Label algebras: A systematic use of terms

  • Gilles Bernot
  • Pascale Le Gall
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 655)


We give the main definitions and results of a new framework for algebraic specifications: the framework of label algebras. The main idea underlying our approach is that the semantics of algebraic specifications can be deeply improved when the satisfaction relation is defined via assignments with range in terms instead of values. Surprisingly, there are several cases where even if two terms have the same value, it is possible that one of them is a suitable instance of a variable in a formula while the other one is not. It is for instance the case for algebraic specifications with exception handling or with observability features. We show that our approach is a useful tool for solving this problem.


algebraic specifications exception handling initial semantics observability subsorting structured specifications 


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  1. [AC91]
    Astesiano E., Cerioli M. Non-strict don't care algebras and specifications. TAPSOFT CAAP, Brighton U.K., April 1991, Springer-Verlag LNCS 493, p.121–142.Google Scholar
  2. [BB91]
    Bernot G., Bidoit M. Proving the correctness of algebraically specified software: Modularity and Observability issues. Proc. of AMAST-2, Second Conference of Algebraic Methodology and Software Technology, Iowa City, Iowa, USA, May 1991.Google Scholar
  3. [BBC86]
    Bernot G., Bidoit M., Choppy C. Abstract data types with exception handling: an initial approach based on a distinction between exceptions and errors. Theoretical Computer Science, Vol.46, n.1, pp.13–45, Elsevier Science Pub. B.V. (North-Holland), November 1986. (Also LRI Report 251, Orsay, Dec. 1985).Google Scholar
  4. [BGM91]
    Bernot G., Gaudel M.C., Marre B. Software testing based on formal specifications: a theory and a tool. to appear in Software Engineering Journal, December 1991.Google Scholar
  5. [Ber92]
    Bernot G. Diplôme d'Habilitation à diriger des Recherches en Sciences, Université de Paris XI, Orsay, 1992.Google Scholar
  6. [BL91]
    Bernot G., Le Gall P. Label algebras and exception handling. To appear in LRI Research Report, Université de Paris XI, Orsay, 1991.Google Scholar
  7. [Bid89]
    Bidoit M. Pluss, un langage pour le développement de spécifications algébriques modulaires. Thèse d'état, University of Orsay Paris XI, 1989.Google Scholar
  8. [Bre91]
    Breu M. Bounded Implementation of Algebraic Specifications. 8th Workshop on Specification od Abstract DataTypes, Dourdan, 1991.Google Scholar
  9. [BW82]
    Broy M., Wirsing M. Partial abstract data types. Acta Informatica, Vol.18-1, Nov. 1982.Google Scholar
  10. [Com90]
    Comon H. Equational formulas in order-sorted algebras. Proc. ICALP, Warwick, Springer-Verlag, July 1990.Google Scholar
  11. [EBCO91]
    Ehrig H., Baldamus M., Cornelius F., Orejas F. Theory of algebraic module specification including behavioural semantics, constraints and aspects of generalized morphisms. Proc. of AMAST-2, Second Conference of Algebraic Methodology and Software Technology, Iowa City, Iowa, USA, May 1991.Google Scholar
  12. [EBO91]
    Ehrig H., Baldamus M., Orejas F. New concepts for amalgamation and extension in the framework of specification logics. Research report Bericht-No 91/05, Technische Universitat Berlin, May 1991.Google Scholar
  13. [EM85]
    Ehrig H., Mahr B. Fundamentals of Algebraic Specification 1. Equations and initial semantics. EATCS Monographs on Theoretical Computer Science, Vol.6, Springer-Verlag, 1985.Google Scholar
  14. [PGJM85]
    Futatsugi K., Goguen J., Jouannaud J-P., Meseguer J. Principles of OBJ2. Proc. 12th ACM Symp. on Principle of Programming Languages, New Orleans, January 1985.Google Scholar
  15. [GB84]
    Goguen J.A., Burstall R.M. Introducing institutions. Proc. of the Workshop on Logics of Programming, Springer-Verlag LNCS 164, pp.221–256, 1984.Google Scholar
  16. [GDLE84]
    Gogolla M., Drosten K., Lipeck U., Ehrich H.D. Algebraic and operational semantics of specifications allowing exceptions and errors. Theoretical Computer Science 34, North Holland, 1984, pp.289–313.Google Scholar
  17. [GM89]
    Goguen J.A., Meseguer J. Order-sorted algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Technical Report SRI-CSL-89-10, SRI, July 1989.Google Scholar
  18. [Gog78]
    Goguen J.A. Order sorted algebras: exceptions and error sorts, coercion and overloading operators. Univ. California Los Angeles, Semantics Theory of Computation Report n.14, Dec. 1978.Google Scholar
  19. [Gog83]
    Gogolla M. Algebraic specification with partially ordered sorts and declarations. Research report Forschungsbericht No 169, University of Dormund, 1983.Google Scholar
  20. [Gog87]
    Gogolla M. On parametric algebraic specifications with clean error handling. Proc. Joint Conf. on Theory and Practice of Software Development, Pisa (1987), Springer-Verlag LNCS 249, pp.81–95.Google Scholar
  21. [GTW78]
    Goguen J.A., Thatcher J.W., Wagner E.G. An Initial Algebra Approach to the Specification, Correctness, and Implementation of Abstract Data Types. Current Trends in Programming Methodology, ed. R.T. Yeh, Printice-Hall, Vol.IV, pp.80–149, 1978. (Also IBM Report RC 6487, October 1976).Google Scholar
  22. [Hen89]
    Hennicker R. Implementation of Parameterized Observational Specifications. TapSoft, Barcelona, LNCS 351, vol.1, pp.290–305, 1989.Google Scholar
  23. [LeG92]
    Le Gall P. Algèbres étiquetées, traitement d'exception et test de logiciel Draft version of Thèse de Doctorat, Université de Paris XI, Orsay, 1992.Google Scholar
  24. [LG86]
    Liskov B., Guttag J. Abstraction and specification in program development. The MIT Press and McGraw-Hill Book Company, 1986.Google Scholar
  25. [Meg90]
    Mégrelis A. Algèbre galactique — Un procédé de calcul formel, relatif aux semi-fonctions, à l'inclusion et à l'égalité Thèse de doctorat, Université Nancy I, September 1990.Google Scholar
  26. [Mos89]
    Mosses P. Unified algebras and Institutions. Proc. of IEEE LICS'89, Fourth Annual Symposium on Logic in Computer Science, June 1989, Asilomar, California.Google Scholar
  27. [MS87]
    Manca V., Salibra A. Soundness and completeness of the Birkhoff equational calculus for many-sorted algebras with possibly empty carrier sets Draft University of Pisa, September 1987, to appear in TCS 1992.Google Scholar
  28. [MSS90]
    Manca V., Salibra A., Scollo G. Equational Type Logic. Conference on Algebraic Methodology and Software Technology, Iowa City, IA, May 1989, TCS 77, p 131–159Google Scholar
  29. [McL71]
    Mac Lane S. Categories for the working mathematician. Graduate texts in mathematics, 5, Springer-Verlag, 1971Google Scholar
  30. [Poi88]
    Poigne A. Partial algebras, Subsorting, and dependent types. 5th Workshop on Specification of Abstract Data Types, Gullane, September 1987, LNCS 332, p. 208–234.Google Scholar
  31. [Sco77]
    Scott D.S. Identity and Existence in Intutionistic Logic. In: Applications of Sheaves, Proc. Durham, Lectures Notes in Mathematics 753.Google Scholar
  32. [Smo86]
    Smolka G. Order-sorted horn logic: semantics and deduction. Research report SR-86-17, Univ. Kaiserslautern, Oct. 1986.Google Scholar
  33. [SS91]
    Salibra A., Scollo G. A soft stairway to institutions 8th Workshop on Specification od Abstract DataTypes, Dourdan, 1991.Google Scholar
  34. [WB80]
    Wirsing M., Broy M. Abstract data types as lattices of finitely generated models. Proc. of the 9th Int. Symposium on Mathematical Foundations of Computer Science (MFCS), Rydzyna, Poland, Sept. 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Gilles Bernot
    • 1
  • Pascale Le Gall
    • 2
  1. 1.LIENS, CNRS URA 1327Paris Cedex 05France
  2. 2.LRI, CNRS URA 410, Bat. 490Université Paris-SudOrsayFrance

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