Ideas for a high-level proof strategy language

ABSTRACT Finding ways to prove theorems mechanically was one of the earliest challenges tackled by the AI community. Notable progress has been made but there is still always a limit to any set of heuristic search techniques. From a proof done by human users, we wish to find out whether AI techniques can also be used to learn from a human user. AI4FM (Artificial Intelligence for Formal Methods) is a four-year project that starts officially in April 2010 (see www.AI4FM.org). It focuses on helping users of "formal methods" many of which give rise to proof obligations that have to be (mechanically) verified (by a theorem prover). In industrial-sized developments, there are often a large number of proof obligations and, whilst many of them succumb to similar proof strategies, those that remain can hold up engineers trying to use formal methods. The goal of AI4FM is to learn enough from one manual proof, to discharge proof obligations automatically that yield to similar proof strategies. To achieve this, a high-level (proof) strategy language is required, and in this paper we outline some ideas of such language, and towards extracting them. * During this work Gudmund Grov has been employed jointly by University of Edinburgh and Newcastle University. and constrained use of Z [FW08] -is the so-called "posit and prove" approach: a designer posits development steps and then justifies that they satisfy earlier specifications by discharging (often automatically generated) proof obligations (POs). A large proportion of these POs can be discharged by automatic theorem provers but "some" proofs require user interaction. Quantifying "some" is hard since it depends on many factors such as the domain, technology and methodology used -it could be as little as 3% or as much as 40%. For example, the Paris Metro line 14, developed in the Bmethod, generated 27, 800 POs (of which around 2, 250 required user-interaction) [Abr07] -the need for interactive proofs is clearly still a bottleneck in industrial application of FM, notwithstanding high degree of automation. THE FORMAL METHODS PROBLE

The development and deployment of formal methods in the UK

UK researchers have made major contributions to the technical ideas underpinning formal approaches to the specification and development of computer systems. Perhaps as a consequence of this, some of the significant attempts to deploy theoretical ideas into practical environments have taken place in the UK. The authors of this paper have been involved in formal methods for many years and both have tracked a significant proportion of the whole story. This paper both lists key ideas and indicates where attempts were made to use the ideas in practice. Not all of these deployment stories have been a complete success and an attempt is made to tease out lessons that influence the probability of long-term impact.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A Rely-Guarantee Specification of Mixed-Criticality Scheduling

The application considered is mixed-criticality scheduling. The core formal approaches used are Rely-Guarantee conditions and the Timeband framework; these are applied to give a layered description of job scheduling which includes resilience to jobs overrunning their expected execution time. A novel formal modelling idea is proposed to handle the relationship between actual time and its approximation in hardware clocks.Comment: This paper will appear in a Festschrift - on publication we will insert a pointer to the boo

Using Rely/Guarantee to Pinpoint Assumptions underlying Security Protocols

The verification of security protocols is essential, in order to ensure the absence of potential attacks. However, verification results are only valid with respect to the assumptions under which the verification was performed. These assumptions are often hidden and are difficult to identify, making it unclear whether a given protocol is safe to deploy into a particular environment. Rely/guarantee provides a mechanism for abstractly reasoning about the interference from the environment. Using this approach, the assumptions are made clear and precise. This paper investigates this approach on the Needham-Schroeder Public Key protocol, showing that the technique can effectively uncover the assumptions under which the protocol can withstand attacks from intruders

Representations of sport in the revolutionary socialist press in Britain, 1988–2012

This paper considers how sport presents a dualism to those on the far left of the political spectrum. A long-standing, passionate debate has existed on the contradictory role played by sport, polarised between those who reject it as a bourgeois capitalist plague and those who argue for its reclamation and reformation. A case study is offered of a political party that has consistently used revolutionary Marxism as the basis for its activity and how this party, the largest in Britain, addresses sport in its publications. The study draws on empirical data to illustrate this debate by reporting findings from three socialist publications. When sport did feature it was often in relation to high profile sporting events with a critical tone adopted and typically focused on issues of commodification, exploitation and alienation of athletes and supporters. However, readers’ letters, printed in the same publications, revealed how this interpretation was not universally accepted, thus illustrating the contradictory nature of sport for those on the far left