Multioperators

Multioperators are operators designed to operate on more than two operands, or on a variable-length sequence of operands. In mathematics and computer science, such operators are commonly described as n-ary operations. An n-ary operation takes exactly n inputs from a set and returns an element of the same set. When the arity is not fixed, the operator is often described as variadic or variadic-like, capable of accepting any finite number of operands.

Common examples include addition and multiplication, which extend naturally to any finite number of terms; the binary version is familiar, while expressions like a1 + a2 + ... + an or a1 × a2 × ... × an use an n-ary form. Logical conjunction and disjunction are also extended to multiple operands. Non-mathematical examples include string or array concatenation, which can take an arbitrary number of operands. In many contexts, multioperators are valued for properties such as associativity, which lets the order of grouping be irrelevant for the result in suitable cases.

Properties and formalization: For an associative multioperator, applying the operator to a sequence of operands yields the same outcome regardless of how the operands are grouped. In formal terms, an n-ary operation is a function from a Cartesian power A^n to A. A signature for an algebra may include operations of varying arities, including nullary operations, which correspond to constants.

Applications: Multioperators underpin expression simplification, variadic functions in programming languages, and parser design. They appear in data aggregation tasks such as sum, min, and max, and in various mathematical and logical formalisms. See also n-ary operation, variadic function, and associative operation.