Simplification Infrastructure for an Implementation of the Chiron Logic
Bibliographic record
Abstract
p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times} Simplification is an important and heavily used facility in many mathematical software systems including both computer algebra systems and computer theorem proving systems. The objective of the MathScheme project is to develop a new generation of mechanized mathematic systems that combines the advantages of both computer algebra and computer theorem proving. Serving as the underlying logic of MathScheme, Chiron is used to formalize mathematics in our project. Therefore, we want to build a simplifier that simplifies Chiron expressions for the MathScheme project. This thesis presents the design and implementation of a simplification infrastructure that allows users to build their own simplifiers. This framework can be viewed as a customizable simplifier. It provides a set of simplification strategies and mechanisms for managing contexts. The rules module of this framework allows future developers to define new simplification rules and add them into the rule library. Using different strategies and optional arguments, developers can build simplifiers that work in various ways. The ultimate goal of this framework is to provide a powerful tool with good flexibility so that other people can use it as a handy building block or an experimental environment in the future development and application of MathScheme.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.038 | 0.009 |
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".