| Stability | experimental |
|---|---|
| Maintainer | ekmett@gmail.com |
| Safe Haskell | None |
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 (Distributive f, Indexable f) => Representable f where
- newtype Rep f a = Rep {
- unrep :: f a
- 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
- liftR2 :: Representable f => (a -> b -> c) -> f a -> f b -> f c
- liftR3 :: Representable f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- 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
- duplicatedRep :: (Representable f, Semigroup (Key f)) => f a -> f (f a)
- extendedRep :: (Representable f, Semigroup (Key f)) => (f a -> b) -> f a -> f b
- duplicateRep :: (Representable f, Monoid (Key f)) => f a -> f (f a)
- extendRep :: (Representable f, Monoid (Key f)) => (f a -> b) -> f a -> f b
- extractRep :: (Indexable f, Monoid (Key f)) => f a -> a
Representable Functors
class (Distributive f, Indexable 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 f => Representable (Rep 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) |
Wrapped representable functors
Instances
| ComonadTrans Rep | |
| (Representable f, ~ * (Key f) a) => MonadReader a (Rep f) | |
| Representable f => Monad (Rep f) | |
| Representable f => Functor (Rep f) | |
| Representable f => Applicative (Rep f) | |
| (Representable f, Monoid (Key f)) => Comonad (Rep f) | |
| Representable f => Distributive (Rep f) | |
| Representable f => Keyed (Rep f) | |
| Representable f => Zip (Rep f) | |
| Representable f => ZipWithKey (Rep f) | |
| Indexable f => Indexable (Rep f) | |
| Indexable f => Lookup (Rep f) | |
| Representable f => Apply (Rep f) | |
| Representable f => Bind (Rep f) | |
| (Representable f, Semigroup (Key f)) => Extend (Rep f) | |
| Representable f => Representable (Rep f) |
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
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
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
duplicatedRep :: (Representable f, Semigroup (Key f)) => f a -> f (f a)Source
extendedRep :: (Representable f, Semigroup (Key f)) => (f a -> b) -> f a -> f bSource
Comonad
duplicateRep :: (Representable f, Monoid (Key f)) => f a -> f (f a)Source
extendRep :: (Representable f, Monoid (Key f)) => (f a -> b) -> f a -> f bSource
extractRep :: (Indexable f, Monoid (Key f)) => f a -> aSource