Two-Level Hybrid: A System for Reasoning Using Higher-Order Abstract Syntax
Bibliographic record
Abstract
Logical frameworks supporting higher-order abstract syntax (HOAS) allow a direct and concise specification of a wide variety of languages and deductive systems. Reasoning about such systems within the same framework is well-known to be problematic. We describe the new version of the Hybrid system, implemented on top of Isabelle/HOL (as well as Coq), in which a de Bruijn representation of λ-terms provides a definitional layer that allows the user to represent object languages in HOAS style, while offering tools for reasoning about them at the higher level. We briefly describe how to carry out two-level reasoning in the style of frameworks such as Linc, and briefly discuss our system's capabilities for reasoning using tactical theorem proving and principles of induction and coinduction.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.004 | 0.008 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 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".