ISABELLE - THE NEXT 700 THEOREM PROVERS

Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory, and higher-order logic. This survey of Isabelle serves as an introduction to the literature. It explains why generic theorem proving is beneficial. It gives a thorough history of Isabelle, beginning with its origins in the LCF system. It presents an account of how logics are represented, illustrated using classical logic. The approach is compared with the Edinburgh Logical Framework. Several of the Isabelle object-logics are presented

Reasoning about order errors in interaction

Reliability of an interactive system depends on users as well as the device implementation. User errors can result in catastrophic system failure. However, work from the field of cognitive science shows that systems can be designed so as to completely eliminate whole classes of user errors. This means that user errors should also fall within the remit of verification methods. In this paper we demonstrate how the HOL theorem prover [7] can be used to detect and prove the absence of the family of errors known as order errors. This is done by taking account of the goals and knowledge of users. We provide an explicit generic user model which embodies theory from the cognitive sciences about the way people are known to act. The user model describes action based on user communication goals. These are goals that a user adopts based on their knowledge of the task they must perform to achieve their goals. We use a simple example of a vending machine to demonstrate the approach. We prove that a user does achieve their goal for a particular design of machine. In doing so we demonstrate that communication goal based errors cannot occur

The Quantum PCP Conjecture

The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop tools that address the question: does a quantum version of the PCP theorem hold? The story of this study starts with classical complexity and takes unexpected turns providing fascinating vistas on the foundations of quantum mechanics, the global nature of entanglement and its topological properties, quantum error correction, information theory, and much more; it raises questions that touch upon some of the most fundamental issues at the heart of our understanding of quantum mechanics. At this point, the jury is still out as to whether or not such a theorem holds. This survey aims to provide a snapshot of the status in this ongoing story, tailored to a general theory-of-CS audience.Comment: 45 pages, 4 figures, an enhanced version of the SIGACT guest column from Volume 44 Issue 2, June 201