Category-theoretic models of Linear Abadi & Plotkin Logic
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This paper presents a sound and complete category-theoretic notion of models for Linear Abadi & Plotkin Logic [Birkedal et al., 2006], a logic suitable for reasoning about parametricity in combination with recursion.A subclass of these called parametric LAPL structures can be seen as an axiomatization of domain theoretic models of parametric polymorphism, and we show how to solve general (nested) recursive domain equations in these.Parametric LAPL structures constitute a general notion of model of parametricity in a setting with recursion.In future papers we will demonstrate this by showing how many different models of parametricity and recursion give rise to parametric LAPL structures, including Simpson and Rosolini's set theoretic models [Rosolini and Simpson, 2004], a syntactic model based on Lily [Pitts, 2000, Bierman et al., 2000] and a model based on admissible pers over a reflexive domain [Birkedal et al., 2007].
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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 | 0.001 |
| 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 it