representable-functors-1.8.0: Representable functors

Stabilityexperimental
Maintainerekmett@gmail.com

Data.Functor.Representable

Contents

Description

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.

Synopsis

Representable Functors

class (Indexable f, Distributive f, Keyed f, Apply f, Applicative f) => Representable f whereSource

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

 tabulate . index = id
 index . tabulate = id
 tabulate . return f = return f

Methods

tabulate :: (Key f -> a) -> f aSource

 fmap f . tabulate = tabulate . fmap f

Representable Lenses

repLens :: Representable f => Lens a b -> Lens (f a) (f b)Source

We extend lens across a representable functor, due to the preservation of limits.

Default definitions

Functor

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

Distributive

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

Keyed

mapWithKeyRep :: Representable f => (Key f -> a -> b) -> f a -> f bSource

Apply/Applicative

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

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

Bind/Monad

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

bindWithKeyRep :: Representable f => f a -> (Key f -> a -> f b) -> f bSource

MonadReader

localRep :: Representable f => (Key f -> Key f) -> f a -> f aSource

Extend

duplicateRep :: (Representable f, Semigroup (Key f)) => f a -> f (f a)Source

extendRep :: (Representable f, Semigroup (Key f)) => (f a -> b) -> f a -> f bSource

Comonad

extractRep :: (Indexable f, Monoid (Key f)) => f a -> aSource