On lists and other abstract data types in the calculus of constructions
Why this work is in the frame
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Bibliographic record
Abstract
The representation of the inductively defined abstract data type for lists was left incomplete in Seldin (1997, Section 9). Here that representation is completed, and it is proved that all extra axioms needed are consistent. Among the innovations of this paper is a definition of cdr , whose definition was left for future work in Seldin (1997, Section 9). The results are then extended to other abstract data types – those of Berardi (1993). The method used to define cdr for lists is extended to obtain the definition of an inverse for each argument of each constructor of an abstract data type. These inverses are used to prove the injective property for the constructors. Also, Dedekind's method of defining the natural numbers is used to define a predicate associated with each abstract data type, and the use of this predicate makes it unnecessary to postulate the induction principle. The only axioms left to be proved are those asserting the disjointness of the co-domains of different constructors, and it is shown that those axioms can be proved consistent.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 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