Data.Bifunctor.Linear.Internal.SymmetricMonoidal

Documentation

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

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 :: ((a `m` b) `m` c) %1 -> a `m` (b `m` c)

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

swap :: (a `m` b) %1 -> b `m` a

Instances

SymmetricMonoidal Either Void

Defined in Data.Bifunctor.Linear.Internal.SymmetricMonoidal

Methods

rassoc :: Either (Either a b) c %1 -> Either a (Either b c)

lassoc :: Either a (Either b c) %1 -> Either (Either a b) c

swap :: Either a b %1 -> Either b a

SymmetricMonoidal (,) ()

Defined in Data.Bifunctor.Linear.Internal.SymmetricMonoidal

Methods

rassoc :: ((a, b), c) %1 -> (a, (b, c))

lassoc :: (a, (b, c)) %1 -> ((a, b), c)

swap :: (a, b) %1 -> (b, a)