Using monads for trivial tasks like list manipulation?

Question

Whenever I read about Monad example, they always present IO as a case study.

Are there any examples of monads doing list manipulation which somebody could present? I apr

Answer 1

A classic example of using the list monad to cleverly write a "simple" list utility function is this:

import Control.Monad (filterM)

-- | Compute all subsets of the elements of a list.
powerSet :: [a] -> [[a]]
powerSet = filterM (\x -> [True, False])

The type of filterM is Monad m => (a -> m Bool) -> [a] -> m [a]. In the context of the list monad, this is a nondeterministic list filter: a filter operation that takes a nondeterministic predicate that returns a list of alternative answers. The result of filterM is in turn a list of alternative possible results.

Or in simpler language, filterM (\x -> [True, False]) means: for each element of the list, I want both to keep it and throw it away. filterM figures out all possible combinations of doing this for each list element.