@hackage functor-apply0.10.1

Haskell 98: Applicative sans pure, Monad sans return, Alternative sans empty

Provides a wide array of semigroup based Functors.

When working with comonads you often have the <*> portion of an Applicative, but not the pure. This was captured in Uustalu and Vene's "Essence of Dataflow Programming" in the form of the ComonadZip class in the days before Applicative. Apply provides a weaker invariant, but for the comonads used for data flow programming (found in the streams package), this invariant is preserved.

Logically:

Functor -> Apply -------> Bind
 |           |             |
 v           v             v
Alt     Applicative ---> Monad
 |           |             |
 v           v             v
Plus -> Alternative -> MonadPlus
Functor
   |
   v
Foldable ----> Foldable1
   |               |
   v               v
Traversable -> Traversable1
Bifunctor -----> Biapply
    |
    v
Bifoldable ----> Bifoldable1
    |                  |
    v                  v
Bitraversable -> Bitraversable1

This lets us remove many of the restrictions from various monad transformers as in many cases the binding operation or <*> operation does not require them.

Finally, to work with these weaker structures it is beneficial to have containers that can provide stronger guarantees about their contents, so versions of Traversable and Foldable that can be folded with just a Semigroup are added.