Report Number: CS-TR-77-614
Institution: Stanford University, Department of Computer Science
Title: The convergence of functions to fixedpoints of recursive definitions
Author: Manna, Z ohar
Author: Shamir, Adi
Date: May 1977
Abstract: The classical method for constructing the least fixedpoint of a recursive definition is to generate a sequence of functions whose initial element is the totally undefined function and which converges to the desired least fixedpoint. This method, due to Kleene, cannot be generalized to allow the construction of other fixedpoints. In this paper we present an alternate definition of convergence and a new fixedpoint access method of generating sequences of functions for a given recursive definition. The initial function of the sequence can be an arbitrary function, and the sequence will always converge to a fixedpoint that is "close" to the initial function. This defines a monotonic mapping from the set of partial functions onto the set of all fixedpoints of the given recursive definition.