Programming with intersection types and bounded polymorphism

This thesis unifies and extends prior work on intersection types and bounded quantification, previously studied only in isolation, by investigating theoretical and practical aspects of a typed $\lambda$-calculus incorporating both. The practical utility of this calculus, called $F\sb{\wedge}$, is established by examples showing, for instance, that it allows a rich form of "coherent overloading" and supports an analog of abstract interpretation during typechecking. More familiar programming examples are presented in terms of an extension of Forsythe, demonstrating how parametric polymorphism can be used to simplify and generalize Forsythe's design. We discuss the novel programming and debugging styles that arise in $F\sb{\wedge}$. We prove the correctness of a simple semi-decision procedure for the subtype relation and the partial correctness of an algorithm for synthesizing minimal types of $F\sb{\wedge}$ terms. Our main tool in this analysis is a notion of "canonical types," which allow proofs to be factored so that intersections are handled separately from the other type constructors. A pair of negative results illustrates some subtle complexities of $F\sb{\wedge}$. First, the subtype relation of $F\sb{\wedge}$ is shown to be undecidable. Second, the failure of an important technical property of the subtype relation--the existence of least upper bounds--indicates that typed semantic models of $F\sb{\wedge}$ will be more difficult to construct and analyze than the known typed models of intersection types. We study the semantics of $F\sb{\wedge}$ from several points of view. An untyped model based on partial equivalence relations demonstrates the consistency of the typing rules and provides a simple interpretation for programs, where "$\sigma$ is a subtype of $\tau$" is read as "$\sigma$ is a subset of $\tau$." More refined models can be obtained using a translation from $F\sb{\wedge}$ into the pure polymorphic $\lambda$-calculus; in these models, "$\sigma$ is a subtype of $\tau$" is interpreted by an explicit coercion function from $\sigma$ to $\tau$. The nonexistence of least upper bounds shows up here in the failure of known techniques for proving the coherence of the translation semantics. Finally, an equational theory of equivalences between $F\sb{\wedge}$ terms is presented and its soundness for both styles of model is verified. (Abstract shortened with permission of author.)