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Automated Correctness Proofs of Machine Code Programs for a Commercial Microprocessor
, 1991
"... We have formally specified a substantial subset of the MC68020, a widely used microprocessor built by Motorola, within the mathematical logic of the automated reasoning system Nqthm, i.e., the BoyerMoore Theorem Prover [4]. Using this MC68020 specification, we have mechanically checked the correctn ..."
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Cited by 32 (2 self)
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We have formally specified a substantial subset of the MC68020, a widely used microprocessor built by Motorola, within the mathematical logic of the automated reasoning system Nqthm, i.e., the BoyerMoore Theorem Prover [4]. Using this MC68020 specification, we have mechanically checked the correctness of MC68020 machine code programs for Euclid's GCD, Hoare's Quick Sort, binary search, and other wellknown algorithms. The machine code for these examples was generated using the Gnu C and the Verdix Ada compilers. We have developed an extensive library of proven lemmas to facilitate automated reasoning about machine code programs. We describe a two stage methodology we use to do our machine code proofs.
A Theorem Prover for a Computational Logic
, 1990
"... We briefly review a mechanical theoremprover for a logic of recursive functions over finitely generated objects including the integers, ordered pairs, and symbols. The prover, known both as NQTHM and as the BoyerMoore prover, contains a mechanized principle of induction and implementations of line ..."
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Cited by 24 (0 self)
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We briefly review a mechanical theoremprover for a logic of recursive functions over finitely generated objects including the integers, ordered pairs, and symbols. The prover, known both as NQTHM and as the BoyerMoore prover, contains a mechanized principle of induction and implementations of linear resolution, rewriting, and arithmetic decision procedures. We describe some applications of the prover, including a proof of the correct implementation of a higher level language on a microprocessor defined at the gate level. We also describe the ongoing project of recoding the entire prover as an applicative function within its own logic.
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
Modular Reasoning in Isabelle
, 1999
"... The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved use ..."
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Cited by 13 (2 self)
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The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved useful in itself, their real power lies in combination. This paper illustrates by examples from abstract algebra how this combination works and argues that it enables modular reasoning.
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,