The views and conclusions contained in this document are those of the authors and should not be interpreted as representing o cial policies, either expressed or implied, of the Advanced Research Projects Agency or the U.S. Government. Any opinions, ndings, and conclusions or recommendations expressed in this material are those of the We study the typing properties of closure conversion for simply-typed and polymorphic-calculi. Unlike most accounts of closure conversion, which only treat the untyped-calculus, we translate well-typed source programs to well-typed target programs. This allows later compiler phases to take advantage of types for representation analysis and tag-free garbage collection, and it facilitates correctness proofs. Our account of closure conversion for the simply-typed language takes advantage of a simple model of objects by mapping closures to existentials. Closure conversion for the polymorphic language requires additional type machinery, namely translucency in the style of Harper and Lillibridge's module calculus, to express the type of a closure.

Compilers for monomorphic languages, such as C and Pascal, take advantage of types to determine data representations, alignment, calling conventions, and register selection. However, these languages lack important features including polymorphism, abstract datatypes, and garbage collection. In contrast, modern programming languages such as Standard ML (SML), provide all of these features, but existing implementations fail to take full advantage of types. The result is that performance of SML code is quite bad when compared to C. In this thesis, I provide a general framework, called type-directed compilation, that allows compiler writers to take advantage of types at all stages in compilation. In the framework, types are used not only to determine efficient representations and calling conventions, but also to prove the correctness of the compiler. A key property of typedirected compilation is that all but the lowest levels of the compiler use typed intermediate languages. An advantage of this approach is that it provides a means for automatically checking the integrity of the resulting code. An important

This paper introduces an operational semantics for call-by-need reduction in terms of Milner's ß-calculus. The functional programming interest lies in the use of ß-calculus as an abstract yet realistic target language. The practical value of the encoding is demonstrated with an outline for a parallel code generator. From a theoretical perspective, the ß-calculus representation of computational strategies with shared reductions is novel and solves a problem posed by Milner [13]. The compactness of the process calculus presentation makes it interesting as an alternative definition of call-by-need. Correctness of the encoding is proved with respect to the call-by-need -calculus of Ariola et al. [3]. 1 Introduction Graph reduction of extended -calculi has become a mature field of applied research. The efficiency of the implementations is due in great measure to a technique known as `sharing', whereby argument values are computed (at most) once and then memoized for future reference. Both...