C. A. R. Hoare’s research while affiliated with University of Oxford and other places

Cognitive computers (κC) are intelligent processors advanced from data and information processing to autonomous knowledge learning and intelligence generation. This study presents a retrospective and prospective review of the odyssey toward κC empowered by transdisciplinary basic research and engineering advances. A wide range of fundamental theories and innovative technologies for κC is explored, and a set of underpinning intelligent mathematics (IM) is created. The architectures of κC for cognitive computing and Autonomous Intelligence Generation (AIG) are designed as a brain-inspired cognitive engine. Applications of κC in autonomous AI (AAI) are demonstrated by pilot projects. This study reveals that AIG will no longer be a privilege restricted only to humans via the odyssey to κC toward training-free and self-inferencing computers.

This paper studies algebraic models for concurrency, in light of recent work on Concurrent Kleene Algebra and Separation Logic. It establishes a strong connection between the Concurrency and Frame Rules of Separation Logic and a variant of the exchange law of Category Theory. We investigate two standard models: one uses sets of traces, and the other is state-based, using assertions and weakest preconditions. We relate the latter to standard models of the heap as a partial function. We exploit the power of algebra to unify models and classify their variations.

It is widely believed that program analysis can be more closely targeted to the needs of programmers if the program is accompanied by further redundant documentation. This may include regression test suites, API protocol usage, and code contracts. To this should be added the largest and most redundant text of all: the previous version of the same program. It is the differences between successive versions of a legacy program already in use which occupy most of a programmer's time. Although differential analysis in the form of equivalence checking has been quite successful for hardware designs, it has not received as much attention in the static program analysis community. This paper briefly summarizes the current state of the art in differential static analysis for software, and suggests a number of promising applications. Although regression test generation has often been thought of as the ultimate goal of differential analysis, we highlight several other applications that can be enabled by differential static analysis. This includes equivalence checking, semantic diffing, differential contract checking, summary validation, invariant discovery and better debugging. We speculate that differential static analysis tools have the potential to be widely deployed on the developer's toolbox despite the fundamental stumbling blocks that limit the adoption of static analysis.

A Concurrent Kleene Algebra offers two composition operators, one that stands for sequential execution and the other for concurrent execution [10]. In this paper we investigate the abstract background of this law in terms of independence relations on which a concrete trace model of the algebra is based. Moreover, we show the interdependence of the basic properties of such relations and two further laws that are essential in the application of the algebra to a Jones style rely/guarantee calculus. Finally we reconstruct the trace model in a more abstract setting based on the notion of atoms from lattice theory.

A team of researchers from SRI International Computer Science Laboratory has proposed a long-term research program toward the construction of error-free software systems. The research project, called the Verified Software Initiative, will make an effort to a comprehensive theory of programming that covers the features needed to build practical and reliable programs. It will focus on a coherent toolset that automates the theory and scales up to the analysis of industrial-strength software. It will also develop a collection of realistic verified programs that can replace unverified programs in existing service and continue to evolve in a verified state. Verification involves the rigorous demonstration of the correctness of software with respect to a specification of its intended behavior. It can be applied at all phases of the software lifecycle including design to maintenance.

C.A.R. Hoare revisits his past Communications article on the axiomatic approach to programming and uses it as a touchstone for the future.

Graphs are used to model control and data flow among events occurring in the execution of a concurrent program. Our treatment of data flow covers both shared storage and external communication. Nevertheless, the laws of Hoare and Jones correctness reasoning remain valid when interpreted in this general model.

We are aiming at a classification of semantical models for Communicating Processes that will enable us to recommend certain models which are just detailed enough for particular applications. But before such an aim can be fully realised, more sophisticated models of processes should be studied. For example, we have not considered the notion of state so far. This would allow to add assignment and explicit value passing between processes, thus combining sequential programs with Communicating Processes. It is also important to ensure that the operators satisfy the usual algebraic laws, for example parallel composition should be associative. And the relationship between specification-oriented denotational semantics used here and the operational semantics used in [12,13,16] should be studied. This requires an explicit concept of divergence. In particular, it is interesting to investigate how the criterion P sat S can be derived systematically from the operational semantics. A significant step in this direction has already been made in [14]. Finally, an explicit syntax for specifications and proof systems for the relation P sat S should be developed. First proposals for such proof systems can be found in [5,9].