Modern type error localization in education
Bibliographic record
Abstract
Learning the functional programming paradigm is often difficult for students.Strong, static type systems with parametric polymorphism are common to functionallanguages such as OCaml and Haskell, but are widely observedto be a major source of difficulty for students and other novices.In this work, we seek to better understand the challenges faced by students and other functionalprogramming novices in order to assist their learning, with a focus on type errors they encounter.Primarily, we explore the ``type error localization'' problem,and develop a tool implementing an improvement on an existing algorithm based on Maximum Satisfiability.We evaluate the tool in the context of student submissions to homework assignments in a functionalprogramming course and determine that, in many cases, our tool would have directed students to the errorin their code when the compiler did not.Our analysis of our approach uses a much larger dataset than previous analyses of similar algorithms,and affirms that Maximum Satisfiability is a practical approach to type error localization.Our tool, Tyro, is available on GitHub
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.022 | 0.153 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.009 | 0.010 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.007 | 0.008 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.014 | 0.005 |
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 source (direct Gemma or distilled Codex), 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".