Actually, arrays in Haskell are automatically memoized and lazily evaluated. So in most practical situations you get memoization for free.

For example, imagine you need to calculate a function f(n) for various values of n (let's say for n ranging from 0 to N). You simply define an array memo_f such that memo_f!n = f(n). ('!' is the array selection operator in Haskell).

Because Haskell evaluates lazily (i.e. not until it absolutely has to), it simply stores a link to the definition of the function for each array element. But once a particular array element is used, that link is replaced by the calculated answer.

I'll post some actual code to demonstrate this in a minute, just in case anyone's interested.