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Record W4412989178 · doi:10.1145/3747532

Type Universes as Kripke Worlds

2025· article· en· W4412989178 on OpenAlex

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueProceedings of the ACM on Programming Languages · 2025
Typearticle
Languageen
FieldComputer Science
TopicLogic, programming, and type systems
Canadian institutionsUniversity of British Columbia
FundersNatural Sciences and Engineering Research Council of CanadaDefense Advanced Research Projects Agency
KeywordsPossible worldKripke structureType (biology)MathematicsEpistemologyPhilosophyGeology

Abstract

fetched live from OpenAlex

What are mutable references; what do they mean? The answers to these questions have spawned lots of important theoretical work and form the foundation of many impactful tools. However, existing semantics collapse a key distinction: which allocations does a reference depend on? In this paper, we deconstruct the space of mutable higher-order references. We formalize a novel distinction–splitting the design space of references not only into higher-order vs (full-)ground references, but also dependency of an allocation on past vs future allocations. This distinction is fundamental to a thorny issue that arises in constructing semantic models of mutable references–the type-world circularity. The issue disappears for what we call predicative references, those that only quantify over past, not future, allocations, and for non-higher-order impredicative references. We design a syntax and semantics for each point in our newly described space. The syntax relies on a type universe hierarchy, à la dependent type theory, to kind the types of allocated terms, and stratify allocations. Each type universe corresponds to a semantic Kripke world, giving a lightweight syntactic mechanism to design and restrict heap shapes. The semantics bear a resemblance to work on regions, and suggest some connection between universe systems and regions, which we describe in some detail.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.733
Threshold uncertainty score0.651

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0040.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.014
GPT teacher head0.272
Teacher spread0.258 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it