Type classes for efficient exact real arithmetic in Coq

Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. Previously, we [Krebbers/Spitters 2011] provided a fast implementation of the exact real numbers in the Coq proof assistant. Our implementation improved on an earlier implementation by O'Connor by using type classes to describe an abstract specification of the underlying dense set from which the real numbers are built. In particular, we used dyadic rationals built from Coq's machine integers to obtain a 100 times speed up of the basic operations already. This article is a substantially expanded version of [Krebbers/Spitters 2011] in which the implementation is extended in the various ways. First, we implement and verify the sine and cosine function. Secondly, we create an additional implementation of the dense set based on Coq's fast rational numbers. Thirdly, we extend the hierarchy to capture order on undecidable structures, while it was limited to decidable structures before. This hierarchy, based on type classes, allows us to share theory on the naturals, integers, rationals, dyadics, and reals in a convenient way. Finally, we obtain another dramatic speed-up by avoiding evaluation of termination proofs at runtime.Comment: arXiv admin note: text overlap with arXiv:1105.275

Reason Maintenance - State of the Art

This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques

A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istv\'an N\'emeti and Gyula D\'avid (2006) have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istv\'an's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in N\'emeti and D\'avid (2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis.Comment: 27 pages, 5 figures. Forthcoming in Synthese. Matches published versio

CPL: A Core Language for Cloud Computing -- Technical Report

Running distributed applications in the cloud involves deployment. That is, distribution and configuration of application services and middleware infrastructure. The considerable complexity of these tasks resulted in the emergence of declarative JSON-based domain-specific deployment languages to develop deployment programs. However, existing deployment programs unsafely compose artifacts written in different languages, leading to bugs that are hard to detect before run time. Furthermore, deployment languages do not provide extension points for custom implementations of existing cloud services such as application-specific load balancing policies. To address these shortcomings, we propose CPL (Cloud Platform Language), a statically-typed core language for programming both distributed applications as well as their deployment on a cloud platform. In CPL, application services and deployment programs interact through statically typed, extensible interfaces, and an application can trigger further deployment at run time. We provide a formal semantics of CPL and demonstrate that it enables type-safe, composable and extensible libraries of service combinators, such as load balancing and fault tolerance.Comment: Technical report accompanying the MODULARITY '16 submissio

The Power of Proofs: New Algorithms for Timed Automata Model Checking (with Appendix)

This paper presents the first model-checking algorithm for an expressive modal mu-calculus over timed automata, $L^{\mathit{rel}, \mathit{af}}_{\nu,\mu}$, and reports performance results for an implementation. This mu-calculus contains extended time-modality operators and can express all of TCTL. Our algorithmic approach uses an "on-the-fly" strategy based on proof search as a means of ensuring high performance for both positive and negative answers to model-checking questions. In particular, a set of proof rules for solving model-checking problems are given and proved sound and complete; we encode our algorithm in these proof rules and model-check a property by constructing a proof (or showing none exists) using these rules. One noteworthy aspect of our technique is that we show that verification performance can be improved with \emph{derived rules}, whose correctness can be inferred from the more primitive rules on which they are based. In this paper, we give the basic proof rules underlying our method, describe derived proof rules to improve performance, and compare our implementation of this model checker to the UPPAAL tool.Comment: This is the preprint of the FORMATS 2014 paper, but this is the full version, containing the Appendix. The final publication is published from Springer, and is available at http://link.springer.com/chapter/10.1007%2F978-3-319-10512-3_9 on the Springer webpag