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A Formal Correspondence Between OMDoc with Alternative Proofs and the \({\overline{\lambda}\mu\tilde{\mu}}\)-Calculus

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Mathematical Knowledge Management (MKM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4108))

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Abstract

We consider an extension of OMDoc proofs with alternative sub-proofs and proofs at different level of detail, and an affine non-deterministic fragment of the \({\overline{\lambda}\mu\tilde{\mu}}\)-calculus seen as a proof format. We provide explanations in pseudo-natural language of proofs in both formats, and a formal correspondence between the two by means of two mutually inverse encodings of one format in the other one.

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References

  1. Autexier, S., Benzmüller, C., Dietrich, D., Meier, A., Wirth, C.: A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity. In: Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, Springer, Heidelberg (2006)

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  3. Kohlhase, M.: OMDoc: An Open Markup Format for Mathematical Documents (Version 1.2)

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  4. Sacerdoti Coen, C.: Explanation in Natural language of terms. In: Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, Springer, Heidelberg (2006)

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  5. Wiedijk, F.: Formal Proof Sketches. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 378–393. Springer, Heidelberg (2004)

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Author information

Authors and Affiliations

  1. DFKI GmbH and Saarland University, Saarbrücken, Germany

    Serge Autexier

  2. Department of Computer Science, University of Bologna, Italy

    Claudio Sacerdoti-Coen

Authors
  1. Serge Autexier
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  2. Claudio Sacerdoti-Coen
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dalhousie University, 6050 University Avenue, Halifax, B3H 1W5, Nova Scotia, Canada

    Jonathan M. Borwein

  2. Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada

    William M. Farmer

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© 2006 Springer-Verlag Berlin Heidelberg

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Autexier, S., Sacerdoti-Coen, C. (2006). A Formal Correspondence Between OMDoc with Alternative Proofs and the \({\overline{\lambda}\mu\tilde{\mu}}\)-Calculus. In: Borwein, J.M., Farmer, W.M. (eds) Mathematical Knowledge Management. MKM 2006. Lecture Notes in Computer Science(), vol 4108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11812289_7

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  • DOI: https://doi.org/10.1007/11812289_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37104-5

  • Online ISBN: 978-3-540-37106-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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