3,720 research outputs found
A theory and its metatheory in FS 0
Feferman has proposed FS0, a theory of finitary inductive systems, as a framework theory suitable for various purposes, including reasoning both in and about encoded theories. I look here at how practical FS0 really is. I formalise of a sequent calculus presentation of classical propositional logic in FS0 and show this can be used for work in both the theory and the metatheory. the latter is illustrated with a discussion of a proof of Gentzen's Hauptsatz
A library of Taylor models for PVS automatic proof checker
We present in this paper a library to compute with Taylor models, a technique
extending interval arithmetic to reduce decorrelation and to solve differential
equations. Numerical software usually produces only numerical results. Our
library can be used to produce both results and proofs. As seen during the
development of Fermat's last theorem reported by Aczel 1996, providing a proof
is not sufficient. Our library provides a proof that has been thoroughly
scrutinized by a trustworthy and tireless assistant. PVS is an automatic proof
assistant that has been fairly developed and used and that has no internal
connection with interval arithmetic or Taylor models. We built our library so
that PVS validates each result as it is produced. As producing and validating a
proof, is and will certainly remain a bigger task than just producing a
numerical result our library will never be a replacement to imperative
implementations of Taylor models such as Cosy Infinity. Our library should
mainly be used to validate small to medium size results that are involved in
safety or life critical applications
Research in mathematical theory of computation
Research progress in the following areas is reviewed: (1) new version of computer program LCF (logic for computable functions) including a facility to search for proofs automatically; (2) the description of the language PASCAL in terms of both LCF and in first order logic; (3) discussion of LISP semantics in LCF and attempt to prove the correctness of the London compilers in a formal way; (4) design of both special purpose and domain independent proving procedures specifically program correctness in mind; (5) design of languages for describing such proof procedures; and (6) the embedding of ideas in the first order checker
Extending ACL2 with SMT Solvers
We present our extension of ACL2 with Satisfiability Modulo Theories (SMT)
solvers using ACL2's trusted clause processor mechanism. We are particularly
interested in the verification of physical systems including Analog and
Mixed-Signal (AMS) designs. ACL2 offers strong induction abilities for
reasoning about sequences and SMT complements deduction methods like ACL2 with
fast nonlinear arithmetic solving procedures. While SAT solvers have been
integrated into ACL2 in previous work, SMT methods raise new issues because of
their support for a broader range of domains including real numbers and
uninterpreted functions. This paper presents Smtlink, our clause processor for
integrating SMT solvers into ACL2. We describe key design and implementation
issues and describe our experience with its use.Comment: In Proceedings ACL2 2015, arXiv:1509.0552
How functional programming mattered
In 1989 when functional programming was still considered a niche topic, Hughes wrote a visionary paper arguing convincingly ‘why functional programming matters’. More than two decades have passed. Has functional programming really mattered? Our answer is a resounding ‘Yes!’. Functional programming is now at the forefront of a new generation of programming technologies, and enjoying increasing popularity and influence. In this paper, we review the impact of functional programming, focusing on how it has changed the way we may construct programs, the way we may verify programs, and fundamentally the way we may think about programs
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