Abstract

ii Programs involving precise types enforce more properties via type-checking, but precise types also prevent the reuse of functions throughout a program since no single precise type is used throughout a large program. My work is a step toward eliminating the underlying dilemma regarding type precision versus func-tion reuse. It culminates in a novel traversal operator that recovers the reuse by automating most of each conversion between “similar ” precise types, for a notion of similarity that I characterize in both the intuitive and technical senses. The benefits of my techniques are clear in side-by-side comparisons; in particular, I apply my techniques to two definitions of lambda-lifting. I present and imple-ment my techniques in the Haskell programming language, but the fundamental ideas are applicable to any statically- and strongly-typed programming functional language with algebraic data types. iii