Embed Size (px)
Citation preview
Linking HOL Light to Mathematica using OpenMath
August26, 2014
Supervised by: Dr. Sofiène Tahar
Department of Electrical and Computer Engineering
Presented by: Ons Seddiki
Introduction
Proposed Methodology
Applications and Demo
Conclusion
Outline
Introduction
3
HOL Light
Mathematical Standard
OpenMath
Returned result
Numerical approaches:
Matlab
Theorem Provers:
Lego, Coq
Computer Algebra Systems:
Mathematica, Maple
Mathematica
OpenMath
4
OpenMath
XML standard
Mathematical objects + semantic
Exchange between programs
Storage in databases
Publication in worldwide web
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.
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.
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
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)
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
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
Applications and Demo
Factoringpolynomials
11
Execution time = 2.355s
Execution time = 2.677s
Applications and Demo
Computation of Eigenvalues and Eigenvectors of a general matrix 2x2
12
Execution time = 2.296s
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
Boundary Condition of an Optical Interface
Applications and Demo
14
Execution time = 2.891s
Applications and Demo
15
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
