[Haskell-beginners] Are monads pure?

[Amy de Buitléir]

When I first started learning Haskell, I was under the impression that
monads provided a way to encapsulate some imperative code so it didn't
"contaminate" your functional code. But I think that's a misconception that
I got because the first monad I dealt with was IO. Lately I've been reading
more about monads, and (aside from IO), they are purely functional, aren't
they? If they have state, they deal with it in a purely functional way.
Behind the scenes, they thread the state through your computations so that
you don't you don't have to bother with it. Is that correct? TIA.
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