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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Asperti, A., Avigad, J.: Zen and the art of formalization. Mathematical Structures in Computer Science 21 (to appear, 2011)
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)
Ciraulo, F., Maietti, M.E., Toto, P.: Constructive version of Boolean Algebra. IGPL (to appear, 2011)
Ciraulo, F., Sambin, G.: The overlap algebra of regular opens. Journal of Pure and Applied Algebra 214, 1988–1995 (2010)
Coen, C.S., Tassi, E.: Formalizing Overlap Algebras in Matita. Mathematical Structures in Computer Science 21, 1–31 (2011)
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)
Maietti, M.E.: A minimalist two-level foundation for constructive mathematics. Annals of Pure and Applied Logic 160(3), 319–354 (2009)
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)
Valentini, S.: Cantor theorem and friends, in logical form. Annals of Pure and Applied Logic 163 (to appear, 2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)