0ary

0ary, also written as zero-ary or nullary, is a term used in logic, mathematics, and computer science to describe an operation, function, or predicate that takes no arguments. In formal languages, such symbols are often called constants.

In logic and mathematics, a 0-ary function symbol is a constant symbol that denotes a fixed element of the domain. For example, in a language with constant symbols c and d, each of these denotes a specific element regardless of any input. A 0-ary relation, or propositional constant, is a predicate that does not depend on any variables and thus has a fixed truth value in a given interpretation; true and false can be treated as 0-ary propositions in propositional logic.

In computer science, a nullary (or zero-argument) function is a function that takes no parameters and returns a value. It is effectively a constant function, often used to compute or retrieve a value without requiring input. Some languages distinction between functions with no parameters and constants, but many treat nullary functions as functions of arity zero.

The terminology extends to data types and algebraic structures, where 0-ary operations correspond to constants within a signature. Higher arities are unary (one argument), binary (two arguments), and so on.

Related concepts include arity, unary and binary operators, and constants in formal languages. While the terms 0-ary and nullary are often interchangeable, “nullary” is more common in programming contexts, and “0-ary” is frequently used in formal logic and algebra to emphasize the lack of input.