Boost C++ Libraries of the most highly regarded and expertly designed C++ library projects in the world. Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

Click here to view the latest version of this page.
C++ Boost


A Monoid is a concept that describes a simple kind of algebraic system. A monoid consists of a set of elements S, a binary operation, and an identity element. The C++ representation of a monoid consists of a function object that implements the binary operation, a set of objects that represent the elements of S, and an object that represents the identity element.

Refinement of

The element type must be a model of Assignable and CopyConstructible. The function object type must be a model of BinaryFunction.


X Is the element type of the Monoid.
a, b are objects of type X.
op Is the function object implementing the Monoid operation.
i is an object of type X and is the identity element for the Monoid.

Valid Expressions

op(a, b) See below for semantics.
Return type: X
a == b Returns true if a and b represent the same element of S.
Return type: bool
a != b Returns true if a and b represent different elements of S.
Return type: bool


Copyright © 2000-2001 Jeremy Siek, Indiana University (
Lie-Quan Lee, Indiana University (
Andrew Lumsdaine, Indiana University (