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.Comment: In Proceedings ACL2 2014, arXiv:1406.123

Enhancements to ACL2 in Versions 6.2, 6.3, and 6.4

We report on improvements to ACL2 made since the 2013 ACL2 Workshop.Comment: In Proceedings ACL2 2014, arXiv:1406.123

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.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

On random models of finite power and monadic logic

AbstractFor any property θ of a model (or graph), let μn(θ) be the fraction of models of power n which satisfy θ, and let μ(θ) = limn →∞ μn(θ) if this limit exists. For first-order properties θ, it is known that μ(θ) must be 0 or 1. We answer a question of K. Compton by proving in a strong way that this 0–1 law can fail if we allow monadic quantification (that is, quantification over sets) in defining the sentence θ. In fact, by producing a monadic sentence which codes arithmetic on n with probability μ = 1, we show that every recursive real is μ(θ) for some monadic θ

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.Comment: In Proceedings ACL2-2023, arXiv:2311.0837