free-applicative-t

This package provides ApT, the "free" "applicative transformer" filling the empty corner in the table below.

Free		-transformer
Monad	Free	FreeT
Applicative	Ap	???

Why not Control.Applicative.Trans.Free?

There already is a type designated to be the free applicative transformer: ApT in the package free. Why do we do it again?

The applicative defined in Control.Applicative.Trans.Free is different to what this package provides. The difference is clear in how it is interpreted to another applicative:

-- "free" Control.Applicative.Trans.Free
runApT :: (Applicative h, Functor g) => (forall a. f a -> h a) -> (forall a. g (h a) -> h a) -> ApT f g b -> h b

-- "free-applicative-t" Control.Applicative.Trans.FreeAp
foldApT :: forall f g h b. Applicative h => (forall a. f a -> h a) -> (forall a. g a -> h a) -> ApT f g b -> h b

Although I (the author) believe this package provides the free applicative transformer under the most natural interpretation of "free" and "applicative transformer," the term "applicative transformer" has never been defined clearly and thus "free" thing of the "applicative transformer" hasn't been too. Because of this ambiguity, I want it to be another take on the Free Applicative Transformer, rather than the patch to the "free" package replacing the current Control.Applicative.Trans.Free.