Why is ListT monad transformer considered buggy - what monad laws it breaks?

functional-programming, haskell, monad-transformers, monads

Solution

A simple example that shows how it fails the associativity law:

v :: Int -> ListT [] Int
v 0 = ListT [[0, 1]]
v 1 = ListT [[0], [1]]

main = do
    print $ runListT $ ((v >=> v) >=> v) 0
    -- = [[0,1,0,0,1],[0,1,1,0,1],[0,1,0,0],[0,1,0,1],[0,1,1,0],[0,1,1,1]]
    print $ runListT $ (v >=> (v >=> v)) 0
    -- = [[0,1,0,0,1],[0,1,0,0],[0,1,0,1],[0,1,1,0,1],[0,1,1,0],[0,1,1,1]]

More examples (mostly using `IO`) and a solution how to fix `ListT` can be found at ListT done right.

Problem

I've seen mentioned that `ListT` is a classic example of a buggy monad transformer that doesn't satisfy the monad laws. Can this be demonstrated by a simple example? Edit: My idea with `ListT []` is a bit wrong, I missed that the documentation requires the inner monad to be commutative. So, is `ListT` buggy just in the sense that has this requirement, or is there another problem? (The examples at Haskell wiki all use `ListT IO` and `IO` is obviously not commutative.)

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