Hi,
In the 'learnyouahaskell' online book the powerset function is described like this -
----
powerset :: [a] -> [[a]]
powerset xs = filterM (\x -> [True, False]) xs
----
And the filterM function is defined like this
filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a]
--
The filterM function is said to be an extension of 'filter' function which maps the monadic predicate over the given list.
Now in powerset function the predicate returns a monad [True,False] for every element of the given list.
So for e.g. if the input list was only [1] the output of filterM will understandably be the cartesian product of [True, False] x [1] = [[1], []].
Extending this if the given input list contains two elements [1,2] the predicate would be mapped one by one on each of the elements and the result combined which means the output should be
[[1], [], [2], []]
But the powerset of [1,2] is definitely not that.
Please could someone help me in getting my head around with how filterM is working in this case.
Thanks,