equivalenceinstances
Equivalenceinstances is a term used in mathematics and computer science to refer to instances of an equivalence relation on a given domain. An equivalence relation E on a set A satisfies reflexivity (aEa for all a), symmetry (if aEb then bEa), and transitivity (if aEb and bEc then aEc). The collection of all related pairs forms a partition of A into equivalence classes, known as the E-classes. This concept appears in discussions of normalization, data deduplication, and formal methods where a consistent notion of indiscernibility is required.
In type theory and programming, an equivalence instance is a decision procedure or a setoid that provides
One can construct quotient structures using equivalence instances, forming A modulo E, denoted A/E, whose elements
Equivalence closures are often used to generate an equivalence instance from a given relation R by taking
Examples include the relation of congruence modulo n on integers, logical equivalence on formulas, and bisimilarity