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View of Computer Algebra Data from Coq

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

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Abstract

Data representation is an important aspect of software composition. It is often the case that different software components are programmed to represent data in the ways which are the most appropriate for their problem domains. Sometimes, converting data from one representation to another is a non-trivial task. This is the case with computer algebra systems and type-theory based interactive theorem provers such as Coq. We provide some custom instrumentation inside Coq to support a computer algebra system (CAS) communication protocol known as SCSCP. We describe general aspects of viewing OpenMath terms produced by a CAS in the calculus of Coq, as well as viewing pure Coq terms in a simpler type system that is behind OpenMath.

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References

  1. Asperti, A., Padovani, L., Sacerdoti Coen, C., Schena, I.: Mathematical knowledge management in HELM. Annals of Mathematics and Artificial Intelligence 38, 27–46 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bertot, Y.: Structural abstract interpretation: A formal study using Coq. In: Bove, A., Barbosa, L.S., Pardo, A., Pinto, J.S. (eds.) Language Engineering and Rigorous Software Development. LNCS, vol. 5520, pp. 153–194. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Bertot, Y., Guilhot, F., Mahboubi, A.: A formal study of Bernstein coefficients and polynomials. Mathematical Structures in Computer Science (2011)

    Google Scholar 

  4. Boulmé, S., Hardin, T., Hirschkoff, D., Ménissier-Morain, V., Rioboo, R.: On the way to certify computer algebra systems. Electronic Notes in Theoretical Computer Science 23(3), 370–385 (1999); CALCULEMUS 1999, Systems for Integrated Computation and Deduction (associated to FLoC 1999, the 1999 Federated Logic Conference)

    Article  MATH  Google Scholar 

  5. Breuer, T., Linton, S.: The GAP 4 type system: organising algebraic algorithms. In: ISSAC 1998: Proceedings of the 1998 international symposium on Symbolic and algebraic computation, pp. 38–45. ACM, New York (1998)

    Chapter  Google Scholar 

  6. Caprotti, O., Geuvers, H., Oostdijk, M.: Certified and portable mathematical documents from formal contexts. In: Electronic Proceedings of the 1st International Workshop on Mathematical Knowledge Management, MKM 2001. RISC, Schloss Hagenberg, Austria (2001)

    Google Scholar 

  7. Caprotti, O., Oostdijk, M.: Formal and efficient primality proofs by use of computer algebra oracles. J. Symbolic Computation 32(1/2), 55–70 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Delahaye, D., Mayero, M.: Quantifier elimination over algebraically closed fields in a proof assistant using a computer algebra system. In: Proc. Calculemus 2005. ENTCS, vol. 151, pp. 57–73 (2006)

    Google Scholar 

  9. Freundt, S., Horn, P., Konovalov, A., Lesseni, S., Linton, S., Roozemond, D.: OpenMath in SCIEnce: Evolving of symbolic computation interaction. In: Davenport, J.H. (ed.) 22nd OpenMath Workshop (July 2009)

    Google Scholar 

  10. Freundt, S., Horn, P., Konovalov, A., Linton, S., Roozemond, D.: Symbolic computation software composability. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC 2008, Calculemus 2008, and MKM 2008. LNCS (LNAI), vol. 5144, pp. 285–295. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.4.12 (2008), http://www.gap-system.org

  12. Garillot, F., Gonthier, G., Mahboubi, A., Rideau, L.: Packaging mathematical structures. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 327–342. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Gonthier, G., Mahboubi, A., Tassi, E.: A Small Scale Reflection Extension for the Coq system. Research Report RR-6455, INRIA (2011)

    Google Scholar 

  14. Grégoire, B., Théry, L., Werner, B.: A computational approach to pocklington certificates in type theory. In: Hagiya, M. (ed.) FLOPS 2006. LNCS, vol. 3945, pp. 97–113. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Horn, P., Roozemond, D.: OpenMath in SCIEnce: SCSCP and POPCORN. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds.) MKM 2009, Held as Part of CICM 2009. LNCS, vol. 5625, pp. 474–479. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  16. Kaliszyk, C., Wiedijk, F.: Certified computer algebra on top of an interactive theorem prover. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 94–105. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Komendantsky, V., Konovalov, A., Linton, S.: Interfacing Coq + Ssreflect with GAP. In: Proc. User Interfaces for Theorem Provers (UITP) 2010. ENTCS, Elsevier, Amsterdam (to appear 2010)

    Google Scholar 

  18. Konovalov, A., Linton, S.: SCSCP – Symbolic Computation Software Composability Protocol, Version 1.2, GAP package (2010), http://www.cs.st-andrews.ac.uk/~alexk/scscp.htm

  19. Leroy, X.: Proving a compiler: Mechanized verification of program transformations and static analyses. Oregon Programming Languages Summer School (2010), http://cristal.inria.fr/~xleroy/courses/Eugene-2010/

  20. OpenMath, http://www.openmath.org/

  21. Saïbi, A.: Typing algorithm in type theory with inheritance. In: Proc. POPL 1997, pp. 292–301 (1997)

    Google Scholar 

  22. Symbolic Computation Software Composability Protocol, http://www.symbolic-computation.org/SCSCP

  23. The Coq development team. The Coq proof assistant reference manual, http://coq.inria.fr/refman/

  24. Wadler, P.: Views: A way for pattern matching to cohabit with data abstraction. In: POPL, pp. 307–313 (1987)

    Google Scholar 

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Komendantsky, V., Konovalov, A., Linton, S. (2011). View of Computer Algebra Data from Coq. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-22673-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22672-4

  • Online ISBN: 978-3-642-22673-1

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