functor-monad

This repository contains multiple (currently: 3) Haskell packages.

free-applicative-t

The package free-applicative-t provides the single module Control.Applicative.Trans.FreeAp for single type: ApT. This type is supposed to represent the "free" "applicative transformer", filling the space in this table:

Free		-transformer
Monad	Free	FreeT
Applicative	Ap	???

More on the README of the package itself.

day-comonoid

The package day-comonoid provides a type class named Comonoid.

class Comonad f => Comonoid f where
    coapply :: f a -> Day f f a

The name "Comonoid" should be read in a context. A functor f being Comonoid means it's a comonoid in the category of Functors equipped with Day as its tensor product.

Comonoid can be seen as "the dual" of Applicative, because Applicative can be seen as the type class for monoids in that category.

functor-monad

The package functor-monad provides FFunctor and FMonad, each corresponds to Functor and Monad but is higher-order.

	a Functor f	a FFunctor ff
Takes	a :: Type	g :: Type -> Type, Functor g
Makes	f a :: Type	ff g :: Type -> Type, Functor (ff g)
Methods	fmap :: (a -> b) -> f a -> f b	ffmap :: (Functor g, Functor h) => (g ~> h) -> (ff g ~> ff h)

	a Monad m	a FMonad mm
Superclass	Functor	FFunctor
Methods	return = pure :: a -> m a	fpure :: (Functor g) => g ~> mm g
	(=<<) :: (a -> m b) -> m a -> m b	fbind :: (Functor g, Functor h) => (g ~> mm h) -> (mm g ~> mm h)
	join :: m (m a) -> m a	fjoin :: (Functor g) => mm (mm g) ~> mm g

More on the README of the package itself.