Data.Field

[auto ekmett@gmail.com**20090402045716] { addfile ./doc/html/monoids/Data-Field.html addfile ./doc/html/monoids/Data-Group-Multiplicative-Sugar.html addfile ./doc/html/monoids/Data-Group-Multiplicative.html addfile ./doc/html/monoids/src/Data-Field.html addfile ./doc/html/monoids/src/Data-Group-Multiplicative-Sugar.html addfile ./doc/html/monoids/src/Data-Group-Multiplicative.html hunk ./doc/html/monoids/Data-Field.html 1 + + +Data.Field

Data.Field

Portability	portable
Stability	experimental
Maintainer	ekmett@gmail.com

Description

Documentation

module Data.Group.Multiplicative

module Data.Ring

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

Source

Produced by Haddock version 2.3.0

hunk ./doc/html/monoids/Data-Group-Combinators.html 22 ->monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework + +Data.Group.Multiplicative.Sugar

Data.Group.Multiplicative.Sugar

Portability	portable
Stability	experimental
Maintainer	ekmett@gmail.com

Description

Syntactic sugar for working with groups that conflicts with names from the Prelude. +

 import Prelude hiding ((-), (+), (*), (/), negate, subtract, recip)
+ import Data.Group.Multiplicative.Sugar
+

Documentation

module Data.Monoid.Multiplicative.Sugar

module Data.Group.Multiplicative

module Data.Group.Sugar

(/) :: MultiplicativeGroup g => g -> g -> g

Source

(\\) :: MultiplicativeGroup g => g -> g -> g

Source

recip :: MultiplicativeGroup g => g -> g

Source

Produced by Haddock version 2.3.0

hunk ./doc/html/monoids/Data-Group-Multiplicative.html 1 + + +Data.Group.Multiplicative

Data.Group.Multiplicative

Portability	portable
Stability	experimental
Maintainer	ekmett@gmail.com

Description

Synopsis

module Data.Monoid.Multiplicative

class Multiplicative g => MultiplicativeGroup g where

over :: g -> g -> g

under :: g -> g -> g

grecip :: g -> g

over :: MultiplicativeGroup g => g -> g -> g

under :: MultiplicativeGroup g => g -> g -> g

grecip :: MultiplicativeGroup g => g -> g

Documentation

module Data.Monoid.Multiplicative

class Multiplicative g => MultiplicativeGroup g where

Source

Minimal definition over or grecip +

Methods

over :: g -> g -> g

Source

x / y

under :: g -> g -> g

Source

x  y

grecip :: g -> g

Source

over :: MultiplicativeGroup g => g -> g -> g

Source

x / y

under :: MultiplicativeGroup g => g -> g -> g

Source

x  y

grecip :: MultiplicativeGroup g => g -> g

Source

Produced by Haddock version 2.3.0

hunk ./doc/html/monoids/Data-Group-Sugar.html 22 ->monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework r m) s r m)monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkLeftSemiNearRing RightSemiNearRing a) => LeftSemiNearRing a) => RightSemiNearRingmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkLeftSemiNearRing RightSemiNearRing a) => LeftSemiNearRing a) => RightSemiNearRingmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework to yield a LeftSemiNearRing +> to yield a RightSemiNearRing hunk ./doc/html/monoids/Data-Monoid-Multiplicative.html 201 - yield a LeftSemiNearRing + yield a RightSemiNearRing hunk ./doc/html/monoids/Data-Monoid-Multiplicative.html 774 ->Module r m => Multiplicative (D r m)Module r m => Multiplicative (D s r m)monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework c r, Reducer c m) => Reducer c (D r m)(Reducer(Reducer c r, Reducer c m) => Reducer c (D s r m)monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework

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

Description r m s r m r m) s r m)Eq r => Eq (D s r m)Fractional a => Fractional (D s a a)Num a => Num (D s a a)Ord r => Ord (D s r m)(Read r, Read m) => Read (D s r m)(Show r, Show m) => Show (D s r m) r m) s r m) r m) s r m) r m) s r m) r m) s r m) r m) s r m) r m) s r m) r m) s r m) r m) s r m) r m) s r m)

d :: (Monoid r, Multiplicative m) => (forall s. D s r m -> D s r m) -> (r, m)

Source

monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkMonoid m => LeftSemiNearRing ([] m) s r m)Monoid m => RightSemiNearRing ([] m) s r m)monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework r m) s r m)monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework r m) s r m)monoids-0.1.21: Monoids, specialized containers and a general map/reduce framework (Index)monoids-0.1.22: Monoids, specialized containers and a general map/reduce framework (Index)monoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework, Data.Ring.Sugar, Data.Ring.Sugar, Data.Group.Multiplicative.Sugar, Data.Monoid.Multiplicative.Sugar, Data.Ring.Sugar, Data.Group.Sugar, Data.Monoid.Multiplicative.Sugar, Data.Ring.Sugar, Data.Group.Sugar, 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Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiationData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiationData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiationData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiationData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, 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Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Fieldrecip, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Group.Multiplicative.SugarData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiationData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiationData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Fieldmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.21: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce framework show/hide

lift :: Monoid m => r -> D s r m

Source

Monoid m => LeftSemiNearRing (Maybe m)

Monoid m => LeftSemiNearRing (Seq m)

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

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

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

r m)

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

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

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

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

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

Monoid m => RightSemiNearRing (Maybe m)

Monoid m => RightSemiNearRing (Seq m)

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

(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 n) => RightSemiNearRing (StateT s m n)

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

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)

Data.Group.Multiplicative.Sugar

Data.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation

Data.Ring.Module.AutomaticDifferentiation

Field

Data.Field

grecip

Data.Group.Multiplicative, Data.Group.Multiplicative.Sugar, Data.Field

lift

Data.Ring.Module.AutomaticDifferentiation

MultiplicativeGroup

Data.Group.Multiplicative, Data.Group.Multiplicative.Sugar, Data.Field

, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation

Data.Group.Multiplicative.Sugar

, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation

under

Data.Group.Multiplicative, Data.Group.Multiplicative.Sugar, Data.Field

Data.Group.Multiplicative.Sugar

Data.Field

Data.Group.Multiplicative

Data.Group.Multiplicative.Sugar

+ + + +Data/Field.hs + + + +

-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Field
+-- Copyright   :  (c) Edward Kmett 2009
+-- License     :  BSD-style
+-- Maintainer  :  ekmett@gmail.com
+-- Stability   :  experimental
+-- Portability :  portable
+--
+-----------------------------------------------------------------------------
+
+module Data.Field
+    ( module Data.Group.Multiplicative
+    , module Data.Ring
+    , Field
+    ) where
+
+import Data.Group.Multiplicative
+import Data.Ring
+
+class (Ring a, MultiplicativeGroup a) => Field a
+

+ hunk ./doc/html/monoids/src/Data-Group-Multiplicative-Sugar.html 1 + + + + +Data/Group/Multiplicative/Sugar.hs + + + +

-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Group.Multiplicative.Sugar
+-- Copyright   :  (c) Edward Kmett 2009
+-- License     :  BSD-style
+-- Maintainer  :  ekmett@gmail.com
+-- Stability   :  experimental
+-- Portability :  portable
+--
+-- Syntactic sugar for working with groups that conflicts with names from the "Prelude".
+--
+-- > import Prelude hiding ((-), (+), (*), (/), negate, subtract, recip)
+-- > import Data.Group.Multiplicative.Sugar
+--
+-----------------------------------------------------------------------------
+
+module Data.Group.Multiplicative.Sugar 
+    ( module Data.Monoid.Multiplicative.Sugar
+    , module Data.Group.Multiplicative
+    , module Data.Group.Sugar
+    , (/)
+    , (\\)
+    , recip
+    ) where
+
+import Data.Group.Multiplicative
+import Data.Monoid.Multiplicative.Sugar
+import Data.Group.Sugar
+import Prelude hiding ((-), (+), (*), (/), negate, subtract, recip)
+
+infixl 7 /
+infixr 7 \\
+
+(/) :: MultiplicativeGroup g => g -> g -> g
+(/) = over
+
+(\\) :: MultiplicativeGroup g => g -> g -> g
+(\\) = under
+
+recip :: MultiplicativeGroup g => g -> g
+recip = grecip
+

+ hunk ./doc/html/monoids/src/Data-Group-Multiplicative.html 1 + + + + +Data/Group/Multiplicative.hs + + + +

-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Group.Multiplicative
+-- Copyright   :  (c) Edward Kmett 2009
+-- License     :  BSD-style
+-- Maintainer  :  ekmett@gmail.com
+-- Stability   :  experimental
+-- Portability :  portable
+--
+-----------------------------------------------------------------------------
+
+module Data.Group.Multiplicative 
+    ( module Data.Monoid.Multiplicative
+    , MultiplicativeGroup
+    , over
+    , under
+    , grecip
+    ) where
+
+import Data.Monoid.Multiplicative
+    
+-- | Minimal definition over or grecip
+class Multiplicative g => MultiplicativeGroup g where
+    -- | @x / y@
+    over :: g -> g -> g
+    -- | @x \ y@
+    under :: g -> g -> g
+    grecip :: g -> g
+
+    x `under` y = grecip x `times` y
+    x `over` y = x `times` grecip y
+    grecip x = one `over` x
+

+ hunk ./doc/html/monoids/src/Data-Monoid-Applicative.html 64 --- and asserts that any 'Alternative' applied to a 'Monoid' forms a 'LeftSemiNearRing' +-- and asserts that any 'Alternative' applied to a 'Monoid' forms a 'RightSemiNearRing' hunk ./doc/html/monoids/src/Data-Monoid-Applicative.html 84 -instance(Alternativef,Monoida)=>LeftSemiNearRing(Altfa) +instance(Alternativef,Monoida)=>RightSemiNearRing(Altfa) hunk ./doc/html/monoids/src/Data-Monoid-Monad.html 67 --- and asserts that any 'MonadPlus' applied to a 'Monoid' forms a 'LeftSemiNearRing' +-- and asserts that any 'MonadPlus' applied to a 'Monoid' forms a 'RightSemiNearRing' hunk ./doc/html/monoids/src/Data-Monoid-Monad.html 94 -instance(MonadPlusm,Monoida)=>LeftSemiNearRing(MonadSumma) +instance(MonadPlusm,Monoida)=>RightSemiNearRing(MonadSumma) hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 33 --- which can be extended if the 'Monad' is a 'MonadPlus' to yield a 'LeftSemiNearRing' +-- which can be extended if the 'Monad' is a 'MonadPlus' to yield a 'RightSemiNearRing' hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 37 --- yield a 'LeftSemiNearRing' +-- yield a 'RightSemiNearRing' hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 233 - --- Numeric instances - -instanceMultiplicativeIntwhere -one=1 -times=(*) - - -instanceMultiplicativeIntegerwhere -one=1 -times=(*) - -instanceIntegralm=>Multiplicative(Ratiom)where -one=1 -times=(*) - +-- Numeric instances +instanceMultiplicativeIntwhere +one=1 +times=(*) + +instanceMultiplicativeIntegerwhere +one=1 +times=(*) + +instanceIntegralm=>Multiplicative(Ratiom)where +one=1 +times=(*) + hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 9 -

{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}
-module Data.Ring.Module.AutomaticDifferentiation 
-    ( module Data.Ring.Module
-    , D
-    ) where
-
-import Prelude hiding ((*),(+),(-),subtract,negate)
-import Data.Ring.Sugar
-import Data.Ring.Module
-import Data.Monoid.Reducer
-import Test.QuickCheck
-import Control.Monad
+{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, RankNTypes, FunctionalDependencies, UndecidableInstances, FlexibleContexts #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Ring.Module.AutomaticDifferentiation
+-- Copyright   :  (c) Edward Kmett 2009
+-- License     :  BSD-style
+-- Maintainer  :  ekmett@gmail.com
+-- Stability   :  experimental
+-- Portability :  portable (instances use MPTCs)
+--
+-----------------------------------------------------------------------------
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 22
-data D r m = D r m
-
-instance (Monoid r, Monoid m) => Monoid (D r m) where
-    mempty = D mempty mempty
-    D x m `mappend` D y n = D (x + y) (m + n)
-
-instance (Module r m) => Multiplicative (D r m) where
-    one = D one zero
-    D x m `times` D y n = D (x * y) (x *. n + m .* y)
-
-instance (Group r, Module r m, Group m) => Group (D r m) where
-    gnegate (D x m) = D (gnegate x) (gnegate m)
-    D x m `minus` D y n = D (x `minus` y) (m `minus` n)
-    D x m `gsubtract` D y n = D (x `gsubtract` y) (m `gsubtract` n)
+module Data.Ring.Module.AutomaticDifferentiation 
+    ( module Data.Ring.Module
+    , D
+    , d
+    , lift
+    ) where
+
+import Prelude
+import Data.Ring.Module
+import Data.Monoid.Reducer
+import Test.QuickCheck
+import Control.Monad
+
+data D s r m = D r m deriving (Show,Read)
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 37
-instance (LeftSemiNearRing r, Module r m) => LeftSemiNearRing (D r m)
-instance (RightSemiNearRing r, Module r m) => RightSemiNearRing (D r m)
-instance (SemiRing r, Module r m) => SemiRing (D r m)
-instance (Ring r, Module r m, Group m) => Ring (D r m)
-
-instance (c `Reducer` r, c `Reducer` m) => Reducer c (D r m) where
-    unit c = D (unit c) (unit c)
-    c `cons` D x m = D (c `cons` x) (c `cons` m)
-    D x m `snoc` c = D (x `snoc` c) (m `snoc` c)
-
-instance (Arbitrary r, Arbitrary m) => Arbitrary (D r m) where
-    arbitrary = liftM2 D arbitrary arbitrary
-    shrink (D r m) = liftM2 D (shrink r) (shrink m)
-
-instance (CoArbitrary r, CoArbitrary m) => CoArbitrary (D r m) where
-    coarbitrary (D r m) = coarbitrary r >< coarbitrary m
-
-{--
-infix 0 ><
+lift :: Monoid m => r -> D s r m
+lift x = D x zero
+
+infinitesimal :: (Monoid r, Multiplicative m) => D s r m
+infinitesimal = D zero one
+
+instance Eq r => Eq (D s r m) where
+    D x _ == D y _ = x == y
+
+instance Ord r => Ord (D s r m) where
+    D x _ `compare` D y _ = compare x y
+
+instance (Monoid r, Monoid m) => Monoid (D s r m) where
+    mempty = D mempty mempty
+    D x m `mappend` D y n = D (x `mappend` y) (m `mappend` n)
+
+instance (r `Module` m) => Multiplicative (D s r m) where
+    one = D one zero
+    D x m `times` D y n = D (x `times` y) (x *. n `plus` m .* y)
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 57
-(><) :: Multiplicatve a => (a -> a) -> (AD a -> AD a) -> AD a -> AD a
-(f >< f') a@(AD a0 a') = D (f a0) (a' * f' a)
-
-data AD r = AD r (Maybe (AD r))
+instance (Group r, r `Module` m, Group m) => Group (D s r m) where
+    gnegate (D x m) = D (gnegate x) (gnegate m)
+    D x m `minus` D y n = D (x `minus` y) (m `minus` n)
+    D x m `gsubtract` D y n = D (x `gsubtract` y) (m `gsubtract` n)
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 62
-instance (Monoid r) => Monoid (AD r) where
-    mempty = K mempty
-    AD x m + AD y n = D (x + y) (m + n)
-
-instance (c `Reducer` r) => Reducer c (AD r) where
-    unit c = c' where c' = AD (unit c) c'
---}
+instance Num a => Num (D s a a) where
+    D x x' + D y y' = D (x + y) (x' + y')
+    D x x' * D y y' = D (x * y) (x * y' + x' * y)
+    D x x' - D y y' = D (x - y) (x' - y')
+    negate (D x x') = D (negate x) (negate x')
+    abs (D x x') = D (abs x) (signum x * x')
+    signum (D x _) = D (signum x) 0
+    fromInteger x = D (fromInteger x) 0
+
+instance Fractional a => Fractional (D s a a) where
+    recip (D x x') = D (recip x) (-x'/x/x)
+    fromRational x = D (fromRational x) 0
+
+instance (LeftSemiNearRing r, Module r m) => LeftSemiNearRing (D s r m)
+instance (RightSemiNearRing r, Module r m) => RightSemiNearRing (D s r m)
+instance (SemiRing r, Module r m) => SemiRing (D s r m)
+instance (Ring r, Module r m, Group m) => Ring (D s r m)
+
+instance (c `Reducer` r, c `Reducer` m) => Reducer c (D s r m) where
+    unit c = D (unit c) (unit c)
+    c `cons` D x m = D (c `cons` x) (c `cons` m)
+    D x m `snoc` c = D (x `snoc` c) (m `snoc` c)
+
+instance (Arbitrary r, Arbitrary m) => Arbitrary (D s r m) where
+    arbitrary = liftM2 D arbitrary arbitrary
+    shrink (D r m) = liftM2 D (shrink r) (shrink m)
+
+instance (CoArbitrary r, CoArbitrary m) => CoArbitrary (D s r m) where
+    coarbitrary (D r m) = coarbitrary r >< coarbitrary m
+
+d :: (Monoid r, Multiplicative m) => (forall s. D s r m -> D s r m) -> (r,m)
+d f = (y,y') where D y y' = f infinitesimal
+
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 71
-instance (Measured v m, Monoid m) => LeftSemiNearRing (FingerTree v m)
+instance (Measured v m, Monoid m) => RightSemiNearRing (FingerTree v m)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 75
--- for 'liftM2 mappend' is a 'LeftSemiNearRing' by 'MonadPlus' left-distributivity
+-- for 'liftM2 mappend' is a 'RightSemiNearRing' by 'MonadPlus' left-distributivity
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 77
-instance Monoid m => LeftSemiNearRing [m]
+instance Monoid m => RightSemiNearRing [m]
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 79
-instance Monoid m => LeftSemiNearRing (Maybe m)
+instance Monoid m => RightSemiNearRing (Maybe m)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 81
-instance Monoid m => LeftSemiNearRing (Seq m)
+instance Monoid m => RightSemiNearRing (Seq m)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 83
-instance (Stream s m t, Monoid a) => LeftSemiNearRing (ParsecT s u m a)
+instance (Stream s m t, Monoid a) => RightSemiNearRing (ParsecT s u m a)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 85
-instance (MonadPlus m, Monoid n) => LeftSemiNearRing (SState.StateT s m n)
+instance (MonadPlus m, Monoid n) => RightSemiNearRing (SState.StateT s m n)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 87
-instance (MonadPlus m, Monoid n) => LeftSemiNearRing (LState.StateT s m n)
+instance (MonadPlus m, Monoid n) => RightSemiNearRing (LState.StateT s m n)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 89
-instance (MonadPlus m, Monoid n) => LeftSemiNearRing (ReaderT e m n)
+instance (MonadPlus m, Monoid n) => RightSemiNearRing (ReaderT e m n)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 91
-instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (SRWS.RWST r w s m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (SRWS.RWST r w s m n)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 93
-instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (LRWS.RWST r w s m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (LRWS.RWST r w s m n)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 95
-instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (SWriter.WriterT w m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (SWriter.WriterT w m n)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near.html 97
-instance (MonadPlus m, Monoid w, Monoid n) => LeftSemiNearRing (LWriter.WriterT w m n)
+instance (MonadPlus m, Monoid w, Monoid n) => RightSemiNearRing (LWriter.WriterT w m n)
hunk ./doc/html/monoids/src/Data-Ring.html 9
-{-# OPTIONS_GHC -fno-warn-orphans #-}
-{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-}
-
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Ring
--- Copyright   :  (c) Edward Kmett 2009
--- License     :  BSD-style
--- Maintainer  :  ekmett@gmail.com
--- Stability   :  experimental
--- Portability :  portable (instances use MPTCs)
---
------------------------------------------------------------------------------
-
-module Data.Ring
-    ( module Data.Group
-    , module Data.Ring.Semi
-    , Ring
-    ) where
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Ring
+-- Copyright   :  (c) Edward Kmett 2009
+-- License     :  BSD-style
+-- Maintainer  :  ekmett@gmail.com
+-- Stability   :  experimental
+-- Portability :  portable (instances use MPTCs)
+--
+-----------------------------------------------------------------------------
+
+module Data.Ring
+    ( module Data.Group
+    , module Data.Ring.Semi
+    , Ring
+    ) where
+
+import Data.Group
+import Data.Ring.Semi
hunk ./doc/html/monoids/src/Data-Ring.html 29
-import Data.Group
-import Data.Ring.Semi
-
-class (Group a, SemiRing a) => Ring a
+class (Group a, SemiRing a) => Ring a
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