217 research outputs found
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
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