A Hoare Logic Contract Theory: An Exercise in Denotational Semantics

Gurov, Dilian; Westman, Jonas

doi:10.1007/978-3-319-98047-8_8

Cited by 6 publications

(5 citation statements)

References 8 publications

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“…This is exactly the correctness notion that is the target of procedure-modular verification. As shown in [12], this notion is sound w.r.t. the original notion S |= par C, in the sense that S |= cr par C entails S |= par C. In other words, verifying a program procedure-modularly establishes that the program is correct w.r.t.…”

Section: Hoare Logic and Contractsmentioning

confidence: 80%

“…In this section we summarise the denotational semantics of Hoare logic and the semantic justification of procedure-modular verification, as developed by the second author in [12]. These formalisations serve as the starting point for the definition of contracts in our contract theory developed in Section 4.2.…”

Section: Hoare Logic and Contractsmentioning

confidence: 99%

“…One can view a Hoare triple {P }S{Q} as a contract C = (P, Q) imposed on the program S. In many contexts it is meaningful to separate the contract from the program; for instance, if the program is yet to be implemented. In our earlier work [12], we gave such contracts a denotational semantics as follows:…”

Section: Hoare Logic and Contractsmentioning

confidence: 99%

“…The key to this is to handle procedure calls by using the contract of the called procedure rather than its body (i.e., by contracting rather than by inlining [7]). In [12], a semantic justification of this is given by means of a contract-relative denotational semantics of statements. The intuition behind this semantics is that procedure calls are given a meaning through the denotation of the contract of the called procedure, rather than through the denotation of its body.…”

Section: Hoare Logic and Contractsmentioning

confidence: 99%

See 3 more Smart Citations

An Abstract Contract Theory for Programs with Procedures

Lidström¹,

Gurov²

2021

Preprint

Self Cite

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Section: Hoare Logic and Contractsmentioning

confidence: 80%

Section: Hoare Logic and Contractsmentioning

confidence: 99%

Section: Hoare Logic and Contractsmentioning

confidence: 99%

Section: Hoare Logic and Contractsmentioning

confidence: 99%

See 2 more Smart Citations

An Abstract Contract Theory for Programs with Procedures

Lidström¹,

Gurov²

2021

Preprint

Self Cite

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show abstract

“…Cyclic proof systems to prove inductive claims, including contracts of recursive procedures, date back to Hoare's axiomatization of recursive procedures [26]. Gurov & Westman [20] provide an abstract framework based on denotational semantics to formally justify (cyclic) proceduremodular verification, while the paper [6] investigates the expressive power of sequent calculi for cyclic and infinite arguments that are often used as a basis in deductive verification. Recursive predicate specifications are standard, for example, in separation logic [39], but not used to specify program traces.…”

Section: Related Workmentioning

confidence: 99%

Trace-based Deductive Verification

Bubel¹,

Gurov²,

Hähnle³

et al.

EPiC Series in Computing

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Contracts specifying a procedure’s behavior in terms of pre- and postconditions are essential for scalable software verification, but cannot express any constraints on the events occurring during execution of the procedure. This necessitates to annotate code with intermediate assertions, preventing full specification abstraction.We propose a logic over symbolic traces able to specify recursive procedures in a mod- ular manner that refers to specified programs only in terms of events. We also provide a deduction system based on symbolic execution and induction that we prove to be sound relative to a trace semantics.Our work generalizes contract-based to trace-based deductive verification by extending the notion of state-based contracts to trace-based contracts.

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An Abstract Contract Theory for Programs with Procedures

Lidström

Gurov

2021

Fundamental Approaches to Software Engineering

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When developing complex software and systems, contracts provide a means for controlling the complexity by dividing the responsibilities among the components of the system in a hierarchical fashion. In specific application areas, dedicated contract theories formalise the notion of contract and the operations on contracts in a manner that supports best the development of systems in that area. At the other end, contract meta-theories attempt to provide a systematic view on the various contract theories by axiomatising their desired properties. However, there exists a noticeable gap between the most well-known contract meta-theory of Benveniste et al. [5], which focuses on the design of embedded and cyber-physical systems, and the established way of using contracts when developing general software, following Meyer’s design-by-contract methodology [18]. At the core of this gap appears to be the notion of procedure: while it is a central unit of composition in software development, the meta-theory does not suggest an obvious way of treating procedures as components.In this paper, we provide a first step towards a contract theory that takes procedures as the basic building block, and is at the same time an instantiation of the meta-theory. To this end, we propose an abstract contract theory for sequential programming languages with procedures, based on denotational semantics. We show that, on the one hand, the specification of contracts of procedures in Hoare logic, and their procedure-modular verification, can be cast naturally in the framework of our abstract contract theory. On the other hand, we also show our contract theory to fulfil the axioms of the meta-theory. In this way, we give further evidence for the utility of the meta-theory, and prepare the ground for combining our instantiation with other, already existing instantiations.

show abstract

A Hoare Logic Contract Theory: An Exercise in Denotational Semantics

Cited by 6 publications

References 8 publications

An Abstract Contract Theory for Programs with Procedures

An Abstract Contract Theory for Programs with Procedures

Trace-based Deductive Verification

An Abstract Contract Theory for Programs with Procedures

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