Eager, lazy, and other executions for predicative programming
Bibliographic record
Abstract
Many programs are executed according to the conventional, eager execution order, for which verification of execution costs is well-understood. However, there are other execution orders in use. One such order in common use is lazy execution or lazy evaluation, which is mostly demanddriven. Laziness supports better decompositions of algorithms, e.g., into modular producers and consumers, which enables compositional reasoning of answer correctness, but then timing correctness is more elusive. This thesis gives a formal method for verifying lazy timing, compositional with respect to program structure; it is an extension of a predicative programming theory. Predicative programming theories are formal methods that unify both specifications and programs as predicates or boolean-typed expressions over memory state and other quantities of interest. Their strengths are mathematical simplicity and support of program development and verification by incremental refinements. Among these theories, Hehner’s a Practical Theory of Programming has the further strength of leaving termination and timing open rather than a built-in, and therefore is a flexible substrate for various timing schemes corresponding to various execution strategies. We use this substrate for our method for lazy timing. This thesis also proves soundness of the eager timing scheme in Hehner’s work with respect to an eager operational semantics, and our lazy timing scheme with respect to a lazy operational semantics. Thus, if refinements promise an upper time bound, then execution actually stops within that time. Lastly, this thesis outlines a space of more operational semantics. It is possible ground for more execution strategies.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".