The data type variety of stack algebras

Abstract

We define and study the class of all stack algebras as the class of all minimal algebras in a variety defined by an infinite recursively enumerable set of equations. Among a number of results, we show that the initial model of the variety is computable, that its equational theory is decidable, but that its equational deduction problem is undecidable. We show that it cannot be finitely axiomatised by equations, but it can be finitely axiomatised by equations with a hidden sort and functions. This class of all stack algebras, together with its specifications, can be used to survey the many models in the literature on stacks in a systematic way, and hence give the study of the stack some mathematical coherence.