This is certainly an intriguing answer, and makes me want to try Haskell sometime, but it also makes me wonder if I can't get the same benefits, with a little effort and discipline, in a "semi-functional" language such as something in the ML family or even (if I can live without static typing) Lisp.

In fact, I've always made a point, when working in a semi-functional language, of writing as much code functionally as possible. My experience is that it has the same benefits as you describe. So I don't know how much more there is to be gotten by actually switching to Haskell. My guess is, most of the additional benefit would come from the type system. But maybe I would be motivated to write even more code functionally.