Advertisement

Relation-sorted algebraic specifications with built-in coercers: Basic notions and results

  • Hans-Jörg Kreowski
  • Zhenyu Qian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 415)

Abstract

A relation-sorted algebraic specification SPEC with built-in coercers is, syntactically seen, quite similar to an order-sorted specification, i.e. SPEC consists of a signature, a set of equations and an arbitrary relation ⊳ on the set of sorts. But our notion of SPEC-algebras is more general. In particular, if two sorts are in the sort relation s⊳s′, then we assume that, in each SPEC-algebra A, the corresponding carriers AS and AS′, are related by an operator AS⊳S′:AS→AS′, which is considered as a component of A, rather than by inclusion AS\(\subseteq\)AS, as required in order-sorted algebras. This allows us to map a sort into a sort and simultaneously forget about some aspects as it occurs in object-oriented programming. Although our approach is more general than order-sorted specification, we et similar results, e.g. concerning the construction of initial algebras and a complete deduction system. Our approach may serve as a general framework for investigating subtypes as injective as well as non-injective conversion.

Keywords

Function Symbol Operational Semantic Full Subcategory Canonical Operator Subtype Relation 
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. Bruce, K.B. and Wegner, P. [86]: "An Algebraic Model for Subtypes in Object-Oriented Languages (Draft) In: SIGPLAN Vol.21, No.10. (1986) 163–172.Google Scholar
  2. Ehrig,H., Mahr,B. [85]: "Fundamentals of Algebraic Specification 1-Equations and Initial Semantics" Springer-Verlag 1985.Google Scholar
  3. Gogolla,M. [84]: "Partially Ordered Sorts in Algebraic Specifications." Proc. 9th CAAP, Cambridge University Press, 139–153. (1984)Google Scholar
  4. Goguen,J.A. [78]: "Order-Sorted Algebra. Semantics and Theory of Computation." Report No. 14, UCLA computer Science Dept. 1978.Google Scholar
  5. Goguen,J.A., Jouannaud,J.-P. and Meseguer,J. [85]: "Operational Semantics of Order-sorted Algebra." In: Proc. International Conference on Automata, Languages and Programming, Springer-LNCS 194. (1985)Google Scholar
  6. Goguen,J.A. and Meseguer,J. [87]: "Order-sorted Algebra Solves the Constructor-Selector, Multiple Representation and Coercion Problems" In: Proc. 1987 Symposium on Logic in Computer Science, Cornell. 1987. 18–29Google Scholar
  7. Goguen,J.A. and Meseguer,J. [88]: "Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Polymorphism, and Partial Operations." Tech. Report SRI (1988).Google Scholar
  8. Kirchner, C., Kirchner,H. and Meseguer,J. [87]: Operational semantics of OBJ3. In: Proc. 15th ICALP (1988)Google Scholar
  9. Qian, Zh. [89]: "Relation-Sorted Algebraic Specifications with Built-in Coercers: Parameterization and Parameter Passing." In: Proc. Categorical Methods in Computer Science with Aspects from Topology, LNCS 393, 244–260. (1989)Google Scholar
  10. Reynolds, J. [80]: "Using category theory to design implicit conversions and generic operations." In: Semantics-Directed Compiler Generation, LNCS 94. (1980) 211–258Google Scholar
  11. Smolka,G., Nutt,W., Goguen,J.A. and Meseguer,J. [87]: "Order-Sorted Equational Computation" SEKI Rep. SR-87-14. In: H.Ait-Kaci, M.Nivat. (eds.) Resolution of Equations in Algebraic Structures; Academic Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Hans-Jörg Kreowski
    • 1
  • Zhenyu Qian
    • 1
  1. 1.Department of Computer ScienceUniversity of BremenBremen 33Fed. Rep. Germany

Personalised recommendations