The Use of Sorts in Algebraic Specifications

Elementary Algebraic Specifications of the Rational Complex Numbers

From the range of techniques available for algebraic specifications we select a core set of features which we define to be the elementary algebraic specifications. These include equational specifications with hidden functions and sorts and initial algebra semantics. We give an elementary equational specification of the field operations and conjugation operator on the rational complex numbers Q(...

Test Selection for Specification-Based Unit Testing of Object-Oriented Software based on Formal Specifications

ion in CO-OPN/2 is provided by two kinds of sorts: algebraic sorts and class types. Not all entities in a CO-OPN/2 system are objects, some of them are merely algebraic values, without identity. Thus CO-OPN/2 stands in the class of hybrid object-oriented specification languages. Sorts provide services, called functions for algebraic sorts, and methods for objects. Methods are special transition...

Augmenting Algebraic Specifications with Structured Sorts and Structural Subsorting

Which data types have w-complete initial algebra specifications?*

Bergstra, J.A. and J. Heering, Which data types have o-complete initial algebra specifications’?, Theoretical Computer Science 124 (1994) 1499168. An algebraic specification is called w-complete or inductively complete if all (open as well as closed) equations valid in its initial model are equationally derivable from it, i.e., if the equational theory of the initial model is identical to the e...

Algebraic Specifications, Higher-Order Types, and Set-Theoretic Models

In most algebraic specification frameworks, the type system is restricted to sorts, subsorts, and first-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higher-order types, interpreted set-theoretically as Cartesian products, function spaces, and power-sets. This paper presents a simple framework for algebraic specifications with higher-...