Functional units for natural numbers

TL;DR

This paper introduces the concept of functional units for natural numbers, establishing the existence of a universal computable functional unit and exploring its properties within the context of thread algebra and execution environments.

Contribution

It defines functional units as a more concrete alternative to services and proves the existence of a universal computable functional unit for natural numbers.

Findings

Existence of a universal computable functional unit for natural numbers

Functional units include an inherent state space

Connections established between functional units and thread algebra

Abstract

Interaction with services provided by an execution environment forms part of the behaviours exhibited by instruction sequences under execution. Mechanisms related to the kind of interaction in question have been proposed in the setting of thread algebra. Like thread, service is an abstract behavioural concept. The concept of a functional unit is similar to the concept of a service, but more concrete. A state space is inherent in the concept of a functional unit, whereas it is not inherent in the concept of a service. In this paper, we establish the existence of a universal computable functional unit for natural numbers and related results.