89 research outputs found
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
Non-Deterministic Kleene Coalgebras
In this paper, we present a systematic way of deriving (1) languages of
(generalised) regular expressions, and (2) sound and complete axiomatizations
thereof, for a wide variety of systems. This generalizes both the results of
Kleene (on regular languages and deterministic finite automata) and Milner (on
regular behaviours and finite labelled transition systems), and includes many
other systems such as Mealy and Moore machines
Enhanced Coalgebraic Bisimulation
International audienceWe present a systematic study of bisimulation-up-to techniques for coalgebras. This enhances the bisimulation proof method for a large class of state based systems, including labelled transition systems but also stream systems and weighted automata. Our approach allows for compositional reasoning about the soundness of enhancements. Applications include the soundness of bisimulation up to bisimilarity, up to equivalence and up to congruence. All in all, this gives a powerful and modular framework for simplified coinductive proofs of equivalence
An introduction to (Co)algebras and (Co)induction and their application to the semantics of programming languages
This report summarizes operational approaches to the formal
semantics of programming languages and shows that they can be
interpreted inductively by least fixed points as well as
coinductively by greatest fixed points. While the inductive
interpretation gives semantics to all terminating programs,
the coinductive one defines moreover also a semantics for all
non-terminating programs. This is especially important in
areas where programs do not terminate in general, e.g. data
bases, operating systems, or control software in embedded
systems. The semantic foundations described in this report can
be used to verify that transformations (e.g. in compilers) of
such software systems are correct.
In the course of this report, coalgebras and coinduction are
introduced, starting with a gentle intuitive motivation and
ending with a detailed mathematical description within the
notions of category theory
Well-Pointed Coalgebras
For endofunctors of varieties preserving intersections, a new description of
the final coalgebra and the initial algebra is presented: the former consists
of all well-pointed coalgebras. These are the pointed coalgebras having no
proper subobject and no proper quotient. The initial algebra consists of all
well-pointed coalgebras that are well-founded in the sense of Osius and Taylor.
And initial algebras are precisely the final well-founded coalgebras. Finally,
the initial iterative algebra consists of all finite well-pointed coalgebras.
Numerous examples are discussed e.g. automata, graphs, and labeled transition
systems
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