Certified Computer Algebra on Top of an Interactive Theorem Prover

  • Cezary Kaliszyk
  • Freek Wiedijk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4573)


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.


Computer Algebra Computer Algebra System Proof Assistant Interactive Theorem Prover Global List 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Cezary Kaliszyk
    • 1
  • Freek Wiedijk
    • 1
  1. 1.Institute for Computing and Information Sciences, Radboud University NijmegenThe Netherlands

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