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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...
A Formal Model of Asynchronous Communication and Its Use in Mechanically Verifying a Biphase Mark Protocol
 Formal Aspects of Computing
, 1992
"... In this paper we present a formal model of asynchronous communication as a function in the BoyerMoore logic. The function transforms the signal stream generated by one processor into the signal stream consumed by an independently clocked processor. This transformation "blurs" edges and "dilates" ti ..."
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Cited by 36 (5 self)
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In this paper we present a formal model of asynchronous communication as a function in the BoyerMoore logic. The function transforms the signal stream generated by one processor into the signal stream consumed by an independently clocked processor. This transformation "blurs" edges and "dilates" time due to differences in the phases and rates of the two clocks and the communications delay. The model can be used quantitatively to derive concrete performance bounds on asynchronous communications at ISO protocol level 1 (physical level). We develop part of the reusable formal theory that permits the convenient application of the model. We use the theory to show that a biphase mark protocol can be used to send messages of arbitrary length between two asynchronous processors. We study two versions of the protocol, a conventional one which uses cells of size 32 cycles and an unconventional one which uses cells of size 18. Our proof of the former protocol requires the ratio of the clock rates of the two processors to be within 3% of unity. The unconventional biphase mark protocol permits the ratio to vary by 5%. At nominal clock rates of 20MHz, the unconventional protocol allows transmissions at a burst rate of slightly over 1MHz. These claims are formally stated in terms of our model of asynchrony; the proofs of the claims have been mechanically checked with the BoyerMoore theorem prover, NQTHM. We conjecture that the protocol can be proved to work under our model for smaller cell sizes and more divergent clock rates but the proofs would be harder. Known inadequacies of our model include that (a) distortion due to the presence of an edge is limited to the time span of the cycle during which the edge was written, (b) both clocks are assumed to be linear functions of time (i....
The BoyerMoore Theorem Prover and Its Interactive Enhancement
, 1995
"... . The socalled "BoyerMoore Theorem Prover" (otherwise known as "Nqthm") has been used to perform a variety of verification tasks for two decades. We give an overview of both this system and an interactive enhancement of it, "PcNqthm," from a number of perspectives. First we introduce the logic in ..."
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Cited by 31 (0 self)
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. The socalled "BoyerMoore Theorem Prover" (otherwise known as "Nqthm") has been used to perform a variety of verification tasks for two decades. We give an overview of both this system and an interactive enhancement of it, "PcNqthm," from a number of perspectives. First we introduce the logic in which theorems are proved. Then we briefly describe the two mechanized theorem proving systems. Next, we present a simple but illustrative example in some detail in order to give an impression of how these systems may be used successfully. Finally, we give extremely short descriptions of a large number of applications of these systems, in order to give an idea of the breadth of their uses. This paper is intended as an informal introduction to systems that have been described in detail and similarly summarized in many other books and papers; no new results are reported here. Our intention here is merely to present Nqthm to a new audience. This research was supported in part by ONR Contract N...
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.
A Mechanically Checked Proof of a Multiprocessor Result via a Uniprocessor View
 Formal Methods in System Design
, 1999
"... We describe a mechanically checked correctness proof for a system of n processes, each running a simple, nonblocking counter algorithm. We prove that if the system runs longer than 5n steps, the counter is increased. The theorem is formalized in applicative Common Lisp and proved with the ACL2 the ..."
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Cited by 14 (6 self)
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We describe a mechanically checked correctness proof for a system of n processes, each running a simple, nonblocking counter algorithm. We prove that if the system runs longer than 5n steps, the counter is increased. The theorem is formalized in applicative Common Lisp and proved with the ACL2 theorem prover. The value of this paper lies not so much in the trivial algorithm addressed as in the method used to prove it correct. The method allows one to reason accurately about the behavior of a concurrent, multiprocess system by reasoning about the sequential computation carried out by a selected process, against a memory that is changed externally. Indeed, we prove general lemmas that allow shifting between the multiprocess and uniprocess views. We prove a safety property using a multiprocess view, project the property to a uniprocess view, and then prove a global progress property via a local, sequential computation argument. 1 Informal Discussion of the Problem Consider a system of ...
A mechanical formalization of several fairness notions
 VDM ’91: Formal Software Development Methods. SpringerVerlag Lecture Notes in Computer Science 551
, 1991
"... The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or ..."
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Cited by 3 (1 self)
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The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or
Mechanically Verifying Safety and Liveness Properties of Delay Insensitive Circuits. Computer Aided Verification
 the BoyerMoore Prover. 1991 International Workshop on Formal Methods in VLSI Design
, 1991
"... The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or ..."
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Cited by 3 (0 self)
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The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or
MachineChecked RealTime System Verificatio
, 1996
"... System Lemma : : : : : : : : : : : : : : : : : : 108 7.4.2 FM9001 Reasonableness Proof : : : : : : : : : : : : : : : 109 7.4.3 FM9001 Program Proof : : : : : : : : : : : : : : : : : : 111 7.4.4 Deriving the Final Theorem : : : : : : : : : : : : : : : : 112 7.5 Invariants Proved in the Quizshow Proo ..."
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Cited by 1 (1 self)
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System Lemma : : : : : : : : : : : : : : : : : : 108 7.4.2 FM9001 Reasonableness Proof : : : : : : : : : : : : : : : 109 7.4.3 FM9001 Program Proof : : : : : : : : : : : : : : : : : : 111 7.4.4 Deriving the Final Theorem : : : : : : : : : : : : : : : : 112 7.5 Invariants Proved in the Quizshow Proof : : : : : : : : : : : : : 113 7.5.1 Abstract System Lemma Invariants : : : : : : : : : : : : 114 7.5.2 FM9001 Reasonableness Lemma Invariants : : : : : : : : 117 7.5.3 Program Correctness Lemma Invariants : : : : : : : : : : 118 7.6 The LightSwitch Example : : : : : : : : : : : : : : : : : : : : : 122 7.6.1 A Correctness Lemma : : : : : : : : : : : : : : : : : : : 122 7.6.2 A LightSwitch Program Specification : : : : : : : : : : : 125 7.6.3 Example Execution of the LightSwitch System : : : : : 126 8. Some Implications of the Proved Realtime System 128 8.1 Execution on the FM9001 Singleboard Computer : : : : : : : : 128 8.2 Comparison with Scheduling Theorem : : : : : : : : : : : : :...