Higher type recursive program schemes and the nested pushdown automaton

When implementing recursive programs on a standard von Neumann random access machine (RAM) it is natural and well known how to use a pushdown store in order to keep track of the recursive procedure calls when the program runs. The more abstract world of program schemes abounds with examples of this pushdown – recursion relation. As a concrete example it is well known how to implement monadic recursive program schemes (de Bakker Scott schemes) on a pushdown automaton with data storage. In this case he reverse direction can be easily proved, too: The pushdown automaton considered has exactly the same computational power as de Bakker Scott schemes. Higher type concepts are at the heart of modern object oriented and functional programming languages in particular. The aim of this paper is to develop a theoretically well founded framework for implementing higher type recursion. We show that a natural generalization of the classical pushdown store, the nested pushdown allows to extend the equivalence above to a natural hierarchy of “higher type de Bakker Scott schemes ”. ∗) e-mail: [email protected]