MATH.23:4.1 - Recover what makes the starting construction work

Write the inputs and the operations that produce the result. Identify a relation the result satisfies and where that relation is used. Separate what has been proved from what has only occurred in inspected cases.

Look inside the operation. Repeated updates may expose a recurrence. Combining two constructions may expose closure or an order dependence. A successful quotient may reveal which distinctions can be discarded. MATH.17 helps make the operations themselves available for this investigation.

When a program supplies examples, recover the class it actually generates. For instance, a generator that produces only trees cannot investigate a claim about arbitrary graphs unless the missing graph classes are handled elsewhere. The representation and evaluator are part of the available mathematical experiment.