Complexity-theoretic aspects of programming language design

Abstract

We survey three of Paris Kanellakis's contributions to the complexity-theoretic analysis of constructs in the design of programming languages. These are (1) his result that first-order unification is complete for polynomial time; (2) his contributions to the complexity analysis of type inference for polymorphicallytyped functional programming languages, which was proven to be complete for exponential time; and (3) his work on expressibility of simply typed lambda calculus when used as a functional database programming language. These research investigations are interrelated, emphasizing common themes and difficulties in the design of programming languages, with concrete implications that can be appreciated by language designers. First-order unification is a ubiquitous building block in implementations of sophisticated programming languages. It is, for example, the workhorse of logic programming engines, and the essential component of compile-time type analysis. The research on unification provided a secure foundation for understanding the complexity of automatic polymorphic type inference in functional languages such as ML and Haskell. Modern functional languages are based on the typed lambda calculus, so it is then natural to consider its computational expressiveness. We describe how the degree of higher-order functionality in simply typed terms can be related directly to well known complexity classes.