Copyright	(c) Edward Kmett 2011-2014
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Safe Haskell	None
Language	Haskell98

Data.Functor.Rep

Contents

Representable Functors
Wrapped representable functors
Default definitions

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 where Source

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 :: * Source

Methods

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

fmap f . tabulate ≡ tabulate . fmap f

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

Instances

Representable Identity
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)) 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

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 Source

Distributive

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

Apply/Applicative

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

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

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

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

Bind/Monad

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

MonadFix

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

MonadZip

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

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

MonadReader

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

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

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 b Source

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 b Source

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

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 b Source

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