History of Interactive Theorem Proving

Harrison, John; Urban, Josef; Wiedijk, Freek

doi:10.1016/b978-0-444-51624-4.50004-6

Cited by 54 publications

(46 citation statements)

References 90 publications

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“…-ITPs (Geuvers, 2009;Harrison et al, 2014), especially: * Coq (Chlipala, 2013a;Pierce et al, 2014;Bertot and Casteran, 2004) * Isabelle/HOL (Wenzel et al, 2004;Nipkow and Klein, 2014) -Automated reasoning (Bradley and Manna, 2007;Kroening and Strichman, 2008) (Chapters 3 and 5) -The Curry-Howard correspondence (Pfenning, 2010;Sørensen and Urzyczyn, 2006) -Dependent and inductive types (Chlipala, 2013a) -Equality (Chlipala, 2013a; nLab authors, 2019a) (Chapters 3 and 4) -Compilers (Cooper and Torczon, 2011) (Chapters 3, 4, and 6)…”

Section: Reading Guidementioning

confidence: 99%

See 1 more Smart Citation

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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Section: Reading Guidementioning

confidence: 99%

“…Edinburgh LCF had case studies for verified programming language implementations (Cohn, 1983), and an important use case of HOL was hardware verification (Boulton et al, 1992). Geuvers (2009) and Harrison et al (2014) provide a more comprehensive description of the history of ITPs.…”

Section: Foundations and Trusted Basesmentioning

confidence: 99%

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

Ringer

Palmskog

Sergey

et al. 2019

FNT in Programming Languages

View full text Add to dashboard Cite

show abstract

“…Readers who want to pursue these topics further will find surveys available on formally verified mathematics [73] and on the history of interactive theorem proving [74,75]. Acknowledgements.…”

Section: The Way Forwardmentioning

confidence: 99%

Computational logic: its origins and applications

Paulson¹

2018

Proc. R. Soc. A.

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Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the ‘logic for computable functions (LCF) approach’ pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users’ code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.

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“…Separating theorem provers from proof checkers using a simple, declarative specification of proof certificates is not new: see [27] for a historical account. For example, the LF dependently typed λ-calculus [25] was originally proposed as a framework for specifying (natural deduction) proofs and the Elf system [41] provided both type checking and inference for LF: the proof-carrying code project of [40] used LF as a target proof language.…”

Section: Introductionmentioning

confidence: 99%

Translating Between Implicit and Explicit Versions of Proof

Blanco

Chihani

Miller

2017

Automated Deduction – CADE 26

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Abstract. The Foundational Proof Certificate (FPC) framework can be used to define the semantics of a wide range of proof evidence. For example, such definitions exist for a number of textbook proof systems as well as for the proof evidence output from some existing theorem proving systems. An important decision in designing a proof certificate format is the choice of how many details are to be placed within certificates. Formats with fewer details are smaller and easier for theorem provers to output but they require more sophistication from checkers since checking will involve some proof reconstruction. Conversely, certificate formats containing many details are larger but are checkable by less sophisticated checkers. Since the FPC framework is based on well-established proof theory principles, proof certificates can be manipulated in meaningful ways. In this paper, we illustrate how it is possible to automate moving from implicit to explicit (elaboration) and from explicit to implicit (distillation) proof evidence via the proof checking of a pair of proof certificates. Performing elaboration makes it possible to transform a proof certificate with details missing into a certificate packed with enough details so that a simple kernel (without support for proof reconstruction) can check the elaborated certificate. We illustrate how trust in only a single, simple checker of explicitly described proofs can be used to provide trust in a range of theorem provers employing a range of proof structures.

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History of Interactive Theorem Proving

Cited by 54 publications

References 90 publications

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

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

Computational logic: its origins and applications

Translating Between Implicit and Explicit Versions of Proof

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