Refinement Calculus for Logic Programming in Isabelle/HOL

Hemer, David; Hayes, Ian J.; Strooper, Paul

doi:10.1007/3-540-44755-5_18

Cited by 4 publications

(6 citation statements)

References 11 publications

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“…Contextual information simplifies the refinement process by allowing individual refinement steps and proof obligations to operate on the predicate level, with minimal reference to the structure of the program. Contextual information is collected via monotonicity laws, which not only simplifies proofs "by-hand", but can also be made transparent to the user when using a refinement tool (Hemer et al 2001). The contextual laws presented in Sect.…”

Section: Discussionmentioning

confidence: 99%

“…In this section we introduce a general notion of context to the calculus, and demonstrate its use with the refinement of a list-reversal procedure. The approach taken is particularly useful when using a refinement tool, as demonstrated in Hemer et al (2001). The tool can manage the context, instead of the user having to explicitly pass the context around in the form of assumptions.…”

Section: Contextual Refinementmentioning

confidence: 99%

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Calculating modules in contextual logic program refinement

Colvin¹,

Hayes²,

Strooper³

2007

Theory and Practice of Logic Programming

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The refinement calculus for logic programs is a framework for deriving logic programs from specifications. It is based on a wide-spectrum language that can express both specifications and code, and a refinement relation that models the notion of correct implementation. In this paper we extend and generalise earlier work on contextual refinement. Contextual refinement simplifies the refinement process by abstractly capturing the context of a subcomponent of a program, which typically includes information about the values of the free variables. This paper also extends and generalises module refinement. A module is a collection of procedures that operate on a common data type; module refinement between a specification module A and an implementation module C allows calls to the procedures of A to be systematically replaced with calls to the corresponding procedures of C . Based on the conditions for module refinement, we present a method for calculating an implementation module from a specification module. Both contextual and module refinement within the refinement calculus have been generalised from earlier work and the results are presented in a unified framework.

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Section: Discussionmentioning

confidence: 99%

Section: Contextual Refinementmentioning

confidence: 99%

Calculating modules in contextual logic program refinement

Colvin¹,

Hayes²,

Strooper³

2007

Theory and Practice of Logic Programming

Self Cite

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“…A tool has been developed to support the refinement calculus [15], based on the Isabelle/HOL theorem prover. By using facilities provided by the theorem prover it is possible to automatically discharge many proof obligations associated with refinement law applications, though the user of the tool guides the refinement by selecting which rules to apply.…”

Section: Discussionmentioning

confidence: 99%

“…A semantics for the refinement calculus has been given which models commands (both specifications and code) as partial functions from sets of bindings of program variables to subsets of those bindings [12]. A tool has been developed to support the refinement calculus [15], based on the Isabelle/HOL theorem prover.…”

Section: Introductionmentioning

confidence: 99%

Developing Logic Programs from Specifications Using Stepwise Refinement

Colvin

Groves

Hayes

et al. 2004

Program Development in Computational Logic

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Abstract.In this paper we demonstrate a refinement calculus for logic programs, which is a framework for developing logic programs from specifications. The paper is written in a tutorial-style, using a running example to illustrate how the refinement calculus is used to develop logic programs. The paper also presents an overview of some of the advanced features of the calculus, including the introduction of higher-order procedures and the refinement of abstract data types.

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“…von Wright (1994) presented a tool for verified program refinement using the refinement calculus in HOL. Since then, there have been a number of refinement tools in Isabelle/HOL with support for logic (Hemer et al, 2001), object-oriented (Liu et al, 2011), functional (Lammich, 2013), and imperative (Lammich, 2015) programs. Cohen et al (2013) developed a framework for Coq called CoqEAL which automates key steps of data refinement.…”

Section: Refinement Of Programs Data and Proofsmentioning

confidence: 99%

QED at Large: A Survey of Engineering of Formally Verified Software

Ringer

Palmskog

Sergey

et al. 2019

FNT in Programming Languages

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Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have been available for over 40 years, but have only recently seen wide practical use. Projects based on construction of machine-checked formal proofs are now reaching an unprecedented scale, comparable to large software projects, which leads to new challenges in proof development and maintenance. Despite its increasing importance, the field of proof engineering is seldom considered in its own right; related theories, techniques, and tools span many fields and venues. This survey of the literature presents a holistic understanding of proof engineering for program correctness, covering impact in practice, foundations, proof automation, proof organization, and practical proof development.

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Refinement Calculus for Logic Programming in Isabelle/HOL

Cited by 4 publications

References 11 publications

Calculating modules in contextual logic program refinement

Calculating modules in contextual logic program refinement

Developing Logic Programs from Specifications Using Stepwise Refinement

QED at Large: A Survey of Engineering of Formally Verified Software

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