The Logic of Hereditary Harrop Formulas as a Specification Logic for Hybrid
Bibliographic record
Abstract
Hybrid is a logical framework that supports the use of higher-order abstract syntax (HOAS) in representing formal systems or "object logics" (OLs). It is implemented in Coq and follows a two-level approach, where a specification logic (SL) is implemented as an inductive type and used to concisely and elegantly encode the inference rules of the formal systems of interest. In this paper, we develop a new higher-order specification logic for Hybrid. By increasing the expressive power of the SL beyond what was considered previously, we increase the flexibility of encoding OLs and thus extend the class of formal systems for which we can reason about efficiently. We focus on formalizing the meta-theory of the SL. We develop an abstract way in which to present an important class of meta-theorems. This class includes properties such as weakening, contraction, exchange, and the admissibility of the cut rule. The cut admissibility theorem establishes consistency and also provides justification for substituting a formula for an assumption in a context of assumptions. It can greatly simplify reasoning about OLs in systems that provide HOAS. We present the abstraction and show how it is used to prove all of these theorems.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".