Calculemus RISC THEOREMA Calculemus at RISC The THEOREMA

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 Copyright Note: This file may be copied and stored under the following conditions: – The file must be kept unchanged and must include the copyright note. – A message is sent to buchberger@risc. uni-linz. ac. at – If you use material from this talk, please, cite the talk appropriately.

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 Ph. D 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 • Ph. D 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 • Open. Math 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: • • • 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: Om. Doc 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: Math. Broker architecture for interchange of mathematical content over the web (Olga Caprotti and Wolfgang Schreiner)

Calculemus RISC THEOREMA Participation in Task 3. 3: Application to Undergraduate Exams • RISC Contribution: Using Theorema in math courses at the U of Linz

Calculemus 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 • Ph. D 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 • Ph. D 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

Calculemus RISC THEOREMA • YVR Laura Kovacs • • Visiting from U of Timisoara, Romania (Prof. S. Maruster) June 2003 – June 2004 Ph. D 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: • • Course was given by A. Trybulec Feb – May 2002 Exercises and discussion over the web Participants: THEOREMA postdocs and Ph. D 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