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The C++ Standard Library provides base classes unary_function and binary_function to simplify the definition of adaptable unary functions and adaptable binary functions. Adaptable function objects are important, because they can be used by function object adaptors: function objects that transform or manipulate other function objects.
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C++11 allowed lambda functions to deduce the return type based on the type of the expression given to the return statement. C++14 provides this ability to all functions. It also extends these facilities to lambda functions, allowing return type deduction for functions that are not of the form return expression;.
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.
A function's identity is based on its implementation. A lambda calculus function (or term) is an implementation of a mathematical function. In the lambda calculus there are a number of combinators (implementations) that satisfy the mathematical definition of a fixed-point combinator.
The term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
This definition recognizes a lambda abstraction with an actual parameter as defining a function. Only lambda abstractions without an application are treated as anonymous functions. lambda-named A named function. An expression like (.) where M is lambda free and N is lambda free or an anonymous function.