eque

Eque is a term encountered in some theoretical discussions to denote the principle of equality among entities in a formal system. It is a neologism inspired by Latin aequus, meaning equal, and is sometimes used as a placeholder name for an equality relation in abstract expositions. Because it is not standardized, its precise interpretation varies by author, but it is usually treated as a binary relation that asserts sameness of value or identity within a given model.

In logic, eque is typically described as a relation between terms. When two terms are related by eque, they are interchangeable under all interpretations, making eque resemble definitional or strict equality in standard treatments. In type theory and programming language semantics, discussions of eque address when two expressions can be substituted for one another without changing observable behavior, though formal treatments often favor explicit equality operators.

Etymology and status: The term remains uncommon in formal literature and is rarely adopted in mainstream textbooks. It is primarily used as a linguistic or pedagogical device to discuss the intuitive notion of identity, rather than as a widely implemented construct.

See also: equality, definitional equality, identity, equivalence relation.