algebra::Monoid< Operation, Element > Struct Template Reference
[Concepts]

Concept Monoid. More...

#include <algebraic_concepts.hpp>

Inherits SemiGroup< Operation, Element >.

Collaboration diagram for algebra::Monoid< Operation, Element >:

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List of all members.

Public Types
typedef associated_type	identity_result_type
	Associated type; if not defined in concept_map automatically detected as result of identity.
Public Member Functions
identity_result_type	identity (Operation, Element)
	Identity element of Operation.

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Detailed Description

template<typename Operation, typename Element>
struct algebra::Monoid< Operation, Element >

Concept Monoid.

Parameters:

	Operation	A functor implementing a binary operation
	Element	The type upon the binary operation is defined

Refinement of:

• SemiGroup

Notation:

op	Object of type Operation
x	Object of type Element

Invariant:

Neutrality from right	op( x, identity(op, x) ) == x
Neutrality from left	op( identity(op, x), x ) == x

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The documentation for this struct was generated from the following file:

• algebraic_concepts.hpp