| Stability | experimental |
|---|---|
| Maintainer | ekmett@gmail.com |
| Safe Haskell | Safe-Infered |
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.
- class (Indexable f, Distributive f, Keyed f, Apply f, Applicative f, ZipWithKey f) => Representable f where
- repLens :: Representable f => Lens a b -> Lens (f a) (f b)
- fmapRep :: Representable f => (a -> b) -> f a -> f b
- distributeRep :: (Representable f, Functor w) => w (f a) -> f (w a)
- mapWithKeyRep :: Representable f => (Key f -> a -> b) -> f a -> f b
- apRep :: Representable f => f (a -> b) -> f a -> f b
- pureRep :: Representable f => a -> f a
- bindRep :: Representable f => f a -> (a -> f b) -> f b
- bindWithKeyRep :: Representable f => f a -> (Key f -> a -> f b) -> f b
- zipWithRep :: Representable f => (a -> b -> c) -> f a -> f b -> f c
- zipWithKeyRep :: Representable f => (Key f -> a -> b -> c) -> f a -> f b -> f c
- askRep :: Representable f => f (Key f)
- localRep :: Representable f => (Key f -> Key f) -> f a -> f a
- duplicateRep :: (Representable f, Semigroup (Key f)) => f a -> f (f a)
- extendRep :: (Representable f, Semigroup (Key f)) => (f a -> b) -> f a -> f b
- extractRep :: (Indexable f, Monoid (Key f)) => f a -> a
Representable Functors
class (Indexable f, Distributive f, Keyed f, Apply f, Applicative f, ZipWithKey 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
Instances
| Representable Identity | |
| Representable ((->) e) | |
| Representable m => Representable (IdentityT m) | |
| Representable f => Representable (Cofree f) | |
| Representable w => Representable (TracedT s w) | |
| Representable m => Representable (ReaderT e m) | |
| (Representable f, Representable g) => Representable (Compose f g) | |
| (Representable f, Representable g) => Representable (Product f g) | |
| (Representable f, Representable m) => Representable (ReaderT f m) |
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
Zip/ZipWithKey
zipWithRep :: Representable f => (a -> b -> c) -> f a -> f b -> f cSource
zipWithKeyRep :: Representable f => (Key f -> a -> b -> c) -> f a -> f b -> f cSource
MonadReader
askRep :: Representable f => f (Key f)Source
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