A Program Construction and Verification Tool for Separation Logic

Dongol, Brijesh; Gomes, Victor B. F.; Struth, Georg

doi:10.1007/978-3-319-19797-5_7

Cited by 21 publications

(36 citation statements)

References 40 publications

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“…However, none of these support data refinement, non-deterministic expression evaluators or time bands. Our logic can be encoded into any existing higher-order theorem prover (e.g., Isabelle [42], KIV [6]), however, we seek to develop further algebraic abstractions of the interval predicate theory and develop an embedding at this algebraic level [18]. Such techniques would enable our proofs to be performed at an even higher level of abstraction.…”

Section: Discussionmentioning

confidence: 99%

Interval-based data refinement: A uniform approach to true concurrency in discrete and real-time systems

Dongol

Derrick

2015

Science of Computer Programming

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The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components observe and modify the state with fine-grained atomicity. Many systems also exhibit truly concurrent behaviour, where multiple events may occur simultaneously. Data refinement, a correctness criterion to compare an abstract and a concrete implementation, normally admits interleaved models of execution only. In this paper, we present a method of data refinement using a framework that allows one to view a component's evolution over an interval of time, simplifying reasoning about true concurrency. By modifying the type of an interval, our theory may be specialised to cover data refinement of both discrete and real-time systems. We develop a sound interval-based forward simulation rule that enables decomposition of data refinement proofs, and apply this rule to verify data refinement for two examples: a simple concurrent program and a more in-depth real-time controller.

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Section: Discussionmentioning

confidence: 99%

Interval-based data refinement: A uniform approach to true concurrency in discrete and real-time systems

Dongol

Derrick

2015

Science of Computer Programming

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“…This approach is taken by [24,15,9,28], and requires a deep model of variables and values, in which concepts such as typing are first-class. This provides a highly expressive model with few limitations on possible manipulations [15].…”

Section: Mechanised State-spacesmentioning

confidence: 99%

“…Whilst we believe our previous work [28] effectively mitigates (1), at the expense of introducing axioms, the complexities associated with (2) still remain. Nevertheless, the approach seems necessary to model dynamic creation of variables, as required, for example, in separation logic [26,9].…”

Section: Mechanised State-spacesmentioning

confidence: 99%

“…Thus one can apply predicate calculus to reason about programs, as well as prove the algebraic laws of programming themselves [19]. These laws can then be applied to construct semantic presentations for the purpose of verification, such as operational semantics, Hoare calculi, separation logic, and refinement calculi, to name a few [2,9]. This further enables the application of automated theorem provers to build program verification tools, an approach which has seen multiple successes [1,22].…”

Section: Introductionmentioning

confidence: 99%

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Unifying Heterogeneous State-Spaces with Lenses

Foster

Zeyda

Woodcock

2016

Theoretical Aspects of Computing – ICTAC 2016

106

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Abstract. Most verification approaches embed a model of program state into their semantic treatment. Though a variety of heterogeneous statespace models exists, they all possess common theoretical properties one would like to abstractly capture, such as the laws of programming. In this paper, we propose lenses as a universal state-space modelling solution. Lenses provide an abstract interface for manipulating data types through spatially-separated views. We define a lens algebra that allow their composition and comparison. We show how this algebra can be used to model variables and alphabets in Hoare and He's Unifying Theories of Programming. The combination of lenses and relational algebra gives rise to a model for UTP in which its fundamental laws can be verified. Moreover, we illustrate how they can be used to model more state complex notions such as memory stores and parallel states. We provide a mechanisation in Isabelle/HOL that validates our theory, and facilitates its use in program verification.

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“…We have already built mathematical components for variants of Kleene algebras, regular algebras and relation algebras in Isabelle [6,17,4,13,2], integrated some of them into verification components for sequential programs [16,5,18], local reasoning with separation logic [12] and the rely-guarantee calculus [3]. In all of them, an abstract algebraic layer has been linked via formal soundness proofs with concrete computational models, e.g.…”

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confidence: 99%

A Discrete Geometric Model of Concurrent Program Execution

Möller

Hoare

Müller

et al. 2017

Unifying Theories of Programming

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Abstract. A trace of the execution of a concurrent object-oriented program can be displayed in two-dimensions as a diagram of a non-metric finite geometry. The actions of a programs are represented by points, its objects and threads by vertical lines, its transactions by horizontal lines, its communications and resource sharing by sloping arrows, and its partial traces by rectangular figures. We prove informally that the geometry satisfies the laws of Concurrent Kleene Algebra (CKA); these describe and justify the interleaved implementation of multithreaded programs on computer systems with a lesser number of concurrent processors. More familiar forms of semantics (e.g., verification-oriented and operational) can be derived from CKA. Programs are represented as sets of all their possible traces of execution, and non-determinism is introduced as union of these sets. The geometry is extended to multiple levels of abstraction and granularity; a method call at a higher level can be modelled by a specification of the method body, which is implemented at a lower level. The final section describes how the axioms and definitions of the geometry have been encoded in the interactive proof tool Isabelle, and reports on progress towards automatic checking of the proofs in the paper.

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A Program Construction and Verification Tool for Separation Logic

Cited by 21 publications

References 40 publications

Interval-based data refinement: A uniform approach to true concurrency in discrete and real-time systems

Interval-based data refinement: A uniform approach to true concurrency in discrete and real-time systems

Unifying Heterogeneous State-Spaces with Lenses

A Discrete Geometric Model of Concurrent Program Execution

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