1. Linking HOL Light to Mathematica using OpenMath Supervised by:Dr. Sofiène Tahar Department of Electrical and Computer Engineering Presented by:Ons Seddiki

2. Introduction Proposed Methodology Applications and Demo ConclusionOutline

3. Introduction3 HOL Light Mathematical Standard OpenMath Returned result Numerical approaches: Matlab Theorem Provers: Lego, Coq Computer Algebra Systems: Mathematica, Maple Mathematica

4. OpenMath4 OpenMath XML standard Mathematical objects + semantic Exchange between programs Storage in databases Publication in worldwide web

5. OpenMath Architecture OpenMath Object Encoding Object Encoding Object OpenMath Object A-Specific Rep Program A B-Specific Rep Program B Phrasebook A +CD General Transport Layer Phrasebook B +CD OpenMath Encoding 5 Dalams (1997) An OpenMath 1.0 Implementation.

6. Proposed Methodology Phrasebook* HOL Light Translator OpenMath Content Dictionaries OpenMath Content Dictionaries OpenMath to HOL Light HOL Light to OpenMath Mathematica to OpenMath OpenMath to Mathematica HOL Light Mathematica 6 * Caprotti (2000) JAVA Phrasebooks for Computer Algebra and automated Deduction.

7. 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 OpenMath Content Dictionaries OpenMath Object Input OpenMath Object Output 7

8. OpenMath Input HOL Light Input Parser & Splitter OpenMath Content Dictionaries OpenMath Object Input Parsing HOL Light input Mapping to OpenMath objects HOL Light Expression ‘‘string’’ Mathematica Function ‘‘string’’ Parser & Splitter 8

9. OpenMath Output OpenMath-Mathematica Phrasebook 9 OpenMath Content Dictionaries OpenMath Object Input OpenMath Object Output Parsing XML file Mapping to Mathematica Calling Mathematica kernel Mapping to OpenMath Object

10. Parser & Collector 10 OpenMath Content Dictionaries OpenMath Object Output Parsing XML file Mapping to HOL Light HOL Light Output theorem Execution time = 2.433s

11. Applications and Demo 11 Execution time = 2.355s

12. Execution time = 2.677s Applications and Demo Computation of Eigenvalues and Eigenvectors of a general matrix 2x2 12 Execution time = 2.296s

13. 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

14. Boundary Condition of an Optical Interface Applications and Demo 14 Execution time = 2.891s

15. Applications and Demo 15

16. 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