Bottom-Up Computation of Recursive Programs

— In this paper, we de fine and study a mechanism for the implementation of recursive programs: we call it production mechanism by opposition to the usual recursion mechanism. It computes bottom-up, starting from the basic values given by halting conditions, and générâtes intermediate values leading to the resuit. We use for this purpose a translation of a recursive program into a system o f équations in a space ofsets. We introducé determinism conditions providing the uniqueness of the set of intermediate values; we study the structure of this set. As an application, we show the opiimality of an implementation of Ackermann program (Rice's algorithm).