Abstract. Building complex software systems necessitates the use of component-based architectures. In theory, of the set of components needed for a design, only some small portion of them are “custom”; the rest are reused or refactored existing pieces of software. Unfortunately, this is an idealized situation. Just because two components should work together does not mean that they will work together. The “glue ” that holds components together is not just technology. The contracts that bind complex systems together implicitly define more than their explicit type. These “conceptual contracts ” describe essential aspects of extra-system semantics: e.g., object models, type systems, data representation, interface action semantics, legal and contractual obligations, and more. Designers and developers spend inordinate amounts of time technologically duct-taping systems to fulfill these conceptual contracts because system-wide semantics have not been rigorously characterized or codified. This paper describes a formal characterization of the problem and discusses an initial implementation of the resulting theoretical system. 1

iii This thesis describes a theory for representing, manipulating, and reasoning about structured pieces of knowledge in open collaborative systems. The theory’s design is motivated by both its general model as well as its target user commu-nity. Its model is structured information, with emphasis on classification, relative structure, equivalence, and interpretation. Its user community is meant to be non-mathematicians and non-computer scientists that might use the theory via computational tool support once inte-grated with modern design and development tools. This thesis discusses a new logic called kind theory that meets these challenges. The core of the work is based in logic, type theory, and universal algebras. The theory is shown to be efficiently implementable, and several parts of a full realization have already been constructed and are reviewed. Additionally, several software engineering concepts, tools, and technologies have been con-structed that take advantage of this theoretical framework. These constructs are discussed as well, from the perspectives of general software engineering and applied formal methods. Acknowledgements iv I am grateful to my initial primary adviser, Prof. K. Mani Chandy, for bringing me to Caltech and his willingness to let me explore many unfamiliar research fields of my own choosing. I am also appreciative of my second adviser, Prof. Jason Hickey, for his support, encouragement, feedback, and patience through the later years of my work. If Jason had not appeared at Caltech in Autumn of 1999, I may well have not finished my Ph.D. I am very much in debt to Joseph Goguen whose inspiring work started me on the path of using algebras and categories. José Meseguer and Francisco (Paco) Duran have been of tremendous help and inspiration in my use of Maude and rewriting logic.

Abstract. We aim to build a denotational semantics for the functional logic programming language Curry, to be used for parametricity and logical relation arguments. First, we investigate only a subset of Curry, but include the important features that separate Curry from a just functional language. We compare a poweralgebraic and a multialgebraic semantic approach and motivate our decision for the multialgebraic one. Afterwards, we describe how general recursion and lists, as an example for algebraic data types, can be added. 1

Abstract. With the aim of putting type-based reasoning for functional logic languages, as recently explored by Christiansen et al. (2010), on a formal basis, we develop a denotational semantics for a typed core language of Curry. Dealing with the core language FlatCurry rather than with full Curry suffices, since there exists a type-preserving translation from the latter into the former. In contrast to existing semantics for functional logic languages, we deliberately approach the problem “from the functional side”. That is, rather than adapting approaches previously known from the study of (resolution-like) semantics for logic languages, we aim for a semantics in the spirit of standard denotational semantics for the polymorphic lambda calculus. We claim and set out to prove that the presented semantics is adequate with respect to an existing operational semantics. A particularly interesting aspect, we think, is that we give the first denotational treatment of recursive let-bindings in combination with call-time choice. 1

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