Canonical Form: Why Choose One Representative for Equivalent Expressions?

One half may be written as 1/2, 2/4 or 50/100. These fractions have the same value but different strings. A canonical form selects one agreed representative from a set of equivalent expressions by a clear rule—for example, reducing a fraction so that its numerator and denominator are coprime and its denominator is positive. Comparison then becomes simpler: convert both expressions, and matching results identify the same equivalence class.

This differs from normalisation. Normalisation often gives one fact an authoritative home so that it is not stored repeatedly; canonical form deals with several expressions of the same object. Nor does it make one spelling more real. It supplies a stable basis for search, caching and deduplication. If the rule does not produce a unique result, or the conversion changes the meaning, it is not doing the required job. Its value is not to erase difference, but to set aside differences in expression that do not matter to the question at hand.