Luke Palmer schrieb:
\begin{code} allPossibilities :: [[a]] -> [[a]] allPossibilities [] = [[]] allPossibilities (l:ls) = [ x : xs | x <- l, xs <- allPossibilities ls]
I am confused. This is exactly sequence. How is this a faster version? Other than maybe avoiding some dictionary-passing?
I suppose, dictionary-passing is really the reason for slower code.
Incidentally there is a "better" version of sequence for finding products of lists:
allPossibilities :: [[a]] -> [[a]] allPossibilities [] = [[]] allPossibilities (l:ls) = [ x : xs | xs <- allPossibilites ls, x <- l ]
I cannot really observe a speed up, with this version, but there are probably examples where any version is faster than the other.
Or, the general form (I don't know of a use other than for lists, however):
"Maybe" should be another useful instance.
sequence' :: Applicative f => [f a] -> f [a] sequence' [] = pure [] sequence' (x:xs) = liftA2 (flip (:)) xs x
The difference is that it binds the tail of the list first, so the generated tails are shared. This means less consing, less GC strain, and a lot less memory usage if you store them.
This argument it too complicated for me.
Mind, the answers come out in a different order.
Yes, thanks. Christian