Higher-Order Beta Matching with Solutions in Long Beta-Eta Normal Form

Higher-order matching is a special case of unification of simply-typed lambda-terms: in a matching equation, one of the two sides contains no unification variables. Loader has recently shown that higher-order matching up to beta equivalence is undecidable, but decidability of higher-order matching up to beta-eta equivalence is a long-standing open problem. We show that higher-order matching up to beta-eta equivalence is decidable if and only if a restricted form of higher-order matching up to beta equivalence is decidable: the restriction is that solutions must be in long beta-eta normal form

Pattern discovery for parallelism in functional languages

No longer the preserve of specialist hardware, parallel devices are now ubiquitous. Pattern-based approaches to parallelism, such as algorithmic skeletons, simplify traditional low-level approaches by presenting composable high-level patterns of parallelism to the programmer. This allows optimal parallel configurations to be derived automatically, and facilitates the use of different parallel architectures. Moreover, parallel patterns can be swap-replaced for sequential recursion schemes, thus simplifying their introduction. Unfortunately, there is no guarantee that recursion schemes are present in all functional programs. Automatic pattern discovery techniques can be used to discover recursion schemes. Current approaches are limited by both the range of analysable functions, and by the range of discoverable patterns. In this thesis, we present an approach based on program slicing techniques that facilitates the analysis of a wider range of explicitly recursive functions. We then present an approach using anti-unification that expands the range of discoverable patterns. In particular, this approach is user-extensible; i.e. patterns developed by the programmer can be discovered without significant effort. We present prototype implementations of both approaches, and evaluate them on a range of examples, including five parallel benchmarks and functions from the Haskell Prelude. We achieve maximum speedups of 32.93x on our 28-core hyperthreaded experimental machine for our parallel benchmarks, demonstrating that our approaches can discover patterns that produce good parallel speedups. Together, the approaches presented in this thesis enable the discovery of more loci of potential parallelism in pure functional programs than currently possible. This leads to more possibilities for parallelism, and so more possibilities to take advantage of the potential performance gains that heterogeneous parallel systems present

Ontology evolution in physics

With the advent of reasoning problems in dynamic environments, there is an increasing need for automated reasoning systems to automatically adapt to unexpected changes in representations. In particular, the automation of the evolution of their ontologies needs to be enhanced without substantially sacrificing expressivity in the underlying representation. Revision of beliefs is not enough, as adding to or removing from beliefs does not change the underlying formal language. General reasoning systems employed in such environments should also address situations in which the language for representing knowledge is not shared among the involved entities, e.g., the ontologies in a multi-ontology environment or the agents in a multi-agent environment. Our techniques involve diagnosis of faults in existing, possibly heterogeneous, ontologies and then resolution of these faults by manipulating the signature and/or the axioms. This thesis describes the design, development and evaluation of GALILEO (Guided Analysis of Logical Inconsistencies Lead to Evolution of Ontologies), a system designed to detect conflicts in highly expressive ontologies and resolve the detected conflicts by performing appropriate repair operations. The integrated mechanism that handles ontology evolution is able to distinguish between various types of conflicts, each corresponding to a unique kind of ontological fault. We apply and develop our techniques in the domain of Physics. This an excellent domain because many of its seminal advances can be seen as examples of ontology evolution, i.e. changing the way that physicists perceive the world, and case studies are well documented – unlike many other domains. Our research covers analysing a wide ranging development set of case studies and evaluating the performance of the system on a test set. Because the formal representations of most of the case studies are non-trivial and the underlying logic has a high degree of expressivity, we face some tricky technical challenges, including dealing with the potentially large number of choices in diagnosis and repair. In order to enhance the practicality and the manageability of the ontology evolution process, GALILEO incorporates the functionality of generating physically meaningful diagnoses and repairs and, as a result, narrowing the search space to a manageable size