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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 ..."
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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 ..."
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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
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 ..."
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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.
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 ..."
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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
From I/O Automata to Timed I/O Automata  A solution to the `Generalized Railroad Crossing' in Isabelle/HOLCF
"... 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 e ..."
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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 verication using I/O automata. We present a modication 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.
State Spaces  The Locale Way
 SSV 2009
, 2009
"... Verification of imperative programs means reasoning about modifications of a program state. So proper representation of state spaces is crucial for the usability of a corresponding verification environment. In this paper we discuss various existing state space models under different aspects like str ..."
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Verification of imperative programs means reasoning about modifications of a program state. So proper representation of state spaces is crucial for the usability of a corresponding verification environment. In this paper we discuss various existing state space models under different aspects like strong typing, modularity and scalability. We also propose a variant based on the locale infrastructure of Isabelle. Thus we manage to combine the advantages of previous formulations (without suffering from their disadvantages), and gain extra flexibility in composing state space components (inherited from the modularity of locales).
A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment
, 2013
"... We present the theory of Simpl, a sequential imperative programming language. We introduce its syntax, its semantics (big and smallstep operational semantics) and Hoare logics for both partial as well as total correctness. We prove soundness and completeness of the Hoare logic. We integrate and auto ..."
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We present the theory of Simpl, a sequential imperative programming language. We introduce its syntax, its semantics (big and smallstep operational semantics) and Hoare logics for both partial as well as total correctness. We prove soundness and completeness of the Hoare logic. We integrate and automate the Hoare logic in Isabelle/HOL to obtain a practically usable verification environment for imperative programs. Simpl is independent of a concrete programming language but expressive enough to cover all common language features: mutually recursive procedures, abrupt termination and exceptions, runtime faults, local and global variables, pointers and heap, expressions with side effects, pointers to procedures, partial application and closures, dynamic
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 ..."
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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.
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 ..."
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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