Why are side-effects modeled as monads in Haskell?

Question

Could anyone give some pointers on why the impure computations in Haskell are modelled as monads?

I mean monad is just an interface with 4 operations, so what was th

Answer 1

Could anyone give some pointers on why the unpure computations in Haskell are modeled as monads?

This question contains a widespread misunderstanding. Impurity and Monad are independent notions. Impurity is not modeled by Monad. Rather, there are a few data types, such as IO, that represent imperative computation. And for some of those types, a tiny fraction of their interface corresponds to the interface pattern called "Monad". Moreover, there is no known pure/functional/denotative explanation of IO (and there is unlikely to be one, considering the "sin bin" purpose of IO), though there is the commonly told story about World -> (a, World) being the meaning of IO a. That story cannot truthfully describe IO, because IO supports concurrency and nondeterminism. The story doesn't even work when for deterministic computations that allow mid-computation interaction with the world.

For more explanation, see this answer.

Edit: On re-reading the question, I don't think my answer is quite on track. Models of imperative computation do often turn out to be monads, just as the question said. The asker might not really assume that monadness in any way enables the modeling of imperative computation.