Why does application of `sequence` on List of Lists lead to computation of its Cartesian Product?

Question

My question is about the sequence function in Prelude, the signature of which is as follows:

sequence :: Monad m => [m a] ->          


        

Answer 1

Just to explain, why the application of sequence to a list of lists is so different from the application of sequence to a list of Maybe-values:

When you apply sequence to a list of lists, then the type of sequence is specialized from

sequence :: Monad m => [m a] -> m [a]

to (with the type constructor m set to [])

sequence :: [[] a] -> [] [a] 

(which is the same as sequence :: [[a]] -> [[a]])

internally, sequence uses (>>=) -- i.e. the monadic bind function. For lists this bind function is implemented completly different than for m set to Maybe!