:: (a -> b -> Maybe a) -> a -> [b] -> Maybe a

The foldM function is analogous to foldl, except that its result is encapsulated in a monad. Note that foldM works from left-to-right over the list arguments. This could be an issue where (>>) and the `folded function' are not commutative.
foldM f a1 [x1, x2, ..., xm]


a2 <- f a1 x1
a3 <- f a2 x2
f am xm
If right-to-left evaluation is required, the input list should be reversed. Note: foldM is the same as foldlM
Left-to-right monadic fold over the elements of a structure. Given a structure t with elements (a, b, ..., w, x, y), the result of a fold with an operator function f is equivalent to:
foldlM f z t = do
aa <- f z a
bb <- f aa b
xx <- f ww x
yy <- f xx y
return yy -- Just @return z@ when the structure is empty
For a Monad m, given two functions f1 :: a -> m b and f2 :: b -> m c, their Kleisli composition (f1 >=> f2) :: a -> m c is defined by:
(f1 >=> f2) a = f1 a >>= f2
Another way of thinking about foldlM is that it amounts to an application to z of a Kleisli composition:
foldlM f z t =
flip f a >=> flip f b >=> ... >=> flip f x >=> flip f y $ z
The monadic effects of foldlM are sequenced from left to right. If at some step the bind operator (>>=) short-circuits (as with, e.g., mzero in a MonadPlus), the evaluated effects will be from an initial segment of the element sequence. If you want to evaluate the monadic effects in right-to-left order, or perhaps be able to short-circuit after processing a tail of the sequence of elements, you'll need to use foldrM instead. If the monadic effects don't short-circuit, the outermost application of f is to the rightmost element y, so that, ignoring effects, the result looks like a left fold:
((((z `f` a) `f` b) ... `f` w) `f` x) `f` y


Basic usage:
>>> let f a e = do { print e ; return $ e : a }

>>> foldlM f [] [0..3]
Monadic fold over the elements of a structure, associating to the left, i.e. from left to right.
O(n) Monadic fold.
O(n) Monadic fold with strict accumulator.
O(n) Monadic fold
O(n) Monadic fold with strict accumulator
Monadic fold over vector.