The literature on programming languages contains an abundance of informal claims on the relative expressive power of programming languages, but there is no framework for formalizing such statements nor for deriving interesting consequences. As a first step in this direction, we develop a formal notion of expressiveness and investigate its properties. To validate the theory, we analyze some widely held beliefs about the expressive power of several extensions of functional languages. Based on these results, we believe that our system correctly captures many of the informal ideas on expressiveness, and that it constitutes a foundation for further research in this direction. 1 Comparing Programming Languages The literature on programming languages contains an abundance of informal claims on the expressive power of programming languages. Arguments in these contexts typically assert the expressibility or non-expressibility of programming constructs relative to a language. Unfortunately, pro...

Abstract. Hygienic macro systems, such as Scheme’s, automatically rename variables to prevent unintentional variable capture—in short, they “just work. ” Yet hygiene has never been formally presented as a specification rather than an algorithm. According to folklore, the definition of hygienic macro expansion hinges on the preservation of alphaequivalence. But the only known notion of alpha-equivalence for programs with macros depends on the results of macro expansion! We break this circularity by introducing explicit binding specifications into the syntax of macro definitions, permitting a definition of alpha-equivalence independent of expansion. We define a semantics for a first-order subset of Scheme-like macros and prove hygiene as a consequence of confluence. The subject of macro hygiene is not at all decided, and more research is needed to precisely state what hygiene formally means and [precisely which] assurances it provides. —Oleg Kiselyov [1]