USING NONSTANDARD ANALYSIS TO ENSURE THE CORRECTNESS OF SYMBOLIC COMPUTATIONS

Abstract

Nonstandard analysis has been put to use in a theorem-prover, where it assists in the analysis of formulae involving limits. The theorem-prover in question is used in the computer program Mathpert to ensure the correctness of calculations in calculus. Although non-standard analysis is widely viewed as non-constructive, it can alternately be viewed as a method of reducing logical manipulation (of formulae with quantifiers) to computation (with rewrite rules). We give a logical theory of nonstandard analysis which is implemented in Mathpert. We describe a procedure for “elimination of infinitesimals” (also implemented in Mathpert) and prove its correctness.