Michael Leuschel

ProB: A Model Checker for B

We present PROB, an animation and model checking tool for the B method. PROB’s animation facilities allow users to gain confidence in their specifications, and unlike the animator provided by the B-Toolkit, the user does not have to guess the right values for the operation arguments or choice variables. PROB contains a model checker and a constraint-based checker, both of which can be used to detect various errors in B specifications. We present our first experiences in using PROB on several case studies, highlighting that PROB enables users to uncover errors that are not easily discovered by existing tools.

ProB : an automated analysis toolset for the B method

We present ProB, a validation toolset for the B method. ProB’s automated animation facilities allow users to gain confidence in their specifications. ProB also contains a model checker and a refinement checker, both of which can be used to detect various errors in B specifications. We describe the underlying methodology of ProB, and present the important aspects of the implementation. We also present empirical evaluations as well as several case studies, highlighting that ProB enables users to uncover errors that are not easily discovered by existing tools.

CONJUNCTIVE PARTIAL DEDUCTION: FOUNDATIONS, CONTROL, ALGORITHMS, AND EXPERIMENTS

Abstract Partial deduction in the Lloyd–Shepherdson framework cannot achieve certain optimisations which are possible by unfold/fold transformations. We introduce conjunctive partial deduction , an extension of partial deduction accommodating such optimisations, e.g., tupling and deforestation. We first present a framework for conjunctive partial deduction, extending the Lloyd–Shepherdson framework by considering conjunctions of atoms (instead of individual atoms) for specialisation and renaming. Correctness results are given for the framework with respect to computed answer semantics, least Herbrand model semantics, and finite failure semantics. Maintaining the well-known distinction between local and global control, we describe a basic algorithm for conjunctive partial deduction, and refine it into a concrete algorithm for which we prove termination. The problem of finding suitable renamings which remove redundant arguments turns out to be important, so we give an independent technique for this. A fully automatic implementation has been undertaken, which always terminates. Differences between the abstract semantics and Prologs left-to-right execution motivate deviations from the abstract technique in the actual implementation, which we discuss. The implementation has been tested on an extensive set of benchmarks which demonstrate that conjunctive partial deduction indeed pays off, surpassing conventional partial deduction on a range of small to medium-size programs, while remaining manageable in an automatic and terminating system.

Controlling generalization and polyvariance in partial deduction of normal logic programs

Given a program and some input data, partial deduction computes a specialized program handling any remaining input more efficiently.However, controlling the process well is a rather difficult problem.In this article, we elaborate global control for partial deduction:for which atoms, among possibly infinitely many, should specialized relations be produced, meanwhile guaranteeing correctness as well as termination? Our work is based on two ingredients. First, we use the concept of a characteristic tree, encapsulating specialization behavior rather than syntactic structure, to guide generalization and polyvariance, and we show how this can be done in a correct andelegant way. Second, we structure combinations of atoms and associated characteristic trees in global trees registering “causal” relationships among such pairs. This allows us to spot looming nontermination and perform proper generalization in order to avert the danger, without having to impose a depth bound on characteristic trees. The practical relevance and benefits of the work areillustrated through extensive experiments. Finally, a similar approach may improve upon current (on-line) control strategies for program transformation in general such as (positive) supercompilation of functional programs. It also seems valuable in the context of abstract interpretation to handle infinite domains of infinite height with more precision.

Combining CSP and b for specification and property verification

ProB is a model checking tool for the B Method. In this paper we present an extension of ProB that supports checking of specifications written in a combination of CSP and B. We explain how the notations are combined semantically and give an overview of the implementation of the combination. We illustrate the benefit that appropriate use of CSP, in conjunction with our tool, gives to B developments both for specification and for verification purposes.

Abstract State Machines, Alloy, B, VDM, and Z

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Logic program specialisation through partial deduction: Control issues

Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial deduction, is to exploit partial knowledge about the input. It is achieved through a well-automated application of parts of the Burstall-Darlington unfold/fold transformation framework. The main challenge in developing systems is to design automatic control that ensures correctness, efficiency, and termination. This survey and tutorial presents the main developments in controlling partial deduction over the past 10 years and analyses their respective merits and shortcomings. It ends with an assessment of current achievements and sketches some remaining research challenges.

On the Power of Homeomorphic Embedding for Online Termination

Recently well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper we investigate and clarify for the first time, both intuitively and formally, the advantages of such an approach over one using well-founded orders. Notably we show that the homeomorphic embedding relation is strictly more powerful than a large class of involved well-founded approaches.

Global Control for Partial Deduction through Characteristic Atoms and Global Trees

Recently, considerable advances have been made in the (online) control of logic program specialisation. A clear conceptual distinction has been established between local and global control and on both levels concrete strategies as well as general frameworks have been proposed. For global control in particular, recent work has developed concrete techniques based on the preservation of characteristic trees (limited, however, by a given, arbitrary depth bound) to obtain a very precise control of polyvariance. On the other hand, the concept of an m-tree has been introduced as a refined way to trace “relationships” of partially deduced atoms, thus serving as the basis for a general framework within which global termination of partial deduction can be ensured in a non ad hoc way.

Validating Z specifications using the PROB animator and model checker

We present the architecture and implementation of the proz tool to validate high-level Z specifications. The tool was integrated into prob, by providing a translation of Z into B and by extending the kernel of prob to accommodate some new syntax and data types. We describe the challenge of going from the tool friendly formalism B to the more specification-oriented formalism Z, and show how many Z specifications can be systematically translated into B. We describe the extensions, such as record types and free types, that had to be added to the kernel to support a large subset of Z. As a side-effect, we provide a way to animate and model check records in prob. By incorporating proz into prob, we have inherited many of the recent extensions developed for B, such as the integration with CSP or the animation of recursive functions. Finally, we present a successful industrial application, which makes use of this fact, and where proz was able to discover several errors in Z specifications containing higher-order recursive functions.