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Automating the Meta Theory of Deductive Systems
, 2000
"... not be interpreted as representing the o cial policies, either expressed or implied, of NSF or the U.S. Government. This thesis describes the design of a metalogical framework that supports the representation and veri cation of deductive systems, its implementation as an automated theorem prover, a ..."
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Cited by 79 (16 self)
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not be interpreted as representing the o cial policies, either expressed or implied, of NSF or the U.S. Government. This thesis describes the design of a metalogical framework that supports the representation and veri cation of deductive systems, its implementation as an automated theorem prover, and experimental results related to the areas of programming languages, type theory, and logics. Design: The metalogical framework extends the logical framework LF [HHP93] by a metalogic M + 2. This design is novel and unique since it allows higherorder encodings of deductive systems and induction principles to coexist. On the one hand, higherorder representation techniques lead to concise and direct encodings of programming languages and logic calculi. Inductive de nitions on the other hand allow the formalization of properties about deductive systems, such as the proof that an operational semantics preserves types or the proof that a logic is is a proof calculus whose proof terms are recursive functions that may be consistent.M +
MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems
, 2000
"... In this article we describe the data model of the MBase system, a webbased, ..."
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Cited by 41 (11 self)
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In this article we describe the data model of the MBase system, a webbased,
Integrating Automated and Interactive Theorem Proving
, 1998
"... Machine code ((Schellhorn and Ahrendt, 1997) and Chapter III.2.6). We use it as a reference or benchmark. Parts of it are repeated every now and then to evaluate the success of our integration concepts, see Section 7. In realistic applications in software verification, proof attempts are more likel ..."
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Cited by 31 (8 self)
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Machine code ((Schellhorn and Ahrendt, 1997) and Chapter III.2.6). We use it as a reference or benchmark. Parts of it are repeated every now and then to evaluate the success of our integration concepts, see Section 7. In realistic applications in software verification, proof attempts are more likely to fail than to go through. This is because specifications, programs, I_3_16mod_a.tex; 9/03/1998; 13:09; p.2 INTEGRATED THEOREM PROVING 549 or userdefined lemmas typically are erroneous. Correct versions usually are only obtained after a number of corrections and failed proof attempts. Therefore, the question is not only how to produce powerful theorem provers but also how to integrate proving and error correction. Current research on this and related topics is discussed in Section 8. There are different approaches of combining interactive methods with automated ones. Their relation to our approach is the subject of Section 9. Finally, in Section 10 we draw conclusions. 2. IDENTIFYING ...
Colouring Terms to Control Equational Reasoning
 Journal of Automated Reasoning
, 1997
"... . In this paper we present an approach to prove the equality between terms in a goaldirected way developed in the field of inductive theorem proving. The two terms to be equated are syntactically split into expressions which are common to both and those which occur only in one term. According to the ..."
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Cited by 25 (13 self)
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. In this paper we present an approach to prove the equality between terms in a goaldirected way developed in the field of inductive theorem proving. The two terms to be equated are syntactically split into expressions which are common to both and those which occur only in one term. According to the computed differences we apply appropriate equations to the terms in order to reduce the differences in a goaldirected way. Although this approach was developed for purposes of inductive theorem proving  we use this technique to manipulate the conclusion of an induction step to enable the use of the hypothesis  it is a powerful method for the control of equational reasoning in general. 1. Introduction The automation of equational reasoning is one of the most important obstacles in the field of automating deductions. Even small equational problems result in a huge search space, and finding a proof often fails due to the combinatorial explosion. Proving (conditional) equations by inductio...
System Description: inka 5.0  A Logic Voyager
, 1999
"... this paper are implemented and used for some example logics and sequent calculus proof search. The core inka is implemented in Allegro Common Lisp. The interface runs on distributed Oz, which is available for Unix and Windows. As a next step we intend to integrate a logic for algorithmic function an ..."
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Cited by 23 (11 self)
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this paper are implemented and used for some example logics and sequent calculus proof search. The core inka is implemented in Allegro Common Lisp. The interface runs on distributed Oz, which is available for Unix and Windows. As a next step we intend to integrate a logic for algorithmic function and predicate definitions as well as the methods to prove their termination as tactics. Termination proofs can be inspected and already proven lemmata can be used during the construction of termination proofs, which are the main advantages wrt. the black box implementation of these methods in the old inka system [8]. References
System Description: MBase, an Open Mathematical Knowledge Base
 CADE17, LNAI 1831
, 2000
"... In this paper we describe the MBase system, a webbased, distributed mathematical knowledge base. This system is a mathematical service in MathWeb that offers ... ..."
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Cited by 21 (9 self)
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In this paper we describe the MBase system, a webbased, distributed mathematical knowledge base. This system is a mathematical service in MathWeb that offers ...
AgentOriented Integration of Distributed Mathematical Services
 Journal of Universal Computer Science
, 1999
"... Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that ..."
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Cited by 19 (10 self)
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Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...
A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity
 Proceedings of MKM’05, volume 3863 of LNAI, IUB
, 2006
"... Abstract. A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components i ..."
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Cited by 15 (6 self)
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Abstract. A practically useful mathematical assistant system requires the sophisticated combination of interaction and automation. Central in such a system is the proof data structure, which has to maintain the current proof state and which has to allow the flexible interplay of various components including the human user. We describe a parameterized proof data structure for the management of proofs, which includes our experience with the development of two proof assistants. It supports and bridges the gap between abstract level proof explanation and lowlevel proof verification. The proof data structure enables, in particular, the flexible handling of lemmas, the maintenance of different proof alternatives, and the representation of different granularities of proof attempts. 1
Conditional Equational Specifications of Data Types with Partial Operations for Inductive Theorem Proving
 PROVING. 8 TH RTA 1997, LNCS 1232
, 1996
"... We propose a specification language for the formalization of data types with partial or nonterminating operations as part of a rewritebased logical framework for inductive theorem proving. The language requires constructors for designating data items and admits positive/negative conditional equati ..."
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Cited by 13 (9 self)
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We propose a specification language for the formalization of data types with partial or nonterminating operations as part of a rewritebased logical framework for inductive theorem proving. The language requires constructors for designating data items and admits positive/negative conditional equations as axioms in specifications. The (total algebra) semantics for such specifications is based on socalled data models. We present admissibility conditions that guarantee the unique existence of a distinguished data model with properties similar to those of the initial model of a usual equational specification. Since admissibility of a specification requires confluence of the induced rewrite relation, we provide an effectively testable confluence criterion which does not presuppose termination.