higherarity

Higherarity is a term used to describe the property of having a higher arity, referring to the number of inputs a function, operation, or relation accepts. Arity is typically categorized as unary (one input), binary (two inputs), ternary (three inputs), and, more generally, n-ary for n inputs. Higherarity commonly means arity greater than two, though some texts use the term more loosely to cover any arity beyond unary.

In mathematics and logic, higher-arity operations and predicates are standard. An n-ary operation f: D^n -> D takes n arguments; a k-ary relation R subset of D^k relates k elements. Ternary and higher-arity constructs appear in algebra, geometry, and computer science; examples include the ternary operator in programming languages, the majority function on three inputs, and relations like R(a,b,c) in databases or logical formulas.

In programming, higher-arity functions can be implemented directly or via currying or partial application; currying converts an n-ary function into a sequence of unary functions, enabling partial application and modular composition. Higherarity can increase expressive power but also complexity in specification, evaluation, testing, and data storage.

Notationally, n-ary and k-ary are standard terms. The adjective higher-arity emphasizes arity beyond binary, while arity itself is a fundamental attribute of functions, operators, and relations in mathematics, logic, and computer science. See also arity, unary, binary, ternary, and n-ary.