Certified Computer Algebra on Top of an Interactive Theorem Prover
We present a prototype of a computer algebra system that is built on top of a proof assistant, HOL Light. This architecture guarantees that one can be certain that the system will make no mistakes. All expressions in the system will have precise semantics, and the proof assistant will check the correctness of all simplifications according to this semantics. The system actually proves each simplification performed by the computer algebra system.
Although our system is built on top of a proof assistant, we designed the user interface to be very close in spirit to the interface of systems like Maple and Mathematica. The system, therefore, allows the user to easily probe the underlying automation of the proof assistant for strengths and weaknesses with respect to the automation of mainstream computer algebra systems. The system that we present is a prototype, but can be straightforwardly scaled up to a practical computer algebra system.
KeywordsComputer Algebra Computer Algebra System Proof Assistant Interactive Theorem Prover Global List
Unable to display preview. Download preview PDF.
- 1.Armando, A., Zini, D.: Towards interoperable mechanized reasoning systems: the logic broker architecture. In: Corradi, A., Omicini, A., Poggi, A. (eds.) WOA, Pitagora Editrice Bologna, pp. 70–75 (2000)Google Scholar
- 8.Buchberger, B., et al.: The Theorema Project: A Progress Report. In: Kerber, M., Kohlhase, M. (eds.) Symbolic Computation and Automated Reasoning (Proceedings of CALCULEMUS, Natick, Massachusetts, A.K. Peters (2000)Google Scholar
- 9.Carette, J., Farmer, W., Wajs, J.: Trustable communication between mathematics systems. In: CALCULEMUS 2003, Rome, Italy, Aracne, pp. 55–68 (2003)Google Scholar
- 10.Carlisle, D., Ion, P., Miner, R., Poppelier, N.: Mathematical Markup Language (MathML) Version 2.0, 2nd edn. (2003)Google Scholar
- 11.Char, B.W., Geddes, K.O., Gentleman, W.M., Gonnet, G.H.: The design of Maple: A compact, portable and powerful computer algebra system. Springer, London (1983)Google Scholar
- 12.Coq Development Team. The Coq Proof Assistant Reference Manual Version 8.0. INRIA-Rocquencourt (January 2005)Google Scholar
- 15.Buswell, S., et al.: The OpenMath Standard, version 2.0 (2002)Google Scholar
- 18.Jackson, P.B.: Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Cornell University, Ithaca, NY, USA (January 1995)Google Scholar
- 19.Lester, D.R.: Effective continued fractions. In: Proceedings 15th IEEE Symposium on Computer Arithmetic, pp. 163–170. IEEE Computer Society Press, Washington (2001)Google Scholar
- 20.Poll, E., Thompson, S.: Adding the axioms to Axiom: Towards a system of automated reasoning in Aldor. In: Calculemus and Types 1998 (July 1998)Google Scholar
- 23.Wester, M.J. (ed.): Contents of Computer Algebra Systems: A Practical Guide, chapter A Critique of the Mathematical Abilities of CA Systems. John Wiley & Sons, Chichester, United Kingdom (1999)Google Scholar