Moduleadjunctions-4.4.3Haskell2010

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.

3 types
1 class
27 values

Packageadjunctions-4.4.3
Exports31
LanguageHaskell2010
LicenceBSD-2-Clause
SourceRep.hs

Representable Functors

2 declarations

classclass Distributive f => Representable (f :: Type -> Type) 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 family Rep (f :: Type -> Type)
If no definition is provided, this will default to GRep.

Methods

tabulate :: (Rep f -> a) -> f a
```
fmap f . tabulate ≡ tabulate . fmap f
```
If no definition is provided, this will default to gtabulate.
index :: f a -> Rep f -> a
If no definition is provided, this will default to gindex.

Instances24Representable, …

Representable ComplexDefined in adjunctions-4.4.3 · Data.Functor.Rep
Representable IdentityDefined in adjunctions-4.4.3 · Data.Functor.Rep
Representable DualDefined in adjunctions-4.4.3 · Data.Functor.Rep
Representable ProductDefined in adjunctions-4.4.3 · Data.Functor.Rep
Representable SumDefined in adjunctions-4.4.3 · Data.Functor.Rep
Representable Par1Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable ProxyDefined in adjunctions-4.4.3 · Data.Functor.Rep
Representable U1Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Representable (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Representable (Cofree f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable (Tagged t)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Representable (Rec1 f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Representable (Backwards f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Representable (Reverse f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable m => Representable (IdentityT m)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable m => Representable (ReaderT e m)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable w => Representable (TracedT s w)Defined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Representable m) => Representable (ReaderT f m)Defined in adjunctions-4.4.3 · Control.Monad.Representable.Reader
Representable ((->) e)Defined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Representable g) => Representable (Product f g)Defined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Representable g) => Representable (f :*: g)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Representable (M1 i c f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Representable g) => Representable (Compose f g)Defined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Representable g) => Representable (f :.: g)Defined in adjunctions-4.4.3 · Data.Functor.Rep

valuetabulated

:: (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

1 declaration

newtypenewtype Co (f :: Type -> Type) a

Constructors

Co
- unCo :: f a

Instances12ComonadTrans, MonadReader, Monad, Functor, Applicative, Distributive, …

ComonadTrans CoDefined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Rep f ~ a) => MonadReader a (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Monad (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Functor f => Functor (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Applicative (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Distributive (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Monoid (Rep f)) => Comonad (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Apply (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Bind (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
(Representable f, Semigroup (Rep f)) => Extend (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
Representable f => Representable (Co f)Defined in adjunctions-4.4.3 · Data.Functor.Rep
type Rep (Co f) = Rep fDefined in adjunctions-4.4.3 · Data.Functor.Rep

Default definitions

0 declarations

Functor

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

Distributive

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

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

Apply/Applicative

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

valuepureRep :: Representable f => a -> f a

valueliftR2 :: Representable f => (a -> b -> c) -> f a -> f b -> f c

valueliftR3 :: Representable f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Bind/Monad

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

MonadFix

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

MonadZip

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

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

MonadReader

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

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

Extend

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

valueextendedRep

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

Comonad

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

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

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

Comonad, with user-specified monoid

valueduplicateRepBy

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

valueextendRepBy

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

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

WithIndex

valueimapRep :: Representable r => (Rep r -> a -> a') -> r a -> r a'

valueifoldMapRep

:: (Representable r, Foldable r, Monoid m)
=> Rep r -> a -> m
-> r a
-> m

valueitraverseRep

:: (Representable r, Traversable r, Applicative f)
=> Rep r -> a -> f a'
-> r a
-> f (r a')

Generics

typetype GRep (f :: Type -> Type) = GRep' (Rep1 f)

A default implementation of Rep for a datatype that is an instance of Generic1. This is usually composed of Either, tuples, unit tuples, and underlying Rep values. For instance, if you have:

data Foo a = MkFoo a (Bar a) (Baz (Quux a)) deriving (Functor, Generic1)
instance Representable Foo

Then you'll get:

GRep Foo = Either () (Either (WrappedRep Bar) (WrappedRep Baz, WrappedRep Quux))

(See the Haddocks for WrappedRep for an explanation of its purpose.)

valuegindex :: (Generic1 f, GRep f ~ Rep f, GIndex (Rep1 f)) => f a -> Rep f -> a

A default implementation of index in terms of GRep.

valuegtabulate

:: (Generic1 f, GRep f ~ Rep f, GTabulate (Rep1 f))
=> Rep f -> a
-> f a

A default implementation of tabulate in terms of GRep.

newtypenewtype WrappedRep (f :: Type -> Type)

On the surface, WrappedRec is a simple wrapper around Rep. But it plays a very important role: it prevents generic Representable instances for recursive types from sending the typechecker into an infinite loop. Consider the following datatype:

data Stream a = a :< Stream a deriving (Functor, Generic1)
instance Representable Stream

With WrappedRep, we have its Rep being:

Rep Stream = Either () (WrappedRep Stream)

If WrappedRep didn't exist, it would be:

Rep Stream = Either () (Either () (Either () ...))

An infinite type! WrappedRep breaks the potentially infinite loop.

Constructors

WrapRep
- unwrapRep :: Rep f