Alternative instance for Compose
Asad Saeeduddin
masaeedu at gmail.com
Thu Jul 16 02:00:22 UTC 2020
Hello folks,
base 4.14 has the following instance for `Compose f g`:
instance (Alternative f, Applicative g) => Alternative (Compose f g) where
empty = Compose empty
(<|>) = coerce ((<|>) :: f (g a) -> f (g a) -> f (g a))
:: forall a . Compose f g a -> Compose f g a -> Compose f g a
This instance doesn't really do anything with the `Applicative g`
constraint it is demanding. It's also kind of unclear what utility it
delivers, given that the resulting Alternative instance is
indistinguishable from the outer functor's Alternative instance. In
other words: `getCompose $ Compose x <|> Compose y == x <|> y`.
It seems to me a more useful instance would be:
instance (Applicative f, Alternative g) => Alternative (Compose f g) where
empty = Compose $ pure empty
(<|>) = _ $ liftA2 (<|>)
This is also nicer in a mathematical sense: `Applicative` functors
correspond to lax monoidal functors from `Hask, (- , -), ()` to `Hask,
(-, -), ()`. We can interpret `Alternative`s as lax monoidal functors
from `Hask, Either - -, Void` to `Hask, (-, -), ()`. Compatible lax
monoidal functors compose, but if you think about the relevant "types"
of the functors a bit, you'll realize that while we can compose an
`Applicative` after an `Alternative` to get another `Alternative`, the
reverse does not work. Hence the instance we have today, which has no
choice but to just ignore the `Applicative` constraint it is demanding.
Does it make sense to replace the instance we have today with the `pure
empty`, `liftA2 (<|>)` one?
Thanks,
Asad
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