BibTeX
@MISC{Gamboa01non-standardanalysis,
author = {Ruben A. Gamboa and Matt Kaufmann},
title = {Non-Standard Analysis in ACL2 },
year = {2001}
}
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Abstract
ACL2 refers to a mathematical logic based on applicative Common Lisp, as well as to an automated theorem prover for this logic. The numeric system of ACL2 reflects that of Common Lisp, including the rational and complex-rational numbers and excluding the real and complex irrationals. In conjunction with the arithmetic completion axioms, this numeric type system makes it possible to prove the non-existence of specific irrational numbers, such as √2. This paper describes ACL2(r), a version of ACL2 with support for the real and complex numbers. The modifications are based on non-standard analysis, which interacts better with the discrete flavor of ACL2 than does traditional analysis.
