Algebra.Functor

A module for functors

Documentation

class Functor f where

Methods

map :: (a -> b) -> f a -> f b

Instances

Functor []

Functor IO

Functor Maybe

Functor Set

Functor Tree

Functor Interleave

Functor OrdList

Functor Id

Functor Strict

Functor ((->) a)

Functor (Either b)

Functor ((,) b)

Functor (Map k)

Functor (Const a)

Functor f => Functor (Backwards f)

Functor f => Functor (Zip f)

Functor m => Functor (MaybeT m)

Functor m => Functor (TreeT m)

Functor m => Functor (ListT m)

(Functor f, Functor g) => Functor (:++: f g)

(Functor f, Functor g) => Functor (:**: f g)

(Functor f, Functor g) => Functor (:.: f g)

(Functor f, Functor g) => Functor (Compose' f g)

Functor f => Functor (Kleisli f a)

Functor m => Functor (StateT s m)

Functor m => Functor (ReaderT r m)

Functor m => Functor (WriterT w m)

Functor f => Functor (ContT r f)

Functor m => Functor (EitherT e m)

Functor m => Functor (ProbT t m)

Functor m => Functor (WriterAccT w acc m)

Functor f => Functor (RWST r w s f)

class Cofunctor f where

Methods

comap :: (a -> b) -> f b -> f a

Instances

(Functor f, Cofunctor g) => Cofunctor (:.: f g)

Cofunctor (Flip (->) a)

class Bifunctor p where

Methods

dimap :: (c -> a) -> (b -> d) -> p a b -> p c d

Instances

Bifunctor (->)

class Commutative f where

Methods

commute :: f a b -> f b a

Instances

Commutative (,)

Commutative Relation

Commutative Bimap

class Functor t => Contravariant t where

Methods

collect :: Functor f => f (t a) -> t (f a)

Instances

Contravariant Id

Contravariant ((->) a)

Contravariant f => Contravariant (Kleisli f a)

newtype Strict a

Constructors

Strict

Fields

lazy :: a

Instances

Unit Strict

Monad Strict

Applicative Strict

Functor Strict

newtype Id a

The Identity Functor

Constructors

Id

Fields

getId :: a

Instances

Unit Id

MonadFix Id

Foldable Id

Monad Id

Applicative Id

Functor Id

Contravariant Id

Isomorphic a b (Id a) (Id b)

Show a => Show (Id a)

newtype Const a b

The Constant Functor

Constructors

Const

Fields

getConst :: a

Instances

Isomorphic a b (Const a c) (Const b c)

Monoid a => Unit (Const a)

Monoid a => Applicative (Const a)

Functor (Const a)

Monoid a => Monoid (Const a b)

Semigroup a => Semigroup (Const a b)

newtype Flip f a b

A motherflippin' functor

Constructors

Flip

Fields

unFlip :: f b a

Instances

Cofunctor (Flip (->) a)

Isomorphic (f a b) (f c d) (Flip f b a) (Flip f d c)

Monoid (f b a) => Monoid (Flip f a b)

Semigroup (f b a) => Semigroup (Flip f a b)

(Ord b, Ord a) => DataMap (Flip Bimap b a) b a

newtype (f :.: g) a

The Composition functor

Constructors

Compose

Fields

getCompose :: f (g a)

Instances

Monad m => ConcreteMonad (:.: m)

Monad m => MonadTrans (:.: m)

Isomorphic (f (g a)) (f' (g' b)) (:.: f g a) (:.: f' g' b)

(Unit f, Unit g) => Unit (:.: f g)

(MonadFix f, Traversable g, Monad g) => MonadFix (:.: f g)

(Traversable f, Traversable g) => Traversable (:.: f g)

(Foldable f, Foldable g) => Foldable (:.: f g)

(Traversable g, Monad f, Monad g) => Monad (:.: f g)

(Applicative f, Applicative g) => Applicative (:.: f g)

(Functor f, Functor g) => Functor (:.: f g)

(Functor f, Cofunctor g) => Cofunctor (:.: f g)

(Applicative f, Monoid (g a)) => Monoid (:.: f g a)

(Applicative f, Semigroup (g a)) => Semigroup (:.: f g a)

data (f :**: g) a

Constructors

(f a) :**: (g a)

Instances

(Unit f, Unit g) => Unit (:**: f g)

(Traversable f, Traversable g) => Traversable (:**: f g)

(Foldable f, Foldable g) => Foldable (:**: f g)

(Applicative f, Applicative g) => Applicative (:**: f g)

(Functor f, Functor g) => Functor (:**: f g)

newtype (f :++: g) a

Constructors

Sum

Fields

getSum :: f a :+: g a

Instances

(Traversable f, Traversable g) => Traversable (:++: f g)

(Foldable f, Foldable g) => Foldable (:++: f g)

(Functor f, Functor g) => Functor (:++: f g)

flip :: (Contravariant c, Functor f) => f (c a) -> c (f a)

project :: (Contravariant c, Functor f) => (a -> c b) -> f a -> c (f b)

The Contravariant version of traverse

(<$>) :: Functor f => (a -> b) -> f a -> f b

(|||) :: (Choice k, Functor (k a), Functor (k b)) => k a c -> k b d -> k (a :+: b) (c :+: d)

(<$) :: Functor f => b -> f a -> f b

(<&>) :: Functor f => f a -> (a -> b) -> f b

void :: Functor f => f a -> f ()

left :: (Choice k, Functor (k a), Functor (k c)) => k a b -> k (a :+: c) (b :+: c)

right :: (Choice k, Functor (k a), Functor (k c)) => k a b -> k (c :+: a) (c :+: b)

promap :: Cofunctor (Flip f c) => (a -> b) -> f b c -> f a c

map2 :: (Functor f, Functor f') => (a -> b) -> f (f' a) -> f (f' b)

map3 :: (Functor f, Functor f', Functor f'') => (a -> b) -> f (f' (f'' a)) -> f (f' (f'' b))