Data.Ring

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.Group

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

class Ringoid m => LeftSemiNearRing m

class Ringoid m => RightSemiNearRing m

class (RightSemiNearRing a, LeftSemiNearRing a) => SemiRing a

class (Group a, SemiRing a) => Ring a

class (Ring a, MultiplicativeGroup a) => DivisionRing a

class (Ring a, MultiplicativeGroup a) => Field a

Documentation

module Data.Group

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

Source

0 annihilates times

Instances

Ringoid Int

Ringoid Integer

Ringoid Natural

Monoid m => Ringoid ([] m)

Monoid m => Ringoid (Maybe m)

Ringoid m => Ringoid (Dual m)

Ringoid m => Ringoid (Self m)

Ringoid m => Ringoid (FromString m)

Num a => Ringoid (FromNum a)

Bits a => Ringoid (Boolean a)

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

Ord a => Ringoid (Priority a)

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

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

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

Ringoid m => Ringoid (ReducedBy m s)

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

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

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

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

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

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

(Ringoid r, Bimodule r m) => Ringoid (D s r m)

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

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

class Ringoid m => LeftSemiNearRing m

Source

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

Instances

LeftSemiNearRing Natural

RightSemiNearRing m => LeftSemiNearRing (Dual m)

LeftSemiNearRing m => LeftSemiNearRing (Self m)

LeftSemiNearRing m => LeftSemiNearRing (FromString m)

Num a => LeftSemiNearRing (FromNum a)

Bits a => LeftSemiNearRing (Boolean a)

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

Ord a => LeftSemiNearRing (Priority a)

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

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

LeftSemiNearRing m => LeftSemiNearRing (ReducedBy m s)

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

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

class Ringoid m => RightSemiNearRing m

Source

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

Instances

RightSemiNearRing Natural

Monoid m => RightSemiNearRing ([] m)

Monoid m => RightSemiNearRing (Maybe m)

LeftSemiNearRing m => RightSemiNearRing (Dual m)

RightSemiNearRing m => RightSemiNearRing (Self m)

RightSemiNearRing m => RightSemiNearRing (FromString m)

Num a => RightSemiNearRing (FromNum a)

Bits a => RightSemiNearRing (Boolean a)

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

Ord a => RightSemiNearRing (Priority a)

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

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

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

RightSemiNearRing m => RightSemiNearRing (ReducedBy m s)

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

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

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

(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 (ReaderT e m n)

(RightSemiNearRing r, Bimodule 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)

class (RightSemiNearRing a, LeftSemiNearRing a) => SemiRing a

Source

A SemiRing is an instance of both Multiplicative and Monoid where times distributes over plus.

Instances

SemiRing Natural

SemiRing r => SemiRing (Dual r)

SemiRing r => SemiRing (Self r)

SemiRing r => SemiRing (FromString r)

Num a => SemiRing (FromNum a)

Bits a => SemiRing (Boolean a)

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

Ord a => SemiRing (Priority a)

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

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

SemiRing r => SemiRing (ReducedBy r s)

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

(SemiRing r, Bimodule r m) => SemiRing (D s r m)

class (Group a, SemiRing a) => Ring a

Source

Instances

Ring r => Ring (Dual r)

Ring r => Ring (Self r)

Ring r => Ring (FromString r)

Num a => Ring (FromNum a)

Bits a => Ring (Boolean a)

Ring r => Ring (ReducedBy r s)

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

(Ring r, Bimodule r m, Group m) => Ring (D s r m)

class (Ring a, MultiplicativeGroup a) => DivisionRing a

Source

Instances

DivisionRing r => DivisionRing (Dual r)

DivisionRing r => DivisionRing (Self r)

DivisionRing r => DivisionRing (FromString r)

DivisionRing r => DivisionRing (ReducedBy r s)

class (Ring a, MultiplicativeGroup a) => Field a

Source

Instances

Field f => Field (Dual f)

Field f => Field (Self f)

Field f => Field (FromString f)

Field f => Field (ReducedBy f s)

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