Bibliographic record
Abstract
Introduction Everything done so far has emphasized the close correspondence between λ and CL, in both motivation and results, but only now do we have the tools to describe this correspondence precisely. This is the aim of the present chapter. The correspondence between the ‘extensional’ equalities will be described first, in Section 9B. The non-extensional equalities are less straightforward. We have = β in λ-calculus and = w in combinatory logic, and despite their many parallel properties, these differ crucially in that rule (ξ) is admissible in the theory λβ but not in CL w . To get a close correspondence, we must define a new relation in CL to be like β-equality, and a new relation in λ to be like weak equality. The former will be done in Section 9D below. (An account of the latter can be found in [ç H98].) Notation 9.1 This chapter is about both λ- and CL-terms, so ‘term’ will never be used without ‘λ-’ or ‘CL-’. For λ-terms we shall ignore changes of bound variables, and ‘ M ≡ α N ’ will be written as ‘ M ≡ N ’. (So, in effect, the word ‘λ-term’ will mean ‘α-convertibility class of λ-terms’, i.e. the class of all λ-terms α- convertible to a given one.) Define ∧ = the class of all (α-convertibility classes of) λ-terms, C = the class of all CL-terms.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.026 | 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".