mapM

mapM is a standard function in Haskell's control of monads. It maps a monadic action over a list and sequences the resulting actions, collecting their results in a single monadic value. In other words, it applies a function that returns a monadic result to each element of a list and runs the actions in order, gathering the results.

The type of mapM is:

mapM :: Monad m => (a -> m b) -> [a] -> m [b]

For each element x in the input list, mapM applies the function to produce an action of type m b, then the actions are executed left to right, and the results are collected in a list inside the monad. It is equivalent to sequence (map f xs).

Example usage in the IO monad:

mapM putStrLn ["hello","world"]

This prints each string on its own line and returns an IO [()] indicating the unit results for each line.

In the Maybe monad, mapM chains optional computations:

mapM (\x -> if x == 0 then Nothing else Just (x * 2)) [1,2]

returns Just [2,4], while any Nothing in the sequence yields Nothing for the whole result.

Related functions include mapM_, which performs the same sequencing but discards the results, and traverse, which generalizes mapM to any traversable structure using an applicative functor.

Overall, mapM is a fundamental tool for combining lists with monadic effects, ensuring effects occur in a defined order while collecting the computed results.