NOT.4:10 - Architectural Rationale

Transformation rules are operations on expressions with an interpretation. Their useful content includes both the replacement and the conditions under which it preserves the relevant consequence. This is why a copied shape or a familiar equality alone is insufficient.

Mathematical construction and computational realization supply different contributions. MATH.17/.18 establishes laws for the transformed operations and interpretations; CMP.12 makes a translation or evaluator effective. The present method constructs a notation-level manipulation for an intended reading or edit. It can be used manually, in an editor or in an automated transformation without identifying those implementations with one another.

The retained observation determines the strength of the rule. Identifying expressions by the same value can discard a derivation, evaluation order or history that another use needs. Selecting that equivalence and respecting it in surrounding constructions makes the limitation explicit. A richer needed result calls for a richer interpretation or another retained form.