Safe Haskell	None
Language	Haskell2010

Data.Bifunctor.Linear

Description

This module provides Bifunctor and related classes.

`Bifunctor`

Use a bifunctor instance to map functions over data structures that have two type paramaters a and b and could be have a functor instance for either the as or bs. For instance, you might want to map a function on either the left or right element of a (Int, Bool):

import Prelude.Linear
import Data.Bifunctor.Linear

-- Map over the second element
negateRight :: (Int, Bool) %1-> (Int, Bool)
negateRight x = second not x

Synopsis

class Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a %1 -> b) -> (c %1 -> d) -> p a c %1 -> p b d
- first :: (a %1 -> b) -> p a c %1 -> p b c
- second :: (b %1 -> c) -> p a b %1 -> p a c
class Bifunctor m => SymmetricMonoidal (m :: Type -> Type -> Type) u | m -> u, u -> m where
- rassoc :: m (m a b) c %1 -> m a (m b c)
- lassoc :: m a (m b c) %1 -> m (m a b) c
- swap :: m a b %1 -> m b a

Documentation

class Bifunctor (p :: Type -> Type -> Type) where Source #

The Bifunctor class

Laws

If bimap is supplied, then bimap id id = id

If first and second are supplied, then first id ≡ id second id ≡ id
If all are supplied, then @bimap f g = first f . second g

Minimal complete definition

bimap | first, second

Methods

bimap :: (a %1 -> b) -> (c %1 -> d) -> p a c %1 -> p b d Source #

first :: (a %1 -> b) -> p a c %1 -> p b c Source #

second :: (b %1 -> c) -> p a b %1 -> p a c Source #

Instances

Instances details

Bifunctor Either Source #
Instance details Defined in Data.Bifunctor.Linear.Internal.Bifunctor Methods bimap :: (a %1 -> b) -> (c %1 -> d) -> Either a c %1 -> Either b d Source # first :: (a %1 -> b) -> Either a c %1 -> Either b c Source # second :: (b %1 -> c) -> Either a b %1 -> Either a c Source #
Bifunctor (,) Source #
Instance details Defined in Data.Bifunctor.Linear.Internal.Bifunctor Methods bimap :: (a %1 -> b) -> (c %1 -> d) -> (a, c) %1 -> (b, d) Source # first :: (a %1 -> b) -> (a, c) %1 -> (b, c) Source # second :: (b %1 -> c) -> (a, b) %1 -> (a, c) Source #

class Bifunctor m => SymmetricMonoidal (m :: Type -> Type -> Type) u | m -> u, u -> m where Source #

A SymmetricMonoidal class

This allows you to shuffle around a bifunctor nested in itself and swap the places of the two types held in the bifunctor. For instance, for tuples:

You can use lassoc :: (a,(b,c)) %1-> ((a,b),c) and then use first to access the a
You can use the dual, i.e., rassoc :: ((a,b),c) %1-> (a,(b,c)) and then second
You can swap the first and second values with swap :: (a,b) %1-> (b,a)

Laws

```
swap . swap = id
```
```
rassoc . lassoc = id
```
```
lassoc . rassoc = id
```

second swap . rassoc . first swap = rassoc . swap . rassoc

Minimal complete definition

swap, (rassoc | lassoc)

Methods

rassoc :: m (m a b) c %1 -> m a (m b c) Source #

lassoc :: m a (m b c) %1 -> m (m a b) c Source #

swap :: m a b %1 -> m b a Source #

Instances

Instances details

SymmetricMonoidal Either Void Source #
Instance details Defined in Data.Bifunctor.Linear.Internal.SymmetricMonoidal Methods rassoc :: Either (Either a b) c %1 -> Either a (Either b c) Source # lassoc :: Either a (Either b c) %1 -> Either (Either a b) c Source # swap :: Either a b %1 -> Either b a Source #
SymmetricMonoidal (,) () Source #
Instance details Defined in Data.Bifunctor.Linear.Internal.SymmetricMonoidal Methods rassoc :: ((a, b), c) %1 -> (a, (b, c)) Source # lassoc :: (a, (b, c)) %1 -> ((a, b), c) Source # swap :: (a, b) %1 -> (b, a) Source #