On the expressive power of finitely typed and universally polymorphic recursive procedures

Abstract

Finitely typed functional programs are naturally classified by their levels. This syntactic classification of functional programs corresponds to a semantical classification: the higher the level of functional programs, the more functions they can compute. We call FL the language of finitely typed functional programs. The halting problem on finite interpretations is elementary recursive for every FL program, i.e. for every FL program P there is an elementary recursive procedure to decide for every finite interpretation $\text{I}$ whether P halts on $\text{I}$.

The well-known programming language ML is essentially FL, augmented with the polymorphic let-in constructor. We show that ML computes the same class of functions as FL. As a consequence.