I've been using haskell for quite a while now, and I've read most of Real World Haskell and Learn You a Haskell. What I want to know is whether there is a point to a language using lazy evaluation, in particular the "advantage" of having infinite lists, is there a task which infinite lists make very easy, or even a task that is only possible with infinite lists?
Here's an utterly trivial but actually day-to-day useful example of where infinite lists specifically come in handy: When you have a list of items that you want to use to initialize some key-value-style data structure, starting with consecutive keys. So, say you have a list of strings and you want to put them into an IntMap counting from 0. Without lazy infinite lists, you'd do something like walk down the input list, keeping a running "next index" counter and building up the IntMap as you go.
With infinite lazy lists, the list itself takes the role of the running counter; just use zip [0..] with your list of items to assign the indices, then IntMap.fromList to construct the final result.
Sure, it's essentially the same thing in both cases. But having lazy infinite lists lets you express the concept much more directly without having to worry about details like the length of the input list or keeping track of an extra counter.