Bibliographic record
Abstract
Coq [1] is a proof assistant which relies on the Curry-Howard isomorphism to construct certified proofs. Proving a theorem is the same thing as providing a term which inhabits a type corresponding to this theorem. In order to trust Coq, it is enough to trust its kernel, which is intentionally kept small enough for a motivated reader to understand and, hopefully, trust it. This approach can have some drawbacks, as high-level constructs have to be translated down to simpler constructs, by the user or by some part of code external to the kernel. For example, writing dependent pattern-matching in Coq can be complicated. Simpifying this task is one of the purposes of the Equations [2] plugin. Given a high-level specification of a function, which can use dependent pattern-matching and complex recursion schemes, it will compile it to pure Coq terms. Equations is the result of the work of Matthieu Sozeau[10], largely based on the research of Goguen et al[7]. This internship revolves around Equations as a tool to benchmark, improve and adapt to new settings. This in turn involves the study of dependent pattern-matching. Research problem The initial goal of this internship was to rewrite a part of Equations, in order to better control the use of the axiom K during the compilation phase. This axiom states that to prove a property depending on a proof of equality, it is enough to consider the case where this proof is the reflexivity. Equivalently, it says that any proof of equality is propositionally equal to the reflexivity. While it is useful in some cases, and even provable for a lot of types, it can be harmful when working in some contexts, like Homotopy Type Theory[12] – abbreviated HoTT. Another problem is that, as an axiom, it will block any computation in Coq that involves it.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.011 |
| Open science | 0.004 | 0.011 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.009 | 0.005 |
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".