Proposal: add foldMapA to Data.Foldable or Control.Applicative

David Feuer david.feuer at
Wed May 8 04:02:49 UTC 2019

On Tue, May 7, 2019 at 11:49 PM Isaac Elliott <isaace71295 at> wrote:

> I've previously suggested similar things, like:
> allA :: (Applicative f, Foldable t) => (a -> f Bool) -> t a -> f Bool
> allA f = fmap getAll . getAp . foldMap (Ap . fmap All . f)
> I think such functions are very convenient.

I think your allA is arguably better-justified than foldMapA because the
implementation you demonstrate could run into trouble if fmap is expensive.

allA :: (Applicative f, Foldable t) => (a -> f Bool) -> t a -> f Bool
allA f = getFall . foldMap (Fall . f)

newtype Fall f = Fall {getFall :: f Bool}
instance Applicative f => Semigroup (Fall f) where
  Fall x <> Fall y = Fall $ liftA2 (&&) x y
instance Applicative f => Monoid (Fall f) where
  mempty = Fall (pure True)

I keep wondering if there's some nice way (short of Coyoneda or similar) to
generalize this
sort of thing. I haven't thought of one yet.
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