Moduleadjunctions-4.4.4Haskell2010

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.

Contents

Representable Functors
Wrapped representable functors
Default definitions
Functor
Distributive
Apply/Applicative
Bind/Monad
MonadFix
MonadZip
MonadReader
Extend
Comonad
Comonad, with user-specified monoid
WithIndex
Generics

Synopsis

class Representable
value tabulated
newtype Co
value fmapRep
value distributeRep
value collectRep
value apRep
value pureRep
value liftR2
value liftR3
value bindRep
value mfixRep
value mzipRep
value mzipWithRep
value askRep
value localRep
value duplicatedRep
value extendedRep
value duplicateRep
value extendRep
value extractRep
value duplicateRepBy
value extendRepBy
value extractRepBy
value imapRep
value ifoldMapRep
value itraverseRep
type GRep
value gindex
value gtabulate
newtype WrappedRep

Packageadjunctions-4.4.4
Exports31
LanguageHaskell2010
LicenceBSD-2-Clause
SourceRep.hs

Representable Functors

classclass Distributive f => Representable (f :: Type -> Type) 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 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-4.4.4 · Data.Functor.Rep
Representable IdentityDefined in adjunctions-4.4.4 · Data.Functor.Rep
Representable DualDefined in adjunctions-4.4.4 · Data.Functor.Rep
Representable ProductDefined in adjunctions-4.4.4 · Data.Functor.Rep
Representable SumDefined in adjunctions-4.4.4 · Data.Functor.Rep
Representable Par1Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable ProxyDefined in adjunctions-4.4.4 · Data.Functor.Rep
Representable U1Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Representable (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Representable (Cofree f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable (Tagged t)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Representable (Rec1 f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Representable (Backwards f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Representable (Reverse f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable m => Representable (IdentityT m)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable m => Representable (ReaderT e m)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable w => Representable (TracedT s w)Defined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Representable m) => Representable (ReaderT f m)Defined in adjunctions-4.4.4 · Control.Monad.Representable.Reader
Representable ((->) e)Defined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Representable g) => Representable (Product f g)Defined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Representable g) => Representable (f :*: g)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Representable (M1 i c f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Representable g) => Representable (Compose f g)Defined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Representable g) => Representable (f :.: g)Defined in adjunctions-4.4.4 · 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))

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

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

Constructors

Co
- unCo :: f a

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

ComonadTrans CoDefined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Rep f ~ a) => MonadReader a (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Monad (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Functor f => Functor (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Applicative (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Distributive (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Monoid (Rep f)) => Comonad (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Apply (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Bind (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
(Representable f, Semigroup (Rep f)) => Extend (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
Representable f => Representable (Co f)Defined in adjunctions-4.4.4 · Data.Functor.Rep
type Rep (Co f) = Rep fDefined in adjunctions-4.4.4 · Data.Functor.Rep

Default definitions

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)

Source#

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

Source#

A default implementation of index in terms of GRep.

valuegtabulate

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

Source#

A default implementation of tabulate in terms of GRep.

newtypenewtype WrappedRep (f :: Type -> Type)

Source#

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