Boost C++ Libraries

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

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C++ Boost

Monoid

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.

Notation

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

Invariants



Copyright © 2000-2001 Jeremy Siek, Indiana University (jsiek@osl.iu.edu)
Lie-Quan Lee, Indiana University (llee@cs.indiana.edu)
Andrew Lumsdaine, Indiana University (lums@osl.iu.edu)