| Copyright | (c) Edward Kmett 2011-2014 |
|---|---|
| License | BSD3 |
| Maintainer | ekmett@gmail.com |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell98 |
Data.Functor.Rep
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 => Representable f where
- tabulated :: (Representable f, Representable g, Profunctor p, Functor h) => p (f a) (h (g b)) -> p (Rep f -> a) (h (Rep g -> b))
- newtype Co f a = Co {
- unCo :: f a
- fmapRep :: Representable f => (a -> b) -> f a -> f b
- distributeRep :: (Representable f, Functor w) => w (f a) -> f (w a)
- 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
- mfixRep :: Representable f => (a -> f a) -> f a
- mzipRep :: Representable f => f a -> f b -> f (a, b)
- mzipWithRep :: Representable f => (a -> b -> c) -> f a -> f b -> f c
- askRep :: Representable f => f (Rep f)
- localRep :: Representable f => (Rep f -> Rep f) -> f a -> f a
- duplicatedRep :: (Representable f, Semigroup (Rep f)) => f a -> f (f a)
- extendedRep :: (Representable f, Semigroup (Rep f)) => (f a -> b) -> f a -> f b
- duplicateRep :: (Representable f, Monoid (Rep f)) => f a -> f (f a)
- extendRep :: (Representable f, Monoid (Rep f)) => (f a -> b) -> f a -> f b
- extractRep :: (Representable f, Monoid (Rep f)) => f a -> a
- duplicateRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> f a -> f (f a)
- extendRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> (f a -> b) -> f a -> f b
- extractRepBy :: Representable f => Rep f -> f a -> a
Representable Functors
class Distributive f => Representable f 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≡ idindex.tabulate≡ idtabulate.return≡return
Associated Types
type Rep f :: *
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))
tabulate and index form two halves of an isomorphism.
This can be used with the combinators from the lens package.
tabulated::Representablef =>Iso'(Repf -> a) (f a)
Wrapped representable functors
newtype Co 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
Distributive
distributeRep :: (Representable f, Functor w) => w (f a) -> f (w a)
Apply/Applicative
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
Bind/Monad
bindRep :: Representable f => f a -> (a -> f b) -> f b
MonadFix
mfixRep :: Representable f => (a -> f a) -> f a
MonadZip
mzipRep :: Representable f => f a -> f b -> f (a, b)
mzipWithRep :: Representable f => (a -> b -> c) -> f a -> f b -> f c
MonadReader
askRep :: Representable f => f (Rep f)
localRep :: Representable f => (Rep f -> Rep f) -> f a -> f a
Extend
duplicatedRep :: (Representable f, Semigroup (Rep f)) => f a -> f (f a)
extendedRep :: (Representable f, Semigroup (Rep f)) => (f a -> b) -> f a -> f b
Comonad
duplicateRep :: (Representable f, Monoid (Rep f)) => f a -> f (f a)
extendRep :: (Representable f, Monoid (Rep f)) => (f a -> b) -> f a -> f b
extractRep :: (Representable f, Monoid (Rep f)) => f a -> a
Comonad, with user-specified monoid
duplicateRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> f a -> f (f a)
extendRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> (f a -> b) -> f a -> f b
extractRepBy :: Representable f => Rep f -> f a -> a