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• W56162016 abstract "ACL2 is a theorem prover over a total, first-order, mostly quantifier-free logic, supporting defined and constrained functions, equality and congruence rewriting, induction, and other reasoning techniques. With its powerful induction engine and direct support for the rational and complex-rational numbers, ACL2 can be used to verify recursive rational algorithms. However, ACL2 can not be used to reason about real-valued algorithms that involve the irrational numbers. For example, there are elegant proofs of the correctness of the Fast Fourier Transform (FFT) which could be formulated in ACL2, but since ACL2's sparse number system permits the proof that the square root of two, and hence the eighth principal root of one, does not exist, it is impossible to reason directly about the FFT in ACL2. This research extends ACL2 to allow reasoning about the real and complex irrational numbers. The modifications are based on non-standard analysis, since infinitesimals are more natural than limits in a quantifier-free context. It is also shown how the trigonometric functions can be defined in the modified ACL2. These definitions are then used to prove that the FFT correctly implements the Fourier Transform.**Dissertation is available in CD-ROM format and requires Windows." @default.
• W56162016 created "2016-06-24" @default.
• W56162016 creator A5016380052 @default.
• W56162016 creator A5051526538 @default.
• W56162016 date "1999-01-01" @default.
• W56162016 modified "2023-09-26" @default.
• W56162016 title "Mechanically verifying real-valued algorithms in acl2" @default.
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