The characterization problem for Hoare logics

Clarke, Edmund M.

doi:10.1098/rsta.1984.0068

Cited by 5 publications

(4 citation statements)

References 15 publications

(19 reference statements)

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“…However, these results do not yield any usable, syntax-directed proof rules that are in the spirit of Hoare-like proof systems that appeared since the publication of [Hoa69]. Therefore Clarke stated in [Cla85]:…”

Section: The Characterization Problemmentioning

confidence: 94%

“…Exploring the border between relative completeness and incompleteness (in the sense of Cook) of Hoare's logics has been the focus of considerable research in the 1980s. Clarke called it the "Characterization Problem for Hoare Logics" in his survey article [Cla85]. The key question is what is meant by a 'Hoare logic'.…”

Section: The Characterization Problemmentioning

confidence: 99%

Fifty years of Hoare’s logic

Apt

Olderog

2019

Form. Asp. Comput.

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“…Other related work includes the proof system of [10], based on "store-models"; in contrast to the approach used there, our underlying semantic model is arguably cleaner, and we believe that our proof rules are more*natural. Our proof system was also based on first order assertion languages, a property that is more in the spirit of Hoare logics, as outlined in [5].…”

Section: Discussionmentioning

confidence: 99%

A fully abstract semantics and a proof system for an algol-like language with sharing

Brookes

1986

Lecture Notes in Computer Science

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Abstract.In this paper we discuss the semantics of a simple block-structured programming language which allows sharing or aliasing. Sharing, which arises naturally in procedural languages which permit certain forms of parameter passing, has typically been regarded as problematical for the semantic treatment of a language. Difficulties have been encountered in both denotational and axiomatic treatments of sharing in the literature. Nevertheless, we find that it is possible to define a clean and elegant formal semantics for sharing. The key to our success is the choice of semantic model; we show that conventional approaches based on locations are less than satisfactory for the purposes of reasoning about partial correctness, and that in a well defined sense locations are unnecessary in a formal treatment of our programming language. In the first part of the paper we describe a denotational semantics for an ALGOL-like language which allows sharing; the semantic model is not based on locations, but instead uses an abstract sharing relation on identifiers to represent the notion of aliasing, and uses an abstract state with a stack-like structure to capture the semantics of blocks. The semantics is shown to be fully abstract with respect to partial correctness properties, in contrast to conventional location-based models. This means that the semantics identifies terms if and only if they induce identical partial correctness behaviour in all program contexts. This property typically fails for locationbased semantics because in such models it is possible to distinguish between terms on the basis of their effect on individual locations, which has no bearing on partial correctness behaviour.In the second part of the paper we demonstrate that our choice of semantic model enables us to design a Hoare-style proof system for our language, and to give relatively straightforward proofs of the soundness and completeness of this system. We claim that our proof rules are conceptually simpler to understand than other rules proposed in the literature, without losing any expressive power. Indeed, we are able to derive some of these proposed rules. We believe that semantically based methods such as ours may lead to improvements and clarifications in the axiomatic and denotational treatment of other programming constructs. The methods by which we construct a proof system will lead us to some general principles which ought to be more widely applicable. We show, for example, that it is possible to define a "generic" inference rule for blocks which is uniformly applicable to blocks headed by different forms of declaration. The important point here is that, unlike the proof systems for these constructs in the literature, we do not have to design a separate rule for blocks for each possible form of declaration. This results in greater flexibility and adaptability in our proof system. In summary, we are advocating a generalization of Hoare logic to encompass the semantics of a wider range of syntactic categories, and we believe that axiomati...

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“…Hoare [16] introduced the notation {P} C {Q} for specifying what a program does 4 . In this notation, C is a program from the programming language whose programs are being specified (the language in Section 2 in our case); and P and Q are conditions on the program variables used in C. The semantics of {P} C {Q} is now described informally.…”

Section: Hoare Logicmentioning

confidence: 99%

Mechanizing Programming Logics in Higher Order Logic

Gordon

1989

Current Trends in Hardware Verification and Automated Theorem Proving

148

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Formal reasoning about computer programs can be based directly on the semantics of the programming language, or done in a special purpose logic like Hoare logic. The advantage of the first approach is that it guarantees that the formal reasoning applies to the language being used (it is well known, for example, that Hoare's assignment axiom fails to hold for most programming languages). The advantage of the second approach is that the proofs can be more direct and natural.In this paper, an attempt to get the advantages of both approaches is described. The rules of Hoare logic are mechanically derived from the semantics of a simple imperative programming language (using the HOL system). These rules form the basis for a simple program verifier in which verification conditions are generated by LCF-style tactics whose validations use the derived Hoare rules. Because Hoare logic is derived, rather than postulated, it is straightforward to mix semantic and axiomatic reasoning. It is also straightforward to combine the constructs of Hoare logic with other application-specific notations. This is briefly illustrated for various logical constructs, including termination statements, VDM-style 'relational' correctness specifications, weakest precondition statements and dynamic logic formulae .The theory underlying the work presented here is well known. Our contribution is to propose a way of mechanizing this theory in a way that makes certain practical details work out smoothly.

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The characterization problem for Hoare logics

Cited by 5 publications

References 15 publications

Fifty years of Hoare’s logic

A fully abstract semantics and a proof system for an algol-like language with sharing

Mechanizing Programming Logics in Higher Order Logic

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