The Convergence of Functions to Fixedpoints of Recursive Definitions
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 Kleen, cannot be generalized to allow the construction of other fixedpoints. This paper presents 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1977
- Accession Number
- ADA049760
Entities
People
- Adi Shamir
- Zohar Manna
Organizations
- Stanford University