Abstract
In this paper, we present an example of the implementation and verification of a functional program. We expose an experience in developing an application in the area of symbolic computation: the computing of Gröbner basis of a set of multivariate polynomials. Our aim is the formal certification of several aspects of the program written in the functional language Caml. In addition, efficient computing of the algorithm is another issue to take into account.
Supported by MCyT TIC2002-02859 and Xunta de Galicia PGIDIT03PXIC10502PN.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Buchberger, B.: An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal. PhD thesis, Univ. of Innsbruck, Austria (1965)
Bird, R., Wadler, P.: Introduction to Functional Programming. Prentice-Hall, Englewood Cliffs (1988)
Hudak, P.: Conception, evolution, and application of functional programming languages. ACM Computing Surveys 21 (1989)
Paulson, L.C.: ML for the Working Programmer, 2nd edn. Cambridge University Press, Cambridge (1996)
Jorge, J.S.: Estudio de la verificación de propíedades de programas funcionales: de las pruebas manuales al uso de asistentes de pruebas. PhD thesis, University of A Coruña, Spain (2004)
Weis, P., Leroy, X.: Le langage Caml, 2nd edn. Dunod (1999)
Leroy, X., et al.: The Objective Caml system: Documentation and User’s Manual, Release 3.08. INRIA (2004), http://caml.inria.fr
The Coq Development Team: The Coq Proof Assistant Reference Manual, Version 7.3. INRIA (2002), http://coq.inria.fr
Bertot, Y., Casteran, P.: Interactive Theorem Proving and Program Development, Coq’Art: The Calculus of Inductive Constructions. Springer, Heidelberg (2004)
Théry, L.: A machine-checked implementation of Buchberger’s algorithm. Journal of Automated Reasoning 26 (2001)
Medina-Bulo, I., Palomo-Lozano, F., Alonso-Jiménez, J.A., Ruiz-Reina, J.-L.: Verified computer algebra in ACL2 (Gröbner bases computation). In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 171–184. Springer, Heidelberg (2004)
Pérez, G.: Bases de Gröbner: Desarrollo formal en Coq. PhD thesis, University of A Coruña, Spain (2005)
Coquand, T., Huet, G.: The calculus of constructions. Information and Computation 76 (1988)
Barja, J.M., Pérez, G.: Demostración en implementaciones concretas de anillos de polinomios. RSME (2000)
Medina-Bulo, I., Alonso-Jiménez, J.A., Palomo-Lozano, F.: Automatic verification of polynomial rings fundamental properties in ACL2. In: 2nd International Workshop on the ACL2 Theorem Prover and Its Applications (2000)
Paulson, L.C.: Constructing recursion operators in intuitionistic type theory. Journal of Symbolic Computation 2 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jorge, J.S., Gulías, V.M., Freire, J.L., Sánchez, J.J. (2005). Towards a Certified and Efficient Computing of Gröbner Bases. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_16
Download citation
DOI: https://doi.org/10.1007/11556985_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29002-5
Online ISBN: 978-3-540-31829-3
eBook Packages: Computer ScienceComputer Science (R0)