CMP.3:4.5 - Recover the value, witness or continuation actually requested

For each return, ask what the recipient must obtain. A dynamic program may return only an optimum value, one attaining sequence of choices, a count, or all attaining sequences. Store a selected predecessor when one witness is required, retain all relevant alternatives when their multiplicity matters, or provide an additional reconstruction procedure.

A small table is not automatically a complete answer. Sometimes an extra pass or a recursive split reconstructs a witness using less storage than retaining all predecessors. Include that work in the cost comparison.

When inputs or requirements change, identify the affected dependencies. Invalidate or recompute their consumers, or show that the changed information cannot alter those results. Choose the simplest reuse boundary that pays for itself; rebuilding a small calculation can be cheaper than maintaining fine-grained dependencies.