Axiomatic domain theory in categories of partial maps
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چکیده
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Axiomatic domain theory in categories of partial maps
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متن کاملCategories and types for axiomatic domain theory
Domain Theory provides a denotational semantics for programming languages and calculi containing fixed point combinators and other so-called paradoxical combinators. This dissertation presents results in the category theory and type theory of Axiomatic Domain Theory. Prompted by the adjunctions of Domain Theory, we extend Benton’s linear/nonlinear dualsequent calculus to include recursive linea...
متن کاملRestriction categories I: categories of partial maps
Given a category with a stable system of monics, one can form the corresponding category of partial maps. To each map in this category there is, on the domain of the map, an associated idempotent, which measures the degree of partiality. This structure is captured abstractly by the notion of a restriction category, in which every arrow is required to have such an associated idempotent. Categori...
متن کاملAxiomatic Domain Theory
The denotational semantics approach to the semantics of programming languages interprets the language constructions by assigning elements of mathematical structures to them. The structures form so-called categories of domains and the study of their closure properties is the subject of domain theory Sco70, Sco82, Plo83, GS90, AJ94]. Typically, categories of domains consist of suitably complete p...
متن کاملOrder-Enrichment for Categories of Partial Maps
Synopsis Motivated by the desire of treating non-termination directly in the semantics of computation, the notion of approximation between programs is studied in the context of categories of partial maps. In particular, contextual approximation and specialisation are considered and shown to coincide. Moreover, after exhibiting the approximation between total maps as a primitive notion, from an ...
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ژورنال
عنوان ژورنال: Science of Computer Programming
سال: 1998
ISSN: 0167-6423
DOI: 10.1016/s0167-6423(98)90035-1