Safe Haskell | Safe-Inferred |
---|---|

Language | Haskell2010 |

## Synopsis

- type Profunctor p = (Cofunctor p, ForallF Functor p)
- class Category (First p) => Cofunctor p where
- (=.) :: (Cofunctor p, Arrow (First p)) => (y -> x) -> p x a -> p y a
- (=:) :: (Cofunctor p, First p ~ Kleisli m) => (y -> m x) -> p x a -> p y a
- cofilter :: (Cofunctor p, First p ~ Kleisli m, Alternative m) => (x -> Bool) -> p x a -> p x a

# Documentation

type Profunctor p = (Cofunctor p, ForallF Functor p) Source #

A `Profunctor`

is a bifunctor `p :: * -> * -> *`

from the product of an
arbitrary category, denoted

, and `First`

p`(->)`

.

This is a generalization of the `profunctors`

package's `Profunctor`

,
where

.`First`

p ~ (->)

A profunctor is two functors on different domains at once, one
contravariant, one covariant, and that is made clear by this definition
specifying `Cofunctor`

and `Functor`

separately.

class Category (First p) => Cofunctor p where Source #

Types `p :: * -> * -> *`

which are contravariant functors
over their first parameter.

Functor laws:

`lmap`

`id`

=`id`

`lmap`

(i`>>>`

j) =`lmap`

i`.`

`lmap`

j

If the domain

is an `First`

p`Arrow`

, and if for every `a`

, the type
`p a`

is an instance of `Applicative`

, then a pure arrow `arr`

f should
correspond to an "applicative natural transformation":

`lmap`

(`arr`

f) (p`<*>`

q) =`lmap`

(`arr`

f) p`<*>`

`lmap`

(`arr`

f) q

`lmap`

(`arr`

f) (`pure`

a) =`pure`

a

The following may not be true in general, but seems to hold in practice,
when the instance

orders effects from left to right,
in particular that should be the case if there is also a `Applicative`

(p a)

:`Monad`

(p a)

`lmap`

(`first`

i) (`lmap`

(`arr`

`fst`

) p`<*>`

`lmap`

(`arr`

`snd`

) q) =`lmap`

(`first`

i`>>>`

`arr`

`fst`

) p`<*>`

`lmap`

(`arr`

`snd`

) q

(=.) :: (Cofunctor p, Arrow (First p)) => (y -> x) -> p x a -> p y a infixl 5 Source #

Mapping with a regular function.