Advertisement

Heterogeneous unified algebras

  • F. Parisi-Presicce
  • S. Veglioni
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)

Abstract

The framework of Unified Algebras, recently developed for the axiomatic specification of ADT, is modified by introducing again the notion of sort as a classification mechanism for elements of a type. While retaining the idea of sorts as values, Heterogeneous Unified Algebras allow the distinction between certain sorts and the definition of subsorts by applying operations to them. A Specification Logic (which can be extended to an Institution using only injective signature morphisms) is defined, and initial algebra and free construction are shown to exist.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H.Ehrig, B.Mahr: Fundamentals of Algebraic Specification 1. Initial Semantics and Equations Springer, EATCS Monographs on Theoretical Computer Science 6 (1985).Google Scholar
  2. 2.
    H.Ehrig, F.Parisi-Presicce: Nonequivalence of categories for equational algebraic specifications. In Proc. 8th Workshop on Abstr. Data Types, 1991, Springer Lecture Notes in Computer Science 665 (1993) 222–235.Google Scholar
  3. 3.
    H.Ehrig, P.Pepper, F.Orejas: On Recent Trends in Algebraic Specification. In ICALP'89 Proc. Int. Coll. on Automata, Languages and Programming, Springer Lecture Notes in Computer Science 372 (1989) 263–288.Google Scholar
  4. 4.
    J.A.Goguen, R.M.Bustrall: Introducing Institutions. Proc. Logics of Programming Workshop, Springer Lecture Notes in Computer Science 164 (1984) 221–256.Google Scholar
  5. 5.
    J.A.Goguen, R.Diaconescu: A Short Oxford Survey of Order Sorted Algebras. Algebraic Specification Column, EATCS Bulletin 48 (1992) 120–133.Google Scholar
  6. 6.
    J.A.Goguen, J.Meseguer: Order Sorted Algebras I: equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoret. Comp. Sci. 105 (1992) 217–273.Google Scholar
  7. 7.
    P.D.Mosses: Unified Algebras and Institutions. In Proc. 4th IEEE Ann. Symp. on Logic in Computer Science, IEEE Press (1989) 304–312.Google Scholar
  8. 8.
    P.D.Mosses: Unified Algebras and Modules. In Proc. 16th Ann. ACM Symp. on Principles of Programming Languages, ACM (1989) 329–343.Google Scholar
  9. 9.
    P.D.Mosses: The use of sorts in algebraic specifications. In Proc. 8th Workshop on Abstr. Data Types, 1991, Springer Lecture Notes in Computer Science 665 (1993) 66–92.Google Scholar
  10. 10.
    F.Parisi-Presicce, S.Veglioni: Heterogeneous Unified Algebras. Tecnical Report 22, Dip. di Matematica, Universit de L'Aquila (1992).Google Scholar
  11. 11.
    A.Poigné: Partial algebras, subsorting and dependent data types. In Proc. 5th Workshop on Abstract Data Types, 1987, Springer Lecture Notes in Computer Science 332 (1988) 208–234.Google Scholar
  12. 12.
    A.Poigné: Parametrization for order-sorted algebraic specifications. J. Comput. System Sci. vol. 40 no. 2 (1990) 229–268.Google Scholar
  13. 13.
    A.Poigné: Once more on order-sorted algebras. In Proc. Symposium on Math. Foundations of Computer Science, Springer Lecture Notes in Computer Science 520 (1991) 397–405.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • F. Parisi-Presicce
    • 1
  • S. Veglioni
    • 1
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversitá degli Studi L'AquilaL'AquilaItaly

Personalised recommendations