[dragonwriter]

> But that doesn't tell me what are they good for. We invent things for a reason, and I don't see the reason. Now I know the reason, it's been told to me many times (some way to wrap I/O while preserving functional purity),

That's an excessively narrow reason. Its certainly a factor of why monads are front-and-center in Haskell, given the goals of the language, but its not really the reason monads are interesting or useful. Monads (and Functors and Applicatives, as well, as more general constructs) are interesting constructs in programming because they are powerful abstractions that unite disparate, useful data types and which, therefore, allow code that works across those data types. They therefore enable library code in circumstances where, in languages without such abstractions, fill-in-the-blanks template code patterns would be required, so they promote code reuse over copy-and-paste coding.

That IO operations are among the things that can be represented by monads is certainly part of their usefulness, but if IO was all they were good for, they wouldn't be all that interesting.