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Nonstandard Analysis in ACL2

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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 nonexistence 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 nonstandard analysis, which interacts better with the discrete flavor of ACL2 than does traditional analysis.

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Authors and Affiliations

  1. Loop One, Inc., 515 Congress Ave., Suite 2500, Austin, TX, 78701, U.S.A.

    Ruben A. Gamboa

  2. Advanced Micro Devices, Inc., 5900 E. Ben White Blvd., M/S 625, Austin, TX, 78741, U.S.A.

    Matt Kaufmann

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  1. Ruben A. Gamboa
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  2. Matt Kaufmann
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Gamboa, R.A., Kaufmann, M. Nonstandard Analysis in ACL2. Journal of Automated Reasoning 27, 323–351 (2001). https://doi.org/10.1023/A:1011908113514

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