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In computer science, function composition is an act or mechanism to combine simple functions to build more complicated ones. Like the usual composition of functions in mathematics, the result of each function is passed as the argument of the next, and the result of the last one is the result of the whole.
The composition of functions is a special case of the composition of relations, sometimes also denoted by . As a result, all properties of composition of relations are true of composition of functions, [2] such as associativity.
Composition over inheritance (or composite reuse principle) in object-oriented programming (OOP) is the principle that classes should favor polymorphic behavior and code reuse by their composition (by containing instances of other classes that implement the desired functionality) over inheritance from a base or parent class. [2]
The C++ Standard Library provides many different function object adaptors, including unary_negate (that returns the logical complement of the value returned by a particular adaptable predicate), and unary_compose and binary_compose, which perform composition of function object.
Higher-order functions are closely related to first-class functions in that higher-order functions and first-class functions both allow functions as arguments and results of other functions. The distinction between the two is subtle: "higher-order" describes a mathematical concept of functions that operate on other functions, while "first-class ...
Composition of functors is associative where defined. Identity of composition of functors is the identity functor. This shows that functors can be considered as morphisms in categories of categories, for example in the category of small categories .
In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure), returns a function or value as its result. All other functions are first-order functions.
A function definition starts with the name of the type of value that it returns or void to indicate that it does not return a value. This is followed by the function name, formal arguments in parentheses, and body lines in braces. In C++, a function declared in a class (as non-static) is called a member function or method.