Categorical foundations for structured specifications in Z
Bibliographic record
Abstract
Abstract In this paper we present a formalization of the Z notation and its structuring mechanisms. One of the main features of our formal framework, based on category theory and the theory of institutions, is that it enables us to provide an abstract view of Z and its related concepts. We show that the main structuring mechanisms of Z are captured smoothly by categorical constructions. In particular, we provide a straightforward and clear semantics for promotion, a powerful structuring technique that is often not presented as part of the schema calculus. Here we show that promotion is already an operation over schemas (and more generally over specifications), that allows one to promote schemas that operate on a local notion of state to operate on a subsuming global state, and in particular can be used to conveniently define large specifications from collections of simpler ones. Moreover, our proposed formalization facilitates the combination of Z with other notations in order to produce heterogeneous specifications, i.e., specifications that are obtained by using various different mathematical formalisms. Thus, our abstract and precise formulation of Z is useful for relating this notation with other formal languages used by the formal methods community. We illustrate this by means of a known combination of formal languages, namely the combination of Z with CSP .
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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 | 0.004 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.006 | 0.008 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 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".