Coalgebraic Methods for Object-Oriented Specification

This thesis is about coalgebraic methods in software specification and verification. It extends known techniques of coalgebraic specification to a more general level to pave the way for real world applications of software verification. There are two main contributions of the present thesis: 1. Chapter 3 proposes a generalisation of the familiar notion of coalgebra such that classes containing methods with arbitrary types (including binary methods) can be modelled with these generalised coalgebras. 2. Chapter 4 presents the specification language CCSL (short for Coalgebraic Class Specification Language), its syntax, its semantics, and a prototype compiler that translates CCSL into higher-order logic.Die Dissertation beschreibt coalgebraische Mittel und Methoden zur Softwarespezifikation und -verifikation. Die Ergebnisse dieser Dissertation vereinfachen die Anwendung coalgebraischer Spezifikations- und Verifikationstechniken und erweitern deren Anwendbarkeit. Damit werden Softwareverifikation im Allgemeinen und im Besonderen coalgebraische Methoden zur Softwareverifikation der praktischen Anwendbarkeit ein Stück nähergebracht. Diese Dissertation enthält zwei wesentliche Beiträge: 1. Im Kapitel 3 wird eine Erweiterung des klassischen Begriffs der Coalgebra vorgestellt. Diese Erweiterung erlaubt die coalgebraische Modellierung von Klassenschnittstellen mit beliebigen Methodentypen (insbesondere mit binären Methoden). 2. Im Kapitel 4 wird die coalgebraische Spezifikationssprache CCSL (Coalgebraic Class Specification Language) vorgestellt. Die Bescheibung umfasst Syntax, Semantik und einen Prototypcompiler, der CCSL Spezifikationen in Logik höherer Ordnung (passend für die Theorembeweiser PVS und Isabelle/HOL) übersetzt

Greatest Bisimulations for Binary Methods

In previous work [14] I introduced a generalised notion of coalgebra that is capable of modelling binary methods as they occur in object-oriented programming. An important problem with this generalisation is that bisimulations are not closed under union and that a greatest bisimulation does not exists in general. There are two possible approaches to improve this situation: First, to strengthen the definition of bisimulation, and second, to place constraints on the coalgebras (i.e., on the behaviour of the binary methods). In this paper I combine both approaches to show that (under reasonable assumptions) the greatest bisimulation does exist for all coalgebras of extended polynomial functors

CMCS'02 Preliminary Version Greatest Bisimulations for Binary Methods

Abstract A generalised notion of coalgebra that is capable of modelling binary methods as theyoccur in object-oriented programming has been introduced in [14]. An important problem with this generalisation is that bisimulations are not closed under union and that a greatestbisimulation does not exists in general. There are two possible approaches to improve this situation: First, to strengthen the definition of bisimulation, and second, to place constraintson the coalgebras (i.e., on the behaviour of the binary methods). In this paper I combine both approaches to show that (under reasonable assumptions) the greatest bisimulation doesexist for all coalgebras of extended polynomial functors. 1 Introduction The term binary method stems from object-oriented programming. A method iscalled a binary method if it takes an additional second argument of its hosting class. The canonical example is the method equal: Self \Theta Self bool Here, Self stands for the type of the current class. In a typical object-orientedlanguage the first argument of typ