A path to DOT: formalizing fully path-dependent types
Why this work is in the frame
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Bibliographic record
Abstract
The Dependent Object Types (DOT) calculus aims to formalize the Scala programming language with a focus on path-dependent types — types such as x . a 1 … a n . T that depend on the runtime value of a path x . a 1 … a n to an object. Unfortunately, existing formulations of DOT can model only types of the form x . A which depend on variables rather than general paths. This restriction makes it impossible to model nested module dependencies. Nesting small components inside larger ones is a necessary ingredient of a modular, scalable language. DOT’s variable restriction thus undermines its ability to fully formalize a variety of programming-language features including Scala’s module system, family polymorphism, and covariant specialization. This paper presents the pDOT calculus, which generalizes DOT to support types that depend on paths of arbitrary length, as well as singleton types to track path equality. We show that naive approaches to add paths to DOT make it inherently unsound, and present necessary conditions for such a calculus to be sound. We discuss the key changes necessary to adapt the techniques of the DOT soundness proofs so that they can be applied to pDOT. Our paper comes with a Coq-mechanized type-safety proof of pDOT. With support for paths of arbitrary length, pDOT can realize DOT’s full potential for formalizing Scala-like calculi.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.009 | 0.010 |
| Research integrity | 0.000 | 0.001 |
| 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