Higher-order term indexing using substitution trees
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We present a higher-order term indexing strategy based on substitution trees for simply typed lambda-terms. There are mainly two problems in adapting first-order indexing techniques. First, many operations used in building an efficient term index and retrieving a set of candidate terms from a large collection are undecidable in general for higher-order terms. Second, the scoping of variables and binders in the higher-order case presents challenges. The approach taken in this article is to reduce the problem to indexing linear higher-order patterns, a decidable fragment of higher-order terms, and delay solving terms outside of this fragment. We present insertion of terms into the index based on computing the most specific linear generalization of two linear higher-order patterns, and retrieval based on matching two linear higher-order patterns. Our theoretical framework maintains that terms are in βη-normal form, thereby eliminating the need to renormalize and raise terms during insertion and retrieval. Finally, we prove correctness of our presented algorithms. This indexing structure is implemented as part of the Twelf system to speed up the execution of the tabled higher-logic programming interpreter.
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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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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