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CCoRN, the Constructive Coq Repository at Nijmegan
"... We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) ..."
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Cited by 19 (9 self)
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We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) applications of such a library.
Assertion application in theorem proving and proof planning
 In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI
, 2003
"... Our work addresses assertion retrieval and application in theorem proving systems or proof planning systems for classical firstorder logic. We propose a distributed mediator M between a mathematical knowledge base KB and a theorem proving system TP which is independent of the particular proof and k ..."
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Cited by 13 (7 self)
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Our work addresses assertion retrieval and application in theorem proving systems or proof planning systems for classical firstorder logic. We propose a distributed mediator M between a mathematical knowledge base KB and a theorem proving system TP which is independent of the particular proof and knowledge representation formats of TP and KB and which applies generalized resolution in order to analyze the logical consequences of arbitrary assertions for a proof context at hand. We discuss the connection to proof planning and motivate an application in a project aiming at a tutorial dialogue system for mathematics. This paper is a short version of [9]. 1 Proof planning at the assertion level Due to Huang [6], the notion of assertion comprises mathematical knowledge from a mathematical knowledge base KB such as axioms, definitions, and theorems. Huang argues that an assertionbased representation, i.e. assertion level, is just
Certifying solutions to permutation group problems
 In F. Baader, ed, CADE19, LNAI 2741
, 2003
"... Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to pr ..."
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Cited by 12 (0 self)
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Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to provide a full proof of correctness of the answer. To guarantee correctness we use proof planning techniques, which construct proofs in a humanoriented reasoning style. This gives the human mathematician the necessary insight into the computed solution, as well as making it feasible to check the solution for relatively large groups. 1
Thoughts on requirements and design issues of user interfaces for proof assistants
 Electronic Notes in Theoretical Computer Science
"... This position paper discusses various issues concerning requirements and design of proof assistant user interfaces (UIs). After a review of some of the difficulties faced by UI projects in academia, it presents a highlevel description of proof assistant interaction. This is followed by an expositio ..."
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Cited by 2 (0 self)
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This position paper discusses various issues concerning requirements and design of proof assistant user interfaces (UIs). After a review of some of the difficulties faced by UI projects in academia, it presents a highlevel description of proof assistant interaction. This is followed by an exposition of use cases and object identification. Several examples demonstrate the usefulness of these requirement elicitation techniques in the theorem proving domain. The second half of the paper begins with a consideration of the “principle of least effort ” for the design of theorem prover user interfaces. This is followed by a brief review of the “GUI versus text mode ” debate, proposals for better use of GUI facilities and a plea for better support of customisation. The paper ends with a discussion of architecture and system design issues. In particular, it argues for a platform architecture with an extensible set of components and the use of XML protocols for communication between UIs and proof assistant backends.