1. Linking HOL Light to Mathematicausing OpenMath Department of Electrical and Computer Engineering Presented by: OnsSeddiki Supervised by: Dr. SofièneTahar August26, 2014

2. Outline

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

4. OpenMath 4

5. OpenMath Architecture Program A • Program B A-SpecificRep • B-SpecificRep Phrasebook A +CD Phrasebook B +CD OpenMath Object • OpenMath Object OpenMathEncoding OpenMathEncoding • Encoding • Object Encoding Object GeneralTransportLayer Dalams (1997) An OpenMath 1.0 Implementation. 5

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

7. Proposed Methodology HOL Light HOL Light Output HOL Light Input OCamlUnits Parser & Collector Parser & Splitter OpenMath Content Dictionaries OpenMath Object Input OpenMath ObjectOutput OpenMath-MathematicaPhrasebook Java Application Mathematica Input Mathematica Output Mathematica 7

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

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

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

11. Applications and Demo • Factoringpolynomials Execution time = 2.355s 11

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

13. Applications and Demo BoundaryConditionof an Optical Interface • 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 13

14. Applications and Demo BoundaryConditionof an Optical Interface Execution time = 2.891s 14

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 HOL Light Returned result Mathematical Standard OpenMath Numerical approaches: Matlab Theorem Provers: Lego, Coq Computer Algebra Systems: Mathematica, Maple Mathematica 16

17. Thank you