Results 11  20
of
31
An Extensible Encoding of Objectoriented Data Models in HOL  with an Application to IMP++
, 2008
"... We present an extensible encoding of objectoriented data models into higherorder logic (HOL). Our encoding is supported by a datatype package that leverages the use of the shallow embedding technique to objectoriented specification and programming languages. The package incrementally compiles an ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
We present an extensible encoding of objectoriented data models into higherorder logic (HOL). Our encoding is supported by a datatype package that leverages the use of the shallow embedding technique to objectoriented specification and programming languages. The package incrementally compiles an objectoriented data model, i. e., a class model, to a theory containing objectuniverses, constructors, accessor functions, coercions (casts) between static types (and providing a foundation for the notion of dynamic types), characteristic sets, and coinductive class invariants. The package is conservative, i. e., all properties are derived entirely from constant definitions, including the constraints over object structures. As an application, we use the package for an objectoriented corelanguage called IMP++, for which we formally prove the correctness of a Hoare logic with respect to a denotational semantics.
B.: System ModelBased Definition of Modeling Language Semantics
 In: Formal Techniques for Distributed Systems 2009 (Proceedings). Volume 5522 of LNCS
, 2009
"... Abstract. In this paper, we present an approach to define the semantics for objectoriented modeling languages. One important property of this semantics is to support underspecified and incomplete models. To this end, semantics is given as predicates over elements of the semantic domain. This domain ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Abstract. In this paper, we present an approach to define the semantics for objectoriented modeling languages. One important property of this semantics is to support underspecified and incomplete models. To this end, semantics is given as predicates over elements of the semantic domain. This domain is called the system model which is a general declarative characterization of object systems. The system model is very detailed since it captures various relevant structural, behavioral, and interaction aspects. This allows us to reuse the system model as a domain for various kinds of objectoriented modeling languages. As a major consequence, the integration of language semantics is straightforward. The whole approach is supported by tools that do not constrain the semantics definition’s expressiveness and flexibility while making it machinecheckable. 1
Extensible universes for objectoriented data models
 Journal of Automated Reasoning
"... Abstract We present a datatype package that enables the shallow embedding technique to objectoriented specification and programming languages. This datatype package incrementally compiles an objectoriented data model to a theory containing objectuniverses, constructors, accessors functions, coerc ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract We present a datatype package that enables the shallow embedding technique to objectoriented specification and programming languages. This datatype package incrementally compiles an objectoriented data model to a theory containing objectuniverses, constructors, accessors functions, coercions between dynamic and static types, characteristic sets, their relations reflecting inheritance, and the necessary class invariants. The package is conservative, i. e., all properties are derived entirely from axiomatic definitions. As an application, we use the package for an objectoriented corelanguage called IMP++, for which correctness of a HoareLogic with respect to an operational semantics is proven. 1
Miscellaneous Isabelle/Isar examples for higherorder logic. Part of the Isabelle distribution, http://isabelle.in.tum.de/library/ HOL/Isar examples/document.pdf
, 2001
"... Isar offers a highlevel proof (and theory) language for Isabelle. We give various examples of Isabelle/Isar proof developments, ranging from simple demonstrations of certain language features to a bit more advanced applications. The “real ” applications of Isabelle/Isar are found elsewhere. Content ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Isar offers a highlevel proof (and theory) language for Isabelle. We give various examples of Isabelle/Isar proof developments, ranging from simple demonstrations of certain language features to a bit more advanced applications. The “real ” applications of Isabelle/Isar are found elsewhere. Contents 1 Basic logical reasoning 3 1.1 Pure backward reasoning.................... 3 1.2 Variations of backward vs. forward reasoning......... 4 1.3 A few examples from “Introduction to Isabelle ”........ 5
Modular Structures as Dependent Types in Isabelle
, 1998
"... This paper describes a method of representing algebraic structures in the theorem prover Isabelle. We use Isabelle's higher order logic extended with set theoretic constructions. Dependent types, constructed as HOL sets, are used to represent modular structures by semantical embedding. The modul ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
This paper describes a method of representing algebraic structures in the theorem prover Isabelle. We use Isabelle's higher order logic extended with set theoretic constructions. Dependent types, constructed as HOL sets, are used to represent modular structures by semantical embedding. The modules remain first class citizen of the logic. Hence, they enable adequate formalization of abstract algebraic structures and a natural proof style. Application examples drawn from abstract algebra and lattice theory  the full version of Tarski's fixpoint theorem  validate the concept.
From I/O Automata to Timed I/O Automata  A solution to the `Generalized Railroad Crossing' in Isabelle/HOLCF
, 1999
"... The model of timed I/O automata represents an extension of the model of I/O automata with the aim of reasoning about realtime systems. A number of case studies using timed I/O automata has been carried out, among them a treatment of the socalled Generalized Railroad Crossing (GRC). An already exist ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
The model of timed I/O automata represents an extension of the model of I/O automata with the aim of reasoning about realtime systems. A number of case studies using timed I/O automata has been carried out, among them a treatment of the socalled Generalized Railroad Crossing (GRC). An already existing formalization of the metatheory of I/O automata within Isabelle/HOLCF allows for fully formal toolsupported verification using I/O automata. We present a modification of this formalization which accomodates for reasoning about timed I/O automata. The guiding principle in choosing the parts of the metatheory of timed I/O automata to formalize has been to provide all the theory necessary for formalizing the solution to the GRC. This leads to a formalization of the GRC, in which not only the correctness proof itself has been formalized, but also the underlying metatheory of timed I/O automata, on which the correctness proof is based.
Mechanical Analysis of UML State Machines and Class Diagrams
 In the Proc. of Workshop on Precise Semantics for the UML. ECOOP2000
, 2000
"... A semantic model for statecharts is used as the basis of a mechanization in Isabelle. Similarly, we build an Isabelle embedding of class diagrams using ideas from a reference semantics for ObjectZ, without using ObjectZ itself, rather expressing the semantics directly in Isabelle's Higher Order Lo ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
A semantic model for statecharts is used as the basis of a mechanization in Isabelle. Similarly, we build an Isabelle embedding of class diagrams using ideas from a reference semantics for ObjectZ, without using ObjectZ itself, rather expressing the semantics directly in Isabelle's Higher Order Logic. The combination of these two mechanized semantical models is intended as a basis for reasoning about combinations of static and dynamic UML design descriptions.
Four approaches to automated reasoning with differential algebraic structures
 AISC 2004, LNAI
, 2004
"... Abstract. While implementing a proof for the Basic Perturbation Lemma (a central result in Homological Algebra) in the theorem prover Isabelle one faces problems such as the implementation of algebraic structures, partial functions in a logic of total functions, or the level of abstraction in formal ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. While implementing a proof for the Basic Perturbation Lemma (a central result in Homological Algebra) in the theorem prover Isabelle one faces problems such as the implementation of algebraic structures, partial functions in a logic of total functions, or the level of abstraction in formal proofs. Different approaches aiming at solving these problems will be evaluated and classified according to features such as the degree of mechanization obtained or the direct correspondence to the mathematical proofs. From this study, an environment for further developments in Homological Algebra will be proposed. 1
A Proof Assistant For Higher Order Logic
, 2008
"... This volume is a selfcontained introduction to interactive proof in higherorder logic (HOL), using the proof assistant Isabelle. It is written for potential users rather than for our colleagues in the research world. The book has three parts. – The first part, Elementary Techniques, shows how to mo ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This volume is a selfcontained introduction to interactive proof in higherorder logic (HOL), using the proof assistant Isabelle. It is written for potential users rather than for our colleagues in the research world. The book has three parts. – The first part, Elementary Techniques, shows how to model functional programs in higherorder logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion. – The second part, Logic and Sets, presents a collection of lowerlevel tactics that you can use to apply rules selectively. It also describes Isabelle/HOL’s treatment of sets, functions and relations and explains how to define sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages. – The third part, Advanced Material, describes a variety of other topics.
Deduction and Computation in Algebraic Topology
 In Proceedings IDEIA 2002, Universidad de Sevilla
"... In this paper, a project to develop a computeraided proof of the Basic Perturbation Lemma is presented. This Perturbation Lemma is one of the central results in algorithmic algebraic topology and to obtain a mechanised proof of it, would be a first step to increase the reliability of several sy ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In this paper, a project to develop a computeraided proof of the Basic Perturbation Lemma is presented. This Perturbation Lemma is one of the central results in algorithmic algebraic topology and to obtain a mechanised proof of it, would be a first step to increase the reliability of several symbolic computation systems in this area. Techniques to encode the necessary algebraic structures in the theorem prover Isabelle are described, and a sequence of high level lemmas designed to reach the proof is included.