Abstract The use of formal method techniques can contribute to the production of more reliable and dependable systems. However, a common bottleneck for industrial adoption of such techniques is the needs for interactive proofs. We use a popular formal method, called Event-B , as our working domain, and set invariant preservation (INV) proofs as targets, because INV proofs can account for a significant proportion of the proofs requiring human interactions. We apply an inductive theorem proving technique, called rippling, for Event-B INV proofs. Rippling automates proofs using meta-level guidance. The guidance is in particular useful to develop proof patches to recover failed proof attempts. We are interested in the case when a missing lemma is required. We combine a scheme-based theory-exploration system, called IsaScheme [ MRMDB10 ], with rippling to develop a proof patch via lemma discovery. We also develop two new proof patches to unfold operator definitions and to suggest case-splits, respectively. The combined use of rippling with these three proof patches as a proof method significantly improves the proof automation for our evaluation set.

We present a computational framework for conceptual blending , a concept invention method that is advocated in cognitive science as a fundamental and uniquely human engine for creative thinking. Our framework treats a crucial part of the blending process, namely the generalisation of input concepts, as a search problem that is solved by means of modern answer set programming methods to find commonalities among input concepts. We also address the problem of pruning the space of possible blends by introducing metrics that capture most of the so-called optimality principles , described in the cognitive science literature as guidelines to produce meaningful and serendipitous blends. As a proof of concept, we demonstrate how our system invents novel concepts and theories in domains where creativity is crucial, namely mathematics and music.

We describe an approach to automatically prove the functional correctness of pointer programs that involve iteration and recursion. Building upon separation logic, our approach has been implemented as a tightly integrated tool chain incorporating a novel combination of proof planning and invariant generation. Starting from shape analysis, performed by the Smallfoot static analyser, we have developed a proof strategy that combines shape and functional aspects of the verification task. By focusing on both iterative and recursive code, we have had to address two related invariant generation tasks, i.e. loop and frame invariants. We deal with both tasks uniformly using an automatic technique called term synthesis, in combination with the IsaPlanner/Isabelle theorem prover. In addition, where verification fails, we attempt to overcome failure by automatically generating missing preconditions. We present in detail our experimental results. Our approach has been evaluated on a range of examples, drawn in part from a functional extension to the Smallfoot corpus.

Pointers are a powerful and widely used programming mechanism, but developing and maintaining correct pointer programs is notoriously hard. Here we describe the CORE1system, which supports the development of provably correct pointer programs. The CORE system combines data structure animation with functional correctness. While the animation component allows a programmer to explore and debug their algorithms, the functional correctness component provides a stronger guarantee via formal proof. CORE builds upon two external reasoning tools, i.e. the Smallfoot family of static analysers and the IsaPlanner proof planner. At the heart of the CORE functional correctness capability lies an integration of planning and term synthesis. The planning subsystem bridges the gap between shape analysis, provided by Smallfoot, and functional correctness. Key to this process is the generation of functional invariants, i.e. both loop and frame invariants. We use term synthesis, coupled with IsaPlanner's capability for reasoning about inductively defined structures, to automate the generation of functional invariants. The formal guarantees constructed by the CORE system take the form of proof tactics.