Are monads expressions, or are there statements in Haskell?

Question

I have an ontological question about monads in haskell; I'm shaky on whether the language makes a distinction between statements and expressions at all. For example, I feel like in most other languages anything with a signature like a -> SomeMonadProbs () would be considered a statement. That said, since haskell is purely functional, and functions are composed of expressions, I'm a wee bit confused on what haskell would say about monads in terms of their expression-hood.

Answer 1

Monad is just one interface for interacting with expressions. For example, consider this list comprehension implemented using do notation:

example :: [(Int, Int)]
example = do
    x <- [1..3]
    y <- [4..6]
    return (x, y)

That desugars to:

[1..3] >>= \x ->
[4..6] >>= \y ->
return (x, y)

... and substituting in the definition of (>>=) for lists gives:

concatMap (\x -> concatMap (\y -> [(x, y)]) [4..6]) [1..3]

The important idea is that anything you can do using do notation can be replaced with calls to (>>=).

The closest thing to "statements" in Haskell are syntactic lines of a do notation block, such as:

x <- [1..3]

These lines do not correspond to isolated expressions, but rather syntactic fragments of an expression which are not self-contained:

[1..3] >>= \x -> ... {incomplete lambda}

So it's really more appropriate to say that everything is an expression in Haskell, and do notation gives you something which appears like a bunch of statements but actually desugars to a bunch of expressions under the hood.