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NonStandard Analysis in ACL2
, 2001
"... 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 complexrational numbers and excluding the real and complex irrationals. In conjunction ..."
Abstract

Cited by 26 (11 self)
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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 complexrational 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.
The Language of Mathematics
, 2009
"... The accompanying thesis is part of a longterm project to enable computers to do mathematics in the same way that humans do. I will sketch something of the nature of mathematics and the project, and then turn to role of the thesis. Mathematics Mathematics arises from the interaction of two dissimila ..."
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Cited by 11 (0 self)
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The accompanying thesis is part of a longterm project to enable computers to do mathematics in the same way that humans do. I will sketch something of the nature of mathematics and the project, and then turn to role of the thesis. Mathematics Mathematics arises from the interaction of two dissimilar modes of reasoning: a ‘soft ’ side, dealing with ideas and analogies, and a ‘hard ’ side, dealing with verification. The ‘hard ’ side is easier to pin down. It consists primarily of formal ‘proofs’, each consisting of a series of assertions. A mathematician can verify that a proof is correct by following it, step by step, checking that each step follows from previous ones via facts already proved to be correct. The ‘soft ’ side is less easily described. It consists of intuitions about the formal objects constructed in mathematical proofs; ideas that one piece of mathematics may analogically correspond to another piece of mathematics; or even analogies between mathematics and objects in the physical world.