Partial higher-order specifications

  • Egidio Astesiano
  • Maura Cerioli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 520)


In this paper we study the classes of extensional models of higher-order partial conditional specifications. After investigating the closure properties of these classes, we show that an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models, can be obtained from any equationally complete inference system for partial conditional specifications. Then, applying some previous results, we propose a deduction system, equationally complete for the class of extensional models of a partial conditional specification.

Finally, turning the attention to the special important case of term-extensional models, we first show a sound and equationally complete inference system and then give necessary and sufficient conditions for the existence of free models, which are also free in the class of term-generated extensional models.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AC1.
    Astesiano, E.; Cerioli, M. “On the Existence of Initial Models for Partial (Higher-Order) Conditional Specifications”, Proc. TAPSOFT'89, vol.1, Lecture Notes in Computer Science n. 351, 1989.Google Scholar
  2. AC2.
    Astesiano, E.; Cerioli, M. “Free Objects and Equational Deduction for Partial Conditional Specifications”, Technical Report n.3, Formal Methods Group, University of Genova, 1990.Google Scholar
  3. AC3.
    Astesiano, E.; Cerioli, M. “Commuting between Institutions via Simulation”, submitted, 1990.Google Scholar
  4. B.
    Burmeister, P. A Model Theoretic Oriented Approach to Partial Algebras, Berlin, Akademie-Verlag, 1986.Google Scholar
  5. BW.
    Broy, M.; Wirsing, M. “Partial abstract types”, Acta Informatica 18, 1982.Google Scholar
  6. C.
    Cerioli, M. “A sound and equationally-complete deduction system for partial conditional (higher order) types”, in Proc.3rd Italian Conference of Theoretical Computer Science, 1989, Singapore, World Scientific.Google Scholar
  7. GB.
    Goguen J.A.; Burstall R.M. “Institutions: Abstract Model Theory for Specification and Programming”. Technical Report of Computer Science Laboratory, SRI International, 1990.Google Scholar
  8. K-B.
    Krieg-Brückner B. “Algebraic Specification and Functionals for Transformational Program and Meta Program Development”, in Proc. TAPSOFT'89, Lecture Notes in Computer Science n. 352, 1989.Google Scholar
  9. M.
    Möller, B. “Algebraic Specification with Higher-Order Operations”, Proc. IFIP TC 2 Working Conference on Program Specification and Transformation, North-Holland, 1987.Google Scholar
  10. Me.
    Meinke, K. “Universal Algebra in Higher Types” to appear in Theoretical Computer Science, 1990.Google Scholar
  11. Mes.
    Meseguer J. “General logic” in Proc. Logic Colloquium '87, North-Holland, '89.Google Scholar
  12. MG.
    Meseguer, J.; Goguen, J.A. “Initiality, Induction and Computability”, in Algebraic Methods in Semantics, Cambridge, Cambridge University Press, 1985.Google Scholar
  13. MTW1.
    Möller B., Tarlecki A., Wirsing M. “Algebraic Specification with Built-in Domain Constructions”, in Proc. of CAAP '88, Lecture Notes in Computer Science n.299, 1988.Google Scholar
  14. MTW2.
    Möller B., Tarlecki A., Wirsing M. “Algebraic Specifications of Reachable Higher-Order Algebras”, in Recent Trends in Data Type Specification, Lecture Notes in Computer Science n.332, 1988.Google Scholar
  15. Q.
    Qian Z. “Higher-Order Order-Sorted Algebras”, Proc. 2nd International Conference on Algebraic and Logic Programming, Nancy Oct. 1990, Lecture Notes in Computer Science, Berlin, Springer-Verlag, 1990Google Scholar
  16. R.
    Reichel H. Initial Computability, Algebraic Specifications, and Partial Algebras, Berlin, Akademie-Verlag, 1986.Google Scholar
  17. T.
    Tarlecki A. “Quasi-varieties in Abstract Algebraic Institutions”, Journal of Computer and System Science, n. 33, 1986.Google Scholar
  18. W.
    Wirsing, M. “Algebraic Specification”, in Handbook of Theoretical Computer Science vol.B, North Holland, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Egidio Astesiano
    • 1
  • Maura Cerioli
    • 1
  1. 1.Dipartimento di MatematicaUniversità di GenovaGenovaItaly

Personalised recommendations