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Towards Formalising Schutz' Axioms for Minkowski Spacetime in Isabelle/HOL [article]

Richard Schmoetten
2021 arXiv   pre-print
We present a mechanisation in Isabelle/HOL of the system of axioms as well as theorems relating to temporal order.  ...  Special Relativity is a cornerstone of modern physical theory. While a standard coordinate model is well-known and widely taught today, several alternative systems of axioms exist.  ...  , provides a reconstruction of the automatic proof in Isabelle/HOL.  ... 
arXiv:2108.10868v2 fatcat:grr4izsqkzdh5knadhq4fzar3u

Formalization of the arithmetization of Euclidean plane geometry and applications

Pierre Boutry, Gabriel Braun, Julien Narboux
2019 Journal of symbolic computation  
To illustrate the concrete use of this formalization, we derived from Tarski's system of geometry a formal proof of the nine-point circle theorem using the Gröbner basis method.  ...  This paper describes the formalization of the arithmetization of Euclidean plane geometry in the Coq proof assistant.  ...  In [MP15] , Marić and Petrović formalized complex plane geometry in the Isabelle/HOL theorem prover.  ... 
doi:10.1016/j.jsc.2018.04.007 fatcat:7lxvzb4akrbnblfsd4nrgpwjrm

Comparing Mathematical Provers [chapter]

Freek Wiedijk
2003 Lecture Notes in Computer Science  
The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their level of automation.  ...  We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs.  ...  automation • • • • • • • • 6 A rather subjective two-dimensional diagram Mizar k Agda k Metamath 6 more automation - more mathematical k ACL2 PVS Isabelle HOL k Ωmega s Otter  ... 
doi:10.1007/3-540-36469-2_15 fatcat:bo4hoan5zrgajada3ejhd7jyni

Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III

Alexander Steen
2019 Künstliche Intelligenz  
A primary focus of this thesis is the provision of evidence that a paramodulation-based proof calculus can effectively be employed for performant equational reasoning in Extensional Type Theory (higher-order  ...  In the practically motivated main part of this thesis, the design and architecture of the new higher-order theorem prover Leo-III is presented.  ...  Isabelle/HOL.  ... 
doi:10.1007/s13218-019-00628-8 fatcat:b6yfenxgxndb3myskqushsm6uy

A Revision of the Proof of the Kepler Conjecture

Thomas C. Hales, John Harrison, Sean McLaughlin, Tobias Nipkow, Steven Obua, Roland Zumkeller
2009 Discrete & Computational Geometry  
The original proof, announced in 1998 and published in 2006, is long and complex. The process of revision and review did not end with the publication of the proof.  ...  A final part of this article lists errata in the original proof of the Kepler conjecture.  ...  The theorem prover that we used, Isabelle/HOL [37] , fulfills this criterion.  ... 
doi:10.1007/s00454-009-9148-4 fatcat:zgy65actvfhlbjjcgsubfv744u

From Tarski to Descartes: Formalization of the Arithmetization of Euclidean Geometry

Pierre Boutry, Gabriel Braun, Julien Narboux
unpublished
use the algebraic automated deduction methods in geometry.We give an example of the use this formalization by deriving from Tarski's system of geometry a formal proof of theorems of nine points using  ...  properties.This work completes our formalization of the two-dimensional results contained in part one of Metamathematische Methoden in der Geometrie.We define the arithmetic operations geometrically and  ...  Isabelle/HOL.  ... 
doi:10.29007/k47p fatcat:5x4xjusgurctpg2vpyxtvxln3a

Primality Testing is Polynomial-time: A Mechanised Verification of the AKS Algorithm [article]

Hing Lun Joseph Chan, University, The Australian National
2019
The entire work is carried out in the HOL4 theorem prover. The correctness of the AKS algorithm relies on a main theorem developed by the AKS team, based on the theory of finite fields.  ...  These slight adjustments are minor in terms of the significance of the AKS achievement, answering the challenge "Is Primes in P?"  ...  These can be handled by the simple recurrence theory outlined in this chapter. The asympotic big-O notation has been formalised in Avigad and Donnelly [2004] using the Isabelle/HOL proof assistant.  ... 
doi:10.25911/5f58b06ca124e fatcat:objty3blpbbyha3evgeduua64a

Test and Verification of Compiler Back Ends with a Cost-Benefit Analysis [article]

Elke Salecker, Sabine Glesner, Technische Universität Berlin, Technische Universität Berlin
2012
We developed a modular, machine-assisted verification approach within the theorem prover Isabelle/HOL.  ...  Der von uns entwickelte Ansatz basiert auf einer Formalisierung im interaktiven Theorembeweiser Isabelle/HOL.  ...  We come back to this point in Chapter 4 where we present our formalization. Isabelle/HOL We developed our formalization in the theorem prover Isabelle [Pau94] .  ... 
doi:10.14279/depositonce-3342 fatcat:pzn735rpinffpdakcsrgbzclqq

Analytical Inductive Functional Programming [chapter]

Emanuel Kitzelmann
2009 Lecture Notes in Computer Science  
Acknowledgement The author would like to thank anonymous reviewers for their constructive and useful comments on the previous version of the paper.  ...  the analytical approach as far as possible in order to be able to induce more complex functions in a reasonable amount of time.  ...  The number of locations in the automaton is Q and number of discrete transitions is ∆. The number of clauses in the translated CLP programs includes the clauses for the delay transitions.  ... 
doi:10.1007/978-3-642-00515-2_7 fatcat:r3xkzawlibfcpluopvlz7ukp4y

Advancing Deductive Program-Level Verification for Real-World Application: Lessons Learned from an Industrial Case Study

Thorsten Bormer
2014
The axioms of the prelude, imported as proof obligations into Isabelle/HOL, are then derived in this theory.  ...  by Boogie which can then be imported into Isabelle/HOL with the help of a loader.  ... 
doi:10.5445/ir/1000049792 fatcat:ibjp7km2onforhv6fjq4bkx54i

Model Transformation Languages with Modular Information Hiding

Andreas Rentschler
2015
All three approaches are tailored to the specific needs of the transformation domain.  ...  Model transformations, together with models, form the principal artifacts in model-driven software development.  ...  There are numerous pieces to the puzzle that had to come together successful for this dissertation project, and I am glad so many people have contributed to the success of this dissertation by adding one  ... 
doi:10.5445/ksp/1000045910 fatcat:uxid36iva5gprkihu6f4ixr3uy

Quality of Experience: From Assessment to Application (Dagstuhl Seminar 15022) Understanding Complexity in Multiobjective Optimization (Dagstuhl Seminar 15031) Model-driven Algorithms and Architectures for Self-Aware Computing Systems (Dagstuhl Seminar 15041) Artificial and Computational Intelligence in Games: Integration (Dagstuhl Seminar 15051)

Michael Philippsen, Pascal Felber, Michael Scott, J Eliot, Katrien De Moor, Markus Fiedler, Peter Reichl, Martín Varela, Salvatore Greco, Kathrin Klamroth, Joshua Knowles, Günter Rudolph (+13 others)
2015 unpublished
The research field of artificial and computational intelligence in games focuses on the wide variety of advanced computational techniques used to create, enhance, and improve the experiences of humans  ...  This includes generalizations to interwoven systems with more than two subproblems, an in-depth analysis of the similarities and the differences between different notions of optimality and between the  ...  I reported on the machine-checked verification of an on-the-fly, concurrent, mark-sweep garbage collector in Isabelle/HOL.  ... 
fatcat:ckaercgotnenhidbwsz7zufttq

Robust Communications in Erlang

Joseph Richard Harrison
2021
This culminates in automatic tooling to detect certain cases of communication discrepancies via static analysis, and automatic instrumentation of concurrent programs to detect and rec [...]  ...  A fragment of the Core Erlang intermediate format is modelled formally so that we can reason about the out-of-order communication in Erlang systems, particularly the dependencies between sent messages  ...  Other Publications Several contributions presented herein are also detailed in other published work, namely: • 'Towards an Isabelle/HOL Formalisation of Core Erlang' (Harrison 2017) contains an earlier  ... 
doi:10.22024/unikent/01.02.87484 fatcat:6jpavcswordzzjtvexzpch6774

2012 Jahresbericht Annual Report Jahresbericht Annual Report

Kontakt Geschäftsstelle, Schloss Dagstuhl, Heike Clemens, Jutka Gasiorowski
2013 unpublished
Acknowledgments Many thanks to the Dagstuhl office and its helpful and patient staff; huge thanks to the organizers of the previous seminars in the series for setting us up for success; and thanks to all  ...  Examples of state-of-the-art interactive theorem provers are ACL2, Isabelle, HOL, Coq and PVS, while E, SPASS, Vampire and Z3 are examples of automatic provers.  ...  be used in analytical reasoning about the model.  ... 
fatcat:qmtsqeo23jcjffzwbvuoasqchq

Interdependent Security and Compliance in Service Selection

Harun Fatih Karataş
2016
Hence this thesis addresses the question of how to consider interdependent security and compliance in service composition.  ...  Instead, compliance is verified afterwards which might necessitate repeating the selection process in case of a non-compliant solution.  ...  Thesis Structure This thesis consists of nine chapters which are organized in four parts.  ... 
doi:10.5283/epub.34763 fatcat:sj4pstjqcndyhkshvnd5ztlixi