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Proof Assistant Decision Procedures for Formalizing Origami
[chapter]

2011
*
Lecture Notes in Computer Science
*

We examine the strength of Gröbner Bases implementations comparing

doi:10.1007/978-3-642-22673-1_4
fatcat:n3dfqj73afgphagwrc3umn4yhi
*proof**assistants*with each other and with the implementations provided*in*computer*algebra*systems. ...*Proofs*performed with computer*algebra*systems can be accompanied by*proof*documents, still they lack complete mathematical rigorousity, like the one provided by*proof**assistant*checked*proofs*. ... Computer*Algebra*functionality*in**Proof**Assistants*Mainstream Computer*Algebra*Systems, for instance Mathematica and Maple, are weakly founded. ...##
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A short proof of the Dimension Conjecture for real hypersurfaces in C^2
[article]

2015
*
arXiv
*
pre-print

Shafikov have settled the so-called Dimension Conjecture, which characterizes spherical hypersurfaces

arXiv:1509.09139v1
fatcat:gfsqdqojcna7xkjfptu2ggorae
*in*C^2 via the dimension of the*algebra*of infinitesimal automorphisms. ...*In*this note, we propose a short argument for obtaining their result. ... Beloshapka for communicating to us an example of a hypersurface*in*C 2 with dim*hol*(M, p) = 1, for which he kindly performed Maple-*assisted*computations. ...##
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Developments in Formal Proofs
[article]

2014
*
arXiv
*
pre-print

Finally, we discuss advances

arXiv:1408.6474v1
fatcat:ho7xhssjurcidhy4yfxphnqbm4
*in*the automation of formal*proofs*, as implemented*in**proof**assistants*such as Mizar, Coq, Isabelle, and*HOL*Light. ... This report describes three particular technological advances*in*formal*proofs*. The*HOL*Light*proof**assistant*will be used to illustrate the design of a highly reliable system. ... I would also like to thank the many speakers and participants at the special program on Semantics of*proofs*and certified math at IHP. ...##
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Reasoning About Algebraic Structures with Implicit Carriers in Isabelle/HOL
[chapter]

2020
*
Lecture Notes in Computer Science
*

We prove Chen and Grätzer's construction theorem for Stone

doi:10.1007/978-3-030-51054-1_14
fatcat:7oikixg6rrdhdeiwl3j7k64fty
*algebras**in*Isabelle/*HOL*. ... The development requires extensive reasoning about*algebraic*structures*in*addition to reasoning*in**algebraic*structures. ...*In*this paper we focus on Isabelle/*HOL*, which is the higherorder logic instance of the generic*proof**assistant*Isabelle [29] . ...##
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Mathematics in the Age of the Turing Machine
[article]

2013
*
arXiv
*
pre-print

The article gives a survey of mathematical

arXiv:1302.2898v1
fatcat:ko2iqnfnq5dlbe6fwirbpvuswy
*proofs*that rely on computer calculations and formal*proofs*. ... The structures of abstract*algebra*-groups, rings, modules,*algebras*,*algebraically*closed fields and so forth -have all been laid out formally*in*the Coq*proof**assistant*. ... Another praiseworthy project is Kaliszyk and Wiedijk's implementation of a computer*algebra*system on top of the*proof**assistant**HOL*Light. ...##
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Interactive Theorem Proving

2016
*
Journal of automated reasoning
*

This special issue collects current efforts towards the construction of formal

doi:10.1007/s10817-016-9363-7
fatcat:cz5nkkk6hfbathwh4rg5s5urum
*proofs*with the use of interactive theorem provers, which combine formal*proof*-checking and prooffinding tools with human ... The paper describes how abstract interpretation can be used to bridge this gap automatically, and how this process has been verified*in*the Coq*proof**assistant*. ... The paper by Bourke, van Glabbeek, and Höfner, "Mechanizing a Process*Algebra*for Network Protocols," describes an approach to modeling Mobile Ad hoc Networks and Wireless Mesh Networks*in*Isabelle/*HOL*...##
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Formalising Mathematics – in Praxis; A Mathematician's First Experiences with Isabelle/HOL and the Why and How of Getting Started

2020
*
Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner)
*

and potential of

doi:10.1365/s13291-020-00221-1
fatcat:pt4sfc3hlvfwlant3b4v2varwu
*proof**assistants*for mathematics. ... This is an account of a mathematician's first experiences with the*proof**assistant*(interactive theorem prover) Isabelle/*HOL*, including a discussion on the rationale behind formalising mathematics and ... The images or other third party material*in*this article are included*in*the article's Creative Commons licence, unless indicated otherwise*in*a credit line to the material. ...##
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Formalisation of Selected Results from Group Theory

2021
*
Zenodo
*

This thesis deals with the formalisation of some group-theoretic results

doi:10.5281/zenodo.4785363
fatcat:ggo4zojijrgk5kfuufsxxsfsgu
*in*Isabelle/*HOL*– an interactive theorem prover that machine-checks every*proof*step. ... – the canonical Isabelle/*HOL*library on abstract*algebra*. ... The Isabelle*proof**assistant*"Isabelle is a generic*proof**assistant*. ...##
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Towards computer aided mathematics

2006
*
Journal of Applied Logic
*

, and computer

doi:10.1016/j.jal.2005.10.001
fatcat:gawws4hbbnappewt2z4dao5loq
*algebra*systems, into interactive*proof**assistants*. ... The aim of this project is to reconstruct, formalize, and fully verify Hales complete*proof**in*the*assistance*system*HOL*-LIGHT. ...##
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Tool-Based Verification of a Relational Vertex Coloring Program
[chapter]

2015
*
Lecture Notes in Computer Science
*

: the automated theorem prover Prover9 and the two

doi:10.1007/978-3-319-24704-5_17
fatcat:v25bbisshfe5feqimxf2u5ocm4
*proof**assistants*Coq and Isabelle/*HOL*. ... We present different approaches of using a special purpose computer*algebra*system and theorem provers*in*software verification. ... Verification of*Proof*Obligations using Isabelle/*HOL**In*this section we discuss the verification of the relational program (VC) by means of Isabelle/*HOL*, a*proof**assistant*that additionally offers support ...##
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Preface

2011
*
Mathematical Structures in Computer Science
*

*in*variants of predicate calculus. ... The best we could do is relative consistency

*proofs*, such as Gödel's result that the continuum hypothesis is indeed consistent with ZFC. ... The full and successful development of this piece of mathematics

*in*the

*HOL*Light

*proof*

*assistant*is thus an important landmark

*in*formal mathematics. ...

##
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Proving Bounds for Real Linear Programs in Isabelle/HOL
[chapter]

2005
*
Lecture Notes in Computer Science
*

For our work described

doi:10.1007/11541868_15
fatcat:7v4m2yzgxnb7deoqie5sqmadqm
*in*this paper, we have chosen the generic*proof**assistant*Isabelle, tailored to Higher-Order Logic (*HOL*) [4] . ...*In*the following, we will refer to this environment as Isabelle/*HOL*. An important step*in*Hales'*proof*is the maximization of about 10 5 real linear programs. ... Using a rewriting oracle that is based on the ideas found*in*[7] , these operations can be performed so quickly that it is projected that the linear programs arising*in*the*proof*of the Kepler conjecture ...##
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Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving
[chapter]

2011
*
Lecture Notes in Computer Science
*

Integrating decision procedures

doi:10.1007/978-3-642-21046-4_3
fatcat:ssvv2zgqena3joe3tdtr7sus6y
*in**proof**assistants**in*a safe way is a major challenge. ... The method is implemented*in*the Coq system but, since our specialised version of Buchberger's algorithm outputs explicit*proof*certificates, it could be easily adapted to other*proof**assistants*. ... We have compared our method with two systems: Macaulay2 [10], a system dedicated to*algebraic*geometry which is very efficient*in*Gröbner bases computations and*HOL*Light [14] , a*proof**assistant*that ...##
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Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL
[article]

2021
*
arXiv
*
pre-print

Our formalizations

arXiv:2101.05257v2
fatcat:ozo6fkwhc5aujaxynmy4a2ztjy
*in*Isabelle/*HOL*can be found on the Archive of Formal*Proofs*. ... We give an overview of our formalizations*in*the*proof**assistant*Isabelle/*HOL*of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erdős and ... The*proof*of this celebrated theorem is long and elaborate; it has not been formalized*in*any*proof**assistant*, to our knowledge. ...##
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A Methodology for the Formal Verification of Dynamic Fault Trees using HOL Theorem Proving

2019
*
IEEE Access
*

*In*this paper, we further enrich the DFT library

*in*

*HOL*by providing the formalization of spare gates with a shared spare and the verification details of their probabilistic behavior. ... Leveraging upon the expressive and sound nature of higher-order logic (

*HOL*) theorem proving, it has been recently proposed for the analysis of DFTs

*algebraically*. ... The

*proof*script for the drive-by-wire system is around 4950 lines long. B. FORMAL VERIFICATION OF CARDIAC

*ASSIST*SYSTEM The DFT for the cardiac

*assist*system (CAS) is shown

*in*Fig. 8 [20] . ...

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