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The KEY Approach: Integrating Object Oriented Design and Formal Verification
, 2000
"... This paper reports on the ongoing KeY project aimed at bridging the gap between (a) objectoriented software engineering methods and tools and (b) deductive verification. A distinctive feature of our approach is the use of a commercial CASE tool enhanced with functionality for formal specifiation an ..."
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Cited by 44 (18 self)
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This paper reports on the ongoing KeY project aimed at bridging the gap between (a) objectoriented software engineering methods and tools and (b) deductive verification. A distinctive feature of our approach is the use of a commercial CASE tool enhanced with functionality for formal specifiation and deductive verification.
History and Future of Implicit and Inductionless Induction: Beware the Old Jade and The Zombie!
, 2005
"... In this survey on implicit induction I recollect some memories on the history of implicit induction as it is relevant for future research on computerassisted theorem proving, esp. memories that significantly differ from the presentation in a recent handbook article on “inductionless induction”. M ..."
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Cited by 6 (3 self)
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In this survey on implicit induction I recollect some memories on the history of implicit induction as it is relevant for future research on computerassisted theorem proving, esp. memories that significantly differ from the presentation in a recent handbook article on “inductionless induction”. Moreover, the important references excluded there are provided here. In order to clear the fog a little, there is a short introduction to inductive theorem proving and a discussion of connotations of implicit induction like “descente infinie”, “inductionless induction”, “proof by consistency”, implicit induction orderings (term orderings), and refutational completeness.
A Firstorder Simplification Rule with Constraints
 3RD INT. WORKSHOP ON FIRSTORDER THEOREM PROVING (FTP
, 2000
"... Several variants of a firstorder simplification rule for nonnormal form tableaux using syntactic constraints are presented. These can be used as a framework for porting refinements of clausal firstorder proof procedures to nonnormal form tableaux. Some experimental results obtained with a protot ..."
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Cited by 3 (3 self)
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Several variants of a firstorder simplification rule for nonnormal form tableaux using syntactic constraints are presented. These can be used as a framework for porting refinements of clausal firstorder proof procedures to nonnormal form tableaux. Some experimental results obtained with a prototypical implementation are given.
The KEY Approach: Integrating Design and Formal Verification of Java Card Programs
, 2000
"... This paper reports on the ongoing KeY project aimed at bridging the gap between (a) objectoriented software engineering methods and tools and (b) deductive verification for the development of JAVA CARD programs. In particular, we describe a Dynamic Logic for JAVA CARD and outline a sequent calculus ..."
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Cited by 3 (0 self)
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This paper reports on the ongoing KeY project aimed at bridging the gap between (a) objectoriented software engineering methods and tools and (b) deductive verification for the development of JAVA CARD programs. In particular, we describe a Dynamic Logic for JAVA CARD and outline a sequent calculus for this logic that axiomatises JAVA CARD and is used in the verification component of the KeY system. 1 Introduction The goal of the project 1 (read "key") is to enhance a commercial CASE tool with functionality for formal specification and deductive verification and, thus, to integrate formal methods into realworld software development processes. Accordingly, the design principles for the software verification component of the KeY system are: The programs to be verified should be written in a "real" objectoriented (OO) programming language. The logical formalism should be as easy as possible to use for software developers (that do not have years of training in formal methods). ...
Hilbert’s ɛTerms in Automated Theorem Proving
"... Abstract. ɛterms, introduced by David Hilbert [8], have the form ɛx.φ, where x is a variable and φ is a formula. Their syntactical structure is thus similar to that of a quantified formulae, but they are terms, denoting ‘an element for which φ holds, if there is any’. The topic of this paper is an ..."
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Abstract. ɛterms, introduced by David Hilbert [8], have the form ɛx.φ, where x is a variable and φ is a formula. Their syntactical structure is thus similar to that of a quantified formulae, but they are terms, denoting ‘an element for which φ holds, if there is any’. The topic of this paper is an investigation into the possibilities and limits of using ɛterms for automated theorem proving. We discuss the relationship between ɛterms and Skolem terms (which both can be used alternatively for the purpose of ∃quantifier elimination), in particular with respect to efficiency and intuition. We also discuss the consequences of allowing ɛterms in theorems (and cuts). This leads to a distinction between (essentially two) semantics and corresponding calculi, one enabling efficient automated proof search, and the other one requiring human guidance but enabling a very intuitive (i.e. semantic) treatment of ɛterms. We give a theoretical foundation of the usage of both variants in a single framework. Finally, we argue that these two approaches to ɛ are just the extremes of a range of ɛtreatments, corresponding to a range of different possible Skolemization variants. 1
Hilbert's epsilonTerms in Automated Theorem Proving
 Automated Reasoning with Analytic
"... . #terms, introduced by David Hilbert [8], have the form #x.#, where x is a variable and # is a formula. Their syntactical structure is thus similar to that of a quantified formulae, but they are terms, denoting `an element for which # holds, if there is any'. The topic of this paper is an inve ..."
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. #terms, introduced by David Hilbert [8], have the form #x.#, where x is a variable and # is a formula. Their syntactical structure is thus similar to that of a quantified formulae, but they are terms, denoting `an element for which # holds, if there is any'. The topic of this paper is an investigation into the possibilities and limits of using #terms for automated theorem proving. We discuss the relationship between #terms and Skolem terms (which both can be used alternatively for the purpose of #quantifier elimination), in particular with respect to e#ciency and intuition. We also discuss the consequences of allowing #terms in theorems (and cuts). This leads to a distinction between (essentially two) semantics and corresponding calculi, one enabling e#cient automated proof search, and the other one requiring human guidance but enabling a very intuitive (i.e. semantic) treatment of #terms. We give a theoretical foundation of the usage of both variants in a singl...
2.2 Why Sequent and Tableau Calculi....................... 5
"... Although induction is omnipresent, inductive theorem proving in the form of descente infinie has not yet been integrated into full firstorder deductive calculi. We present such an integration that even works for higherorder logic. This integration is based on lemma and induction hypothesis applica ..."
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Although induction is omnipresent, inductive theorem proving in the form of descente infinie has not yet been integrated into full firstorder deductive calculi. We present such an integration that even works for higherorder logic. This integration is based on lemma and induction hypothesis application for free variable sequent and tableau calculi. We discuss the appropriateness of these types of calculi for this integration. The deductive part of this integration requires the first combination of raising, explicit variable dependency representation, the liberalized rule, and preservation of solutions.
Taclets and the KeY Prover
, 2003
"... We give a short overview of the KeY prover  which is the proof system belonging to the KeY tool [1]  from a user interface perspective. In particular, we explain the concept of taclets, which are the basic building blocks for proofs in the KeY prover. Key words: interactive theorem proving, user ..."
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We give a short overview of the KeY prover  which is the proof system belonging to the KeY tool [1]  from a user interface perspective. In particular, we explain the concept of taclets, which are the basic building blocks for proofs in the KeY prover. Key words: interactive theorem proving, user interface, taclets 1
Mathematical Knowledge Archives in Theorema
"... Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambigu ..."
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Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces, addressing the domains of categories and functors as namespaces with variable opera− tions. All constructs are logic–internal in the sense that they have a natural translation to higher–order logic so that �mathematical knowledge management � can be treated by the object logic itself. 1