Calculemus RISC THEOREMA Calculemus at RISC: The THEOREMA Project Bruno Buchberger OVR (“Old Visiting Researcher”) Talk at the Calculemus Midterm Review

CalculemusRISC THEOREMA

Calculemus at RISC:The THEOREMA Project

Bruno BuchbergerOVR (“Old Visiting Researcher”)

Talk at the Calculemus Midterm ReviewSaarland University and DFKI, Saarbruecken, Germany

March 30, 2003


Copyright Bruno Buchberger 2003

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• 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


• The Goal of RISC:

• research• education• application

in symbolic computation.

• The YVR program is integrated into RISC education.


• 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 internshipRISC graduates now founded SWpark in Romania!)


• 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


• THEOREMA involvements in EU-Programs:

• Calculemus TMR

• OpenMath Thematic Net• MKM (Mathematical Knowledge Management) Thematic Net• Socrates


• 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


• THEOREMA cooperation with other groups:

• 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


• 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


• 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


• 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)


Participation in Task 3.3: Application to Undergraduate Exams

• RISC Contribution: Using Theorema in math courses at the U of Linz


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 !


• 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


• 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


• 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


• 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


• YVR Laura Kovacs

• 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


• Remote MIZAR course for THEOREMA young researchers:

• Course was given by A. Trybulec• Feb – May 2002• Exercises and discussion over the web• Participants: THEOREMA postdocs and PhD students.


• 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


• 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

Documents

Calculemus RISC THEOREMA Calculemus at RISC: The THEOREMA Project Bruno Buchberger OVR (“Old Visiting Researcher”) Talk at the Calculemus Midterm Review