Calculemus
RISC THEOREMA
Calculemus at RISC:
The THEOREMA Project
Bruno Buchberger
OVR (“Old Visiting Researcher”)
Talk at the Calculemus Midterm Review
Saarland University and DFKI, Saarbruecken, Germany
March 30, 2003
Calculemus
RISC THEOREMA
Copyright Bruno Buchberger 2003
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Calculemus
RISC THEOREMA
• RISC:
Research Institute for Symbolic Computation
Johannes Kepler University
Linz, Austria
Founded in 1987 by B. Buchberger
• THEOREMA:
A project at RISC on formal mathematics
(computer-supported proving, solving, computing)
Project leader: B. Buchberger
Calculemus
RISC THEOREMA
• The Goal of RISC:
• research
• education
• application
in symbolic computation.
• The YVR program is integrated into RISC education.
Calculemus
RISC THEOREMA
• Education at RISC:
• permanently ~ 25 international PhD students
• emphasis on basic research
• educate also in research management
(e.g. J of SC, e.g. int’l conferences)
• educate also in application management
(e.g. Softwarepark Hagenberg, a RISC spin-off,
possibilities for internship
RISC graduates now founded SWpark in Romania!)
Calculemus
RISC THEOREMA
• THEOREMA Group:
• Senior researchers: B. Buchberger, T. Jebelean, W.
Windsteiger
• Postdocs: Temur Kutsia, Koji Nakagawa, Mircea Marin, Judit
Robu
• PhD students: Florina Piroi, Markus Rosenkranz, Adrian
Craciun, Laura Kovacs, Nikolaj Popov, Gabor Kusper
• Socrates students: Cornel Izbasa, Diana Dubu, Sorin Cira,
Camelia Kocsis
Calculemus
RISC THEOREMA
• THEOREMA involvements in EU-Programs:
• Calculemus TMR
• OpenMath Thematic Net
• MKM (Mathematical Knowledge Management) Thematic Net
• Socrates
Calculemus
RISC THEOREMA
• THEOREMA tasks within Calculemus:
• Task leader for Task 2.2: Enhance Computer Algebra
Systems by Reasoning Power
• Task leader in Task 3.1: Case Studies in Writing
Mathematical Publications
• Participation in Task 1.2: Definition of Mathematical Services
• Participation in Task 3.3: Application to Undergraduate
Exams
Calculemus
RISC THEOREMA
• THEOREMA cooperation with other groups:
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U of Karlsruhe 2.2
U of Bialystok 3.1
U of Edinburgh 2.2
U of Genova 2.2
U of Saarbrücken 3.1
U of Bialystok: 3.1
Calculemus
RISC THEOREMA
• Task 2.2: Enhance Computer Algebra Systems by Reasoning
Power
• Participants: THEOREMA, U of Karlsruhe, U of Edinburgh,
(U of Genova)
• Current computer algebra systems: solving and computing
• Future math systems: proving, solving, and computing
• THEOREMA was chosen as a prototype for this task
(the entire functionality of Mathematica is preserved and
powerful proving functionality is added)
• External links to other proving systems are possible
Calculemus
RISC THEOREMA
• Task 3.1: Case Studies in Writing Mathematical Publications
• Participants: THEOREMA, U of Bialystok, U of Saarbrücken
• U of Bialystok: MIZAR library is currently the most extensive
verified math knowledge base (J of Formalized Mathematics)
• Within THEOREMA:
• Lecture notes on predicate logic as a working language
• Lecture notes on algorithmic methods in math
• All publications on THEOREMA were written within
THEOREMA
• U of Saarbrücken: OmDoc language for describing
semantics and structure of mathematical documents on the
web
Calculemus
RISC THEOREMA
• Participation in Task 1.2: Definition of Mathematical
Services
• RISC Contribution: MathBroker architecture for interchange
of mathematical content over the web (Olga Caprotti and
Wolfgang Schreiner)
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RISC THEOREMA
Participation in Task 3.3: Application to
Undergraduate Exams
• RISC Contribution: Using Theorema in math courses at the
U of Linz
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RISC THEOREMA
The Ultimate Scientific Goal of Calculemus (and
THEOREMA):
• Automate the management of mathematical knowledge
(not only methods!):
• invention
• verification
• re-use (over the web)
• Why? Efficiency (of spending funds) !
• Calculemus  Math / CS  Applications
• Europe is leading !
Calculemus
RISC THEOREMA
• THEOREMA Training within Calculemus:
• YVR Program:
• In:
• Adrian Craciun: 17 mo
• Out:
• Markus Rosenkranz: 1 mo (to U of Nijmegen)
• In (starting April 2003):
• Laura Kovacs: 16 mo
• Camelia Kocsis: 16 mo
Calculemus
RISC THEOREMA
• THEOREMA Training within Calculemus:
• Remote Mizar course for THEOREMA young researchers
• Tutorial on THEOREMA at Calculemus Workshop in Pisa
• THEOREMA training for high school teachers and math
students
• Train Socrates students in the THEOREMA group
Calculemus
RISC THEOREMA
• YVR Adrian Craciun
• Visiting from U of Timisoara (Romania)
• Sep 2001 – June 2003
• PhD topic: Theory Exploration and Algorithm Synthesis
within Theorema
• Work at RISC:
• with B. Buchberger: induction provers, case study merge
sort, conjecture generator
• with W. Windsteiger: implementation techniques in
Mathematica
• with T. Kutsia: simplification techniques using sequence
variables
Calculemus
RISC THEOREMA
• YVR Markus Rosenkranz
• Visiting U of Nijmegen (Prof. Barendregt)
• April 2002
• PhD topic: Non-commutative Gröbner bases for boundary
value problems (differential equations)
• Work at U of N:
• with H. Barendregt: formalizing differential operators in
Coq
• with F. Wiedijk: comparison of 15 theorem proving
systems
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RISC THEOREMA
• YVR Laura Kovacs
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•
•
•
Visiting from U of Timisoara, Romania (Prof. S. Maruster)
June 2003 – June 2004
PhD topic: Algorithm Verification in Theorema
Work at U of N.:
• with B. Buchberger: formal proving
• with T. Jebelean: inductive assertion method
• with W. Windsteiger: implementation techniques in
Mathematica
Calculemus
RISC THEOREMA
• Remote MIZAR course for THEOREMA young
researchers:
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•
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Course was given by A. Trybulec
Feb – May 2002
Exercises and discussion over the web
Participants: THEOREMA postdocs and PhD students.
Calculemus
RISC THEOREMA
• Socrates students in THEOREMA:
• Cornel Izbasa (U of Timisoara, Romania): Oct 2001 - March
2002, work with W. Windsteiger on the kernel of the
Theorema system
• Diana Dubu (U of Timisoara, Romania): Oct 2001 – March
2002, work with T. Jebelean on predicate proving in natural
style
• Sorin Cira (U of Timisoara, Romania): Oct 2002 - June
2003, work with B. Buchberger on developing a
mathematical knowledge base for Hilbert spaces theory
• Camelia Kocsis (U Cluj-Napoca, Romania): Feb 2003 - June
2003, work with B. Buchberger on retrieval of logical
formulae from a mathematical knowledge base
Calculemus
RISC THEOREMA
• Practical problems with YVR program:
• Conditions for candidates are too restrictive
• age limits (example: Judit Robu)
• countries (examples: K. Nakagawa - Japan, T. Kutsia Georgia)
• too long stay in Austria (example Florina Piroi)
• Rates come many months too late
• we cannot hire people taking a financial risk