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Matt Kaufmann

Publications and source records attributed to Matt Kaufmann.

At least 19 recordsLinked to original sources
arXiv2025

Extended Abstract: Mutable Objects with Several Implementations

This extended abstract outlines an ACL2 feature, attach-stobj, that first appeared in ACL2 Version 8.6 (October, 2024). This feature supports different executable operations for a given abstract stobj, without requiring recertification of the book that introduces that stobj or theorems about it. The paper provides background as well as a user-level overview and some implementation notes.

cs.PL↗
arXiv2023

Advances in ACL2 Proof Debugging Tools

The experience of an ACL2 user generally includes many failed proof attempts. A key to successful use of the ACL2 prover is the effective use of tools to debug those failures. We focus on changes made after ACL2 Version 8.5: the improved break-rewrite utility and the new utility, with-brr-data.

cs.AI↗
arXiv2020

Iteration in ACL2

Iterative algorithms are traditionally expressed in ACL2 using recursion. On the other hand, Common Lisp provides a construct, loop, which -- like most programming languages -- provides direct support for iteration. We describe an ACL2 analogue loop$ of loop that supports efficient ACL2 programming and reasoning with iteration.

cs.LO↗
arXiv2017

Iterated Ultrapowers for the Masses

We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown to provide smooth proofs of several results in general model theory.

math.LO↗
arXiv2017

Meta-extract: Using Existing Facts in Meta-reasoning

ACL2 has long supported user-defined simplifiers, so-called metafunctions and clause processors, which are installed when corresponding rules of class :meta or :clause-processor are proved. Historically, such simplifiers could access the logical world at execution time and could call certain built-in proof tools, but one could not assume the soundness of the proof tools or the truth of any facts extracted from the world or context when proving a simplifier correct. Starting with ACL2 Version 6.0, released in December 2012, an additional capability was added which allows the correctness proofs of simplifiers to assume the correctness of some such proof tools and extracted facts. In this paper we explain this capability and give examples that demonstrate its utility.

cs.LO↗
arXiv2017

A Versatile, Sound Tool for Simplifying Definitions

We present a tool, simplify-defun, that transforms the definition of a given function into a simplified definition of a new function, providing a proof checked by ACL2 that the old and new functions are equivalent. When appropriate it also generates termination and guard proofs for the new function. We explain how the tool is engineered so that these proofs will succeed. Examples illustrate its utility, in particular for program transformation in synthesis and verification.

cs.PL↗
arXiv2016

Efficient Certified RAT Verification

Clausal proofs have become a popular approach to validate the results of SAT solvers. However, validating clausal proofs in the most widely supported format (DRAT) is expensive even in highly optimized implementations. We present a new format, called LRAT, which extends the DRAT format with hints that facilitate a simple and fast validation algorithm. Checking validity of LRAT proofs can be implemented using trusted systems such as the languages supported by theorem provers. We demonstrate this by implementing two certified LRAT checkers, one in Coq and one in ACL2.

cs.LO↗
arXiv2016

Largest initial segments pointwise fixed by automorphisms of models of set theory

Given a model $\mathcal{M}$ of set theory, and a nontrivial automorphism $j$ of $\mathcal{M}$, let $\mathcal{I}_{\mathrm{fix}}(j)$ be the submodel of $\mathcal{M}$ whose universe consists of elements $m$ of $\mathcal{M}$ such that $j(x)=x$ for every $x$ in the transitive closure of $m$ (where the transitive closure of $m$ is computed within $\mathcal{M}$). Here we study the class $\mathcal{C}$ of structures of the form $\mathcal{I}_{\mathrm{fix}}(j)$, where the ambient model $\mathcal{M}$ satisfies a frugal yet robust fragment of $\mathrm{ZFC}$ known as $\mathrm{MOST}$, and $j(m)=m$ whenever $m$ is a finite ordinal in the sense of $\mathcal{M}$. We show that every structure in $\mathcal{C}$ satisfies $\mathrm{MOST}+Δ_0^\mathcal{P}\textrm{-Collection}$. We also show that the following countable structures are in $\mathcal{C}$: (a) transitive models of $\mathrm{MOST}+Δ_0^\mathcal{P}\textrm{-Collection}$, (b) recursively saturated models of $\mathrm{MOST}+Δ_0^\mathcal{P}\textrm{-Collection}$, (c) models of $\mathrm{ZFC}$. It follows from (b) that the theory of $\mathcal{C}$ is precisely $\mathrm{MOST+Δ}_{0}^{\mathcal{P}}$-Collection. We conclude by proving a refinement of a result due to Amir Togha.

math.LO↗
arXiv2015

Fourier Series Formalization in ACL2(r)

We formalize some basic properties of Fourier series in the logic of ACL2(r), which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r). Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.

cs.LO↗
arXiv2015

Proceedings Thirteenth International Workshop on the ACL2 Theorem Prover and Its Applications

This volume contains the proceedings of the Thirteenth International Workshop on the ACL2 Theorem Prover and Its Applications, ACL2 2015, a two-day workshop held in Austin, Texas, USA, on October 1-2, 2015. ACL2 workshops occur at approximately 18-month intervals and provide a major technical forum for researchers to present and discuss improvements and extensions to the theorem prover, comparisons of ACL2 with other systems, and applications of ACL2 in formal verification. ACL2 is a state-of-the-art automated reasoning system that has been successfully applied in academia, government, and industry for specification and verification of computing systems and in teaching computer science courses. In 2005, Boyer, Kaufmann, and Moore were awarded the 2005 ACM Software System Award for their work on ACL2 and the other theorem provers in the Boyer-Moore family.

cs.LO↗
arXiv2014

Industrial-Strength Documentation for ACL2

The ACL2 theorem prover is a complex system. Its libraries are vast. Industrial verification efforts may extend this base with hundreds of thousands of lines of additional modeling tools, specifications, and proof scripts. High quality documentation is vital for teams that are working together on projects of this scale. We have developed XDOC, a flexible, scalable documentation tool for ACL2 that can incorporate the documentation for ACL2 itself, the Community Books, and an organization's internal formal verification projects, and which has many features that help to keep the resulting manuals up to date. Using this tool, we have produced a comprehensive, publicly available ACL2+Books Manual that brings better documentation to all ACL2 users. We have also developed an extended manual for use within Centaur Technology that extends the public manual to cover Centaur's internal books. We expect that other organizations using ACL2 will wish to develop similarly extended manuals.

cs.SE↗
arXiv2013

Enhancements to ACL2 in Versions 5.0, 6.0, and 6.1

We report on highlights of the ACL2 enhancements introduced in ACL2 releases since the 2011 ACL2 Workshop. Although many enhancements are critical for soundness or robustness, we focus in this paper on those improvements that could benefit users who are aware of them, but that might not be discovered in everyday practice.

cs.MS↗
arXiv2013

Abstract Stobjs and Their Application to ISA Modeling

We introduce a new ACL2 feature, the abstract stobj, and show how to apply it to modeling the instruction set architecture of a microprocessor. Benefits of abstract stobjs over traditional ("concrete") stobjs can include faster execution, support for symbolic simulation, more efficient reasoning, and resilience of proof developments under modeling optimization.

cs.LO↗
arXiv2011

Integrating Testing and Interactive Theorem Proving

Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often spend considerable effort examining the theorem prover's output before realizing this. We present a synergistic integration of testing with theorem proving, implemented in the ACL2 Sedan (ACL2s), for automatically generating concrete counterexamples. Our method uses the full power of the theorem prover and associated libraries to simplify conjectures; this simplification can transform conjectures for which finding counterexamples is hard into conjectures where finding counterexamples is trivial. In fact, our approach even leads to better theorem proving, e.g. if testing shows that a generalization step leads to a false conjecture, we force the theorem prover to backtrack, allowing it to pursue more fruitful options that may yield a proof. The focus of the paper is on the engineering of a synergistic integration of testing with interactive theorem proving; this includes extending ACL2 with new functionality that we expect to be of general interest. We also discuss our experience in using ACL2s to teach freshman students how to reason about their programs.

cs.SE↗