CMP.Preface:5 - Use checks, assumptions and recurring failures
The worked cases use small inputs and explicit operations so that a reader can reconstruct the method and change a premise. A physical machine can provide different arithmetic, atomicity or memory behavior. An empirical data source can violate the probability or feedback assumptions used by an algorithmic argument. Carry those requirements to the appropriate implementation or subject inquiry when they matter to use.
For a combination of methods, check the following substantive questions:
- Does the original question require a value, a witness, complete enumeration, an approximation or a continuing behavior?
- Can each contribution actually obtain what the next one consumes, under the same input, meaning and resource conditions?
- What is retained or discarded by sharing, compression, relaxation, sampling, learning or translation, and can that change the requested answer?
- Which argument covers correctness and which covers termination or continuing progress? Are their operations and assumptions available in this setting?
- When a condition changes, which dependent conclusion must be revised and which earlier work remains useful?
Use the relevant body’s checks where its operation enters; an unchanged supplier need not be rederived. Whole-computation costs can include simultaneously retained tables, repeated conversions or shared communication, even when each local operation is affordable.
| Failure invited by the construction | Practical correction |
|---|---|
| Memoization identifies calls by visible arguments while ignoring changing state or effects | Include the consequential context or avoid that reuse. |
| An optimum value is taken to supply every optimal witness | Preserve or reconstruct every required choice; account for output size. |
| Local improvement or training fit is treated as a guarantee about a different target | Recover the actual neighborhood, feedback and performance claim. |
| A stationary sampling law is treated as a finite-run independent sample | Establish the finite-run distribution or use an applicable dependence bound. |
| A translation or composition is checked only by its final value | Include the intermediate observations, failures and progress on which its context relies. |
| A model-specific limit is treated as an unrestricted impossibility | State the access and cost model, error and input promises, then examine which change escapes the bound. |
Being able to repeat a trace is useful preparation but leaves transfer to be tried. Ask the learner or assisting agent to change an input promise, required output or execution rule and recover the affected construction. Human learning, an AI agent’s immediate performance and a learned rule’s statistical generalization are different capability questions; their assessment should fit the intended work.