Reduce Once, Verify Many: Verifying Isolation Guarantees via Hierarchical Abstractions

2026-08-07

AI Summary

This work addresses the inefficiency and redundancy in verifying correctness across multiple isolation levels in database systems by proposing a systematic, hierarchy-based verification methodology. Leveraging refinement and generic reduction theory, the approach constructs a reusable hierarchy of abstractions within Isabelle/HOL, elucidating the fundamental differences in verification mechanisms between strong and weak isolation levels. By establishing a single high-level reduction proof for weak isolation once and then refining it stepwise down to concrete implementations, users need only supply lightweight refinement proofs at the lowest layer. This framework unifies the formal verification of seven distinct isolation levels, substantially reducing both the complexity and manual effort traditionally required for such tasks.

Abstract

We present a mathematically rigorous, systematic approach for the verification of database isolation guarantees, which (i) supports a spectrum of seven isolation levels, (ii) uncovers a fundamental dichotomy among isolation levels: stronger levels can be verified via refinement alone, whereas weaker levels additionally require reduction, and (iii) provides a hierarchy of abstract models that substantially simplifies proofs by factoring out their most labor-intensive parts. In particular, we eliminate the need for per-protocol reduction proofs for the weaker class of isolation levels by performing a once-and-for-all reduction at a high level of abstraction in our hierarchy. To achieve this, we develop and apply a generic theory of reduction, which is also of more general interest. Overall, our approach minimizes the user's proof effort to a single, simpler refinement of the most concrete model in our hierarchy. All our results are formalized in Isabelle/HOL.

Problem

• isolation guarantees
• verification
• reduction
• refinement
• abstract models

Innovation

• hierarchical abstractions
• isolation guarantees
• refinement
• reduction
• formal verification