CMP.2:1 - Problem frame

Use this when you can state the answer required from a finite input, but a procedure for obtaining it is missing or unaffordable. Parts of the task resemble the whole, or a transformation produces another instance whose answer could help. You need to choose those subproblems and determine what they must return.

An engineer, researcher or AI agent may recognize a recursive formula yet be unable to turn an unfamiliar problem into one. A common difficulty appears at recombination: each part returns a correct answer to its own question, but those answers omit information needed for the whole. Another appears at progress: a call changes its input without bringing computation closer to a return.

The gain is a recursive procedure with usable base cases, a reason its calls return, a justified way of combining their results and an initial account of its cost. The reader needs to follow finite case distinctions, functions and a simple inductive argument. MATH.4 can supply that argument; C.29.2 supplies the relation between a computational answer and the question it is meant to settle.

Use a suitable existing procedure directly when it already answers the question within the available resources. This method develops recursion for obtaining a finite answer. A server, stream or other intentionally continuing process needs a progress condition appropriate to that behavior.