In chapter 4 of his book, Okasaki defines a type of both finite and infinite streams (which is really just the type of Haskell &quot;lists&quot;), and, in the remainder of the book, he only uses finite ones.<p>A stream of infinite length, which you call &quot;stream&quot; without qualification, is what I call &quot;a function on the natural numbers&quot;. (Well, up to isomorphism.)