A single complete relational rule for coalgebraic refinement

A transition system can be presented either as a binary relation or as a coalgebra for the powerset functor, each representation being obtained from the other by transposition. More generally, a coalgebra for a functor F generalises transition systems in the sense that a shape for transitions is determined by F, typically encoding a signature of methods and observers. This paper explores such a duality to frame in purely relational terms coalgebraic refinement, showing that relational (data) refinement of transition relations, in its two variants, downward and upward (functional) simulations, is equivalent to coalgebraic refinement based on backward and forward morphisms, respectively. Going deeper, it is also shown that downward simulation provides a complete relational rule to prove coalgebraic refinement. With such a single rule the paper defines a pre-ordered calculus for refinement of coalgebras, with bisimilarity as the induced equivalence. The calculus is monotonic with respect to the main relational operators and arbitrary relator F, therefore providing a framework for structural reasoning about refinement

Strategic term rewriting and its application to a VDM-SL to SQL conversion

We constructed a tool, called VooDooM, which converts datatypes in Vdm-sl into Sql relational data models. The conversion involves transformation of algebraic types to maps and products, and pointer introduction. The conversion is specified as a theory of refinement by calculation. The implementation technology is strategic term rewriting in Haskell, as supported by the Strafunski bundle. Due to these choices of theory and technology, the road from theory to practise is straightforward.Fundação para a Ciência e a Tecnologia (FCT) - POSI/ICHS/44304/2002Agência de Inovação (ADI) - ∑!223

Idempotent Turing Machines

A function f is said to be idempotent if f(f(x)) = f(x) holds whenever f(x) is defined. This paper presents a computation model for idempotent functions, called an idempotent Turing machine. The computation model is necessarily and sufficiently expressive in the sense that not only does it always compute an idempotent function but also every idempotent computable function can be computed by an idempotent Turing machine. Furthermore, a few typical properties of the computation model such as robustness and universality are shown. Our computation model is expected to be a basis of special-purpose (or domain-specific) programming languages in which only but all idempotent computable functions can be defined

Rhodes University Research Report 2006

[From Preface] Rhodes University defines as one of its three core activities the production of knowledge through stimulating imaginative and rigorous research of all kinds (fundamental, applied, policy-oriented, etc.), and in all disciplines and fields. Though a small university with less than 6 000 students, the student profile and research output (publications, Master’s and Doctoral graduates) of Rhodes ensures that it occupies a distinctive place in the overall South African higher education landscape. For one, almost 25% of Rhodes’ students are postgraduates. Coming from a diversity of countries, these postgraduates ensure that Rhodes is a cosmopolitan and fertile environment of thinking and ideas. For another, Rhodes has the best research output of all South African universities, a testimony to the dedication and passion of its academics for research and the commitment of the University to nurture and cultivate knowledge production of all kinds. During 2006, Rhodes academics published 113 books and book chapters, 312 articles, and contributed 636 papers to conferences. One hundred and seventy students graduated with Master’s degrees and 47 with Doctorates. In a number of areas Rhodes’ academics are at the cutting-edge of research, pushing the frontiers knowledge production. The award of a Department of Science and Technology sponsored Research Chair in Chemistry to Professor Nyokong is one indicator of national recognition of this reality. Rhodes researchers are at the forefront of a number of national projects, and also continue to attract research funding from a variety of international and national research agencies and industry. Rhodes possesses an admirable research culture, and provides the intellectual space for the flourishing and debate of ideas, as evidenced by the number and diversity of seminars, public lectures, and the quality of local and international academics that visit Rhodes. A number of Rhodes academics also make important contributions to national public debate, enhancing the visibility of Rhodes in the intellectual life of South Africa. Rhodes University is committed to maintain and, in the years to come, to enhance its research output, to broaden its research base, to bring on steam new generations of researchers (who are also increasing women and black), and to continue being a distinctive South African university in the domain of knowledge production

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.