Program schemas with equality

We discuss the class of program schemas augmented with equality tests, that is, tests of equality between terms. In the first part of the paper we discuss and illustrate the “power” of equality tests. It turns out that the class of program schemas with equality is more powerful than the “maximal” classes of schemas suggested by other investigators. In the second part of the paper we discuss the decision problems of program schemas with equality. It is shown for example that while the decision problems normally considered for schemas (such as halting, divergence, equivalence, isomorphism and freedom) are solvable for Ianov schemas, they all become unsolvable if general equality tests are added. We suggest, however, limited equality tests which can be added to certain subclasses of program schemas while preserving their solvable properties.