Arity

In logic, mathematics, and computer science, the arity i/ˈærɨti/ of a function or operation is the number of arguments or operands that the function takes. The arity of a relation is the dimension of the domain in the corresponding Cartesian product. The term springs from such words as unary, binary, ternary, etc.

The term "arity" is primarily used with reference to functions of the form f : V → S, where V ⊂ Sn, and S is some set. Such a function is often called an operation on S, and n is its arity.

The logarithm function has an argument and a base: log_b(N). Arities greater than 3 are seldom encountered except in theoretical computer science. In computer programming, there is often a syntactical distinction between operators and functions; syntactical operators usually have arity 0, 1, or 2. Functions vary widely in the number of arguments, though large numbers can become unwieldy.

In mathematics, depending on the branch, arity may be called type, adicity, or rank.

In computer science, arity may be called adicity, a function that takes a variable number of arguments being called variadic. Unary functions may also be called "monadic"; similarly, binary functions may be called "dyadic".

In linguistics and in logic, arity is sometimes called valency, not to be confused with valency in graph theory.