A rewriting logic approach to operational semantics

Şerbănuţă, Traian Florin; Roşu, Grigore; Meseguer, José

doi:10.1016/j.ic.2008.03.026

Cited by 55 publications

(11 citation statements)

References 66 publications

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“…We here discuss the definition of KernelC using K [10], a technique for defining languages within the Rewriting Logic Semantics [6,14]. Within this framework, languages L are defined as rewrite theories (Σ L , E L , R L ), where Σ L is a signature extending the syntax of L, E L is a set of Σ L -equations, which are thought of as structural rearrangements preparing the context for rules and carrying no computational meaning, while R L is a set of Σ L -rules, used to model irreversible computational steps.…”

Section: Formal Semantics Of Kernelcmentioning

confidence: 99%

Runtime Verification of C Memory Safety

Roşu

Schulte

Şerbănuţă

2009

Lecture Notes in Computer Science

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C is the most widely used imperative system's implementation language. While C provides types and high-level abstractions, its design goal has been to provide highest performance which often requires low-level access to memory. As a consequence C supports arbitrary pointer arithmetic, casting, and explicit allocation and deallocation. These operations are difficult to use, resulting in programs that often have software bugs like buffer overflows and dangling pointers that cause security vulnerabilities. We say a C program is memory safe, if at runtime it never goes wrong with such a memory access error. Based on standards for writing "good" C code, this paper proposes strong memory safety as the least restrictive formal definition of memory safety amenable for runtime verification. We show that although verification of memory safety is in general undecidable, even when restricted to closed, terminating programs, runtime verification of strong memory safety is a decision procedure for this class of programs. We verify strong memory safety of a program by executing the program using a symbolic, deterministic definition of the dynamic semantics. A prototype implementation of these ideas shows the feasibility of this approach.

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Section: Formal Semantics Of Kernelcmentioning

confidence: 99%

Runtime Verification of C Memory Safety

Roşu

Schulte

Şerbănuţă

2009

Lecture Notes in Computer Science

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“…The full details on the syntax and semantics of IMP are formally given in Section 2. However, we note that it is possible to faithfully model a variety of languages in this manner, as shown in [24]. Given a language semantics S as a parameter, reachability logic (defined in [14]) can prove sequents of the form…”

Section: Introductionmentioning

confidence: 99%

Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Buruiana

Ciobâcă

2019

Electron. Proc. Theor. Comput. Sci.

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We give a language-parametric solution to the problem of total correctness, by automatically reducing it to the problem of partial correctness, under the assumption that an expression whose value decreases with each program step in a well-founded order is provided. Our approach assumes that the programming language semantics is given as a rewrite theory. We implement a prototype on top of the RMT tool and we show that it works in practice on a number of examples.

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“…Several Coq mechanisations of soundness proofs for RL proof systems are presented, but Coq's coinduction is absent from them. In [3,7] coinduction is used for formalising RL and for proving RL properties for programs and for term-rewriting systems, but their approach is not mechanised in a proof assistant. More closely related work to ours is reported in [9]; they attack, however, the problem exactly in the opposite way: they develop a general theory of coinduction in Coq and use it to verify programs directly based on the semantics of programming languages, i.e., without using a proof system.…”

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confidence: 99%

(Co)inductive Proof Systems for Compositional Proofs in Reachability Logic

Rusu¹,

Nowak²

2019

Electron. Proc. Theor. Comput. Sci.

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Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and inherit the coinductive nature of the logic. The proof systems differ, however, in several aspects. First, they use induction and coinduction in different proportions. The second aspect regards compositionality, broadly meaning their ability to prove simpler formulas on smaller systems, and to reuse those formulas as lemmas for more complex formulas on larger systems. The third aspect is the difficulty of their soundness proofs. We show that the more induction a proof system uses, and the more specialised is its use of coinduction (with respect to our problem domain), the more compositional the proof system is, but the more difficult its soundness proof becomes. We also briefly present mechanisations of these results in the Isabelle/HOL and Coq proof assistants.testing of the final running software; but it enables the early catching of errors and the early discovery of key functional-correctness properties, all of which are known to have practical, cost-effective benefits.Contributions. We further study RL on transition systems (TS). We propose three proof systems for RL, and formalise them in the Coq [1] and Isabelle/HOL [10] proof assistants. One may naturally ask: why having several proof systems and proof assistants -why not one of each? The answer is manyfold:• the proof systems we propose have some common features: the soundness and completenes metaproperties, and the coinductiveness nature inherited from RL. However, they do differ in others aspects: (i) the "amount" of induction they contain; (ii) their degree of compositionality (i.e., their ability to prove local formulas on "components" of a TS, and then to use those formulas as lemmas in proofs of global formulas on the TS); and (iii) the difficulty level of their soundness proofs.• we show that the more induction a proof system uses, and the closest its coinduction style to our problem domain of proving reachability-logic formulas, the more compositional the proof system is, but the more difficult its soundness proof. There is a winner: the most compositional proof system of the three, but we found that the other ones exhibit interesting, worth-presenting features as well. • Coq and Isabelle/HOL have different styles of coinduction: Knaster-Tarski style vs. Curry-Howard style. Experiencing this first-hand with the nontrivial examples constituted by proof systems suggested a spinoff project, which amounts to porting some of the features of one proof assistant into the other one. For the moment, porting Knaster-Tarski features into the Curry-Howard coinduction of Coq produced promising results, with possible practical impact for a broader class of Coq users.Related Work. Regarding RL, most papers in the above-given list of references mention its coinductive nature, but do not actually use it. Several Coq mechanisatio...

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A rewriting logic approach to operational semantics

Cited by 55 publications

References 66 publications

Runtime Verification of C Memory Safety

Runtime Verification of C Memory Safety

Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

(Co)inductive Proof Systems for Compositional Proofs in Reachability Logic

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