Theoretical Computer Science 93 (1992) l-41 Elsevier 1 Fundamental Study On the expressive power of finitely tvDed and universally polymorphic r&rsive procedures* A.J. Kfoury Boston Unioersity, Computer Science Department, Ill Cummington Street, Boston, MA 02215, USA J. Tiuryn* * Unioersity of Warsaw, Institute of Mathematics, PKiN. 00-901 Warszawa, Poland P. Urzyczyn University of Warsaw, Institute of Mathematics, PKiN, 00-901 Warszawa. Poland Communicated by M. Nivat Received December 1989 Abstract Kfoury, A.J., J. Tiuryn and P. Urzyczyn, On the expressive power of finitely typed and universally polymorphic recursive procedures, Theoretical Computer Science 93 (1992) l-41. Finitely typed functional programs are naturally classified by their levels. This syntactic classifica- tion 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 9 whether P halts on 9. 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, *This research was partly supported by NSF grant CCR-8901647 and by a grant of the Polish Ministry of National Education, no. R.P.I.09. Some of the results in this paper have been presented at the Symposiums “Logic in Computer Science” in 1987 and 1988 (see 1173 and [18]). ** Part of the work was done when the author was visiting Computer Science Department of Washing- ton State University, Pullman, WA. 0304-3975/92/$05.00 0 1992-Elsevier Science Publishers B.V. All rights reserved