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25
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.
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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Cited by 21 (2 self)
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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...
A Grand Challenge Proposal for Formal Methods: A Verified Stack
"... We propose a grand challenge for the formal methods community: build and mechanically verify a practical embedded system, from transistors to software. We propose that each group within the formal methods community design and verify, by the methods appropriate to that group, an embedded system of ..."
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Cited by 20 (1 self)
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We propose a grand challenge for the formal methods community: build and mechanically verify a practical embedded system, from transistors to software. We propose that each group within the formal methods community design and verify, by the methods appropriate to that group, an embedded system of their choice. The point is not to have just one integrated formal method or just one verified application, but to encourage groups to develop the techniques and methodologies necessary for systemlevel verification.
Proving theorems about Java and the JVM with ACL2
 Models, Algebras and Logic of Engineering Software
, 2003
"... We describe a methodology for proving theorems mechanically about Java methods. The theorem prover used is the ACL2 system, an industrialstrength version of the BoyerMoore theorem prover. An operational semantics for a substantial subset of the Java Virtual Machine (JVM) has been defined in ACL2. ..."
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Cited by 18 (9 self)
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We describe a methodology for proving theorems mechanically about Java methods. The theorem prover used is the ACL2 system, an industrialstrength version of the BoyerMoore theorem prover. An operational semantics for a substantial subset of the Java Virtual Machine (JVM) has been defined in ACL2. Theorems are proved about Java methods and classes by compiling them with javac and then proving the corresponding theorem about the JVM. Certain automatically applied strategies are implemented with rewrite rules (and other proofguiding pragmas) in ACL2 “books” to control the theorem prover when operating on problems involving the JVM model. The Java Virtual Machine or JVM [27] is the basic abstraction Java [17] implementors are expected to respect. We speculate that the JVM is an appropriate level of abstraction at which to model Java programs with the intention of mechanically verifying their properties. The most complex features of the Java subset we handle – construction and initialization of new objects, synchronization, thread management, and virtual method invocation – are all supported directly and with full abstraction as single atomic instructions in the JVM. The complexity of verifying JVM bytecode program stems from the complexity of Java’s semantics, not
Formal verification of IA64 division algorithms
 Proceedings, Theorem Proving in Higher Order Logics (TPHOLs), LNCS 1869
, 2000
"... Abstract. The IA64 architecture defers floating point and integer division to software. To ensure correctness and maximum efficiency, Intel provides a number of recommended algorithms which can be called as subroutines or inlined by compilers and assembly language programmers. All these algorithms ..."
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Cited by 18 (4 self)
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Abstract. The IA64 architecture defers floating point and integer division to software. To ensure correctness and maximum efficiency, Intel provides a number of recommended algorithms which can be called as subroutines or inlined by compilers and assembly language programmers. All these algorithms have been subjected to formal verification using the HOL Light theorem prover. As well as improving our level of confidence in the algorithms, the formal verification process has led to a better understanding of the underlying theory, allowing some significant efficiency improvements. 1
Modular Verification of SRT Division
, 1996
"... . We describe a formal specification and mechanized verification in PVS of the general theory of SRT division along with a specific hardware realization of the algorithm. The specification demonstrates how attributes of the PVS language (in particular, predicate subtypes) allow the general theory to ..."
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Cited by 16 (1 self)
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. We describe a formal specification and mechanized verification in PVS of the general theory of SRT division along with a specific hardware realization of the algorithm. The specification demonstrates how attributes of the PVS language (in particular, predicate subtypes) allow the general theory to be developed in a readable manner that is similar to textbook presentations, while the PVS table construct allows direct specification of the implementation's quotient lookup table. Verification of the derivations in the SRT theory and for the data path and lookup table of the implementation are highly automated and performed for arbitrary, but finite precision; in addition, the theory is verified for general radix, while the implementation is specialized to radix 4. The effectiveness of the automation stems from the tight integration in PVS of rewriting with decision procedures for equality, linear arithmetic over integers and rationals, and propositional logic. This example demonstrates t...
MultiProver Verification of FloatingPoint Programs ⋆
"... Abstract. In the context of deductive program verification, supporting floatingpoint computations is tricky. We propose an expressive language to formally specify behavioral properties of such programs. We give a firstorder axiomatization of floatingpoint operations which allows to reduce verifica ..."
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Cited by 15 (3 self)
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Abstract. In the context of deductive program verification, supporting floatingpoint computations is tricky. We propose an expressive language to formally specify behavioral properties of such programs. We give a firstorder axiomatization of floatingpoint operations which allows to reduce verification to checking the validity of logic formulas, in a suitable form for a large class of provers including SMT solvers and interactive proof assistants. Experiments using the FramaC platform for static analysis of C code are presented. 1
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 ...
Verification of IEEE Compliant Subtractive Division Algorithms
 FORMAL METHODS IN COMPUTERAIDED DESIGN (FMCAD '96)
, 1996
"... A parameterized definition of subtractive floating point division algorithms is presented and verified using PVS. The general algorithm is proven to satisfy a formal definition of an IEEE standard for floating point arithmetic. The utility of the general specification is illustrated using a numb ..."
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Cited by 11 (1 self)
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A parameterized definition of subtractive floating point division algorithms is presented and verified using PVS. The general algorithm is proven to satisfy a formal definition of an IEEE standard for floating point arithmetic. The utility of the general specification is illustrated using a number of different instances of the general algorithm.
Verification of Pipeline Circuits
 In ACL2 Workshop 2000 (proceedings are available as UTCS
, 2000
"... The use of pipelines is an important technique in contemporary hardware design, particularly at the level of registertransfer logic (RTL). Earlier formal analysis (e.g., [4]) using the ACL2 theorem prover showed correctness of pipelined floatingpoint RTL. This paper extends that work by consid ..."
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Cited by 5 (3 self)
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The use of pipelines is an important technique in contemporary hardware design, particularly at the level of registertransfer logic (RTL). Earlier formal analysis (e.g., [4]) using the ACL2 theorem prover showed correctness of pipelined floatingpoint RTL. This paper extends that work by considering a notion of a conditional pipeline, essentially the result of sharing hardware among several distinct pipelines. We have employed a pipeline tool, written in ACL2 but completely unverified, to find a pipelinerelated bug in an industrial hardware design, which has since been corrected.