A Structural Proof of the Soundness of Rely/guarantee Rules

Coleman, Joey W.; Jones, Cliff B.

doi:10.1093/logcom/exm030

Cited by 56 publications

(62 citation statements)

References 31 publications

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“…The formal similarity of our abstract locations with the rely-guarantee formalism [12,32] suggests the intriguing possibility of an extension to concurrency.…”

Section: Discussionmentioning

confidence: 94%

Abstract effects and proof-relevant logical relations

Benton

Hofmann

Nigam

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Abstract. We introduce a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proof-relevant generalisation thereof, namely setoids. The objects of a setoid establish that values inhabit semantic types, whilst its morphisms are understood as proofs of semantic equivalence. The transition to proof-relevance solves two well-known problems caused by the use of existential quantification over future worlds in traditional Kripke logical relations: failure of admissibility, and spurious functional dependencies. We illustrate the novel format with two applications: a direct-style validation of Pitts and Stark's equivalences for "new" and a denotational semantics for a region-based effect system that supports type abstraction in the sense that only externally visible effects need to be tracked; non-observable internal modifications, such as the reorganisation of a search tree or lazy initialisation, can count as 'pure' or 'read only'. This 'fictional purity' allows clients of a module soundly to validate more effect-based program equivalences than would be possible with traditional effect systems.

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“…The formal similarity of our abstract locations with the rely-guarantee formalism [12,32] suggests the intriguing possibility of an extension to concurrency.…”

Section: Discussionmentioning

confidence: 94%

Abstract effects and proof-relevant logical relations

Benton

Hofmann

Nigam

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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“…Our presentation separates a core algebraic theory of processes from an instantiation of that theory as a relational model similar to that used by Jones [CJ07]. Section 2.1 introduces the operators in our language.…”

Section: Basic Commands and Refinementmentioning

confidence: 99%

Generalised rely-guarantee concurrency: an algebraic foundation

Hayes

2016

Form. Asp. Comput.

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Abstract. The rely-guarantee technique allows one to reason compositionally about concurrent programs. To handle interference the technique makes use of rely and guarantee conditions, both of which are binary relations on states. A rely condition is an assumption that the environment performs only atomic steps satisfying the rely relation and a guarantee is a commitment that every atomic step the program makes satisfies the guarantee relation. In order to investigate rely-guarantee reasoning more generally, in this paper we allow interference to be represented by a process rather than a relation and hence derive more general rely-guarantee laws. The paper makes use of a weak conjunction operator between processes, which generalises a guarantee relation to a guarantee process, and introduces a rely quotient operator, which generalises a rely relation to a process. The paper focuses on the algebraic properties of the general rely-guarantee theory. The Jones-style rely-guarantee theory can be interpreted as a model of the general algebraic theory and hence the general laws presented here hold for that theory.

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“…Following Jones [12,31,38,39], to enable compositionality, the behaviour of the environment of an action system is formalised by its rely condition. However, unlike Jones, who assumes rely conditions are interleaved with those of the component under consideration, we assume rely conditions are interval predicates that are assumed to hold over the interval in which an action executes.…”

Section: Action Systems With Time Bandsmentioning

confidence: 99%

“…To enable compositionality, we use rely/guarantee-style reasoning [12,31,38,39], where the rely condition is an interval predicate that specifies the behaviour of the environment. Unlike Jones, [12,38] who defines rely-guarantee reasoning in a relational setting, we asume that rely conditions are interval predicates that may specify real-time behaviour [21].…”

Section: Introductionmentioning

confidence: 99%

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Deriving real-time action systems with multiple time bands using algebraic reasoning

Dongol

Hayes

Derrick

2014

Science of Computer Programming

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The verify-while-develop paradigm allows one to incrementally develop programs from their specifications using a series of calculations against the remaining proof obligations. This paper presents a derivation method for real-time systems with realistic constraints on their behaviour. We develop a high-level intervalbased logic that provides flexibility in an implementation, yet allows algebraic reasoning over multiple granularities and sampling multiple sensors with delay. The semantics of an action system is given in terms of interval predicates and algebraic operators to unify the logics for an action system and its properties, which in turn simplifies the calculations and derivations.

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A Structural Proof of the Soundness of Rely/guarantee Rules

Abstract: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Logic and Computation following peer review. The definitive publisher-authenticated version (Coleman JW, Jones CB. A structural proof of the soundness of rely/guarantee rules.

Cited by 56 publications

References 31 publications

Abstract effects and proof-relevant logical relations

Abstract effects and proof-relevant logical relations

Generalised rely-guarantee concurrency: an algebraic foundation

Deriving real-time action systems with multiple time bands using algebraic reasoning

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