Data.Monoid.Multiplicative

When dealing with a Ring or other structure, you often need a pair of Monoid instances that are closely related. Making a newtype for one is unsatisfying and yields an unnatural programming style.

A Multiplicative is a Monoid that is intended for use in a scenario that can be extended to have another Monoid slot in for addition. This enables one to use common notation.

Any Multiplicative can be turned into a Monoid using the Log wrapper.

Any Monoid can be turned into a Multiplicative using the Exp wrapper.

Instances are supplied for common Monads of Monoids, in a fashion which can be extended if the Monad is a MonadPlus to yield a RightSemiNearRing

Instances are also supplied for common Applicatives of Monoids, in a fashion which can be extended if the Applicative is Alternative to yield a RightSemiNearRing

Documentation

class Multiplicative m where

Methods

one :: m

times :: m -> m -> m

Instances

Multiplicative Int

Multiplicative Integer

Monoid m => Multiplicative [m]

Integral m => Multiplicative (Ratio m)

Monoid n => Multiplicative (IO n)

Monoid n => Multiplicative (ZipList n)

Multiplicative m => Multiplicative (Dual m)

Monoid m => Multiplicative (Maybe m)

Monoid m => Multiplicative (Seq m)

Multiplicative m => Multiplicative (Self m)

Monoid m => Multiplicative (Exp m)

Monoid m => Multiplicative (Const m a)

(Measured v m, Monoid m) => Multiplicative (FingerTree v m)

(Applicative f, Monoid a) => Multiplicative (Alt f a)

(Monad m, Monoid a) => Multiplicative (MonadSum m a)

Multiplicative to Monoid

data Log m

Convert a Multiplicative into a Monoid. Mnemonic: Log a + Log b = Log (a * b)

Constructors

Log

Fields

getLog :: m

Instances

Multiplicative m => Monoid (Log m)

MultiplicativeGroup g => Group (Log g)

Monoid to Multiplicative

data Exp m

Convert a Monoid into a Multiplicative. Mnemonic: Exp a * Exp b = Exp (a + b)

Constructors

Exp

Fields

getExp :: m

Instances

Monoid m => Multiplicative (Exp m)

Group g => MultiplicativeGroup (Exp g)