Control.Comonad.Cofree

Documentation

newtype BiffB p f g a b

Constructors

BiffB

Fields

runBiffB :: p (f a) (g b)

Instances

(Functor f, Bifunctor p, Functor g) => Bifunctor (BiffB p f g)

Functor f => PCopointed (BiffB (,) Identity f)

Functor f => PPointed (BiffB Either Identity f)

FunctorPlus f => PPointed (BiffB (,) Identity f)

(Functor f, Symmetric p) => Symmetric (BiffB p f f)

(Functor f, Braided p) => Braided (BiffB p f f)

Functor f => PComonad (BiffB (,) Identity f)

Functor f => PApplicative (BiffB Either Identity f)

FunctorPlus f => PApplicative (BiffB (,) Identity f)

Functor f => PMonad (BiffB Either Identity f)

FunctorPlus f => PMonad (BiffB (,) Identity f)

(Bizip p, Zip f, Zip g) => Bizip (BiffB p f g)

(BiZap p q, Zap f g, Zap i j) => BiZap (BiffB p f i) (BiffB q g j)

(Functor f, Bifunctor p, Functor g) => Functor (BiffB p f g a)

newtype FixB s a

Constructors

InB

Fields

outB :: s a (FixB s a)

Instances

PMonad f => Monad (FixB f)

Bifunctor s => Functor (FixB s)

PCopointed f => Copointed (FixB f)

PPointed f => Pointed (FixB f)

PComonad f => Comonad (FixB f)

Bizip p => Zip (FixB p)

class Bifunctor f => PCopointed f where

Methods

pextract :: f a c -> a

Instances

Functor f => PCopointed (BiffB (,) Identity f)

class PCopointed f => PComonad f where

Methods

pextend :: (f b c -> a) -> f b c -> f a c

Instances

Functor f => PComonad (BiffB (,) Identity f)

newtype Identity a

Identity wrapper. Abstraction for wrapping up a object. If you have an monadic function, say:

   example :: Int -> Identity Int
   example x = return (x*x)

you can "run" it, using

 Main> runIdentity (example 42)
 1764 :: Int

A typical use of the Identity monad is to derive a monad from a monad transformer.

-- derive the Control.Monad.State.State monad using the Control.Monad.State.StateT monad transformer
type Control.Monad.State.State s a = Control.Monad.State.StateT s Identity a

The runIdentity label is used in the type definition because it follows a style of monad definition that explicitly represents monad values as computations. In this style, a monadic computation is built up using the monadic operators and then the value of the computation is extracted using the run****** function. Because the Identity monad does not do any computation, its definition is trivial. For a better example of this style of monad, see the Control.Monad.State.State monad.

Constructors

Identity

Fields

runIdentity :: a

Instances

Monad Identity

Functor Identity

MonadFix Identity

Copointed Identity

Pointed Identity

Comonad Identity

ComonadFix Identity

Cozip Identity

Zip Identity

Zap Identity Identity

Functor f => PCopointed (BiffB (,) Identity f)

Functor f => PPointed (BiffB Either Identity f)

FunctorPlus f => PPointed (BiffB (,) Identity f)

Functor f => PComonad (BiffB (,) Identity f)

Functor f => PApplicative (BiffB Either Identity f)

FunctorPlus f => PApplicative (BiffB (,) Identity f)

Functor f => PMonad (BiffB Either Identity f)

FunctorPlus f => PMonad (BiffB (,) Identity f)

type CofreeB f a b = BiffB (,) Identity f a b

type Cofree f a = FixB (BiffB (,) Identity f) a

outCofree :: Cofree f a -> f (Cofree f a)

runCofree :: Cofree f a -> (a, f (Cofree f a))

anaCofree :: Functor f => (a -> c) -> (a -> f a) -> a -> Cofree f c

cofree :: a -> f (Cofree f a) -> Cofree f a