Oracle-based Differential Operational Semantics (long version)
Bibliographic record
Abstract
Program dierences are pervasive in software development and understanding them is crucial. However, such changes are usually represented as textual dierences with no regard to the syntactic nature of programs or their semantics. Such a representation may be hard to read or reason about and often fails to convey insight on the semantic implications of a change. In this paper, we propose a formal framework to characterize the dierence of behavior between two close programs equivalent or notin terms of their small-step semantics. To this end, we introduce small-step-prediction oracles that consume one reduction step of one program and produce a sequence of reduction steps of the other. Such oracles are operational, handle diverging or stuck computations, and are well-suited for describing local changes, while expressive enough to describe arbitrary ones. They can also be composed, to characterize a dierence as a sequence of simpler dierences. Last but not least, small-prediction-step oracles can be explained to programmers in terms of evaluation of the compared programs. We illustrate this framework by instantiating it on the Imp imperative language, with oracles ranging from trivial equivalence-preserving syntactic transformations to characterized semantic dierences. Through these examples, we show how our framework can be used to relate syntactic changes with their eect on the semantics, or to describe higher-level changes by abstracting away from the small-step semantics presentation. We have dened and proved the framework and the presented examples in the Coq proof assistant, and implemented a proof-of-concept inference tool for the Imp language.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
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".