CMP.2:10 - Architectural Rationale

Subproblem meaning, recombination, progress and cost belong together because changing one can force a change in the others. Starting from a recursive syntax would obscure the discovery of the required question and summary. Starting from an induction proof alone can leave the effective decomposition and cost unresolved.

MATH.4 supplies witness construction by induction; MATH.12 supplies extraction from a proof. This pattern constructs and compares recursive obtaining procedures, including decompositions that do not follow the input’s constructors. CMP.3 changes how repeated calls are evaluated without silently changing what they ask. C.29.2 retains the common computational formulation and its connection to the receiving question.