Calculating fault propagation in functional programs

Abstract

The production of safety critical software is bound to a number of safety and certification standards in which estimating the risk of failure plays a central role. Yet risk estimation seems to live outside most programmers’ core practice, involving simulation techniques and worst case analysis performed a posteriori. In this paper we propose that risk be constructively handled in functional programming by writing programs which choose between expected and faulty be- haviour and by reasoning about them in a linear algebra extension to the standard algebra of programming. In particular, the paper calculates propagation of faults across standard program transformation techniques known as tupling and fusion, enabling the fault of the whole to be expressed in terms of the faults of its parts.