Copyright	(c) Henning Thielemann 2009-2010 Mikael Johansson 2006
Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability
Safe Haskell	Safe-Inferred
Language	Haskell98

Algebra.Monoid

Description

Abstract concept of a Monoid. Will be used in order to generate type classes for generic algebras. An algebra is a vector space that also is a monoid. Should we use the Monoid class from base library despite its unfortunate method name mappend?

Synopsis

class C a where
- idt :: a
- (<*>) :: a -> a -> a
- cumulate :: [a] -> a

Documentation

class C a where Source #

We expect a monoid to adher to associativity and the identity behaving decently. Nothing more, really.

Minimal complete definition

idt, (<*>)

Methods

idt :: a Source #

(<*>) :: a -> a -> a Source #

cumulate :: [a] -> a Source #

Instances

Instances details

C All Source #
Instance details Defined in Algebra.Monoid Methods idt :: All Source # (<*>) :: All -> All -> All Source # cumulate :: [All] -> All Source #
C Any Source #
Instance details Defined in Algebra.Monoid Methods idt :: Any Source # (<*>) :: Any -> Any -> Any Source # cumulate :: [Any] -> Any Source #
C T Source #
Instance details Defined in Number.Peano Methods idt :: T Source # (<*>) :: T -> T -> T Source # cumulate :: [T] -> T Source #
C (First a) Source #
Instance details Defined in Algebra.Monoid Methods idt :: First a Source # (<*>) :: First a -> First a -> First a Source # cumulate :: [First a] -> First a Source #
C (Last a) Source #
Instance details Defined in Algebra.Monoid Methods idt :: Last a Source # (<*>) :: Last a -> Last a -> Last a Source # cumulate :: [Last a] -> Last a Source #
C a => C (Dual a) Source #
Instance details Defined in Algebra.Monoid Methods idt :: Dual a Source # (<*>) :: Dual a -> Dual a -> Dual a Source # cumulate :: [Dual a] -> Dual a Source #
C (Endo a) Source #
Instance details Defined in Algebra.Monoid Methods idt :: Endo a Source # (<*>) :: Endo a -> Endo a -> Endo a Source # cumulate :: [Endo a] -> Endo a Source #
C a => C (Sum a) Source #
Instance details Defined in Algebra.Monoid Methods idt :: Sum a Source # (<*>) :: Sum a -> Sum a -> Sum a Source # cumulate :: [Sum a] -> Sum a Source #
C a => C (Product a) Source #
Instance details Defined in Algebra.Monoid Methods idt :: Product a Source # (<*>) :: Product a -> Product a -> Product a Source # cumulate :: [Product a] -> Product a Source #
C a => C (T a) Source #
Instance details Defined in Number.NonNegative Methods idt :: T a Source # (<*>) :: T a -> T a -> T a Source # cumulate :: [T a] -> T a Source #
Ord a => C (Max a) Source #
Instance details Defined in MathObj.Monoid Methods idt :: Max a Source # (<*>) :: Max a -> Max a -> Max a Source # cumulate :: [Max a] -> Max a Source #
Ord a => C (Min a) Source #
Instance details Defined in MathObj.Monoid Methods idt :: Min a Source # (<*>) :: Min a -> Min a -> Min a Source # cumulate :: [Min a] -> Min a Source #
C a => C (LCM a) Source #
Instance details Defined in MathObj.Monoid Methods idt :: LCM a Source # (<*>) :: LCM a -> LCM a -> LCM a Source # cumulate :: [LCM a] -> LCM a Source #
C a => C (GCD a) Source #
Instance details Defined in MathObj.Monoid Methods idt :: GCD a Source # (<*>) :: GCD a -> GCD a -> GCD a Source # cumulate :: [GCD a] -> GCD a Source #
C a => C (T a) Source #
Instance details Defined in Number.NonNegativeChunky Methods idt :: T a Source # (<*>) :: T a -> T a -> T a Source # cumulate :: [T a] -> T a Source #
Ix i => C (T i) Source #
Instance details Defined in MathObj.Permutation.CycleList.Check Methods idt :: T i Source # (<*>) :: T i -> T i -> T i Source # cumulate :: [T i] -> T i Source #