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A mechanism for generating verification conditions (VCs) for the iteration-free fragment of an imperative language is fundamental in any deductive program verification system. In this paper we revisit symbolic execution, weakest preconditions, and bounded model checking as VC-generation mechanisms, and propose a uniform presentation of the corresponding sets of VCs, in terms of (logical encodings of) paths in the control-flow graph of a single-assignment form of the program under analysis. This allows us to compare the mechanisms, in particular with respect to the size of the generated formulas. © 2012 ACM.

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This paper is a systematic study of verification conditions and their use in the context of program verification. We take Hoare logic as a starting point and study in detail how a verification conditions generator can be obtained from it. The notion of program annotation is essential in this process. Weakest preconditions and the use of updates are also studied as alternative approaches to verification conditions. Our study is carried on in the context of a While language. Important extensions to this language are considered toward the end of the paper. We also briefly survey modern program verification tools and their approaches to the generation of verification conditions. © 2011 Elsevier Inc.

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With the incresasing importance of program verification, an issue that has been receiving more attention is the certification of verification tools, addressing the vernacular question: Who verifies the verifier?. In this paper we approach this meta-verification problem by focusing on a fundamental component of program verifiers: the Verification Conditions Generator (VCGen), responsible for producing a set of proof obligations from a program and a specification. The semantic foundations of VCGens lie in program logics, such as Hoare logic, Dynamic logic, or Separation logic, and related predicate transformers. Dynamic logic is the basis of the KeY system, one of the foremost deductive verifiers, whose logic makes use of the notion of update, which is quite intricate to formalize. In this paper we derive systematically, based on a KeY-style dynamic logic, a correct-by-construction VCGen for a toy programming language. Our workflow covers the entire process, from the logic to the VCGen. It is implemented in the Why3 tool, which is itself a program verifier. We prove the soundness and (an appropriate notion of) completeness of the logic, then define a VCGen for our language and establish its soundness. Dynamic logic is one of a variety of research topics that our dear friend and colleague Luis Soares Barbosa has, over the years, initiated and promoted at the University of Minho. It is a pleasure for us to dedicate this work to him on the occasion of his 60th birthday.

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In the context of intuitionistic sequent calculus, naturality means permutation-freeness (the terminology is essentially due to Mints). We study naturality in the context of the lambda-calculus with generalized applications and its multiary extension, to cover, under the Curry-Howard correspondence, proof systems ranging from natural deduction (with and without general elimination rules) to a fragment of sequent calculus with an iterable left-introduction rule, and which can still be recognized as a call-by-name lambda-calculus. In this context, naturality consists of a certain restricted use of generalized applications. We consider the further restriction obtained by the combination of naturality with normality w.r.t. the commutative conversion engendered by generalized applications. This combination sheds light on the interpretation of naturality as a vectorization mechanism, allowing a multitude of different ways of structuring lambda-terms, and the structuring of a multitude of interesting fragments of the systems under study. We also consider a relaxation of naturality, called weak naturality: this not only brings similar structural benefits, but also suggests a new weak system of natural deduction with generalized applications which is exempt from commutative conversions. In the end, we use all of this evidence as a stepping stone to propose a computational interpretation of generalized application (whether multiary or not, and without any restriction): it includes, alongside the argument(s) for the function, a general list - a new, very general, vectorization mechanism, that structures the continuation of the computation.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Abstract