Certified Computer Algebra on Top of an Interactive Theorem Prover

  • Authors:

  • Cezary Kaliszyk;Freek Wiedijk

  • Affiliations:

  • Institute for Computing and Information Sciences, Radboud University Nijmegen, The Netherlands;Institute for Computing and Information Sciences, Radboud University Nijmegen, The Netherlands

  • Venue:
  • Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
  • Year:
  • 2007

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Abstract

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 proveseach 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.