Operandides

Operandides are a class of abstract algebraic constructs proposed to model the role of operands in binary operations within formal semantics and algebraic theories. In this framework, an operandide encapsulates the data and the structural position that an operand occupies in a fixed binary operation on a set. Each operandide carries two distinguished position markers corresponding to the left and right operands, and a rule that combines two operandides to produce a new operandide reflecting the result of applying the operation to the two inputs.

The term was introduced in theoretical literature in the early 2010s, combining the word operand with the -ide suffix to signal a distinct mathematical object that resembles an operand but behaves according to its own internal composition laws. The motivation was to separate the notion of the data carried by an operand from the structural role it plays within a given operation, enabling a uniform study of how operands are substituted and composed across different contexts.

Formally, an operandide consists of a carrier set equipped with two distinguished projection maps representing the left and right operand slots and a binary composition rule that assigns to a pair of operandides a new operandide compatible with the underlying operation. In simple cases, identity and associativity conditions translate into identity or associative properties for the operandide composition. Isomorphisms that preserve left and right positions define equivalence classes of operandides.

Applications of operandides appear mainly in niche areas of theoretical computer science and algebraic semantics, particularly in discussions of evaluation order and operand substitution. They are related to, but distinct from, standard product constructions and from operad-like frameworks that model compositional structure.

See also: operand, algebraic structure, formal semantics, operads.