Copyright | (c) Edward Kmett 2011-2014 |
---|---|

License | BSD3 |

Maintainer | ekmett@gmail.com |

Stability | experimental |

Safe Haskell | Trustworthy |

Language | Haskell98 |

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`

≡ id`index`

.`tabulate`

≡ id`tabulate`

.`return`

≡`return`

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`

.

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`

::`Representable`

f =>`Iso'`

(`Rep`

f -> a) (f a)

# Wrapped representable functors

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`

) 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.)

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`

) 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.