Filters








38 Hits in 4.2 sec

Programming and certifying a CAD algorithm in the Coq system

Assia Mahboubi, Thierry Coquand, Henri Lombardi, Marie-Françoise Roy
2006
Our aim is to program a reflectional decision procedure for the Coq system, using the CAD, to decide whether a (possibly multivariate) system of polynomial inequalities with rational coefficients has a  ...  The introduction of the Cylindrical Algebraic Decomposition (CAD) method has later allowed to design rather feasible algorithms.  ...  Our aim in this project is to program a generic algorithm of CAD to build the expected decisions procedure, using Coq as a functional typed programming language.  ... 
doi:10.4230/dagsemproc.05021.17 fatcat:iwiezllajbalxlfk5hkka64krq

A constructive formalisation of Semi-algebraic sets and functions

Boris Djalal
2018 Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018  
We formally define in Coq the base operations on semi-algebraic sets and functions using embedded firstorder formulae over the language of real closed fields, and we prove the correctness of their geometrical  ...  Semi-algebraic sets and semi-algebraic functions are essential to specify and certify cylindrical algebraic decomposition algorithms.  ...  the MAP working group about real geometry, including Marie-Françoise Roy and Henri Lombardi.  ... 
doi:10.1145/3176245.3167099 fatcat:bpdry2qnsbfyrgwzdxfkbofw5i

A constructive formalisation of Semi-algebraic sets and functions

Boris Djalal
2018 Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018  
We formally define in Coq the base operations on semi-algebraic sets and functions using embedded firstorder formulae over the language of real closed fields, and we prove the correctness of their geometrical  ...  Semi-algebraic sets and semi-algebraic functions are essential to specify and certify cylindrical algebraic decomposition algorithms.  ...  the MAP working group about real geometry, including Marie-Françoise Roy and Henri Lombardi.  ... 
doi:10.1145/3167099 dblp:conf/cpp/Djalal18 fatcat:cf35odpsirfjbhuxs2i4les7ne

Proof Assistant Decision Procedures for Formalizing Origami [chapter]

Cezary Kaliszyk, Tetsuo Ida
2011 Lecture Notes in Computer Science  
We examine the strength of Gröbner Bases implementations comparing proof assistants with each other and with the implementations provided in computer algebra systems.  ...  We show how a equation system solving mechanism can be embedded in a CAS decision procedure of a proof assistant.  ...  McLaughlin and Harrison [16] have implemented a proof producing CAD algorithm that follows the Hörmander's CAD algorithm.  ... 
doi:10.1007/978-3-642-22673-1_4 fatcat:n3dfqj73afgphagwrc3umn4yhi

A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations

Érik Martin-Dorel, Pierre Roux
2017 Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017  
We develop a reflexive tactic for the Coq proof assistant allowing one to automatically discharge polynomial positivity proofs.  ...  State of the art methods rely on heuristic roundings to exact solutions in the rational field. These solutions are then easy to verify in a proof assistant.  ...  This illustrates that the Coq system may lack a way to load (untrusted) proof elements other than hard coding them in the sources.  ... 
doi:10.1145/3018610.3018622 dblp:conf/cpp/Martin-DorelR17 fatcat:tuauz6kkzjdihbanfk4t2hrzse

Deciding Univariate Polynomial Problems Using Untrusted Certificates in Isabelle/HOL

Wenda Li, Grant Olney Passmore, Lawrence C. Paulson
2017 Journal of automated reasoning  
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition.  ...  This allows us to exploit highly-tuned computer algebra systems like Mathematica to guide our procedure without impacting the correctness of its results.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10817-017-9424-6 fatcat:hmwbpdzomvf4vgctwnerib4tp4

Formalization of Wu's Simple Method in Coq [chapter]

Jean-David Génevaux, Julien Narboux, Pascal Schreck
2011 Lecture Notes in Computer Science  
We present in this paper the integration within the Coq proof assistant, of a method for automatic theorem proving in geometry. We use an approach based on the validation of a certificate.  ...  The certificate is generated by an implementation in Ocaml of a simple version of Wu's method.  ...  We wish to thank Loïc Pottier and Laurent Théry for having made their work publicly available and for the discussions we had.  ... 
doi:10.1007/978-3-642-25379-9_8 fatcat:yk3yueuenreatdwxiiumaosc3e

Recent Advances in Real Geometric Reasoning [chapter]

James H. Davenport, Matthew England
2015 Lecture Notes in Computer Science  
In the 1930s Tarski showed that real quantifier elimination was possible, and in 1975 Collins gave a remotely practicable method, albeit with doubly-exponential complexity, which was later shown to be  ...  We discuss some of the recent major advances in Collins method: such as an alternative approach based on passing via the complexes, and advances which come closer to "solving the question asked" rather  ...  Acknowledgements This work was supported by the EPSRC (grant number EP/J003247/1). The  ... 
doi:10.1007/978-3-319-21362-0_3 fatcat:kyr53ossuzccrcdffp5ipmucfa

Certifying Standard and Stratified Datalog Inference Engines in SSReflect [chapter]

Véronique Benzaken, Évelyne Contejean, Stefania Dumbrava
2017 Lecture Notes in Computer Science  
As such, we propose a deep specification of a stratified Datalog inference engine in the SSReflect extension [15] of the Coq proof-assistant [27] .  ...  We propose a SSReflect library for logic programming in the Datalog setting. As part of this work, we give a first mechanization of standard Datalog and of its extension with stratified negation.  ...  Proof by Theorems 5 and 6, using a corrolary of the Knaster-Tarski result, as established in Coq by [11] .  ... 
doi:10.1007/978-3-319-66107-0_12 fatcat:32wdsbjjprhddnyyex3sjzrypq

Towards formal proofs of feedback control theory

Omar A. Jasim, Sandor M. Veres
2017 2017 21st International Conference on System Theory, Control and Computing (ICSTCC)  
Other examples are statements on robust control performance in the face of dynamical uncertainties and disturbances in sensing and actuation.  ...  The most basic of such property is the stability of a control subsystem or the overall system.  ...  In this paper we are interested in formal verification algorithms, which aims to check the correctness of control design (CAD) in Stage 2.  ... 
doi:10.1109/icstcc.2017.8107009 fatcat:q4mfpuohkfeete525amndwjljq

Formal Methods for Smartcard Security [chapter]

Gilles Barthe, Guillaume Dufay
2005 Lecture Notes in Computer Science  
Such an increased flexibility raises concerns about the possibility of logical attacks that could affect a very large number of devices, and requires the development of techniques and tools that can be  ...  The objective of this chapter is to describe some applications of formal methods to increase the reliability of smartcards and trusted personal devices.  ...  The authors are partially supported by the European IST project INSPIRED, the RNTL project CASTLES and the ACI Sécurité SPOPS and GECCOO.  ... 
doi:10.1007/11554578_5 fatcat:4y7miflopjhs7ik5wvacpen7f4

Compositional safety verification with Max-SMT

Marc Brockschmidt, Daniel Larra, Albert Oliveras, Enric Rodrıguez-Carbonell, Albert Rubio
2015 2015 Formal Methods in Computer-Aided Design (FMCAD)  
For a given program part (e.g., a single loop) and a postcondition ϕ, we show how to, using a Max-SMT solver, an inductive invariant together with a precondition can be synthesized so that the precondition  ...  The derived conditions can be viewed as implicit contracts between different parts of the program, and thus enable an incremental program analysis.  ...  IV-A, and then present the algorithm that combines these local analyses to construct a global safety proof in Sect. IV-B. A.  ... 
doi:10.1109/fmcad.2015.7542250 fatcat:vl7e6bnhvrhifmdvg2nvvidxga

Dependent types in practical programming

Hongwei Xi, Frank Pfenning
1999 Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '99  
A major complication resulting from introducing dependent types is that pure type inference for the enriched system is no longer possible, but we show that type-checking a sufficiently annotated program  ...  We present an approach to enriching the type system of ML with a restricted form of dependent types, where type index objects are drawn from a constraint domain C, leading to the DML(C) language schema  ...  We also would like to thank Chad Brown for proofreading a draft and providing us with many helpful comments, and the referees for their highly constructive suggestions.  ... 
doi:10.1145/292540.292560 dblp:conf/popl/XiP99 fatcat:xphj4iccpfbjdnv3ooyz72ccai

The mitochondrial carrier SFXN1 is critical for Complex III integrity and cellular metabolism [article]

Michelle Grace Acoba, Ebru S. Selen Alpergin, Santosh Renuse, Lucía Fernández-del-Río, Ya-Wen Lu, Catherine F Clarke, Akhilesh Pandey, Michael J. Wolfgang, Steven M Claypool
2020 bioRxiv   pre-print
We find that SFXN1, an integral membrane protein in the IMM with an uneven number of transmembrane domains, is a novel TIM22 substrate.  ...  Instead, SFXN1 supports CIII function by participating in heme and central carbon metabolism.  ...  We therefore measured its two isoforms in humans: CoQ 9 and CoQ 10 .  ... 
doi:10.1101/2020.06.18.157495 fatcat:khavzdtsznayfoetvlisglzqui

Applying Formal Methods to Networking: Theory, Techniques, and Applications

Junaid Qadir, Osman Hasan
2015 IEEE Communications Surveys and Tutorials  
In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.  ...  The Internet which began as a research experiment was never designed to handle the users and applications it hosts today.  ...  Coq also supports extracting certified programs to popular functional languages like OCaml, Haskell, etc.  ... 
doi:10.1109/comst.2014.2345792 fatcat:oc6l6pn4tnddjbbr5v4gbbuycq
« Previous Showing results 1 — 15 out of 38 results