Skip to main content

A simple abstract semantics for equational theories

  • Communications
  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 965))

Included in the following conference series:

  • 145 Accesses

Abstract

We show that a suitable abstraction of the notion of termalgebra, called compositum, can be used to capture in a precise mathematical way the intuition that the category of algebras of most (order-sorted) equational theories is completely characterised by their term-model. We also use the relationship between composita and order-sorted equational theories to show that every order-sorted compositum can be canonically embedded into an unsorted one.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. P.Aczel. Term Declaration Logic and Generalised Composita, in: Proceedings of the sixth Symposium on Logic and Computer Science, I.E.E.E. Computer Society Press, 1991.

    Google Scholar 

  2. G.Barthe. Term Declaration Logic and Generalised Composita, Ph.D thesis, University of Manchester, 1993.

    Google Scholar 

  3. G.Barthe. A simple abstract semantics for equational theories, to appear as a technical report, University of Nijmegen, 1995.

    Google Scholar 

  4. J.Goguen. Order-sorted algebra, Technical report, UCLA, 1968.

    Google Scholar 

  5. J.Goguen. What is Unification?, in Hassan Ait-Kaci and Maurice Nivat editors, Resolution of Equations in Algebraic Structures, Vol. 1, pp 217–261, Academic Press, 1989.

    Google Scholar 

  6. J.Goguen and R.Diaconescu. An Oxford survey of Order Sorted Algebra, Mathematical Structures in Computer Science, Vol. 4, pp 363–392, 1994

    Google Scholar 

  7. J.Goguen and J.Meseguer. Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations, Theoretical Computer Science, Vol. 105, pp 217–273, 1992.

    Google Scholar 

  8. S.Mac Lane. Categories for the Working Mathematician, Graduate Texts in Mathematics, Vol. 5, Springer Verlag, 1971.

    Google Scholar 

  9. A.Nerode. Composita, Equations and Freely Generated Algebras, Transactions of the American Mathematical Society, pp 139–151, 1959.

    Google Scholar 

  10. D.Rydeheard and R.Burstall. Computational Category Theory, International Series in Computer Science, Prenctice-Hall, 1988.

    Google Scholar 

  11. M.Schmidt-Schauß. Computational Aspects of Order-Sorted Logic with Term Declarations, Springer Lecture Notes in Artificial Intelligence, Vol. 395, 1989.

    Google Scholar 

  12. M.Schmidt-Schauß and J.Siekmann. Unification Algebras: An Axiomatic Approach to Unification, Equation Solving and Constraint Solving, Universität Kaiserslautern, SEKI-REPORT SR-88-23, 1988.

    Google Scholar 

  13. G.Smolka, W.Nutt, J.Goguen and J.Meseguer. Order-Sorted Equational Computation, in Hassan Ait-Kaci and Maurice Nivat editors, Resolution of Equations in Algebraic Structures, Vol. 2, Academic Press, 1989.

    Google Scholar 

  14. J.Williams. Instantiation Theory, Springer Lecture Notes in Artificial Intelligence, Vol. 518, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Horst Reichel

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barthe, G. (1995). A simple abstract semantics for equational theories. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_45

Download citation

  • DOI: https://doi.org/10.1007/3-540-60249-6_45

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60249-1

  • Online ISBN: 978-3-540-44770-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics