A Layered Approach to Intensional Analysis in Type Theory
Why this work is in the frame
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Bibliographic record
Abstract
We introduce layering to modal type theory to support meta-programming and intensional analysis coherently. In particular, we demonstrate this idea by developing a 2-layered modal type theory. At the core of this type theory (layer 0) is a simply typed λ -calculus with no modality. Layer 1 is obtained by extending the core language with one layer of contextual ◻ types to support pattern matching on potentially open code from layer 0 while retaining normalization. Although both layers fundamentally share a uniform syntax and the same typing judgment, we only allow computation at layer 1. As a consequence, layer 0 accurately captures the syntactic representation of code in contrast to the computational behaviors at layer 1. Moreover, the uniform syntax at both layers enables quotation and code running. The system is justified by normalization by evaluation (NbE) using a presheaf model. The normalization algorithm extracted from the model is sound and complete and is implemented in Agda. Layered modal type theory provides a uniform foundation for meta-programming with intensional analysis. We see this work as an important step towards a foundational way to support meta-programming in proof assistants.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 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