Cogent: uniqueness types and certifying compilation

This paper presents a framework aimed at significantly reducing the cost of proving functional correctness for low-level operating systems components. The framework is designed around a new functional programming language, Cogent. A central aspect of the language is its uniqueness type system, which eliminates the need for a trusted runtime or garbage collector while still guaranteeing memory safety, a crucial property for safety and security. Moreover, it allows us to assign two semantics to the language: The first semantics is imperative, suitable for efficient C code generation, and the second is purely functional, providing a user-friendly interface for equational reasoning and verification of higher-level correctness properties. The refinement theorem connecting the two semantics allows the compiler to produce a proof via translation validation certifying the correctness of the generated C code with respect to the semantics of the Cogent source program. We have demonstrated the effectiveness of our framework for implementation and for verification through two file system implementations

Cogent: uniqueness types and certifying compilation.

This paper presents a framework aimed at significantly reducing the cost of proving functional correctness for low-level operating systems components. The framework is designed around a new functional programming language, Cogent. A central aspect of the language is its uniqueness type system, which eliminates the need for a trusted runtime or garbage collector while still guaranteeing memory safety, a crucial property for safety and security. Moreover, it allows us to assign two semantics to the language: The first semantics is imperative, suitable for efficient C code generation, and the second is purely functional, providing a user-friendly interface for equational reasoning and verification of higher-level correctness properties. The refinement theorem connecting the two semantics allows the compiler to produce a proof via translation validation certifying the correctness of the generated C code with respect to the semantics of the Cogent source program. We have demonstrated the effectiveness of our framework for implementation and for verification through two file system implementations

Saturation-based decision procedures for extensions of the guarded fragment

We apply the framework of Bachmair and Ganzinger for saturation-based theorem proving to derive a range of decision procedures for logical formalisms, starting with a simple terminological language EL, which allows for conjunction and existential restrictions only, and ending with extensions of the guarded fragment with equality, constants, functionality, number restrictions and compositional axioms of form S ◦ T ⊆ H. Our procedures are derived in a uniform way using standard saturation-based calculi enhanced with simplification rules based on the general notion of redundancy. We argue that such decision procedures can be applied for reasoning in expressive description logics, where they have certain advantages over traditionally used tableau procedures, such as optimal worst-case complexity and direct correctness proofs.Wir wenden das Framework von Bachmair und Ganzinger für saturierungsbasiertes Theorembeweisen an, um eine Reihe von Entscheidungsverfahren für logische Formalismen abzuleiten, angefangen von einer simplen terminologischen Sprache EL, die nur Konjunktionen und existentielle Restriktionen erlaubt, bis zu Erweiterungen des Guarded Fragment mit Gleichheit, Konstanten, Funktionalität, Zahlenrestriktionen und Kompositionsaxiomen der Form S ◦ T ⊆ H. Unsere Verfahren sind einheitlich abgeleitet unter Benutzung herkömmlicher saturierungsbasierter Kalküle, verbessert durch Simplifikationsregeln, die auf dem Konzept der Redundanz basieren. Wir argumentieren, daß solche Entscheidungsprozeduren für das Beweisen in ausdrucksvollen Beschreibungslogiken angewendet werden können, wo sie gewisse Vorteile gegenüber traditionell benutzten Tableauverfahren besitzen, wie z.B. optimale worst-case Komplexität und direkte Korrektheitsbeweise

Relations between Modern Mathematics and Poetry: Czesław Miłosz; Zbigniew Herbert; Ion Barbu/Dan Barbilian

This doctoral thesis is an examination of the relationship between poetry and mathematics, centred on three twentieth-century case studies: the Polish poets Czesław Miłosz (1911-2004) and Zbigniew Herbert (1924-1998), and the Romanian mathematician and poet Dan Barbilian/Ion Barbu (1895-1961). Part One of the thesis is a review of current scholarly literature, divided into two chapters. The first chapter looks at the nature of mathematics, outlining its historical developments and describing some major mathematical concepts as they pertain to the later case studies. This entails a focus on non-Euclidean geometries, modern algebra, and the foundations of mathematics in Europe; the nature of mathematical truth and language; and the modern historical evolution of mathematical schools in Poland and Romania. The second chapter examines some existing attempts to bring together mathematics and poetry, drawing on literature and science as an academic field; the role of the imagination and invention in the languages of both poetics and mathematics; the interest in mathematics among certain Symbolist poets, notably Mallarmé; and the experimental work of the French groups of mathematicians and mathematician-poets, Bourbaki and Oulipo. The role of metaphor is examined in particular. Part Two of the thesis is the case studies. The first presents the ethical and moral stance of Czesław Miłosz, investigating his attitudes towards classical and later relativistic science, in the light of the Nazi occupation and the Marxist regimes in Poland, and how these are reflected in his poetry. The study of Zbigniew Herbert is structured around a wide selection of his poetic oeuvre, and identifying his treatment of evolving and increasingly more complex mathematical concepts. The third case study, on Dan Barbilian, who published his poetry under the name Ion Barbu, begins with an examination of the mathematical school at Göttingen in the 1920s, tracing the influence of Gauss, Riemann, Klein, Hilbert and Noether in Barbilian’s own mathematical work, particularly in the areas of metric spaces and axiomatic geometry. In the discussion, the critical analysis of the mathematician and linguist Solomon Marcus is examined. This study finishes with a close reading of seven of Barbu’s poems. The relationship of mathematics and poetry has rarely been studied as a coherent academic field, and the relevant scholarship is often disconnected. A feature of this thesis is that it brings together a wide range of scholarly literature and discussion. Although primarily in English, a considerable amount of the academic literature collated here is in French, Romanian, Polish and some German. The poems themselves are presented in the original Polish and Romanian with both published and working translations appended in the footnotes. In the case of the two Polish poets, one a Nobel laureate and the other a multiple prize-winning figure highly regarded in Poland, this thesis is unusual in its concentration on mathematics as a feature of the poetry which is otherwise much-admired for its politically-engaged and lyrical qualities. In the case of the Romanian, Dan Barbilian, he is widely known in Romania as a mathematician, and most particularly as the published poet Ion Barbu, yet his work is little studied outside that country, and indeed much of it is not yet translated into English. This thesis suggests at an array of both theoretical and specific starting points for examining the multi-stranded and intricate relationship between mathematics and poetry, pointing to a number of continuing avenues of further research

Sight, sound, the chicken and the egg: Audio-visual co-dependency in music

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Amongst the modern day abundance of audio-visual media, where sounds represent everything from the swooping of virtual cameras through 3D spaces to the pressing of buttons and receiving of emails, and conversely where VJs routinely accompany live musical performance with an increasingly sophisticated language of abstract computer animation, the notion of music as a necessarily exclusively aural medium seems somewhat out of place. Psychological theories relating to the cognition of sound, in particular physical schema, accounting for the ubiquity of vertical plane pitch metaphors in most musical cultures, provide evidence of a deep-rooted spatially informed understanding of sound thus providing a common ground for both sound and vision in music. Furthermore, Western Classical composition is rife with examples of visually conceived forms from Bach’s Crab Canon (1747) to Xenakis’ architecturally inspired Metastasis (1954). However, in practice the gap between the listener’s auditory experience and the composer’s visual concept is often insurmountable. Rising to Schaeffer’s call for “Primacy to the ear!” (Schaeffer, 1967, pp. 28-30), acousmatic composers have sought to derive music exclusively from experientially verifiable criteria. However, in its pervasiveness of other musical genres, no doubt aided by technologically and commercially driven domination of the pre-recorded over the live listening experience in the latter half of the twentieth century, such an approach has lead to the neglect of visual aspects in the live performance of much art-music. This research aims to begin to redress this balance through the composition of, largely computer realised, audio-visual works whose conception arises not from a superimposition of one medium upon another, but through the very relations between the media themselves. Utilising modern computers’ ability to synchronise physical and virtual visual events with synthesised sound in real time not only affords composers an invaluable tool for enhancing listener’s perception of formal structures but also implies causal relationships between the sonic and the visual which can provide a base of intuitive understanding on which more complex formal ideas can be built.Sponsored by the Brunel University Isambard Scholarship

Discovering Causal Relations and Equations from Data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.Comment: 137 page

Holistic Approach for Authoring Immersive and Smart Environments for the Integration in Engineering Education

Die vierte industrielle Revolution und der rasante technologische Fortschritt stellen die etablierten Bildungsstrukturen und traditionellen Bildungspraktiken in Frage. Besonders in der Ingenieurausbildung erfordert das lebenslange Lernen, dass man sein Wissen und seine Fähigkeiten ständig verbessern muss, um auf dem Arbeitsmarkt wettbewerbsfähig zu sein. Es besteht die Notwendigkeit eines Paradigmenwechsels in der Bildung und Ausbildung hin zu neuen Technologien wie virtueller Realität und künstlicher Intelligenz. Die Einbeziehung dieser Technologien in ein Bildungsprogramm ist jedoch nicht so einfach wie die Investition in neue Geräte oder Software. Es müssen neue Bildungsprogramme geschaffen oder alte von Grund auf umgestaltet werden. Dabei handelt es sich um komplexe und umfangreiche Prozesse, die Entscheidungsfindung, Design und Entwicklung umfassen. Diese sind mit erheblichen Herausforderungen verbunden, die die Überwindung vieler Hindernisse erfordert. Diese Arbeit stellt eine Methodologie vor, die sich mit den Herausforderungen der Nutzung von Virtueller Realität und Künstlicher Intelligenz als Schlüsseltechnologien in der Ingenieurausbildung befasst. Die Methodologie hat zum Ziel, die Hauptakteure anzuleiten, um den Lernprozess zu verbessern, sowie neuartige und effiziente Lernerfahrungen zu ermöglichen. Da jedes Bildungsprogramm einzigartig ist, folgt die Methodik einem ganzheitlichen Ansatz, um die Erstellung maßgeschneiderter Kurse oder Ausbildungen zu unterstützen. Zu diesem Zweck werden die Wechselwirkung zwischen verschiedenen Aspekten berücksichtigt. Diese werden in den drei Ebenen - Bildung, Technologie und Management zusammengefasst. Die Methodik betont den Einfluss der Technologien auf die Unterrichtsgestaltung und die Managementprozesse. Sie liefert Methoden zur Entscheidungsfindung auf der Grundlage einer umfassenden pädagogischen, technologischen und wirtschaftlichen Analyse. Darüber hinaus unterstützt sie den Prozess der didaktischen Gestaltung durch eine umfassende Kategorisierung der Vor- und Nachteile immersiver Lernumgebungen und zeigt auf, welche ihrer Eigenschaften den Lernprozess verbessern können. Ein besonderer Schwerpunkt liegt auf der systematischen Gestaltung immersiver Systeme und der effizienten Erstellung immersiver Anwendungen unter Verwendung von Methoden aus dem Bereich der künstlichen Intelligenz. Es werden vier Anwendungsfälle mit verschiedenen Ausbildungsprogrammen vorgestellt, um die Methodik zu validieren. Jedes Bildungsprogramm hat seine eigenen Ziele und in Kombination decken sie die Validierung aller Ebenen der Methodik ab. Die Methodik wurde iterativ mit jedem Validierungsprojekt weiterentwickelt und verbessert. Die Ergebnisse zeigen, dass die Methodik zuverlässig und auf viele Szenarien sowie auf die meisten Bildungsstufen und Bereiche übertragbar ist. Durch die Anwendung der in dieser Arbeit vorgestellten Methoden können Interessengruppen immersiven Technologien effektiv und effizient in ihre Unterrichtspraxis integrieren. Darüber hinaus können sie auf der Grundlage der vorgeschlagenen Ansätze Aufwand, Zeit und Kosten für die Planung, Entwicklung und Wartung der immersiven Systeme sparen. Die Technologie verlagert die Rolle des Lehrenden in eine Moderatorrolle. Außerdem bekommen die Lehrkräfte die Möglichkeit die Lernenden individuell zu unterstützen und sich auf deren kognitive Fähigkeiten höherer Ordnung zu konzentrieren. Als Hauptergebnis erhalten die Lernenden eine angemessene, qualitativ hochwertige und zeitgemäße Ausbildung, die sie qualifizierter, erfolgreicher und zufriedener macht