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

sequence acts as if it were defined like this.

sequence [] = return []
sequence (m:ms) = do
    x <- m
    xs <- sequence ms
    return (x:xs)

(Or sequence = foldr (liftM2 (:)) (return []) but anyhow…)

Just think about what happens when applied to a list of lists.

sequence [] = [[]]
sequence (list : lists) =
    [ x : xs
    | x <- list
    , xs <- sequence lists
    ]