Is there a standard name or implementation of the

Question

I frequently find use for what I call the "purely applicative Either", i.e. Either with the Applicative instance available so long as we don't implement a Monad instance as well.

newtype AEither e a = AEither { unAEither :: Either e a }
  deriving Functor

-- technically we only need Semigroup
instance Monoid e => Applicative (AEither e) where
  pure a = AEither (pure a)
  AEither e1 <*> AEither e2 = AEither (combine e1 e2) where
    combine (Right f) (Right a) = Right (f a)
    combine (Left m1) (Left m2) = Left (m1 <> m2)
    combine (Left m ) _         = Left m
    combine _         (Left m ) = Left m

It's a really useful Applicative as it provides a more powerful notion of "summarization of error" than Either's Monad instance can do. To that end, I find myself implementing it over-and-over again.

Is there a standard instance somewhere? Is there even a standard name?

Answer 1

This looks pretty similar to the AccValidation type in the validation package: http://hackage.haskell.org/package/validation-0.3.1/docs/Data-Validation.html

Edit:

In particular the following instance declaration:

instance Semigroup err => Apply (AccValidation err) where
  AccFailure e1 <.> AccFailure e2 =
    AccFailure (e1 <> e2)
  AccFailure e1 <.> AccSuccess _  =
    AccFailure e1
  AccSuccess _  <.> AccFailure e2 =
    AccFailure e2
  AccSuccess f  <.> AccSuccess a  =
    AccSuccess (f a)