CMP.3:4.2 - Define reuse by the answer the continuation needs

Choose a representation of subproblem identity, often called a key. Equal keys must imply interchangeable answers for the intended continuation. The key can contain input values, an immutable object’s identity, a data revision, parameters and relevant assumptions. A cache local to one fixed computation may keep some of these implicit in its scope.

MATH.2 supplies the reasoning behind an identification: the operation used after identification must give the same required result whichever representative was used. An implementation also needs an effective way to recognize the keys. A hash narrows candidates; resolve collisions before treating different data as identical.

Distinguish completed answers from computations that have merely begun. Reading an unfinished entry as a result can introduce circular reasoning. In parallel evaluation, decide whether repeated demand waits for one producer or safely computes another copy; preserve the meaning of completion in either case.

For an operation with effects, state what reuse preserves. Replacing two reads of a changing sensor by one stored reading changes the observation sequence. Repeating a random draw and reusing one sample changes dependence. Sharing a pure calculation on an already obtained reading or sample can be valid. Select the intended operation before choosing the reuse rule.