Copyright	(c) 2015 diagrams-core team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	Safe
Language	Haskell2010

Data.Monoid.Coproduct.Strict

Contents

Description

A strict coproduct of two monoids.

Synopsis

data m :+: n
inL :: m -> m :+: n
inR :: n -> m :+: n
prependL :: Semigroup m => m -> (m :+: n) -> m :+: n
prependR :: Semigroup n => n -> (m :+: n) -> m :+: n
killL :: (Action m n, Monoid' n) => (m :+: n) -> n
killR :: Monoid m => (m :+: n) -> m
untangle :: (Action m n, Monoid m, Monoid' n) => (m :+: n) -> (m, n)
untangled :: (Action m n, Monoid m, Monoid' n) => Lens (m :+: n) (m' :+: n') (m, n) (m', n')
_L :: (Action m n, Monoid m, Semigroup n) => Lens (m :+: n) (m' :+: n) m m'
_R :: (Action m n, Monoid' n) => Lens (m :+: n) (m :+: n') n n'

Coproduct

data m :+: n Source #

m :+: n is the coproduct of monoids m and n. Concatentation is equivilent to

(m1 :+: n1) <> (m2 :+: n2) = (m1 <> m2) :+: (n1 <> act m1 n2)@

but has a more efficient internal implimentation.

Instances

(Action m n, Monoid m, Monoid' n, Show m, Show n) => Show (m :+: n) Source #
Instance details Defined in Data.Monoid.Coproduct.Strict Methods showsPrec :: Int -> (m :+: n) -> ShowS # show :: (m :+: n) -> String # showList :: [m :+: n] -> ShowS #
(Action m n, Semigroup m, Semigroup n) => Semigroup (m :+: n) Source #
Instance details Defined in Data.Monoid.Coproduct.Strict Methods (<>) :: (m :+: n) -> (m :+: n) -> m :+: n # sconcat :: NonEmpty (m :+: n) -> m :+: n # stimes :: Integral b => b -> (m :+: n) -> m :+: n #
(Action m n, Semigroup m, Semigroup n) => Monoid (m :+: n) Source #
Instance details Defined in Data.Monoid.Coproduct.Strict Methods mempty :: m :+: n # mappend :: (m :+: n) -> (m :+: n) -> m :+: n # mconcat :: [m :+: n] -> m :+: n #
(Action m n, Action m r, Action n r, Semigroup n) => Action (m :+: n) r Source #	Coproducts act on other things by having each of the components act individually.
Instance details Defined in Data.Monoid.Coproduct.Strict Methods act :: (m :+: n) -> r -> r Source #

inL :: m -> m :+: n Source #

Construct a coproduct with a left value.

inR :: n -> m :+: n Source #

Construct a coproduct with a right value.

prependL :: Semigroup m => m -> (m :+: n) -> m :+: n Source #

Prepend a value from the left.

prependR :: Semigroup n => n -> (m :+: n) -> m :+: n Source #

Prepend a value from the right.

killL :: (Action m n, Monoid' n) => (m :+: n) -> n Source #

Extract n from a coproduct.

killR :: Monoid m => (m :+: n) -> m Source #

Extract m from a coproduct.

untangle :: (Action m n, Monoid m, Monoid' n) => (m :+: n) -> (m, n) Source #

Lenses

untangled :: (Action m n, Monoid m, Monoid' n) => Lens (m :+: n) (m' :+: n') (m, n) (m', n') Source #

Lens onto the both m and n.

_L :: (Action m n, Monoid m, Semigroup n) => Lens (m :+: n) (m' :+: n) m m' Source #

Lens onto the left value of a coproduct.

_R :: (Action m n, Monoid' n) => Lens (m :+: n) (m :+: n') n n' Source #

Lens onto the right value of a coproduct.