Calculating risk in functional programming

TL;DR

This paper introduces a method for estimating and managing risk in functional programming by extending algebraic reasoning to include fault propagation, especially useful on unreliable hardware.

Contribution

It proposes a novel approach to handle risk constructively in functional programming through an algebraic extension that models fault propagation during program transformations.

Findings

Fault propagation can be calculated across program transformations.

Risk can be expressed in terms of component faults.

Method supports reasoning about unreliable hardware environments.

Abstract

In the trend towards tolerating hardware unreliability, accuracy is exchanged for cost savings. Running on less reliable machines, "functionally correct" code becomes risky and one needs to know how risk propagates so as to mitigate it. Risk estimation, however, seems to live outside the average programmer's technical competence and core practice. In this paper we propose that risk be constructively handled in functional programming by (a) writing programs which may choose between expected and faulty behaviour, and by (b) reasoning about them in a linear algebra extension to standard, a la Bird-Moor algebra of programming. In particular, the propagation of faults across standard program transformation techniques known as tupling and fusion is calculated, enabling the fault of the whole to be expressed in terms of the faults of its parts.