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Transcript of Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of...
![Page 1: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/1.jpg)
Linking HOL Light to Mathematica using OpenMath
August26, 2014
Supervised by: Dr. Sofiène Tahar
Department of Electrical and Computer Engineering
Presented by: Ons Seddiki
![Page 2: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/2.jpg)
Introduction
Proposed Methodology
Applications and Demo
Conclusion
Outline
![Page 3: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/3.jpg)
Introduction
3
HOL Light
Mathematical Standard
OpenMath
Returned result
Numerical approaches:
Matlab
Theorem Provers:
Lego, Coq
Computer Algebra Systems:
Mathematica, Maple
Mathematica
![Page 4: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/4.jpg)
OpenMath
4
OpenMath
XML standard
Mathematical objects + semantic
Exchange between programs
Storage in databases
Publication in worldwide web
![Page 5: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/5.jpg)
OpenMath Architecture
OpenMath Object
EncodingObject
EncodingObject
OpenMath Object
A-Specific Rep
Program A
B-Specific Rep
Program B
Phrasebook A+CD
General Transport Layer
Phrasebook B+CD
OpenMath Encoding
OpenMath Encoding
5
Dalams (1997) An OpenMath 1.0 Implementation.
![Page 6: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/6.jpg)
Proposed Methodology
Phrasebook*
HOL Light TranslatorOpenMath
Content Dictionaries
OpenMath to HOL LightHOL Light to OpenMath
Mathematica to OpenMathOpenMath to Mathematica
HOL Light
Mathematica
6
* Caprotti (2000) JAVA Phrasebooks for Computer Algebra and automated Deduction.
![Page 7: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/7.jpg)
Proposed Methodology
Java Application
OCaml Units
HOL Light
Mathematica
HOL Light Input HOL Light Output
Parser & Splitter Parser & Collector
OpenMath-Mathematica Phrasebook
Mathematica Input Mathematica Output
OpenMathContent
Dictionaries
OpenMath
Object Input
OpenMath
Object Output
7
![Page 8: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/8.jpg)
OpenMath Input
HOL Light Input
Parser & Splitter
OpenMathContent
Dictionaries
OpenMath Object Input
Parsing HOL Light input
Mapping to OpenMath objects
HOL Light Expression
‘‘string’’
Mathematica Function ‘‘string’’
Parser & Splitter
8
∫1
10
(𝑥3+2𝑥2−2𝑥+𝑦)
![Page 9: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/9.jpg)
OpenMath Output
OpenMath-Mathematica Phrasebook
OpenMath-Mathematica Phrasebook
9
OpenMathContent
Dictionaries
OpenMathObject Input
OpenMath Object Output
Parsing XML file
Mapping to Mathematica
Calling Mathematica kernel
Mapping to OpenMath Object
![Page 10: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/10.jpg)
Parser & Collector
10
Parser & Collector
OpenMathContent
Dictionaries
OpenMath Object Output
Parsing XML file
Mapping to HOL Light
HOL Light Output theorem
Execution time = 2.433s
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Applications and Demo
Factoringpolynomials
11
Execution time = 2.355s
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Execution time = 2.677s
Applications and Demo
Computation of Eigenvalues and Eigenvectors of a general matrix 2x2
12
Execution time = 2.296s
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Boundary Condition of an Optical Interface
Applications and Demo
13
• The electromagnetic field satisfies the boundary condition
• Cross product between the normal to the interface and the summation of the electric fields and the magnetic fields at the interface
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Boundary Condition of an Optical Interface
Applications and Demo
14
Execution time = 2.891s
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Applications and Demo
15
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Conclusion
Tool linking HOL Light to Mathematica using OpenMath
Improve and extend the grammar of the HOL Light translator
Implement a web service to access Mathematica
Implement connection to an open source CAS
16
HOL Light
Mathematical Standard
OpenMath
Returned result
Numerical approaches:
Matlab
Theorem Provers:
Lego, Coq
Computer Algebra
Systems:Mathematica, Maple
Mathematica
![Page 17: Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki.](https://reader038.fdocuments.net/reader038/viewer/2022110322/56649d035503460f949d6495/html5/thumbnails/17.jpg)