Bimonadic Semantics for Basic Pattern Matching Calculi
Bibliographic record
Abstract
The pattern matching calculi introduced by the first author are a refinement of the λ-calculus that integrates mechanisms appropriate for fine-grained modelling of non-strict pattern matching. While related work in the literature only uses a single monad, typically Maybe, for matchings, we present an axiomatic approach to semantics of these pattern matching calculi using two monads, one for expressions and one for matchings. Although these two monads only need to be relatively lightly coupled, this semantics implies soundness of all core PMC rules, and is a useful tool for exploration of the design space for pattern matching calculi. Using lifting and Maybe monads, we obtain standard Haskell semantics, and by adding another level of Maybe to both, we obtain a denotational semantics of the “matching failure as exceptions” approach of Erwig and Peyton Jones. Using list-like monads opens up interesting extensions in the direction of functional-logic programming. A short version of this report appears as [Kahl, Carette + 2006].
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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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".