A simple blame calculus for explicit nulls
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Gradual typing provides a model for when a legacy language with less precise types interacts with a newer language with more precise types. Casts mediate between types of different precision, allocating blame when a value fails to conform to a type. The blame theorem asserts that blame always falls on the less-precisely typed side of a cast. One instance of interest is when a legacy language (such as Java) permits null values at every type, while a newer language (such as Scala or Kotlin) explicitly indicates which types permit null values. Nieto et al. in 2020 introduced a gradually typed calculus for just this purpose. The calculus requires three distinct constructors for function types and a non-standard proof of the blame theorem; it can embed terms from the legacy language into the newer language (or vice versa) only when they are closed. Here, we define a simpler calculus that is more orthogonal, with one constructor for function types and one for possibly nullable types, and with an entirely standard proof of the blame theorem; it can embed terms from the legacy language into the newer language (and vice versa) even if they are open. All results in the paper have been mechanized in Coq.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| 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