Modulemonoid-extras-0.6.2Haskell2010

Data.Monoid.Coproduct.Strict

A strict coproduct of two monoids.

Coproduct

8 declarations

datadata (:+:) m n

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.

Instances4Show, Semigroup, Monoid, Action

(Action m n, Monoid m, Monoid' n, Show m, Show n) => Show (m :+: n)Defined in monoid-extras-0.6.2 · Data.Monoid.Coproduct.Strict
(Action m n, Semigroup m, Semigroup n) => Semigroup (m :+: n)Defined in monoid-extras-0.6.2 · Data.Monoid.Coproduct.Strict
(Action m n, Semigroup m, Semigroup n) => Monoid (m :+: n)Defined in monoid-extras-0.6.2 · Data.Monoid.Coproduct.Strict
(Action m n, Action m r, Action n r, Semigroup n) => Action (m :+: n) rDefined in monoid-extras-0.6.2 · Data.Monoid.Coproduct.Strict
Coproducts act on other things by having each of the components act individually.

valueinL :: m -> m :+: n

Construct a coproduct with a left value.

valueinR :: n -> m :+: n

Construct a coproduct with a right value.

valueprependL :: Semigroup m => m -> m :+: n -> m :+: n

Prepend a value from the left.

valueprependR :: Semigroup n => n -> m :+: n -> m :+: n

Prepend a value from the right.

valuekillL :: (Action m n, Monoid' n) => m :+: n -> n

Extract n from a coproduct.

valuekillR :: Monoid m => m :+: n -> m

Extract m from a coproduct.

valueuntangle :: (Action m n, Monoid m, Monoid' n) => m :+: n -> (m, n)

valueuntangled :: (Action m n, Monoid m, Monoid' n) => Lens (m :+: n) (m' :+: n') (m, n) (m', n')

Lens onto the both m and n.

value_L :: (Action m n, Monoid m, Semigroup n) => Lens (m :+: n) (m' :+: n) m m'

Lens onto the left value of a coproduct.

value_R :: (Action m n, Monoid' n) => Lens (m :+: n) (m :+: n') n n'

Lens onto the right value of a coproduct.