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

Algebra.Monoid

Description

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

Documentation

class C a where #

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

Minimal complete definition

idt, (<*>)

Methods

idt :: a #

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

cumulate :: [a] -> a #

Instances

C All #
Methods idt :: All # (<*>) :: All -> All -> All # cumulate :: [All] -> All #
C Any #
Methods idt :: Any # (<*>) :: Any -> Any -> Any # cumulate :: [Any] -> Any #
C T #
Methods idt :: T # (<*>) :: T -> T -> T # cumulate :: [T] -> T #
C a => C (Dual a) #
Methods idt :: Dual a # (<*>) :: Dual a -> Dual a -> Dual a # cumulate :: [Dual a] -> Dual a #
C (Endo a) #
Methods idt :: Endo a # (<*>) :: Endo a -> Endo a -> Endo a # cumulate :: [Endo a] -> Endo a #
C a => C (Sum a) #
Methods idt :: Sum a # (<*>) :: Sum a -> Sum a -> Sum a # cumulate :: [Sum a] -> Sum a #
C a => C (Product a) #
Methods idt :: Product a # (<*>) :: Product a -> Product a -> Product a # cumulate :: [Product a] -> Product a #
C (First a) #
Methods idt :: First a # (<*>) :: First a -> First a -> First a # cumulate :: [First a] -> First a #
C (Last a) #
Methods idt :: Last a # (<*>) :: Last a -> Last a -> Last a # cumulate :: [Last a] -> Last a #
Ord a => C (Max a) #
Methods idt :: Max a # (<*>) :: Max a -> Max a -> Max a # cumulate :: [Max a] -> Max a #
Ord a => C (Min a) #
Methods idt :: Min a # (<*>) :: Min a -> Min a -> Min a # cumulate :: [Min a] -> Min a #
C a => C (LCM a) #
Methods idt :: LCM a # (<*>) :: LCM a -> LCM a -> LCM a # cumulate :: [LCM a] -> LCM a #
C a => C (GCD a) #
Methods idt :: GCD a # (<*>) :: GCD a -> GCD a -> GCD a # cumulate :: [GCD a] -> GCD a #
C a => C (T a) #
Methods idt :: T a # (<*>) :: T a -> T a -> T a # cumulate :: [T a] -> T a #
Ix i => C (T i) #
Methods idt :: T i # (<*>) :: T i -> T i -> T i # cumulate :: [T i] -> T i #