First-class citizen

https://en.wikipedia.org/wiki/Functional_programming

https://en.wikipedia.org/wiki/First-class_citizen

In programming language design, a first-class citizen (also type, object, entity, or value) in a given programming language is an entity which supports all the operations generally available to other entities. These operations typically include being passed as an argument, returned from a function, modified, and assigned to a variable.^[1]

First-class and higher-order functions[edit]

Main articles: First-class function and Higher-order function

Higher-order functions are functions that can either take other functions as arguments or return them as results. In calculus, an example of a higher-order function is the differential operator ddx, which returns the derivative of a function f.

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" is a computer science term that describes programming language entities that have no restriction on their use (thus first-class functions can appear anywhere in the program that other first-class entities like numbers can, including as arguments to other functions and as their return values).

Higher-order functions enable partial application or currying, a technique in which a function is applied to its arguments one at a time, with each application returning a new function that accepts the next argument. This allows one to succinctly express, for example, the successor function as the addition operator partially applied to the natural number one.

Many programming languages support passing and returning function values, which can be applied to arguments. Whether this suffices to call function values first-class is disputed.

Some authors require it be possible to create new functions at runtime to call them 'first-class'. As a result, functions in C are not first-class objects; instead, they are sometimes called second-class objects, because they can still be manipulated in most of the above fashions (via function pointers).

In Smalltalk, functions (methods) are first-class objects, just like Smalltalk classes. Since Smalltalk operators (+, -, etc.) are methods, they are also first-class objects.