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Formalization of Formal Topology by Means of the Interactive Theorem Prover Matita

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Intelligent Computer Mathematics (CICM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6824))

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Abstract

The project entitled “Formalization of Formal Topology by means of the interactive theorem prover Matita” is an official bilateral project between the Universities of Padova and Bologna, funded by the former, active from March 2008 until August 2010. The project aimed to bring together and exploit the synergic collaboration of two communities of researchers, both centered around constructive type theory: on one side the Logic Group at the University of Padova, focused on developing formal, pointfree topology within a constructive and predicative framework; on the other side, the Helm group at the University of Bologna, developing the Matita Interactive Theorem Prover [2], a young proof assistant based on the Calculus of Inductive Constructions as its logical foundation.

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References

  1. Asperti, A., Avigad, J.: Zen and the art of formalization. Mathematical Structures in Computer Science 21 (to appear, 2011)

    Google Scholar 

  2. Asperti, A., Coen, C.S., Tassi, E., Zacchiroli, S.: User interaction with the Matita proof assistant. Journal of Automated Reasoning 39(2), 109–139 (2007)

    Article  MATH  Google Scholar 

  3. Ciraulo, F., Maietti, M.E., Toto, P.: Constructive version of Boolean Algebra. IGPL (to appear, 2011)

    Google Scholar 

  4. Ciraulo, F., Sambin, G.: The overlap algebra of regular opens. Journal of Pure and Applied Algebra 214, 1988–1995 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Coen, C.S., Tassi, E.: Formalizing Overlap Algebras in Matita. Mathematical Structures in Computer Science 21, 1–31 (2011)

    Article  MATH  Google Scholar 

  6. Coen, C.S., Valentini, S.: General recursion and formal topology. In: Proceedings Workshop on Partiality and Recursion in Interactive Theorem Provers. EPTCS, vol. 43, pp. 65–75 (2010)

    Google Scholar 

  7. Maietti, M.E.: A minimalist two-level foundation for constructive mathematics. Annals of Pure and Applied Logic 160(3), 319–354 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Maietti, M.E., Sambin, G.: From Sets and Types to Topology and Analysis. In: Toward A Minimalist Foundation for Constructive Mathematics, ch. 6. Oxford University Press, Oxford (2005)

    Google Scholar 

  9. Valentini, S.: Cantor theorem and friends, in logical form. Annals of Pure and Applied Logic 163 (to appear, 2011)

    Google Scholar 

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Asperti, A., Maietti, M.E., Sacerdoti Coen, C., Sambin, G., Valentini, S. (2011). Formalization of Formal Topology by Means of the Interactive Theorem Prover Matita. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds) Intelligent Computer Mathematics. CICM 2011. Lecture Notes in Computer Science(), vol 6824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22673-1_20

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  • DOI: https://doi.org/10.1007/978-3-642-22673-1_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22672-4

  • Online ISBN: 978-3-642-22673-1

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