x <|> (y <|> z) = (x <|> y) <|> z empty <|> x = x = x <|> emptyThis makes your coalesce a valid (<|>) if you take empty = [], but as Chris points out it's not as intuitive from the perspective of certain other nice-to-have properties.
The usual intuition behind the list Functor/Applicative/Monad instances are that they represents non-deterministic values, which can have any of some list of possible values. In this case, the natural interpretation of <|> is as a non-deterministic choice of two possible computations. So the list of possible results would include anything from either computation. Your implementation, on the other hand, would represent a left-biased choice, where the right alternative is only used if the left is impossible.
It's hard to look at laws, because there's apparently little agreement on the proper laws for Alternative. It looks possible that as an Applicative and Alternative, this would be fine; but the Alternative instance you propose would work in odd ways with the Monad instance. That is, if f x == [] for any x in (non-empty) xs, then something like (xs <|> ys) >>= f would yield an empty list, while (xs >>= f) <|> (ys >>= f) would not. But, this isn't a law or anything, you could chalk it up as counter-intuitive, but not disqualifying.
On Fri, May 5, 2017 at 11:12 PM, Theodore Lief Gannon <tanuki@gmail.com> wrote:
Fiddling around, I found myself wanting:
coalesce :: [a] -> [a] -> [a]-- or -- :: (Foldable t) => t a -> t a -> t acoalesce a b = if null a then b else a
I expected this to be (<|>) (it is for Maybe!) but instead I find no canonical implementation of it anywhere, and what seems like a useless instance Alternative []. What's the rationale?
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