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

Structure preserving specification languages for knowledge-based systems

Much of the work on validation and verification of knowledge based systems (KBSs) has been done in terms of implementation languages (mostly rule-based languages). Recent papers have argued that it is advantageous to do validation and verification in terms of a more abstract and formal specification of the system. However, constructing such formal specifications is a difficult task. This paper proposes the use of formal specification languages for KBS-development that are closely based on the structure of informal knowledge-models. The use of such formal languages has as advantages that (i) we can give strong support for the construction of a formal specification, namely on the basis of the informal description of the system; and (ii) we can use the structural correspondence to verify that the formal specification does indeed capture the informally stated requirements

A method for maintaining new software

This thesis describes a novel method for perfective maintenance of software which has been developed from specifications using formal transformations. The list of applied transformations provides a suitable derivation history to use when changes are made to the software. The method uses transformations which have been implemented in a tool called the Maintainer's Assistant for the purposes of restructuring code. The method uses these transformations for refinement. Comparisons are made between sequential transformations, refinement calculi and standard proof based refinement techniques for providing a suitable derivation history to use when changes are made in the requirements of a system. Two case studies are presented upon which these comparisons are based and on which the method is tested. Criteria such as saleability, speed, ease, design improvements and software quality is used to argue that transformations are a more favourable basis of refinement. Metrics are used to evaluate the complexity of the code developed using the method. Conclusions of how to develop different types of specifications into code and on how best to apply various changes are presented. An approach which is recommended is to use transformations for splitting the specification so that original refinement paths can still be used. Using transformations for refining a specification and recording this path produces software of a better structure and of higher maintainability. Having such a path improves the speed and ease of future alterations to the system. This is more cost effective than redeveloping the software from a new specification

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

A Graphical Environment Supporting the Algebraic Specification of Abstract Data Types

Abstract Data Types (ADTs) are a powerful conceptual and practical device for building high-quality software because of the way they can describe objects whilst hiding the details of how they are represented within a computer. In order to implement ADTs correctly, it is first necessary to precisely describe their properties and behaviour, typically within a mathematical framework such as algebraic specification. These techniques are no longer merely research topics but are now tools used by software practitioners. Unfortunately, the high level of mathematical sophistication required to exploit these methods has made them unattractive to a large portion of their intended audience. This thesis investigates the use of computer graphics as a way of making the formal specification of ADTs more palatable. Computer graphics technology has recently been explored as a way of making computer programs more understandable by revealing aspects of their structure and run-time behaviour that are usually hidden in textual representations. These graphical techniques can also be used to create and edit programs. Although such visualisation techniques have been incorporated into tools supporting several phases of software development, a survey presented in this thesis of existing systems reveals that their application to supporting the formal specification of ADTs has so far been ignored. This thesis describes the development of a prototype tool (called VISAGE) for visualising and visually programming formally-specified ADTs. VISAGE uses a synchronised combination of textual and graphical views to illustrate the various facets of an ADT's structure and behaviour. The graphical views use both static and dynamic representations developed specifically for this domain. VISAGE's visual programming facility has powerful mechanisms for creating and manipulating entire structures (as well as their components) that make it at least comparable with textual methods. In recognition of the importance of examples as a way of illustrating abstract concepts, VISAGE provides a dedicated tool (called the PLAYPEN) that allows the creation of example data by the user. These data can then be transformed by the operations belonging to the ADT with the result shown by means of a dynamic, graphical display. An evaluation of VISAGE was conducted in order to detect any improvement in subjects' performance, confidence and understanding of ADT specifications. The subjects were asked to perform a set of simple specification tasks with some using VISAGE and the others using manual techniques to act as a control. An analysis of the results shows a distinct positive reaction from the VISAGE group that was completely absent in the control group thereby supporting the thesis that the algebraic specification of ADTs can be made more accessible and palatable though the use of computer graphic techniques

A Conceptual Framework for Adapation

This paper presents a white-box conceptual framework for adaptation that promotes a neat separation of the adaptation logic from the application logic through a clear identification of control data and their role in the adaptation logic. The framework provides an original perspective from which we survey archetypal approaches to (self-)adaptation ranging from programming languages and paradigms, to computational models, to engineering solutions