Graduation date: 1981

Thesis (M.A.)--Oregon State University, 1988. / Typescript (photocopy). Mounted photographs. Includes bibliographical references (leaves 95-104). Also available online.

Thesis (Ph.D.) - University of St Andrews, April 2007.

Truth and falsehood, questions and answers, construction and deconstruction; most things come in dual pairs. Duality is a mirror that reveals the new from the old via opposition. This idea appears pervasively in logic, where duality inverts "true" with "false" and "and" with "or." However, even though programming languages are closely connected to logics, this kind of strong duality is not so apparent in practice. Sum types (disjoint tagged unions) and product types (structures) are dual concepts, but in the realm of programming, natural biases obscure their duality. To better understand the role of duality in programming, we shift our perspective. Our approach is based on the Curry-Howard isomorphism which says that programs following a specification are the same as proofs for mathematical theorems. This thesis explores Gentzen's sequent calculus, a logic steeped in duality, as a model for computational duality. By applying the Curry-Howard isomorphism to the sequent calculus, we get a language that combines dual programming concepts as equal opposites: data types found in functional languages are dual to co-data types (interface-based objects) found in object-oriented languages, control flow is dual to information flow, induction is dual to co-induction. This gives a duality-based semantics for reasoning about programs via orthogonality: checking safety and correctness based on a comprehensive test suite. We use the language of the sequent calculus to apply ideas from logic to issues relevant to program compilation. The idea of logical polarity reveals a symmetric basis of primitive programming constructs that can faithfully represent all user-defined data and co-data types. We reflect the lessons learned back into a core language for functional languages, at the cost of symmetry, with the relationship between the sequent calculus and natural deduction. This relationship lets us derive a pure lambda calculus with user-defined data and co-data which we further extend by bringing out the implicit control-flow in functional programs. Explicit control-flow lets us share and name control the same way we share and name data, enabling a direct representation of join points, which are essential for tractable optimization and compilation.

A study of 80 clay figurines from aboriginal sites in the upper Rogue River Valley in southwestern Oregon fails to reveal any connection with other figurines found in the Pacific Northwest and northern California. A preference for animal rather than human representations is demonstrated. The temporal distribution of the figurines is not known, but spatial distribution appears roughly coextensive with territories occupied by the upland Takelma at the time of Euro-American contact during the second quarter of the nineteenth century.

The original purpose of this study was a detailed structural analysis of the Jurassic Otter Point Formation in order to determine if the Canyonville Fault Zone, which forms the northern boundary of the Klamath Mountains in the Riddle - Canyonville area (Benson and Perttu, 1980), extends westward to the coast and, if possible, to characterize the structure of the Otter Point Formation. Further, a detailed examination of the structural and stratigraphic relationships between the Otter Point Formation and the Eocene Roseburg and Lookingglass Formations was to be performed in an attempt to determine the tectonic history of the area.

Dependently typed programming languages allow the type system to express arbitrary propositions of intuitionistic logic, thanks to the Curry-Howard isomorphism. Taking full advantage of this type system requires defining more types than usual, in order to encode logical correctness criteria into the definitions of datatypes. While an abundance of specialized types helps ensure correctness, it comes at the cost of needing to redefine common functions for each specialized type. This dissertation makes an effort to attack the problem of code reuse in dependently typed languages. Our solution is to write generic functions, which can be applied to any datatype. Such a generic function can be applied to datatypes that are defined at the time the generic function was written, but they can also be applied to any datatype that is defined in the future. Our solution builds upon previous work on generic programming within dependently typed programming. Type theory supports generic programming using a construction known as a universe. A universe can be considered the model of a programming language, such that writing functions over it models writing generic programs in the programming language. Historically, there has been a trade-off between the expressive power of the modeled programming language, and the kinds of generic functions that can be written in it. Our dissertation shows that no such trade-off is necessary, and that we can write future-proof generic functions in a model of a dependently typed programming language with a rich collection of types.

Cette thèse étudie différents aspects de la réalisabilité classique due à Jean-Louis Krivine. Celle-ci permet de mettre en oeuvre l'isomorphisme de Curry-Howard: on peut ainsi associer un programme à chaque démonstration mathématique, et considérer chaque théorème comme une spécification. Dans un premier temps, on rappelle le formalisme de la réalisabilité classique ainsi que certains de ses résultats fondamentaux. On s'attache ensuite à l'analyse des contenus opérationnels obtenus suivant deux méthodes différentes d'étude des entiers des modèles de la réalisabilité. Dans un second temps, on rappelle la notion de jeu qui peut être associée à chaque formule du premier ordre dans ce cadre. Ces jeux permettent d'établir une correspondance entre les formules valides du calcul des prédicats et les protocoles de la couche transport des réseaux, que l'on peut spécifier de manière claire et précise par ce biais. La dernière partie est consacrée à l'étude de l'axiome du choix dépendant. On montre que la méthode développée pour le réaliser s'adapte à une expression simple de celui-ci au niveau des individus d'un modèle. On utilise enfin l'instruction associée pour réaliser un cas particulier du théorème de Herbrand. Le terme obtenu effectue une opération très générale, qui peut être interprétée dans le cadre des protocoles réseaux.

Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 383-401). Also available online in ProQuest, free to University of Oregon users.

Thesis (Ph. D.)--University of Wisconsin, 1958. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves [362]-371).