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On the Versatility of Open Logical Relations: Continuity, Automatic Differentiation, and a Containment Theorem [article]

Gilles Barthe, Raphaëlle Crubillé, Ugo Dal Lago, Francesco Gavazzo
2020 arXiv   pre-print
Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation.  ...  To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property  ...  This witnesses, on yet another situation, the versatility of open logical relations.  ... 
arXiv:2002.08489v1 fatcat:wayjsmoewfgyrf5n7iokv27wee

On the Versatility of Open Logical Relations [chapter]

Gilles Barthe, Raphaëlle Crubillé, Ugo Dal Lago, Francesco Gavazzo
2020 Lecture Notes in Computer Science  
Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation.  ...  To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property  ...  On the Versatility of Logical Relations  ... 
doi:10.1007/978-3-030-44914-8_3 fatcat:k6qdai3k5vdkrnhayohebr6ygi

Predicate Transformer Semantics for Hybrid Systems: Verification Components for Isabelle/HOL [article]

Jonathan Julián Huerta y Munive, Georg Struth
2021 arXiv   pre-print
It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or invariant sets for vector fields.  ...  We present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL.  ...  We would also like to thank our referees for pointers to related work and many suggestions that helped us to improve the presentation of this work and reflect on its contributions.  ... 
arXiv:1909.05618v3 fatcat:7lnrnamltvcutgxfezop4akt7q

Sharing HOL4 and HOL Light proof knowledge [article]

Thibault Gauthier, Cezary Kaliszyk
2015 arXiv   pre-print
Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises.  ...  In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers.  ...  Acknowledgments This work has been supported by the Austrian Science Fund (FWF): P26201.  ... 
arXiv:1509.03527v1 fatcat:pguhm3mu75bhzi625u63jyaxbi

Sharing HOL4 and HOL Light Proof Knowledge [chapter]

Thibault Gauthier, Cezary Kaliszyk
2015 Lecture Notes in Computer Science  
Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises.  ...  In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers.  ...  Acknowledgments This work has been supported by the Austrian Science Fund (FWF): P26201.  ... 
doi:10.1007/978-3-662-48899-7_26 fatcat:tdutfexmfzfdbjxla4mx4yvu7q

Hybrid Systems Verification with Isabelle/HOL: Simpler Syntax, Better Models, Faster Proofs [article]

Simon Foster, Jonathan Julián Huerta y Munive, Mario Gleirscher, Georg Struth
2021 arXiv   pre-print
The new store model yields clean separations and dynamic local views of variables, e.g. discrete/continuous, mutable/immutable, program/logical, and enhanced ways of manipulating them using combinators  ...  We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and  ...  Programme (AAIP; grant CSI:Cobot), a partnership between Lloyd's Register Foundation and the University of York.  ... 
arXiv:2106.05987v1 fatcat:7nuhzdtenjbcdlsyvnw2zvwwgq

Probabilistic Relational Reasoning for Differential Privacy

Gilles Barthe, Boris Köpf, Federico Olmedo, Santiago Zanella-Béguelin
2013 ACM Transactions on Programming Languages and Systems  
The central component of CertiPriv is a quantitative extension of a probabilistic relational Hoare logic that enables one to derive differential privacy guarantees for programs from first principles.  ...  We report on CertiPriv, a machine-checked framework for reasoning about differential privacy built on top of the Coq proof assistant.  ...  and French project ANR SESUR-012 SCALP.  ... 
doi:10.1145/2492061 fatcat:6ts2xg6zm5duzey2ob7t3hvggq

Probabilistic relational reasoning for differential privacy

Gilles Barthe, Boris Köpf, Federico Olmedo, Santiago Zanella Béguelin
2012 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '12  
The central component of CertiPriv is a quantitative extension of a probabilistic relational Hoare logic that enables one to derive differential privacy guarantees for programs from first principles.  ...  We report on CertiPriv, a machine-checked framework for reasoning about differential privacy built on top of the Coq proof assistant.  ...  and French project ANR SESUR-012 SCALP.  ... 
doi:10.1145/2103656.2103670 dblp:conf/popl/BartheKOB12 fatcat:xr2gadhd75dkpeyeaaqsejn5za

Probabilistic relational reasoning for differential privacy

Gilles Barthe, Boris Köpf, Federico Olmedo, Santiago Zanella Béguelin
2012 SIGPLAN notices  
The central component of CertiPriv is a quantitative extension of a probabilistic relational Hoare logic that enables one to derive differential privacy guarantees for programs from first principles.  ...  We report on CertiPriv, a machine-checked framework for reasoning about differential privacy built on top of the Coq proof assistant.  ...  and French project ANR SESUR-012 SCALP.  ... 
doi:10.1145/2103621.2103670 fatcat:j7tcpaj5dfd67i5xclew3gj3ha

Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity

Ioannis Raptis
2007 International Journal of Theoretical Physics  
This topos is seen to be a finitary instance of both an elementary and a Grothendieck topos, generalizing in a differential geometric setting, as befits ADG, Sorkin's finitary substitutes of continuous  ...  quantum causal sets involved therein, on which a finitary (:locally finite), singularity-free, background manifold independent and geometrically prequantized version of the gravitational vacuum Einstein  ...  Acknowledgments The author is indebted to Chris Isham for once mentioning to him the possibility of adopting and developing a generalized, Grothendieck-type of perspective on Sorkin's work [94] , as well  ... 
doi:10.1007/s10773-006-9240-y fatcat:cktkvpcmrfazvj4clbhyg3ljlq

Regular search spaces and constructive negation

A Momigliano
1997 Journal of Logic and Computation  
It is based on a simple logical framework that goes under the name of regular search spaces.  ...  Section 3 formulates the theory of Regular AA/?-Systems. Section 4 deals with the proof-theory of NF and the related soundness and completeness problem.  ...  Acknowledgements We would like to thank Roy Dyckhoff, Frank Pfenning, Robert Stark and two anonymous referees for helpful comments on various drafts of this paper.  ... 
doi:10.1093/logcom/7.3.367 fatcat:brky6qozs5g55dflenbeyt2c5e

Book Reviews

1961 Management science  
problems and on partial differential equations.  ...  The inclusion of a chapter on error and error propagation would have in- creased the value of the book for the computer men who are continuously faced with this type of problem.  ... 
doi:10.1287/mnsc.7.2.187 fatcat:325atncunvb4xiqpuv7ipwzz5y

Four Lessons in Versatility or How Query Languages Adapt to the Web [chapter]

François Bry, Tim Furche, Benedikt Linse, Alexander Pohl, Antonius Weinzierl, Olga Yestekhina
2009 Lecture Notes in Computer Science  
Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends.  ...  It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers.  ...  , but each relation is organised in such a way that all elements related to one element of its parent step are in a single continuous interval.  ... 
doi:10.1007/978-3-642-04581-3_2 fatcat:tyjxlcot7bgztckkzfw6vqq24m

Formally Verified Architecture Patterns of Hybrid Systems Using Proof and Refinement with Event-B [chapter]

Guillaume Dupont, Yamine Aït-Ameur, Marc Pantel, Neeraj K. Singh
2020 Lecture Notes in Computer Science  
We validate the approach and illustrate the use of the defined pattern on an extension of a very common case study, borrowed from literature.  ...  Hybrid systems show continuous-time dynamics depending on mode that is required in several stages of the architecture of Cyber-Physical Systems.  ...  Hoang for his help with Rodin's Theory plug-in and R. Banach for the helpful discussions related to Event-B hybridation.  ... 
doi:10.1007/978-3-030-48077-6_12 fatcat:xxrzy5w5jnhltamvb6sh4xm2ua

Book Review: Primzahlverteilung

Albert Leon Whiteman
1958 Bulletin of the American Mathematical Society  
Round-off, truncation, and instability, the three devils of numerical analysis, are introduced in such a way as to drive the student from the paradise of infinitely precise computation, without plunging  ...  There are a good many references to the recent literature on numerical analysis, and this way, the student should get the feeling that numerical analysis did not come to an end with Horner.  ...  The author proceeds to the development of a body of theorems related to and logically interdependent with the prime number theorem. / tx dt - + R(x) 2 log t for sufficiently large x } with | R(x)\ <cixe  ... 
doi:10.1090/s0002-9904-1958-10183-4 fatcat:kr7y4ptlujeyjkbfyr7is5vot4
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