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

Clemens Ballarin, Lawrence C. Paulson
1998 Lecture Notes in Computer Science  
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
more » ... anket 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.
doi:10.1007/bfb0055902 fatcat:3y4foskxojaanofx67uk2ageyi