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An Industrial Strength Theorem Prover for a Logic Based on Common Lisp
 IEEE Transactions on Software Engineering
, 1997
"... ACL2 is a reimplemented extended version of Boyer and Moore's Nqthm and Kaufmann's PcNqthm, intended for large scale verification projects. This paper deals primarily with how we scaled up Nqthm's logic to an "industrial strength" programming language  namely, a large applicative subset of Comm ..."
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Cited by 107 (5 self)
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ACL2 is a reimplemented extended version of Boyer and Moore's Nqthm and Kaufmann's PcNqthm, intended for large scale verification projects. This paper deals primarily with how we scaled up Nqthm's logic to an "industrial strength" programming language  namely, a large applicative subset of Common Lisp  while preserving the use of total functions within the logic. This makes it possible to run formal models efficiently while keeping the logic simple. We enumerate many other important features of ACL2 and we briefly summarize two industrial applications: a model of the Motorola CAP digital signal processing chip and the proof of the correctness of the kernel of the floating point division algorithm on the AMD5K 86 microprocessor by Advanced Micro Devices, Inc.
ACL2: An Industrial Strength Version of Nqthm
, 1996
"... ACL2 is a reimplemented extended version of Boyer and Moore's Nqthm and Kaufmann's PcNqthm, intended for large scale verification projects. However, the logic supported by ACL2 is compatible with the applicative subset of Common Lisp. The decision to use an "industrial strength" programming languag ..."
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Cited by 58 (5 self)
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ACL2 is a reimplemented extended version of Boyer and Moore's Nqthm and Kaufmann's PcNqthm, intended for large scale verification projects. However, the logic supported by ACL2 is compatible with the applicative subset of Common Lisp. The decision to use an "industrial strength" programming language as the foundation of the mathematical logic is crucial to our advocacy of ACL2 in the application of formal methods to large systems. However, one of the key reasons Nqthm has been so successful, we believe, is its insistence that functions be total. Common Lisp functions are not total and this is one of the reasons Common Lisp is so efficient. This paper explains how we scaled up Nqthm's logic to Common Lisp, preserving the use of total functions within the logic but achieving Common Lisp execution speeds. 1 History ACL2 is a direct descendent of the BoyerMoore system, Nqthm [8, 12], and its interactive enhancement, PcNqthm [21, 22, 23]. See [7, 25] for introductions to the two ancestr...
Design Goals for ACL2
, 1994
"... ACL2 is a theorem proving system under development at Computational Logic, Inc., by the authors of the BoyerMoore system, Nqthm, and its interactive enhancement, PcNqthm, based on our perceptions of some of the inadequacies of Nqthm when used in largescale verification projects. Foremost among th ..."
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Cited by 36 (5 self)
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ACL2 is a theorem proving system under development at Computational Logic, Inc., by the authors of the BoyerMoore system, Nqthm, and its interactive enhancement, PcNqthm, based on our perceptions of some of the inadequacies of Nqthm when used in largescale verification projects. Foremost among those inadequacies is the fact that Nqthm's logic is an inefficient programming language. We now recognize that the efficiency of the logic as a programming language is of great importance because the models of microprocessors, operating systems, and languages typically constructed in verification projects must be executed to corroborate them against the realities they model. Simulation of such large scale systems stresses the logic in ways not imagined when Nqthm was designed. In addition, Nqthm does not adequately support certain proof techniques, nor does it encourage the reuse of previously developed libraries or the collaboration of semiautonomous workers on different parts of a verifica...
Mechanizing set theory: Cardinal arithmetic and the axiom of choice
 Journal of Automated Reasoning
, 1996
"... Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving this resu ..."
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Cited by 16 (9 self)
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Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving this result required developing theories of orders, orderisomorphisms, order types, ordinal arithmetic, cardinals, etc.; this covers most of Kunen, Set Theory, Chapter I. Furthermore, we have proved the equivalence of 7 formulations of the Wellordering Theorem and 20 formulations of AC; this covers the first two chapters of Rubin and Rubin, Equivalents of the Axiom of Choice, and involves highly technical material. The definitions used in the proofs are
Computer Theorem Proving in Math
"... We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context. ..."
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Cited by 1 (0 self)
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We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context.
Using Theorem Proving and Algorithmic Decision Procedures for LargeScale System Verification
, 2005
"... To the few people who believed I could do it even when I myself didn’t Acknowledgments This dissertation has been shaped by many people, including my teachers, collaborators, friends, and family. I would like to take this opportunity to acknowledge the influence they have had in my development as a ..."
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To the few people who believed I could do it even when I myself didn’t Acknowledgments This dissertation has been shaped by many people, including my teachers, collaborators, friends, and family. I would like to take this opportunity to acknowledge the influence they have had in my development as a person and as a scientist. First and foremost, I wish to thank my advisor J Strother Moore. J is an amazing advisor, a marvellous collaborator, an insightful researcher, an empathetic teacher, and a truly great human being. He gave me just the right balance of freedom, encouragement, and direction to guide the course of this research. My stimulating discussions with him made the act of research an experience of pure enjoyment, and helped pull me out of many low ebbs. At one point I used to believe that whenever I was stuck with a problem one meeting with J would get me back on track. Furthermore, my times together with J and Jo during Thanksgivings and other occasions always made me feel part of his family. There was no problem, technical or otherwise, that I could not discuss with J, and there was no time when
Mechanising Set Theory: Cardinal Arithmetic and the Axiom of Choice
, 1995
"... A growing corpus of mathematics has been checked by machine. Researchers have constructed computer proofs of results in logic [23], number theory [22], group theory [25],calculus [9], etc. An especially wide variety of results have been mechanised using the Mizar Proof Checker and published in the ..."
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A growing corpus of mathematics has been checked by machine. Researchers have constructed computer proofs of results in logic [23], number theory [22], group theory [25],calculus [9], etc. An especially wide variety of results have been mechanised using the Mizar Proof Checker and published in the Mizar journal [6]. However,