Abstract: "The failure to make explicit two different notions of subtype, a subtype as inclusion notion originally proposed by Goguen [18] and a subtype as implicit conversion notion originally proposed by Reynolds [44], leads to unsatisfactory situations in present approaches to subtyping. We...

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Bibliographic Details

Main Authors:	Martí-Oliet, Narciso (Author), Meseguer, José (Author)
Format:	Book
Language:	English
Published:	Stanford, Calif. 1990
Series:	Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL 90,16
Subjects:	Logic, Symbolic and mathematical Semantics
Summary:	Abstract: "The failure to make explicit two different notions of subtype, a subtype as inclusion notion originally proposed by Goguen [18] and a subtype as implicit conversion notion originally proposed by Reynolds [44], leads to unsatisfactory situations in present approaches to subtyping. We argue that choosing either notion at the expense of the other would be mistaken and limiting, and propose a framework in which two subtype relations [tau less than or equal to tau prime] (inclusion) and [tau less than or equal to]: [tau prime] (implicit conversion) are distinguished and integrated Most of the paper is devoted to extending the first-order theory of subtypes as inclusions already developed in [23] to a higher-order context; this involves providing a higher-order equational logic for (inclusive) subtypes, a categorical semantics for such a logic that is complete and has initial models, and a proof that this higher-order logic is a conservative extension of its first-order counterpart. We then give axioms that integrate the [less than or equal to] and [less than or equal to]: relations in a unified categorical semantics Besides enjoying the benefits provided by each of the notions without their respective limitations, our framework supports rules for structural subtyping that are more informative and can discriminate between inclusions and implicit conversions.
Physical Description:	62 S.