Elements of generalized ultrametric domain theory
نویسندگان
چکیده
منابع مشابه
Elements of Generalized Ultrametric Domain Theory
Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces, as was observed by Lawvere (1973). Guided by his enriched-categorical view on (ultra)metric spaces, we generalize the standard notions of Cauchy sequence and limit in an (ultra)metric space, and of adjoint pair between preorders. This leads to a solution method for recursive domain equations...
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Abstract Domains and metric spaces are two central tools for the study of denotational semantics in computer science, but are otherwise very different in many fundamental aspects. A construction that tries to establish links between both paradigms is the space of formal balls, a continuous poset which can be defined for every metric space and that reflects many of its properties. On the other h...
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We present a Coq formalization of ultrametric spaces and of ultrametric-enriched categories, up to and including the construction of solutions to recursive domain equations in ultrametric-enriched categories. We then show how to apply this semantic setup for giving semantics to a programming language with higher-order store. Specifically, we define a step counting operational semantics for a fu...
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Γ-ultrametric spaces are spaces which satisfy all the axioms of an ultrametric space except that the distance function takes values in a complete lattice Γ instead of R≥0. Γ-ultrametric spaces have been extensively studied as a way to weaken the notion of an ultrametric space while still providing enough structure to be useful (see for example [17], [18], [8]). The many uses of Γ-ultrametric sp...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1996
ISSN: 0304-3975
DOI: 10.1016/0304-3975(95)00013-5