Abstract

This paper presents a technique for preserving the power of general program transformations in the presence of a rich collection of distinguishable error values. This is accomplished by introducing an annotation, "Safe", to mark occurrences of functions that cannot produce errors. Succinct and general algebraic laws can be expressed using Safe, thereby giving program transformations in a language with many error values the same power and generality as program transformations in a language with only a single error value (such as FP [Bac78]). In fact, the Safe mechanism accomplishes much more. It actually strengthens equational reasoning by providing a sufficient condition on a program context E(\Delta) and functions f and g; such that E(f) j E(g) even if f 6j g:

Citations