On the Expressive Power of Programming Languages

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 rst 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, programming language theory does not provide a formal framework for specifying and verifying such statements. Comparing the set of computable functions that a language can represent is useless because the languages in question are usually universal; other measures do not exist. The lack of a comparison relation makes it impossible to draw any rm conclusions from expressiveness claims or to use them for an objective decision about the use of a programming language. Supported in part by NSF grant CCR 89-17022 and Darpa/NSF grant CCR 87-20277.