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45
Tutorial dialogs on mathematical proofs
 In Proceedings of the IJCAI Workshop on Knowledge Representation
, 2003
"... The representation of knowledge for a mathematical proof assistant is generally used exclusively for the purpose of proving theorems. Aiming at a broader scope, we examine the use of mathematical knowledge in a mathematical tutoring system with flexible natural language dialog. Based on an analysis ..."
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The representation of knowledge for a mathematical proof assistant is generally used exclusively for the purpose of proving theorems. Aiming at a broader scope, we examine the use of mathematical knowledge in a mathematical tutoring system with flexible natural language dialog. Based on an analysis of a corpus of dialogs we collected with a simulated tutoring system for teaching proofs in naive set theory, we identify several interesting problems which lead to requirements for mathematical knowledge representation. This includes resolving reference between natural language expressions and mathematical formulas, determining the semantic role of mathematical formulas in context, and determining the contribution of inference steps specified by the user. 1
Protocol switching: Exploiting metaproperties
 In Proc. 21st IEEE Intl. Conf. on Distributed Computing Systems Workshops (ICDCSW’01), Intl. Workshop on Applied Reliable Group Communication (WARGC
, 2001
"... As we see a growing variety of network and application behaviors, it becomes more important that protocols adapt to their surroundings. Building adaptive protocols is complicated, and therefore we have considered building hybrid protocols that switch between specialized protocols. In this paper, we ..."
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Cited by 14 (6 self)
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As we see a growing variety of network and application behaviors, it becomes more important that protocols adapt to their surroundings. Building adaptive protocols is complicated, and therefore we have considered building hybrid protocols that switch between specialized protocols. In this paper, we show for which communication properties this is a correct solution, and classify these using a new concept called metaproperties. We also show how well these switches perform. 1 Introduction and Related Work Many networking protocols accomplish the same thing, such as recovery from message loss, but are optimized for different environments or applications. Developing hybrid protocols that combine the advantages of the various
Proof Development with ΩMEGA
 PROCEEDINGS OF THE 18TH CONFERENCE ON AUTOMATED DEDUCTION (CADE–18), VOLUME 2392 OF LNAI
, 2002
"... ..."
Handling polymorphism in automated deduction
 In 21th International Conference on Automated Deduction (CADE21), volume 4603 of LNCS (LNAI
, 2007
"... Abstract. Polymorphism has become a common way of designing short and reusable programs by abstracting generic definitions from typespecific ones. Such a convenience is valuable in logic as well, because it unburdens the specifier from writing redundant declarations of logical symbols. However, top ..."
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Abstract. Polymorphism has become a common way of designing short and reusable programs by abstracting generic definitions from typespecific ones. Such a convenience is valuable in logic as well, because it unburdens the specifier from writing redundant declarations of logical symbols. However, top shelf automated theorem provers such as Simplify, Yices or other SMTLIB ones do not handle polymorphism. To this end, we present efficient reductions of polymorphism in both unsorted and manysorted first order logics. For each encoding, we show that the formulas and their encoded counterparts are logically equivalent in the context of automated theorem proving. The efficiency keynote is to disturb the prover as little as possible, especially the internal decision procedures used for special sorts, e.g. integer linear arithmetic, to which we apply a special treatment. The corresponding implementations are presented in the framework of the Why/Caduceus toolkit. 1
A Computational Approach to Reflective MetaReasoning about Languages with Bindings
 In MERLIN ’05: Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized
, 2005
"... We present a foundation for a computational metatheory of languages with bindings implemented in a computeraided formal reasoning environment. Our theory provides the ability to reason abstractly about operators, languages, openended languages, classes of languages, etc. The theory is based on th ..."
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Cited by 12 (2 self)
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We present a foundation for a computational metatheory of languages with bindings implemented in a computeraided formal reasoning environment. Our theory provides the ability to reason abstractly about operators, languages, openended languages, classes of languages, etc. The theory is based on the ideas of higherorder abstract syntax, with an appropriate induction principle parameterized over the language (i.e. a set of operators) being used. In our approach, both the bound and free variables are treated uniformly and this uniform treatment extends naturally to variablelength bindings. The implementation is reflective, namely there is a natural mapping between the metalanguage of the theoremprover and the object language of our theory. The object language substitution operation is mapped to the metalanguage substitution and does not need to be defined recursively. Our approach does not require designing a custom type theory; in this paper we describe the implementation of this foundational theory within a generalpurpose type theory. This work is fully implemented in the MetaPRL theorem prover, using the preexisting NuPRLlike MartinL ofstyle computational type theory. Based on this implementation, we lay out an outline for a framework for programming language experimentation and exploration as well as a general reflective reasoning framework. This paper also includes a short survey of the existing approaches to syntactic reflection. 1
Userspecified adaptive scheduling in a streaming media network
 In: IEEE Conference on Open Architectures and Network Programming
, 2003
"... Abstract — In disaster and combat situations, mobile cameras and other sensors transmit realtime data, used by many operators or analysis tools. Unfortunately, in the face of limited, unreliable resources, and varying demands, not all users may be able to get the fidelity they require. This paper d ..."
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Abstract — In disaster and combat situations, mobile cameras and other sensors transmit realtime data, used by many operators or analysis tools. Unfortunately, in the face of limited, unreliable resources, and varying demands, not all users may be able to get the fidelity they require. This paper describes MediaNet, a distributed stream processing system designed with the above scenarios in mind. Unlike past approaches, MediaNet’s users can intuitively specify how the system should adapt based on their individual needs. MediaNet uses both local and online global resource scheduling to improve user performance and network utilization, and adapts without requiring underlying support for resource reservations. Performance experiments show that our scheduling algorithm is reasonably fast, and that user performance and network utilization are both significantly improved. I.
Bridging theorem proving and mathematical knowledge retrieval
 In Festschrift in Honour of Jörg Siekmann, LNAI
, 2004
"... Abstract. Accessing knowledge of a single knowledge source with different client applications often requires the help of mediator systems as middleware components. In the domain of theorem proving large efforts have been made to formalize knowledge for mathematics and verification issues, and to str ..."
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Cited by 9 (5 self)
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Abstract. Accessing knowledge of a single knowledge source with different client applications often requires the help of mediator systems as middleware components. In the domain of theorem proving large efforts have been made to formalize knowledge for mathematics and verification issues, and to structure it in databases. But these databases are either specialized for a single client, or if the knowledge is stored in a general database, the services this database can provide are usually limited and hard to adjust for a particular theorem prover. Only recently there have been initiatives to flexibly connect existing theorem proving systems into networked environments that contain large knowledge bases. An intermediate layer containing both, search and proving functionality can be used to mediate between the two. In this paper we motivate the need and discuss the requirements for mediators between mathematical knowledge bases and theorem proving systems. We also present an attempt at a concurrent mediator between a knowledge base and a proof planning system. 1
MetaPRL  A Modular Logical Environment
, 2003
"... MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive ..."
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Cited by 8 (2 self)
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MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive LCFstyle tacticbased proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit. MetaPRL is distributed under an opensource license and can be downloaded from http://metaprl.org/. This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.
An experiment in formal design using metaproperties
 In Proc. DISCEXII ’01: The 2nd DARPA Information Survivability Conference and Exposition. IEEE
, 2001
"... Formal methods tools have greatly influenced our ability to increase the reliability of software and hardware systems by revealing errors and clarifying critical concepts. In this article we show how a rich specification language and a theorem prover for it have contributed to the design and impleme ..."
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Cited by 8 (2 self)
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Formal methods tools have greatly influenced our ability to increase the reliability of software and hardware systems by revealing errors and clarifying critical concepts. In this article we show how a rich specification language and a theorem prover for it have contributed to the design and implementation of verifiably correct adaptive protocols. The protocol building team included experts in formal methods who were able to use the theorem prover to help guide protocol construction at the pace of implementation that is not formally assisted. This example shows that formal methods can have a large impact when being engaged at the earliest stages of design and implementation, because they add value to all subsequent stages, including the creation of informative documentation needed for the maintenance and evolution of software. 1.
Extracting Programs from Constructive HOL Proofs via IZF SetTheoretic Semantics
"... Abstract. Church’s Higher Order Logic is a basis for proof assistants — HOL and PVS. Church’s logic has a simple settheoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, Z ..."
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Cited by 7 (1 self)
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Abstract. Church’s Higher Order Logic is a basis for proof assistants — HOL and PVS. Church’s logic has a simple settheoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, ZFC, into a constructive core, IZF, and axioms of excluded middle and choice. Then we provide the standard settheoretic semantics in such a way that the constructive core of HOL is mapped into IZF. We use the disjunction, numerical existence and term existence properties of IZF to provide a program extraction capability from proofs in the constructive core. We can implement the disjunction and numerical existence properties in two different ways: one modifying Rathjen’s realizability for CZF and the other using a new direct weak normalization result for intensional IZF by Moczyd̷lowski. The latter can also be used for the term existence property. 1