Functional programming paradigm key terms

Domain

The set from which a function's input values are chosen; in f: A → B, it is A.

Co-domain

The set from which a function's output values are chosen; in f: A → B, it is B. Not every co-domain member needs to be an output.

First-class object

An object that may appear in expressions, be assigned to a variable, be assigned as an argument, or be returned in a function call.

First-class function

A function treated as a first-class object, so it can be passed as an argument to another function and returned as the result of a function call.

Function application

The process of giving particular inputs to a function.

Cartesian product

The product of two sets; integer x integer is the Cartesian product of the set integer with itself and represents pairs of integers.

Partial function application

Applying fewer arguments than a function requires, producing another function that accepts the remaining arguments.

Function type notation

Notation using arrows to show the sequence of argument types and the final result type, such as integer → integer → integer.

Composition of functions

An operation that combines two functions to create a new function by applying one function and then applying the other to its result.

Co-domain

The set identified as the possible output set of a function; for f: A → B, B is the co-domain.