MATH.17:10 - Architectural Rationale

Separating membership, closure and higher-order transformation locates three different sources of failure. Combining them into a generic instruction to “check composition” would leave the repair unclear.

MATH.16 supplies the function-object construction. Here the practitioner selects a collection of allowable operations and constructs further operations whose arguments are members of that collection. Monoid and category language make the established composition reusable; the derivative example shows why other higher-order operations need other laws. The choice follows the problem about rules.

The same structure can support mathematical work, computational transformations and mathematical accounts of methods. Its applicability in the latter two depends on the interpretation of operations and consequences, which remains the responsibility of the receiving method.