Abstract
While implementing a proof for the Basic Perturbation Lemma (a central result in Homological Algebra) in the theorem prover Isabelle one faces problems such as the implementation of algebraic structures, partial functions in a logic of total functions, or the level of abstraction in formal proofs. Different approaches aiming at solving these problems will be evaluated and classified according to features such as the degree of mechanization obtained or the direct correspondence to the mathematical proofs. From this study, an environment for further developments in Homological Algebra will be proposed.
Partially supported by MCyT, project TIC2002-01626 and by CAR ACPI-2002/06.
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References
Ballarin, C.: Locales and Locale Expressions in Isabelle/Isar. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 34–50. Springer, Heidelberg (2004)
Berghofer, S.: Program Extraction in Simply-Typed Higher Order Logic. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 21–38. Springer, Heidelberg (2003)
Brown, R.: The twisted Eilenberg-Zilber theorem, Celebrazioni Arch. Secolo XX, Simp. Top, pp. 34-37 (1967)
Calmet, J.: Some Grand Mathematical Challenges in Mechanized Mathematics. In: Hardin, T., Rioboo, R. (eds.) Calculemus 2003, pp. 137–141 (2003)
Dousson, X., Sergeraert, F., Siret, Y.: The Kenzo program, http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/
Glimming, J.: Logic and Automation for Algebra of Programming, Master Thesis, Maths Institute, University of Oxford (August 2001), available at http://www.nada.kth.se/~glimming/publications.shtml
Gugenheim, V.K.A.M.: On the chain complex of a fibration. Illinois Journal of Mathematics 16, 398–414 (1972)
Kobayashi, H., Suzuki, H., Murao, H.: Rings and Modules in Isabelle/HOL. In: Hardin, T., Rioboo, R. (eds.) Calculemus 2003, pp. 124–129 (2003)
Lambán, L., Pascual, V., Rubio, J.: An object-oriented interpretation of the EAT system. Appl. Algebra Eng. Commun. Comput. 14(3), 187–215
Mac Lane, S.: Homology. Springer, Heidelberg (1994)
Naraschewski, W., Wenzel, M.: Object-Oriented Verification based on Record Subtyping in Higher-Order Logic. In: Grundy, J., Newey, M. (eds.) TPHOLs 1998. LNCS, vol. 1479, pp. 349–366. Springer, Heidelberg (1998)
Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Paulson, L.: Defining Functions on Equivalence Classes, Report, available at http://www.cl.cam.ac.uk/users/lcp/papers/Reports/equivclasses.pdf
Rubio, J., Sergeraert, F.: Constructive Algebraic Topology. Lecture Notes Summer School in Fundamental Algebraic Topology, Institut Fourier (1997)
Rubio, J., Sergeraert, F., Siret, Y.: EAT: Symbolic Software for Effective Homology Computation, Institut Fourier, Grenoble (1997)
Shih, W.: Homologie des espaces fibrés, Publications Math.ématiques de l’I.H.E.S. 13 (1962)
Théry, L.: Proving and computing: A certified version of the Buchberger’s algorithm. In: Kirchner, C., Kirchner, H. (eds.) CADE 1998. LNCS (LNAI), vol. 1421, p. 349. Springer, Heidelberg (1998)
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Aransay, J., Ballarin, C., Rubio, J. (2004). Four Approaches to Automated Reasoning with Differential Algebraic Structures. In: Buchberger, B., Campbell, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2004. Lecture Notes in Computer Science(), vol 3249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30210-0_19
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DOI: https://doi.org/10.1007/978-3-540-30210-0_19
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