Data.Functor.Rep

Representable endofunctors over the category of Haskell types are isomorphic to the reader monad and so inherit a very large number of properties for free.

Representable Functors

class Distributive f => Representable f where

A Functor f is Representable if tabulate and index witness an isomorphism to (->) x.

Every Distributive Functor is actually Representable.

Every Representable Functor from Hask to Hask is a right adjoint.

tabulate . index  ≡ id
index . tabulate  ≡ id
tabulate . return ≡ return

Associated Types

type Rep f :: *

Methods

tabulate :: (Rep f -> a) -> f a

fmap f . tabulate ≡ tabulate . fmap f

index :: f a -> Rep f -> a

Instances

Representable Identity

Representable Complex

Representable Dual

Representable Sum

Representable Product

Representable ((->) e)

Representable (Proxy *)

Representable m => Representable (IdentityT m)

Representable f => Representable (Cofree f)

Representable f => Representable (Co f)

Representable w => Representable (TracedT s w)

Representable m => Representable (ReaderT e m)

(Representable f, Representable g) => Representable (Compose f g)

Representable (Tagged * t)

(Representable f, Representable g) => Representable (Product f g)

(Representable f, Representable m) => Representable (ReaderT f m)

tabulated :: (Representable f, Representable g, Profunctor p, Functor h) => p (f a) (h (g b)) -> p (Rep f -> a) (h (Rep g -> b))

tabulate and index form two halves of an isomorphism.

This can be used with the combinators from the lens package.

tabulated :: Representable f => Iso' (Rep f -> a) (f a)

Wrapped representable functors

newtype Co f a

Constructors

Co

Fields

unCo :: f a

Instances

ComonadTrans Co

(Representable f, (~) * (Rep f) a) => MonadReader a (Co f)

Representable f => Monad (Co f)

Functor f => Functor (Co f)

Representable f => Applicative (Co f)

(Representable f, Monoid (Rep f)) => Comonad (Co f)

Representable f => Distributive (Co f)

Representable f => Apply (Co f)

Representable f => Bind (Co f)

(Representable f, Semigroup (Rep f)) => Extend (Co f)

Representable f => Representable (Co f)

type Rep (Co f) = Rep f

Default definitions

Functor

fmapRep :: Representable f => (a -> b) -> f a -> f b

Distributive

distributeRep :: (Representable f, Functor w) => w (f a) -> f (w a)

Apply/Applicative

apRep :: Representable f => f (a -> b) -> f a -> f b

pureRep :: Representable f => a -> f a

liftR2 :: Representable f => (a -> b -> c) -> f a -> f b -> f c

liftR3 :: Representable f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Bind/Monad

bindRep :: Representable f => f a -> (a -> f b) -> f b

MonadFix

mfixRep :: Representable f => (a -> f a) -> f a

MonadZip

mzipRep :: Representable f => f a -> f b -> f (a, b)

mzipWithRep :: Representable f => (a -> b -> c) -> f a -> f b -> f c

MonadReader

askRep :: Representable f => f (Rep f)

localRep :: Representable f => (Rep f -> Rep f) -> f a -> f a

Extend

duplicatedRep :: (Representable f, Semigroup (Rep f)) => f a -> f (f a)

extendedRep :: (Representable f, Semigroup (Rep f)) => (f a -> b) -> f a -> f b

Comonad

duplicateRep :: (Representable f, Monoid (Rep f)) => f a -> f (f a)

extendRep :: (Representable f, Monoid (Rep f)) => (f a -> b) -> f a -> f b

extractRep :: (Representable f, Monoid (Rep f)) => f a -> a

Comonad, with user-specified monoid

duplicateRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> f a -> f (f a)

extendRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> (f a -> b) -> f a -> f b

extractRepBy :: Representable f => Rep f -> f a -> a