Advertisement

Hidden Specification of a Functional System

  • César Domínguezand
  • Laureano Lambán
  • Vico Pascual
  • Julio Rubio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2178)

Abstract

This paper is devoted to the formal study of the data structures appearing in a symbolic computation system, namely the EAT system. One of the main features of the EAT system is that it intensively uses functional programming techniques. This implies that some formalisms for the algebraic specification of systems must be adapted to this functional setting. Specifically, this work deals with hidden and coalgebraic methodologies through an institutional framework. As a byproduct, the new concept of coalgebraic institution associated to an institution is introduced. Then, the problem of modeling functorial relationships between data structures is tackled, giving a hidden specification for this aspect of the EAT system and proving the existence of final objects in convenient categories, which accurately model the EAT way of working.

Keywords

Chain Complex Institutional Framework Natural Transformation Algebraic Topology Data Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Abbadi, L. Cardelli, A Theory of objects, Springer, 1996.Google Scholar
  2. 2.
    R. Burstall, R. Diaconescu, Hiding and behaviour: an institutional approach, in A Classical Mind: Essays in Honour of C.A.R. Hoare, Prentice-Hall (1994) 75–92.Google Scholar
  3. 3.
    C. Cîrstea, Coalgebra semantics for hidden algebra: parameterised objects and inheritance, Lecture Notes in Computer Science 1376 (1997) 174–189.Google Scholar
  4. 4.
    C. Domínguez, J. Rubio,Modeling inheritance as coercion in a symbolic computation system, in Proceedings ISSAC’2001, ACM Press (2001).Google Scholar
  5. 5.
    J. Goguen, R. Burstall, Institutions: Abstract model theory for specification and programming, Journal of the Association for Computing Machinery 39(1) (1992) 95–146.zbMATHMathSciNetGoogle Scholar
  6. 6.
    J. Goguen, R. Diaconescu, Towards an algebraic semantics for the object paradigm, Lecture Notes in Computer Science 785 (1994) 1–29.Google Scholar
  7. 7.
    J. Goguen, G. Malcolm, A hidden agenda, Theoretical Computer Science 245 (2000) 55–101.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    P. Hudak, S.L. Peyton Jones, P. Wadler, et al. Report on the functional language Haskell: a non-strict, purely functional language, Version 1.2., SIGPLAN Notices 27(5) (1992) Ri-Rxii, R1-R164.Google Scholar
  9. 9.
    B. Jacobs, J. Rutten, A tutorial on (co)algebras and (co)induction, EATCS Bulletin 62 (1997) 222–259.zbMATHGoogle Scholar
  10. 10.
    L. Lambán, V. Pascual, J. Rubio, Specifying implementations, in Proceedings ISSAC’ 99, ACM Press (1999) 245–251.Google Scholar
  11. 11.
    L. Lambán, V. Pascual, J. Rubio, An object-oriented interpretation of the EAT system. Preprint.Google Scholar
  12. 12.
    J. Loeckx, H. D. Ehrich, M. Wolf, Specification of Abstract Data Types, Wiley-Teubner, 1996.Google Scholar
  13. 13.
    J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, 1967.Google Scholar
  14. 14.
    J. Rubio, F. Sergeraert, Locally effective objects and Algebraic Topology, in Computational Algebraic Geometry, Birkhäuser (1993) 235–251.Google Scholar
  15. 15.
    J. Rubio, F. Sergeraert, Y. Siret, EAT: Symbolic Software for Effective Homology Computation, http://ftp://fourier.ujf-grenoble.fr/pub/EAT, Institut Fourier, Grenoble, 1997.Google Scholar
  16. 16.
    F. Sergeraert, Y. Siret, Kenzo: Symbolic Software for Effective Homology Computation, http://ftp://fourier.ujf-grenoble.fr/pub/KENZO, Institut Fourier, Grenoble, 1999.Google Scholar
  17. 17.
    G. Steele Jr., Common Lisp. The language, Second Edition, Digital Press (1990).Google Scholar
  18. 18.
    J. Rutten, Universal coalgebra: a theory of systems, Theoretical Computer Science 249 (2000) 3–80.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    P. Wadler, S. Blott, How to make ad hoc polymorphism less ad hoc, in Proceedings of the 16th ACM Symposium on Principles of Programming Languages (1989) 60–76.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • César Domínguezand
    • 1
  • Laureano Lambán
    • 1
  • Vico Pascual
    • 1
  • Julio Rubio
    • 1
  1. 1.Departamento de Matemáticas y ComputaciónUniversidad de La RiojaLogroño, La RiojaSpain

Personalised recommendations