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.
The research of the second author has been partially supported by the Commission of the European Communities under the ESPRIT Programme in the PROSPECTRA Project, ref #390.
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References
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.
Ehrig,H., Mahr,B. [85]: "Fundamentals of Algebraic Specification 1-Equations and Initial Semantics" Springer-Verlag 1985.
Gogolla,M. [84]: "Partially Ordered Sorts in Algebraic Specifications." Proc. 9th CAAP, Cambridge University Press, 139–153. (1984)
Goguen,J.A. [78]: "Order-Sorted Algebra. Semantics and Theory of Computation." Report No. 14, UCLA computer Science Dept. 1978.
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)
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. 18–29
Goguen,J.A. and Meseguer,J. [88]: "Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Polymorphism, and Partial Operations." Tech. Report SRI (1988).
Kirchner, C., Kirchner,H. and Meseguer,J. [87]: Operational semantics of OBJ3. In: Proc. 15th ICALP (1988)
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)
Reynolds, J. [80]: "Using category theory to design implicit conversions and generic operations." In: Semantics-Directed Compiler Generation, LNCS 94. (1980) 211–258
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.
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Kreowski, HJ., Qian, Z. (1990). Relation-sorted algebraic specifications with built-in coercers: Basic notions and results. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_40
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DOI: https://doi.org/10.1007/3-540-52282-4_40
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