aridades

Aridades, or arity, is the property of a function, operation, predicate, or verb that specifies the number of arguments it takes. In formal contexts, arity is a fixed attribute: a function f: X1 × X2 × ... × Xn → Y has arity n. A 0-ary function is a constant; a unary function takes one input; a binary function takes two; higher arities exist (ternary, quaternary, etc.).

In programming and logic, arity helps define the structure of expressions and computations. Some functions have fixed arity, while others are variadic or polyadic, able to accept a variable number of arguments. Variadic operations are common for summing an arbitrary list of numbers or printing values; some languages support techniques like currying to transform an n-ary function into a sequence of unary functions.

In linguistics, arity (often linked to valency) describes how many arguments a verb or predicate requires in its semantic and syntactic structure. Monadic (one participant), dyadic (two), and triadic (three) are common terms. A transitive verb has two core participants (subject and object); a ditransitive verb has three (subject, indirect object, direct object). The concept extends to other predicates and, in some frameworks, to how different syntactic arguments are realized and labeled with semantic roles such as agent, patient, or recipient.

Across disciplines, arity provides a concise way to express how many inputs are essential for a given operator, function, or predicate to constitute a complete, meaningful unit.