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14
Structured Theory Development for a Mechanized Logic
 Journal of Automated Reasoning
, 1999
"... Experience has shown that large or multiuser interactive proof efforts can benefit significantly from structuring mechanisms, much like those available in many modern programming languages. Such a mechanism can allow some lemmas and definitions to be exported, and others not. In this paper we addre ..."
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Experience has shown that large or multiuser interactive proof efforts can benefit significantly from structuring mechanisms, much like those available in many modern programming languages. Such a mechanism can allow some lemmas and definitions to be exported, and others not. In this paper we address two such structuring mechanisms for the ACL2 theorem prover: encapsulation and books. After presenting an introduction to ACL2, this paper justifies the implementation of ACL2's structuring mechanisms and, more generally, formulates and proves highlevel correctness properties of ACL2. The issues in the present paper are relevant not only for ACL2 but also for other theoremproving environments.
A generic library of floatingpoint numbers and its application to exact computing
 In 14th International Conference on Theorem Proving in Higher Order Logics
, 2001
"... Abstract. In this paper we present a general library to reason about floatingpoint numbers within the Coq system. Most of the results of the library are proved for an arbitrary floatingpoint format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i. ..."
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Abstract. In this paper we present a general library to reason about floatingpoint numbers within the Coq system. Most of the results of the library are proved for an arbitrary floatingpoint format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors. 1
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 ..."
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Cited by 28 (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.
Symbolic Simulation: an ACL2 Approach
 Proceedings of the Second International Conference on Formal Methods in ComputerAided Design (FMCAD'98), volume LNCS 1522
, 1998
"... . Executable formal specification can allow engineers to test (or simulate) the specified system on concrete data before the system is implemented. This is beginning to gain acceptance and is just the formal analogue of the standard practice of building simulators in conventional programming languag ..."
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. Executable formal specification can allow engineers to test (or simulate) the specified system on concrete data before the system is implemented. This is beginning to gain acceptance and is just the formal analogue of the standard practice of building simulators in conventional programming languages such as C. A largely unexplored but potentially very useful next step is symbolic simulation, the "execution" of the formal specification on indeterminant data. With the right interface, this need not require much additional training of the engineers using the tool. It allows many tests to be collapsed into one. Furthermore, it familiarizes the working engineer with the abstractions and notation used in the design, thus allowing team members to speak clearly to one another. We illustrate these ideas with a formal specification of a simple computing machine in ACL2. We sketch some requirements on the interface, which we call a symbolic spreadsheet. 1 Introduction The use of formal methods...
A Case Study in Formal Verification of RegisterTransfer Logic with ACL2: The Floating Point Adder of the AMD Athlon
"... . As an alternative to commercial hardware description languages, AMD 1 has developed an RTL language for microprocessor designs that is simple enough to admit a clear semantic definition, providing a basis for formal verification. We describe a mechanical proof system for designs represented in t ..."
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. As an alternative to commercial hardware description languages, AMD 1 has developed an RTL language for microprocessor designs that is simple enough to admit a clear semantic definition, providing a basis for formal verification. We describe a mechanical proof system for designs represented in this language, consisting of a translator to the ACL2 logical programming language and a methodology for verifying properties of the resulting programs using the ACL2 prover. As an illustration, we present a proof of IEEE compliance of the floatingpoint adder of the AMD Athlon processor. 1 Introduction The formal hardware verification effort at AMD has emphasized theorem proving using ACL2 [3], and has focused on the elementary floatingpoint operations. One of the challenges of our earlier work was to construct accurate formal models of the targeted circuit designs. These included the division and square root operations of the AMDK5 processor [4, 6], which were implemented in microcode, a...
Trustworthy Numerical Computation in Scala
"... Modern computing has adopted the floating point type as a default way to describe computations with real numbers. Thanks to dedicated hardware support, such computations are efficient on modern architectures, even in double precision. However, rigorous reasoning about the resulting programs remains ..."
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Modern computing has adopted the floating point type as a default way to describe computations with real numbers. Thanks to dedicated hardware support, such computations are efficient on modern architectures, even in double precision. However, rigorous reasoning about the resulting programs remains difficult. This is in part due to a large gap between the finite floating point representation and the infiniteprecision realnumber semantics that serves as the developers’ mental model. Because programming languages do not provide support for estimating errors, some computations in practice are performed more and some less precisely than needed. We present a library solution for rigorous arithmetic computation. Our numerical data type library tracks a (double) floating point value, but also a guaranteed upper bound on the error between this value and the ideal value that would be computed in the realvalue semantics. Our implementation involves a set of linear approximations based on an extension of affine arithmetic. The derived approximations cover most of the standard mathematical operations, including trigonometric functions, and are more comprehensive than any publicly available ones. Moreover, while interval arithmetic rapidly yields overly pessimistic estimates, our approach remains precise for several computational tasks of interest. We evaluate the library on a number of examples from numerical analysis and physical simulations. We found it to be a useful tool for gaining confidence in the correctness of the computation.
SingleThreaded Objects in ACL2
 Practical Aspects of Declarative Languages (PADL), volume 2257 of LNCS
, 1999
"... ACL2 is a firstorder applicative programming language based on Common Lisp. It is also a mathematical logic for which a mechanical theoremprover has been implemented in the style of the BoyerMoore theorem prover. The ACL2 system is used primarily in the modeling and verification of computer hardwa ..."
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ACL2 is a firstorder applicative programming language based on Common Lisp. It is also a mathematical logic for which a mechanical theoremprover has been implemented in the style of the BoyerMoore theorem prover. The ACL2 system is used primarily in the modeling and verification of computer hardware and software, where the executability of the language allows models to be used as prototype designs or "simulators." To support efficient execution of certain kinds of models, especially models of microprocessors, ACL2 provides "singlethreaded objects," structures with the usual "copy on write" applicative semantics but for which writes are implemented destructively. Syntactic restrictions insure consistency between the formal semantics and the implementation. The design of singlethreaded objects has been influenced both by the need to make execution efficient and the need to make proofs about them simple. We discuss the issues. 1 Background "ACL2" stands for "A Computational Logic for...
A Framework for Verifying BitLevel Pipelined Machines Based on Automated Deduction and Decision Procedures
 Journal of Automated Reasoning
, 2006
"... Abstract. We describe an approach to verifying bitlevel pipelined machine models using a combination of deductive reasoning and decision procedures. While theorem proving systems such as ACL2 have been used to verify bitlevel designs, they typically require extensive expert user support. Decision ..."
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Abstract. We describe an approach to verifying bitlevel pipelined machine models using a combination of deductive reasoning and decision procedures. While theorem proving systems such as ACL2 have been used to verify bitlevel designs, they typically require extensive expert user support. Decision procedures such as those implemented in UCLID can be used to automatically and efficiently verify termlevel pipelined machine models, but these models use numerous abstractions, implement a subset of the instruction set, and are far from executable. We show that by integrating UCLID with the ACL2 theorem proving system, we can use ACL2 to reduce the proof that an executable, bitlevel machine refines its instruction set architecture to a proof that a termlevel abstraction of the bitlevel machine refines the instruction set architecture, which is then handled automatically by UCLID. We demonstrate the efficiency of our approach by applying it to verify a complex seven stage bitlevel interface pipelined machine model that implements 593 instructions and has features such as branch prediction, exceptions, and predicated instruction execution. Such a proof is not possible using UCLID and would require prohibitively more effort using just ACL2.
An ACL2 Proof of Write Invalidate Cache Coherence
 In Proc. CAV'98, volume 1427 of LNCS
, 1998
"... . As a pedagogical exercise in ACL2, we formalize and prove the correctness of a write invalidate cache scheme. In our formalization, an arbitrary number of processors, each with its own local cache, interact with a global memory via a bus which is snooped by the caches. 1 Ongoing Industrial Applica ..."
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. As a pedagogical exercise in ACL2, we formalize and prove the correctness of a write invalidate cache scheme. In our formalization, an arbitrary number of processors, each with its own local cache, interact with a global memory via a bus which is snooped by the caches. 1 Ongoing Industrial Applications of ACL2 The ACL2 theorem proving system is finding use in industrialscale verification projects. Two significant projects which have been reported previously are  the mechanical verification of the floatingpoint division microcode for the AMDK5 TM [6], and  the ACL2 modeling of the Motorola CAP digital signal processor and its use to prove that a pipeline hazard detection predicate was correct and that several DSP microcode applications were correct [1]. The abstract of a recent talk given by David Russinoff of Advanced Micro Devices, Inc., summarizes the current AMD work with ACL2: Formal design verification at AMD has focused on the elementary arithmetic floating point op...