A logic covering undefinedness in program proofs

Barringer, Howard; Cheng, J. H.; Jones, Cliff B.

doi:10.1007/bf00264250

Cited by 144 publications

(63 citation statements)

References 9 publications

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“…It is therefore not surprising that different logics are based on different semantics: Event-B [12] and PVS [17] choose SW-semantics; LPF [4], the logic underlying VDM, is based on SS-semantics; Owe [16] favors WS-semantics. To our best knowledge, only Owe explains his choice by a comparison between the four semantics.…”

Section: Term Rewritingmentioning

confidence: 99%

Term Rewriting in Logics of Partial Functions

Schmalz¹

2011

Formal Methods and Software Engineering

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Abstract. We devise a theoretical foundation of directed rewriting, a term rewriting strategy for logics of partial functions, inspired by term rewriting in the Rodin platform. We prove that directed rewriting is sound and show how to supply new rewrite rules in a soundness preserving fashion. In the context of Rodin, we show that directed rewriting makes a significant number of conditional rewrite rules unconditional. Our work not only allows us to point out a number of concrete ways of improving directed rewriting in Rodin, but also has applications in other logics of partial functions. Additionally, we give a semantics for the logic of Event-B.

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Section: Term Rewritingmentioning

confidence: 99%

Term Rewriting in Logics of Partial Functions

Schmalz¹

2011

Formal Methods and Software Engineering

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“…In the existing literature, this has been done in two ways. The first is based on using a partial logic, with formulas getting no value in case of a computation error -like in [BCJ84,Ho87,Owe85]. The second employs a three-valued logic with the third,"undefined" value representing a computation error -see e.g.…”

Section: Introductionmentioning

confidence: 99%

Proof Systems for Reasoning about Computation Errors

Avron

Konikowska

2009

Stud Logica

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Abstract. In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents.

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“…There is a significant body of work on the LPF [Che86], its proof theory [BCJ84], its typed form [JM94], its mechanisation in a proof support environment [JJLM91] and its use for reasoning about models and refinements in VDM [BFL + 94, Jon06,Fit07]. A full description is not attempted here but the cited papers and references therein provide a history and link LPF to mainstream writings on logic.…”

Section: Introductionmentioning

confidence: 99%

The connection between two ways of reasoning about partial functions

Fitzgerald

Jones

2008

Information Processing Letters

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Undefined terms involving the application of partial functions and operators are common in program specifications and in discharging proof obligations that arise in design. One way of reasoning about partial functions with classical First-order Predicate Calculus (FoPC ) is to use a non-strict equality notion so as to insulate logical operators from undefined operands. An alternative approach is to work only with strict (weak) equality but use an alternative Logic of Partial Functions (LPF ) -a logic in which the "Law of the Excluded Middle" does not hold. This paper explores the relationships between the theorems that can be proved in the two approaches. The main result is that theorems in LPF using weak equality can be straightforwardly translated into ones that are true in FoPC ; translation in the other direction results, in general, in more complicated expressions but in many cases these can be readily simplified. Such results are important if the laudable move towards interworking of formal methods tools is to be sound.

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A logic covering undefinedness in program proofs

Cited by 144 publications

References 9 publications

Term Rewriting in Logics of Partial Functions

Term Rewriting in Logics of Partial Functions

Proof Systems for Reasoning about Computation Errors

The connection between two ways of reasoning about partial functions

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