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Proof Assistant Decision Procedures for Formalizing Origami
[chapter]
2011
Lecture Notes in Computer Science
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We examine the strength of Gröbner Bases implementations comparing 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. ...
doi:10.1007/978-3-642-22673-1_4
fatcat:n3dfqj73afgphagwrc3umn4yhi
A short proof of the Dimension Conjecture for real hypersurfaces in C^2
[article]
2015
arXiv
pre-print
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Shafikov have settled the so-called Dimension Conjecture, which characterizes spherical hypersurfaces 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. ...
arXiv:1509.09139v1
fatcat:gfsqdqojcna7xkjfptu2ggorae
Developments in Formal Proofs
[article]
2014
arXiv
pre-print
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Finally, we discuss advances 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. ...
arXiv:1408.6474v1
fatcat:ho7xhssjurcidhy4yfxphnqbm4
Reasoning About Algebraic Structures with Implicit Carriers in Isabelle/HOL
[chapter]
2020
Lecture Notes in Computer Science
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We prove Chen and Grätzer's construction theorem for Stone 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] . ...
doi:10.1007/978-3-030-51054-1_14
fatcat:7oikixg6rrdhdeiwl3j7k64fty
Mathematics in the Age of the Turing Machine
[article]
2013
arXiv
pre-print
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The article gives a survey of mathematical 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. ...
arXiv:1302.2898v1
fatcat:ko2iqnfnq5dlbe6fwirbpvuswy
Interactive Theorem Proving
2016
Journal of automated reasoning
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This special issue collects current efforts towards the construction of formal 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 ...
doi:10.1007/s10817-016-9363-7
fatcat:cz5nkkk6hfbathwh4rg5s5urum
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)
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and potential of 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. ...
doi:10.1365/s13291-020-00221-1
fatcat:pt4sfc3hlvfwlant3b4v2varwu
Formalisation of Selected Results from Group Theory
2021
Zenodo
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This thesis deals with the formalisation of some group-theoretic results 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. ...
doi:10.5281/zenodo.4785363
fatcat:ggo4zojijrgk5kfuufsxxsfsgu
Towards computer aided mathematics
2006
Journal of Applied Logic
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, and computer 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. ...
doi:10.1016/j.jal.2005.10.001
fatcat:gawws4hbbnappewt2z4dao5loq
Tool-Based Verification of a Relational Vertex Coloring Program
[chapter]
2015
Lecture Notes in Computer Science
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: the automated theorem prover Prover9 and the two 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 ...
doi:10.1007/978-3-319-24704-5_17
fatcat:v25bbisshfe5feqimxf2u5ocm4
Preface
2011
Mathematical Structures in Computer Science
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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. ...
doi:10.1017/s0960129511000235
fatcat:f5ehf7oyjjdrffke7wt3lpujc4
Proving Bounds for Real Linear Programs in Isabelle/HOL
[chapter]
2005
Lecture Notes in Computer Science
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For our work described 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 ...
doi:10.1007/11541868_15
fatcat:7v4m2yzgxnb7deoqie5sqmadqm
Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving
[chapter]
2011
Lecture Notes in Computer Science
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Integrating decision procedures 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 ...
doi:10.1007/978-3-642-21046-4_3
fatcat:ssvv2zgqena3joe3tdtr7sus6y
Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL
[article]
2021
arXiv
pre-print
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Other Versions
Our formalizations 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. ...
arXiv:2101.05257v2
fatcat:ozo6fkwhc5aujaxynmy4a2ztjy
A Methodology for the Formal Verification of Dynamic Fault Trees using HOL Theorem Proving
2019
IEEE Access
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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] . ...
doi:10.1109/access.2019.2942829
fatcat:27c4t2ss7rawhhj5so2x6d6w6a
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