| Copyright | (c) Edward Kmett 2011-2014 |
|---|---|
| License | BSD3 |
| Maintainer | ekmett@gmail.com |
| Stability | experimental |
| Safe Haskell | Trustworthy |
| 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)
- collectRep :: (Representable f, Functor w) => (a -> f b) -> w a -> f (w 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
- 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
- imapRep :: Representable r => (Rep r -> a -> a') -> r a -> r a'
- ifoldMapRep :: forall r m a. (Representable r, Foldable r, Monoid m) => (Rep r -> a -> m) -> r a -> m
- itraverseRep :: forall r f a a'. (Representable r, Traversable r, Applicative f) => (Rep r -> a -> f a') -> r a -> f (r a')
- type GRep f = GRep' (Rep1 f)
- gindex :: (Generic1 f, GRep f ~ Rep f, GIndex (Rep1 f)) => f a -> Rep f -> a
- gtabulate :: (Generic1 f, GRep f ~ Rep f, GTabulate (Rep1 f)) => (Rep f -> a) -> f a
- newtype WrappedRep f = WrapRep {}
Representable Functors
class Distributive f => Representable f 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≡ idindex.tabulate≡ idtabulate.return≡return
Methods
tabulate :: (Rep f -> a) -> f a Source #
tabulate :: (Generic1 f, GRep f ~ Rep f, GTabulate (Rep1 f)) => (Rep f -> a) -> f a Source #
index :: f a -> Rep f -> a Source #
If no definition is provided, this will default to gindex.
index :: (Generic1 f, GRep f ~ Rep f, GIndex (Rep1 f)) => f a -> Rep f -> a Source #
If no definition is provided, this will default to gindex.
Instances
tabulated :: (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::Representablef =>Iso'(Repf -> a) (f a)
Wrapped representable functors
Instances
| ComonadTrans Co Source # | |
| (Representable f, (~) * (Rep f) a) => MonadReader a (Co f) Source # | |
| Representable f => Monad (Co f) Source # | |
| Functor f => Functor (Co f) Source # | |
| Representable f => Applicative (Co f) Source # | |
| (Representable f, Monoid (Rep f)) => Comonad (Co f) Source # | |
| Representable f => Distributive (Co f) Source # | |
| Representable f => Apply (Co f) Source # | |
| Representable f => Bind (Co f) Source # | |
| (Representable f, Semigroup (Rep f)) => Extend (Co f) Source # | |
| Representable f => Representable (Co f) Source # | |
| type Rep (Co f) Source # | |
Default definitions
Functor
fmapRep :: Representable f => (a -> b) -> f a -> f b Source #
Distributive
distributeRep :: (Representable f, Functor w) => w (f a) -> f (w a) Source #
collectRep :: (Representable f, Functor w) => (a -> f b) -> w a -> f (w b) Source #
Apply/Applicative
apRep :: Representable f => f (a -> b) -> f a -> f b Source #
pureRep :: Representable f => a -> f a Source #
liftR2 :: Representable f => (a -> b -> c) -> f a -> f b -> f c Source #
liftR3 :: Representable f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d Source #
Bind/Monad
bindRep :: Representable f => f a -> (a -> f b) -> f b Source #
MonadFix
mfixRep :: Representable f => (a -> f a) -> f a Source #
MonadZip
mzipRep :: Representable f => f a -> f b -> f (a, b) Source #
mzipWithRep :: Representable f => (a -> b -> c) -> f a -> f b -> f c Source #
MonadReader
askRep :: Representable f => f (Rep f) Source #
Extend
duplicatedRep :: (Representable f, Semigroup (Rep f)) => f a -> f (f a) Source #
extendedRep :: (Representable f, Semigroup (Rep f)) => (f a -> b) -> f a -> f b Source #
Comonad
duplicateRep :: (Representable f, Monoid (Rep f)) => f a -> f (f a) Source #
extractRep :: (Representable f, Monoid (Rep f)) => f a -> a Source #
Comonad, with user-specified monoid
duplicateRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> f a -> f (f a) Source #
extendRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> (f a -> b) -> f a -> f b Source #
extractRepBy :: Representable f => Rep f -> f a -> a Source #
WithIndex
imapRep :: Representable r => (Rep r -> a -> a') -> r a -> r a' Source #
ifoldMapRep :: forall r m a. (Representable r, Foldable r, Monoid m) => (Rep r -> a -> m) -> r a -> m Source #
itraverseRep :: forall r f a a'. (Representable r, Traversable r, Applicative f) => (Rep r -> a -> f a') -> r a -> f (r a') Source #
Generics
type GRep f = 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) instanceRepresentableFoo
Then you'll get:
GRepFoo = Either () (Either (WrappedRepBar) (WrappedRepBaz,WrappedRepQuux))
(See the Haddocks for WrappedRep for an explanation of its purpose.)
newtype WrappedRep f 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) instanceRepresentableStream
With WrappedRep, we have its Rep being:
RepStream =Either() (WrappedRepStream)
If WrappedRep didn't exist, it would be:
Rep Stream = Either () (Either () (Either () ...))
An infinite type! WrappedRep breaks the potentially infinite loop.