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Reasoning about coding theory: The benefits we get from computer algebra

  • Clemens Ballarin
  • Lawrence C. Paulson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1476)

Abstract

The use of computer algebra is usually considered beneficial for mechanised reasoning in mathematical domains. We present a case study, in the application domain of coding theory, that supports this claim: the mechanised proofs depend on non-trivial algorithms from computer algebra and increase the reasoning power of the theorem prover. The unsoundness of computer algebra systems is a major problem in interfacing them to theorem provers. Our approach to obtaining a sound overall system is not blanket distrust but based on the distinction between algorithms we call sound and ad hoc respectively. This distinction is blurred in most computer algebra systems. Our experimental interface therefore uses a computer algebra library. It is based on theorem templates, which provide formal specifications for the algorithms.

Keywords

Computer algebra mechanised reasoning combining systems soundness of computer algebra systems specialisation problem coding theory 

AISC topics

Integration of logical reasoning and computer algebra automated theorem provers 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Clemens Ballarin
    • 1
  • Lawrence C. Paulson
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK

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