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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.

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.

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 and elegant 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 are illustrated 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.