A Machine-checked Categorial Formalisation of Term Graph Rewriting with Semantics Preservation
Bibliographic record
Abstract
Term graph rewriting is important as "conceptual implementation" of the execution of functional programs, and of data-flow optimisations in compilers. Since term graphs were introduced into the literature, various flavours of term graph rewriting have been investigated mainly as implementation of term rewriting. One way to define term graph rewriting rule application is via the well-established and intuitively accessible double-pushout (DPO) approach. It uses the abstraction of category theory to define matching and replacement on a black-box level through basic categorial theoretic concepts like pushouts. However, the semantics preservation of DPO term graph rewriting, to our knowledge, has never been formalised before. In this thesis, we show the gs-monoidal categories proposed by Andrea Corradini and Fabio Gadducci serves not only as a category-theoretic interface for programming "on top of" term graphs with sequential and parallel composition, but also as the necessary link relating our formalisation of DPO term graph rewriting to the categorial description for program semantics. One achievement of our work is the representation of term graphs employed by the dependently-typed programming language Agda on a suitable level of abstraction from the concrete choice of set representation for graph nodes and edges through the novel category-theoretic abstraction of dependent objects. Another result is the formalisation of the functor from gs-monoidal category of term graphs to any gs-monoidal categories which enables us to obtain the semantics of term graphs. Finally, we present a new result proving the semantics preservation for such DPO-based term graph rewriting.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| 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".