**Axiomatic Domain Theory in Categories of Partial Maps ...**

Marcel0 Fiore, Axiomatic Domain Theory in Categories of Partial Maps (Cambridge University Press, 1996), ISBN 0 521 57188 Domains are the mathematical structures used in denotational semantics to inter- pret programming languages and domain theory is the mathematical theory of such structures.

**Cambridge University Press 0521602777 Axiomatic Domain ...**

Cambridge University Press 0521602777 - Axiomatic Domain Theory in Categories of Partial Maps - Marcelo P. Fiore Excerpt More information ... Cambridge University Press 0521602777 - Axiomatic Domain Theory in Categories of Partial Maps - Marcelo P. Fiore Excerpt More information.

**Categories and Types for Axiomatic Domain Theory**

Categories and Types for Axiomatic Domain Theory Adam Eppendahl Abstract Domain Theory provides a denotational semantics for programming languages and calculi con-taining ﬁxed point combinators and other so-called paradoxical combinators. This dissertation presents results in the category theory and type theory of Axiomatic Domain Theory.

**Domain Theory for Concurrency —New Categorical Foundations**

PhD thesis “Axiomatic Domain Theory in Categories of Partial Maps” published in the British Computer So-ciety Distinguished Dissertation series in 1995. He is currently working to extend the foundations of seman-tics of functional and concurrent computation towards a mathematical theory of general processes encompass-

**Formalizing Restriction Categories cs.ioc.ee**

more synthetic and concrete partial map categories. A partial map category is based on a given category (of total maps) and a map in it is a map from a subobject of the domain. In this paper, we report on an Agda formalization of the rst chapters of the theory of restriction categories, including the challenging completeness result. We explain ...

**An Extension of Models of Axiomatic Domain Theory to ...**

An Extension of Models of Axiomatic Domain Theory to Models of Synthetic Domain Theory ... x Axiomatic Domain Theory]). Models of axiomatic domain theory are given with respect to an enrichment ... 1,! ƒ in a category C allows one to consider partial maps with domain of deﬁnition a >-subobject and action a C-map. To this

**Symposium for Gordon Plotkin Edinburgh 07 08/09/2006 From ...**

1983 categories of partial maps for computability [dPH86, LM84] ... 1984 reformulation of domain theory using partial continuous maps [Plo85] Hand-written notes for the TPG course ... jlet [x] be e in e0 and its interpretation in Cpop Axiomatic Domain Theory [Fio94] inﬂuenced by reformulation: Cpop paradigmatic example of algebraically ...

**An Axiomatisation of Computationally Adequate Domain ...**

3 Partial maps For a thorough survey of categories of partial maps consult [RR88]. Deﬁnition 3.1 [Mog86, Ros86] A domain structure is a pair (K;D) consisting of a category K and a well-powered category D, such that D is a full-on-objects subcategory of K all of whose morphisms are monos in K, with the following closure property: every diagram X •!f A n

**Domain theoretic models of parametric polymorphism**

phism. By studying various categories of admissible and chain complete per’s and their relations, we discover a picture very similar to that of domain theory. 1 Introduction In this paper we show how to deﬁne parametric domain-theoretic models of polymorphic intuitionistic / linear lambda calculus.

**Some Reasons for Generalizing Domain Theory**

Some Reasons for Generalizing Domain Theory Martin Hyland Received 9 October 2009 One natural way to generalize Domain Theory is to replace partially ordered sets by categories. This kind of generalization has recently found application in the study of concurrency. An outline is given of the elegant mathematical foundations which have been ...