Pure Type Systems for Functional Programming

We present a functional programming language based on Pure Type Systems (PTSs). We show how we can de ne such a language by extending the PTS framework with algebraic data types, case expressions and de nitions. Furthermore, we present an e cient type checking algorithm and an interpreter for this language. PTSs are well suited as a basis for a functional programming language because they are at the top of a hierarchy of increasingly stronger type systems. The concepts of `existential types', `rank-n polymorphism' and `dependent types' arise naturally in functional programming languages based on the systems in this hierarchy. There is no need for ad-hoc extensions to incorporate these features. The type system of our language is more powerful than the Hindley-Milner system. We illustrate this fact by giving a number of meaningful programs that cannot be typed in Haskell but are typable in our language.