Set'') that has the function <hask>insert :: Int -> Set -> Set</hask>, which takes an integer and a set, and returns the set created by inserting the given integer into the given set. And suppose you have ''mySet'' and ''myList,'' a set and a list of values to be added to the set, respectively. One could write a function to recurse over the list of integers, each time inserting a single member of ''myList,'' but with first-class functions this is not necessary. Look at the expression <hask>map insert myList</hask> -- what is the type of the list which it produces? Since ''insert'' takes an ''Int'' and a ''Set'', but only ''Int''s were given, the resulting list will be of functions that take a set and return a set. Conceptually, the code <hask>map insert [1,2,3]</hask> will return the list <hask>[(insert 1) (insert 2) (insert 3)]</hask>.