Error Algebras

Abstract

In computations over many-sorted algebras, one typically encounters error cases, caused by attempting to evaluate an operation outside its domain (e.g. division by the integer 0; taking the square root of a negative integer; popping an empty stack). We present a method for systematically dealing with such error cases, namely the construction of an "error algebra" based on the original algebra. As an application of this method, we show that it provides a good semantics for (possibly improper) function tables.