Data.Semigroup.Act

Documentation

class Semigroup g => SemigroupAct g a where

Represents an action of semigroup g to set a.

Laws: Endo . act must be a homomorphism of semigroups.

Methods

act :: g -> a -> a

Instances

(Semigroup (Sum n), Bounded a, Enum a, Integral n) => SemigroupAct (Sum n) (EnumBoundedIntAct a)

(Semigroup (Sum n), Integral n, Enum a) => SemigroupAct (Sum n) (EnumIntAct a)

(Semigroup (Product n), Monoid w, Whole n) => SemigroupAct (Product n) (Repeat w)

The implementation uses times1p which is defined very efficiently for most semigroups.

(Semigroup (SelfAct g), Semigroup g) => SemigroupAct (SelfAct g) (SelfAct g)

(Semigroup (Option g), SemigroupAct g a, Semigroup g) => SemigroupAct (Option g) (OptionSet g a)

class (Monoid g, SemigroupAct g a) => MonoidAct g a

Represents an action of monoid g to set a.

Laws: Endo . act must be a homomorphism of monoids.

Instances

(Monoid (SelfAct g), SemigroupAct (SelfAct g) (SelfAct g), Semigroup g, Monoid g) => MonoidAct (SelfAct g) (SelfAct g)

(Monoid (Option g), SemigroupAct (Option g) (OptionSet g a), SemigroupAct g a, Monoid g) => MonoidAct (Option g) (OptionSet g a)

newtype OptionSet g a

A wrapper for constructing a monoid action from Option.

Constructors

OptionSet

Fields

getOptionSet :: a

Instances

(Monoid (Option g), SemigroupAct (Option g) (OptionSet g a), SemigroupAct g a, Monoid g) => MonoidAct (Option g) (OptionSet g a)

(Semigroup (Option g), SemigroupAct g a, Semigroup g) => SemigroupAct (Option g) (OptionSet g a)

newtype SelfAct a

A wrapper for a group acting on itself.

Constructors

SelfAct a

Instances

Functor SelfAct

Eq a => Eq (SelfAct a)

(Eq (SelfAct a), Ord a) => Ord (SelfAct a)

Read a => Read (SelfAct a)

Show a => Show (SelfAct a)

Monoid g => Monoid (SelfAct g)

Semigroup g => Semigroup (SelfAct g)

(Monoid (SelfAct g), SemigroupAct (SelfAct g) (SelfAct g), Semigroup g, Monoid g) => MonoidAct (SelfAct g) (SelfAct g)

(Semigroup (SelfAct g), Semigroup g) => SemigroupAct (SelfAct g) (SelfAct g)

newtype Repeat a

A wrapper for represeting the action of natural numbers with multiplication on a monoid.

Constructors

Repeat

Fields

unwrapRepeat :: a

Instances

Functor Repeat

Eq a => Eq (Repeat a)

(Eq (Repeat a), Ord a) => Ord (Repeat a)

Read a => Read (Repeat a)

Show a => Show (Repeat a)

(Semigroup (Product n), Monoid w, Whole n) => SemigroupAct (Product n) (Repeat w)

The implementation uses times1p which is defined very efficiently for most semigroups.