Calculating risk in functional programming

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.