Haskell: firstLeft
I found myself recently reaching for a firstLeft function. The idea was that using Either to model failure/success of a function, you either want to get the first error back (Left) or all the results (Right).
firstLeft :: [Either a b] -> Either a [b]
Prelude> firstLeft [Right 1, Right 2, Right 3]
Right [1,2,3]
Prelude> firstLeft [Right 1, Right 2, Right 3, Left "gah!"]
Left "gah!"
Prelude> firstLeft [Right 1, Left "ooh!", Right 2, Right 3, Left "gah!"]
Left "ooh!"
Benl immediately pointed out to me, this is in fact sequence:
sequence :: (Monad m, Traversable t) => t (m a) -> m (t a)
Prelude> sequence [Right 1, Right 2, Right 3]
Right [1,2,3]
Prelude> sequence [Right 1, Right 2, Right 3, Left "gah!"]
Left "gah!"
Prelude> sequence [Right 1, Left "ooh!", Right 2, Right 3, Left "gah!"]
Left "ooh!"
If this is not immediately obvious as to why these two are equivalent, see below. Type variables can effectively be curried:
sequence :: (Monad m, Traversable t) => t (m a) -> m (t a)
-- m = Either a:
sequence' :: (Traversable t) => t ((Either a) b) -> (Either a) (t b)
-- t = []:
sequence'' :: [Either a b] -> Either a [b]
firstLeft :: [Either a b] -> Either a [b]
The term sequence seems a bit confusing, I generally thought of this as a kind of collect operation. Interestingly, the documentation for sequence refers to this term too in describing it:
Evaluate each [..] action in the structure [..] and collect the results.
