Data.Ring.Semi.Near

monoids-0.1.31: Monoids, specialized containers and a general map/reduce framework

Data.Ring.Semi.Near

Portability	portable (instances use MPTCs)
Stability	experimental
Maintainer	ekmett@gmail.com

Description

Defines left- and right- seminearrings. Every MonadPlus wrapped around a Monoid qualifies due to the distributivity of (>>=) over mplus.

See http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WordNumbers1/

Synopsis

module Data.Monoid.Multiplicative

class (Multiplicative m, Monoid m) => LeftSemiNearRing m

class (Multiplicative m, Monoid m) => RightSemiNearRing m

Documentation

module Data.Monoid.Multiplicative

class (Multiplicative m, Monoid m) => LeftSemiNearRing m

a * (b + c) = (a * b) + (a * c)

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Instances

LeftSemiNearRing BoolRing

LeftSemiNearRing Natural

RightSemiNearRing m => LeftSemiNearRing (Dual m)

LeftSemiNearRing m => LeftSemiNearRing (Self m)

LeftSemiNearRing m => LeftSemiNearRing (FromString m)

Ord a => LeftSemiNearRing (Priority a)

(Bounded a, Ord a) => LeftSemiNearRing (Order a)

(Ord a, Num a) => LeftSemiNearRing (Tropical a)

Num a => LeftSemiNearRing (FromNum a)

(Bounded a, Enum a) => LeftSemiNearRing (BitSet a)

LeftSemiNearRing m => LeftSemiNearRing (ReducedBy m s)

(Modular s a, Integral a) => LeftSemiNearRing (Mod a s)

(LeftSemiNearRing r, Module r m) => LeftSemiNearRing (D s r m)

class (Multiplicative m, Monoid m) => RightSemiNearRing m

(a + b) * c = (a * c) + (b * c)

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Instances

RightSemiNearRing BoolRing

RightSemiNearRing Natural

Monoid m => RightSemiNearRing ([] m)

Monoid m => RightSemiNearRing (Maybe m)

LeftSemiNearRing m => RightSemiNearRing (Dual m)

Monoid m => RightSemiNearRing (Seq m)

RightSemiNearRing m => RightSemiNearRing (Self m)

RightSemiNearRing m => RightSemiNearRing (FromString m)

Ord a => RightSemiNearRing (Priority a)

(Bounded a, Ord a) => RightSemiNearRing (Order a)

(Ord a, Num a) => RightSemiNearRing (Tropical a)

Num a => RightSemiNearRing (FromNum a)

(Bounded a, Enum a) => RightSemiNearRing (BitSet a)

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

RightSemiNearRing m => RightSemiNearRing (ReducedBy m s)

(Modular s a, Integral a) => RightSemiNearRing (Mod a s)

(Alternative f, Monoid a) => RightSemiNearRing (Alt f a)

(MonadPlus m, Monoid a) => RightSemiNearRing (MonadSum m a)

(MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (WriterT w m n)

(MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (WriterT w m n)

(MonadPlus m, Monoid n) => RightSemiNearRing (StateT s m n)

(MonadPlus m, Monoid n) => RightSemiNearRing (StateT s m n)

(MonadPlus m, Monoid n) => RightSemiNearRing (ReaderT e m n)

(RightSemiNearRing r, Module r m) => RightSemiNearRing (D s r m)

(Stream s m t, Monoid a) => RightSemiNearRing (ParsecT s u m a)

(MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (RWST r w s m n)

(MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (RWST r w s m n)

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