Data.Functor.Cofree

A cofree functor is right adjoint to a forgetful functor. In this package the forgetful functor forgets class constraints.

Documentation

data Cofree c b where

The cofree functor for constraint c.

Constructors

Cofree :: c a => (a -> b) -> a -> Cofree c b

Instances

(forall x. c (Identity x), forall x. c (Compose (Cofree c) (Cofree c) x)) => Monad (Cofree c)

Defined in Data.Functor.Cofree

Methods

(>>=) :: Cofree c a -> (a -> Cofree c b) -> Cofree c b

(>>) :: Cofree c a -> Cofree c b -> Cofree c b

return :: a -> Cofree c a

Functor (Cofree c)

Defined in Data.Functor.Cofree

Methods

fmap :: (a -> b) -> Cofree c a -> Cofree c b

(<$) :: a -> Cofree c b -> Cofree c a

(forall x. c (Identity x), forall x. c (Compose (Cofree c) (Cofree c) x)) => Applicative (Cofree c)

Defined in Data.Functor.Cofree

Methods

pure :: a -> Cofree c a

(<*>) :: Cofree c (a -> b) -> Cofree c a -> Cofree c b

liftA2 :: (a -> b -> c0) -> Cofree c a -> Cofree c b -> Cofree c c0

(*>) :: Cofree c a -> Cofree c b -> Cofree c b

(<*) :: Cofree c a -> Cofree c b -> Cofree c a

Comonad (Cofree c)

Defined in Data.Functor.Cofree

Methods

extract :: Cofree c a -> a

duplicate :: Cofree c a -> Cofree c (Cofree c a)

extend :: (Cofree c a -> b) -> Cofree c a -> Cofree c b

deriveCofreeInstance :: Name -> Q [Dec]

Derive the instance of Cofree c a for the class c.

counit :: Cofree c b -> b

leftAdjunct :: c a => (a -> b) -> a -> Cofree c b

unit :: c b => b -> Cofree c b

unit = leftAdjunct id

rightAdjunct :: (a -> Cofree c b) -> a -> b

rightAdjunct f = counit . f

convert :: (c (w a), Comonad w) => w a -> Cofree c a

Products

type Product c m n = Cofree c (m, n)

product :: c a => (a -> m) -> (a -> n) -> a -> Product c m n

outL :: Product c m n -> m

outR :: Product c m n -> n

type TerminalObject c = Cofree c ()

terminal :: c a => a -> TerminalObject c