The Nuprl Open Logical Environment

Allen, Stuart F.; Constable, Robert L.; Eaton, Rich; Kreitz, Christoph; Lorigo, Lori

doi:10.1007/10721959_12

Cited by 38 publications

(39 citation statements)

References 10 publications

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“…As a platform for the implementation of our proof calculus we have selected the Nuprl proof development system [9,2,19,1]. Nuprl is an environment for the development of formalized mathematical knowledge that supports interactive and tactic-based reasoning, decision procedures, language extensions through user-defined concepts, and an extendable library of verified formal knowledge.…”

Section: Implementation Of the Formal Theorymentioning

confidence: 99%

Automating Proofs in Category Theory

Kozen¹,

Kreitz²,

Richter³

2006

Automated Reasoning

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Abstract. We introduce a semi-automated proof system for basic category-theoretic reasoning. It is based on a first-order sequent calculus that captures the basic properties of categories, functors and natural transformations as well as a small set of proof tactics that automate proof search in this calculus. We demonstrate our approach by automating the proof that the functor categories Fun[C × D, E] and Fun [C, Fun[D, E]] are naturally isomorphic.

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Section: Implementation Of the Formal Theorymentioning

confidence: 99%

Automating Proofs in Category Theory

Kozen¹,

Kreitz²,

Richter³

2006

Automated Reasoning

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“…The Nuprl system (Constable et al, 1986;Allen et al, 2000;Nuprl) supports an interactive development of formal mathematical theories and program verifications. It provides a highly visual proof editor , a tactic mechanism for the development of proof strategies through programmed application of inference rules, decision procedures for standard arithmetic and equality reasoning, mechanisms for extracting programs from proofs and evaluating programs, and an extendable library of verified knowledge from various domains.…”

Section: Nuprlmentioning

confidence: 99%

“…In its newest release (Allen et al, 2000), Nuprl features an open, distributed architecture that is organized as a collection of independent communicating processes centered around a persistent knowledge base (or library). This enables users to connect external proof tools to Nuprl and to use them simultaneously and asynchronously in complex proofs.…”

Section: Nuprlmentioning

confidence: 99%

“…In this article we will demonstrate that formal logical methods based on expressive type systems are capable of supporting the formal design and implementation In particular we will show that linking the Ensemble group communication toolkit (Hayden, 1998;Birman et al, 2000) to the Nuprl proof development system (Constable et al, 1986;Allen et al, 2000) provides an infrastructure for the application of logical inference techniques to a real-world system. We call this infrastructure a logical programming environment for Ensemble (Kreitz et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

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Building reliable, high-performance networks with the Nuprl proof development system

Kreitz¹

2004

J. Funct. Prog.

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Proof systems for expressive type theories provide a foundation for the verification and synthesis of programs. But despite their successful application to numerous programming problems there remains an issue with scalability. Are proof environments capable of reasoning about large software systems? Can the support they offer be useful in practice?In this article we answer this question by showing how the Nuprl proof development system and its rich type theory have contributed to the design of reliable, high-performance networks by synthesizing optimized code for application configurations of the Ensemble group communication toolkit. We present a type-theoretical semantics of OCaml, the implementation language of Ensemble, and tools for automatically importing system code into the Nuprl system. We describe reasoning strategies for generating verifiably correct fast-path optimizations of application configurations that substantially reduce end-to-end latency in Ensemble. We also discuss briefly how to use Nuprl for checking configurations against specifications and for the design of reliable adaptive network protocols.

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“…The Nuprl Logical Programming Environment (LPE) [10,3] is a framework for the development of formalized mathematical knowledge that is well suited to support such a formal design of software systems. It provides an expressive formal language and a substantial body of formal knowledge that was accumulated in increasingly large applications, such as verifications of a logic synthesis tool [1] and of the SCI cache coherency protocol [13] as well as the verification and optimization of communication protocols [17,12,18].…”

Section: Introductionmentioning

confidence: 99%

Proving Hybrid Protocols Correct

Bickford

Kreitz

Renesse

et al. 2001

Lecture Notes in Computer Science

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Abstract. We describe a generic switching protocol for the construction of hybrid protocols and prove it correct with the Nuprl proof development system. For this purpose we introduce the concept of metaproperties and use them to formally characterize communication properties that can be preserved by switching. We also identify switching invariants that an implementation of the switching protocol must satisfy in order to work correctly.

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The Nuprl Open Logical Environment

Cited by 38 publications

References 10 publications

Automating Proofs in Category Theory

Automating Proofs in Category Theory

Building reliable, high-performance networks with the Nuprl proof development system

Proving Hybrid Protocols Correct

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