Abstract
The study of models based on partial equivalence relations (per) and the analysis of the interpretation of inheritance that arises in these structures (Bruce&Longo[88]) leads us to reconsider the classical problem of type-assignment in this framework. Moreover we introduce:
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(1)
A natural generalization of type-assignment systems to typed-equivalence systems that is suggested by the permodels.
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(2)
A specialization of the type-assignment system to a type-containment system that is motivated by the search for a “complete” theory of inheritance.
In the last section we show that a fragment of such theory of inheritance can be fully automated.
Parts of this chapter appeared as TR 28/89 "Formal Theories of Inheritance for Typed Functional Languages", Dipartimento di Informatica, Universita' di Pisa and was presented at the EEC Jumelage meeting on typed λ-calculi (Nijmegen, November 1988) and at the Workshop on Conditional and Typed Rewriting Systems '90, Montreal.
Work done while on leave from Dipartimento di Informatica, Universita' di Pisa.
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© 1991 Springer-Verlag Berlin Heidelberg
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Amadio, R.M. (1991). Typed equivalence, type assignment, and type containment. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_105
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DOI: https://doi.org/10.1007/3-540-54317-1_105
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