[maxiepoo]

"Just Wrong" is a bit harsh. Monads are there to simulate side effects within the language, as opposed to the side effects that are built in to the language.

WARNING: the below contains math. Ignore if math makes you mad.

If "side effects" means the availability of certain operations such as mutating state, throwing errors etc, then monads certainly do have something to do with side effects in that these operations can often be described by an algebraic theory and algebraic theories have a direct correspondence to certain kinds of monads (the monad of free algebras of the theory).

[jerf]

No, they aren't. This is like saying "Iterators are in the language to walk over hash tables." No, they aren't. It is one of the things they can do, but it isn't what they are there for. What they are there for is to present a sequence of values. They aren't there to walk over trees, or walk over hash tables, or indeed, walk over data structures at all. Even if you think that last one, you don't understand them, because there are iterators that don't involve data structures at all.

You'll be stuck with a wrong understanding of them as long as you think that's what they are. That is one of the things they can be used for, but that's all. It isn't what they are. There are plenty of "monads" that are not being used for "side effects" and are perfectly pure no matter how you look at them, such as the list instance of monad. Rather than arguing with me about how if you bend the list a bit and sort of redefine "side effect" and if you squint a bit, the list instance really is related to "side effects", just don't look at it that way.