Since we're going for precision, I note that monads have nothing to do with impurity (https://wiki.haskell.org/What_a_Monad_is_not#Monads_are_not_...). It just happens that IO, in which the impurity lives, is a monad. It is also a functor (in the category-theory, not Prolog or C++, sense), but that doesn't make functors impure, and it doesn't make monads impure (or impurity inherently monadic: https://wiki.haskell.org/What_a_Monad_is_not#Haskell_doesn.2...).

> To say it more correctly (hopefully): Haskell contains a purely functional sub-language. It also has impure parts. Just like most programming languages have pure and impure parts. The difference is that Haskell employs the type system to segregate the two parts.

(Anyway I'd be interested in how to access IO without using the IO monad; is there a lower-level type to use instead?)