MATH.1:4.4 - Use the path at the needed level

Return the path that answers the immediate composition question, or the formation and composition rules when the receiving work needs a reusable family.

If each generator has a supplied additive cost, obtain a path’s cost by adding the costs of its generators; the empty path has cost zero. Keep the path as well when the receiver needs to execute it or inspect why it is available. Two paths with the same cost can contain different generators.

If a representation hides an intermediate object, test the attempted composition that made the distinction matter. Refine the objects or retain the paths until the subsequent operation is well defined. MATH.2 constructs an identification that preserves selected operations; it can later reduce the structure deliberately.

An interpretation can associate generators with transformations in another setting. The mathematical path then specifies their composition. Whether those transformations are available and adequate in that setting is the application’s question, using such common methods as FPF C.29 and B.5.MPC.

Stop when the receiving question has a permitted path, a reusable construction, or a specific failed connection. Constructing every possible path or proving an unchanged concatenation law again adds no result to that use.