Trillium: Higher-Order Concurrent and Distributed Separation Logic for Intensional Refinement

Expressive state-of-the-art separation logics rely on step-indexing to model semantically complex features and to support modular reasoning about imperative higher-order concurrent and distributed programs. Stepindexing comes, however, with an inherent cost: it restricts the adequacy theorem of prog...

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Bibliographic Details
Published in:Proceedings of ACM on programming languages Vol. 8; no. POPL; pp. 241 - 272
Main Authors: Timany, Amin, Gregersen, Simon Oddershede, Stefanesco, Léo, Hinrichsen, Jonas Kastberg, Gondelman, Léon, Nieto, Abel, Birkedal, Lars
Format: Journal Article
Language:English
Published: New York, NY, USA ACM 02.01.2024
Subjects:
Abstraction
Higher order logic
Hoare logic
Invariants
Logic and verification
Pre- and post-conditions
Program specifications
Program verification
Programming logic
Separation logic
Theory of computation
higher-order logic
refinement
formal verification
Distributed systems
separation logic
concurrency
ISSN:2475-1421, 2475-1421
Online Access:Get full text
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Summary:Expressive state-of-the-art separation logics rely on step-indexing to model semantically complex features and to support modular reasoning about imperative higher-order concurrent and distributed programs. Stepindexing comes, however, with an inherent cost: it restricts the adequacy theorem of program logics to a fairly simple class of safety properties. In this paper, we explore if and how intensional refinement is a viable methodology for strengthening higher-order concurrent (and distributed) separation logic to prove non-trivial safety and liveness properties. Specifically, we introduce Trillium, a language-agnostic separation logic framework for showing intensional refinement relations between traces of a program and a model. We instantiate Trillium with a concurrent language and develop Fairis, a concurrent separation logic, that we use to show liveness properties of concurrent programs under fair scheduling assumptions through a fair liveness-preserving refinement of a model. We also instantiate Trillium with a distributed language and obtain an extension of Aneris, a distributed separation logic, which we use to show refinement relations between distributed systems and TLA+ models.
ISSN:2475-1421
2475-1421
DOI:10.1145/3632851