F-Calculus: A Universal Programming Language of Self-Stabilizing Computational Fields

Abstract

This paper proposes a new programming language F-calculus (digamma-calculus). F-calculus is an effective tool to construct self-stabilizing computational fields. A computational field is a data structure representing a network composed of asynchronously running devices that have low computational ability and independent states. The research on computational fields has been getting more advanced recently due to the rise of distributed computing and the internet of things. Self-stabilizing computational fields are important especially for practice. Our main contribution is to clarify the class of self-stabilizing computational fields, about which little has been known since the research field was established. In this paper, we introduce our new calculus and prove that it has the same expressive power to the self-stabilizing fragment of the field calculus on condition that termination is guaranteed. Furthermore, we discuss formal verification of self-stabilization using a type-theoretic approach.