arity

Arity is a term used in mathematics, logic, and computer science to designate the number of arguments or operands that a function, operation, or relation takes. The word derives from French arité, ultimately from Latin aritas, and is used to classify expressions by their input requirements.

In mathematics and logic, the arity of a function is the number of inputs it consumes; a k-ary relation relates k elements. Unary operations take one operand, binary take two, ternary take three, and so on. Many standard operations are fixed-arity, such as unary negation and binary addition. Some operators are variadic or n-ary, taking an arbitrary number of arguments, such as summation over a list or logical conjunction over a set of propositions.

In programming, arity refers to the number of parameters a function or method expects. Most languages support fixed-arity functions or variadic functions; examples include C's varargs, Python's *args, and JavaScript's rest parameters. Some languages support currying and partial application to convert a function of several arguments into a sequence of unary functions, while others enforce explicit arity at declaration and do not provide built-in partial application.

In databases, a relation's arity is the number of attributes (columns) in that relation. Arity concepts help describe the structural complexity of mathematical objects, programming interfaces, and data schemas, and they influence how operations are composed and applied across disciplines.