Equalvalue

Equalvalue is a term used in mathematics and computer science to denote that two values are considered identical in terms of their evaluated outcome within a given domain or formal system. It emphasizes semantic equality, ignoring differences in representation, type, or structure when a suitable equality relation is defined.

In formal terms, equalvalue is defined by an equivalence relation E on a set D. For elements a and b in D, equalvalue(a,b) holds if E(a,b) is true. In programming, equalvalue is often implemented as a comparator function that returns true when two inputs are equal under a chosen notion of equality, possibly with normalization, tolerance, or type handling.

Value equality is distinct from reference equality, which considers two values equal only if they refer to the same object or memory location. Depending on the domain, equalvalue may or may not apply type coercion and may incorporate numeric tolerance, canonicalization, or structural normalization.

Examples include: in arithmetic, 2+2 and 4 have equalvalue under standard numeric equality; in strings, "04" and "4" are not equalvalue unless a normalization step converts them to a common representation; in floating point, 0.1+0.2 and 0.3 may be treated as equalvalue within a specified tolerance.

Applications of equalvalue include data deduplication, database key equivalence, testing frameworks that check semantic results, and formal verification where a robust notion of value equivalence is needed.

See also: equality relation, equivalence relation, strict equality, deep equality, normalization, type coercion, tolerance.