Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either equations or type assignments. Models of this logic are type algebras, viz. universal algebras equipped with a binary relation-to support type assignment. Equational type logic has a sound and complete calculus, and initial models exist. The use of equational type logic is illustrated by means of simple examples, where all of the aforementioned phenomena occur. Formal notions of reduction and extension are introduced, and their relationship to free constructions is investigated. Computational aspects of equational type logic are investigated in the framework of conditional term rewriting systems, genera!izing known results on confluence of these systems. Finally, some closely related work is reviewed and future research directions are outlined in the conclusions. * 41, Ird.wy'~~-rted (conditional) equational logic is the most established basis to the algebraic approach to abstract data type (ADT) specification [ 15,9]. algebras [ 17,4] are the standard models of this lo&c, extending u structures in a straightforward way. In algebraic specification, however, several phenomena indicate that this logic encounters limitations in practice. We mention a few, most interesting of these phenomena (which are discussed in Section 2): partiaiity, exception handling, extension, type polymorphism, dependent types. Several formal frameworks have been designed to solve the problems that are raised by e&r& of these phenomena. In particular, many of these frameworks are based on extensions of equational logic in various forms. Most of these approaches address the phenomena of their interest at a rather high level of generality. Yet, a unifying approach, where all of these phenomena can be dealt with, does not seem to have emerged. The following problem is addressed in this paper: to nd and investigate a parsimonious logic of types where al2 of the aforementioned phenomena can be dealt with in an algebraic setting. In Section 2 we further motivate our irwstigation ng, for each of those phenomena, rt discussion an a simple exam@ational type logic
