adjunctions-4.2: Adjunctions and representable functors

Stabilityexperimental
Maintainerekmett@gmail.com
Safe HaskellNone

Data.Functor.Rep

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 Distributive f => Representable f whereSource

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 . returnreturn

Associated Types

type Rep f :: *Source

Methods

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

 fmap f . tabulatetabulate . fmap f

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

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

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 Source

Constructors

Co 

Fields

unCo :: f a
 

Instances

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

Apply/Applicative

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

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

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

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

Bind/Monad

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

MonadFix

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

MonadZip

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

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

MonadReader

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

Extend

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

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

Comonad

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

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

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

Comonad, with user-specified monoid

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

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

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