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The Nuprl Open Logical Environment
, 2000
"... The Nuprl system is a framework for reasoning about mathematics and programming. Over the years its design has been substantially improved to meet the demands of largescale applications. Nuprl LPE, the newest release, features an open, distributed architecture centered around a flexible knowled ..."
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Cited by 44 (16 self)
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The Nuprl system is a framework for reasoning about mathematics and programming. Over the years its design has been substantially improved to meet the demands of largescale applications. Nuprl LPE, the newest release, features an open, distributed architecture centered around a flexible knowledge base and supports the cooperation of independent formal tools. This paper gives a brief overview of the system and the objectives that are addressed by its new architecture.
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 20 (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...
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 8 (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
Integrating TPS and ΩMEGA
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 1999
"... This paper reports on the integration of the higherorder theorem proving environment Tps [Andrews et al., 1996] into the mathematical assistant Ωmega [Benzmuller et al., 1997]. Tps can be called from mega either as a black box or as an interactive system. In black box mode, the user has control ov ..."
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Cited by 7 (4 self)
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This paper reports on the integration of the higherorder theorem proving environment Tps [Andrews et al., 1996] into the mathematical assistant Ωmega [Benzmuller et al., 1997]. Tps can be called from mega either as a black box or as an interactive system. In black box mode, the user has control over the parameters which control proof search in Tps; in interactive mode, all features of the Tpssystem are available to the user. If the subproblem which is passed to Tps contains concepts defined in Ωmega's database of mathematical theories, these definitions are not instantiated but are also passed to Tps. Using a special theory which contains proof tactics that model the NDcalculus variant of Tps within mega, any complete or partial proof generated in Tps can be translated one to one into an mega proof plan. Proof transformation is realised by proof plan expansion in Ωmega's 3dimensional proof data structure, and remains transparent to the user.
A Classical SetTheoretic Model of Polymorphic Extensional Type Theory
, 1997
"... . We give a new semantic foundation for type theories in the lineage of MartinLof's "polymorphic extensional" type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. These type theories are based on an operational seman ..."
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Cited by 6 (1 self)
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. We give a new semantic foundation for type theories in the lineage of MartinLof's "polymorphic extensional" type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. These type theories are based on an operational semantics of an untyped programming language. We show how to integrate classical settheoretic objects, such as functionsasgraphs and equivalence classes, into this operational framework. The new semantics is dramatically simpler than the previous ones, and enables direct reasoning about classical mathematics. A practical consequence is that it justifies a useful embedding of the logic of the HOL theorem prover that gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the years. 1 Introduction The socalled "polymorphic extensional" type theory of MartinLof (MartinLof, 1982) has two features that set it apart from other constructive type t...
Importing Isabelle Formal Mathematics into NuPRL
, 1999
"... Isabelle and NuPRL are two theorem proving environments that are written in different dialects of ML using different formula syntaxes and different logical foundations. In spite of this, they have similar sets of basic theories, representing the same mathematical concepts. ..."
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Cited by 6 (0 self)
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Isabelle and NuPRL are two theorem proving environments that are written in different dialects of ML using different formula syntaxes and different logical foundations. In spite of this, they have similar sets of basic theories, representing the same mathematical concepts.
Changing Data Structures in Type Theory: a study of natural numbers
 Types for Proofs and Programs, Intl. Workshop (TYPES 2000), LNCS 2277
, 2000
"... In typetheory based proof systems that provide inductive structures, computation tools are automatically associated to inductive de nitions. Choosing a particular representation for a given concept has a strong inuence on proof structure. We propose a method to make the change from one represe ..."
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Cited by 3 (0 self)
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In typetheory based proof systems that provide inductive structures, computation tools are automatically associated to inductive de nitions. Choosing a particular representation for a given concept has a strong inuence on proof structure. We propose a method to make the change from one representation to another easier, by systematically translating proofs from one context to another. We show how this method works by using it on natural numbers, for which a unary representation (based on Peano axioms) and a binary representation are available. This method leads to an automatic translation tool that we have implemented in Coq and successfully applied to several arithmetical theorems.
An interpretation of isabelle/hol in hol light
 In Furbach and Shankar [20
"... Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabe ..."
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Cited by 2 (1 self)
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Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabelle logic that cannot be represented directly are elaborated to functors in OCaml. We demonstrate the effectiveness of the interpretation via an implementation, translating a significant part of the Isabelle standard library into HOL Light. 1
Integrating TPS with ΩMEGA
, 1998
"... We report on the integration of Tps as an external reasoning component into the mathematical assistant system Ωmega. Thereby Tps can be used both as an automatic theorem prover for higher order logic as well as interactively employed from within the Ωmega environment. Tps proofs can be directly inc ..."
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Cited by 2 (1 self)
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We report on the integration of Tps as an external reasoning component into the mathematical assistant system Ωmega. Thereby Tps can be used both as an automatic theorem prover for higher order logic as well as interactively employed from within the Ωmega environment. Tps proofs can be directly incorporated into Ωmega on a tactic level enabling their visualization and verbalization. Using an example we show how Tps proofs can be inserted into Ωmega's knowledge base by expanding them to calculus level using both Ωmega's tactic mechanism and the first order theorem prover Otter. Furthermore we demonstrate how the facts from Ωmega's knowledge base can be used to build a Tps library.