Haskell Language Monads List Monad
Example
The lists form a monad. They have a monad instantiation equivalent to this one:
instance Monad [] where return x = [x] xs >>= f = concat (map f xs)
We can use them to emulate non-determinism in our computations. When we use xs >>= f, the function f :: a -> [b] is mapped over the list xs, obtaining a list of lists of results of each application of f over each element of xs, and all the lists of results are then concatenated into one list of all the results. As an example, we compute a sum of two non-deterministic numbers using do-notation, the sum being represented by list of sums of all pairs of integers from two lists, each list representing all possible values of a non-deterministic number:
sumnd xs ys = do
x <- xs
y <- ys
return (x + y)
Or equivalently, using liftM2 in Control.Monad:
sumnd = liftM2 (+)
we obtain:
> sumnd [1,2,3] [0,10]
[1,11,2,12,3,13]
