I show how monads in Haskell can be used to structure infinite search algorithms, and indeed get them for free. This is a follow-up to my blog post Seemingly impossible functional programs. In the two papers Infinite sets that admit fast exhaustive search (LICS07) and Exhaustible sets in higher-type computation (LMCS08), I discussed what kinds of infinite sets admit exhaustive search in finite time, and how to systematically build such sets. Here I build them using monads, which makes the algorithms more transparent (and economic). Continue reading A Haskell monad for infinite search in finite time