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The largest Cartesian closed category of domains, considered constructively

DIETER SPREEN
2005 Mathematical Structures in Computer Science  
Theorem The category of constructive SFP domains is the largest constructively Cartesian closed weakly indexed full subcategory of the category of constructive domains that have a computable completeness  ...  Corollary The category of effective SFP objects and continuous maps is the largest Cartesian closed full subcategory of the category of ω-algebraic cpo's that have a computable completeness test.  ...  It is shown that the category of constructive SFP domains is the largest constructively Cartesian closed weakly indexed full subcategory of the category of constructive domains having a computable completeness  ... 
doi:10.1017/s0960129504004591 fatcat:vp4xagskqzhqzhemvfwih46msy

On the Largest Cartesian Closed Category of Stable Domains

Xiaoyong Xi, Guohua Wu
2014 Electronical Notes in Theoretical Computer Science  
Zhang showed that the category of dI-domains is the largest cartesian closed subcategory of ω-SABC and ω-SABC, with the exponential being the stable function space, where ω-SABC and ω-SABC are full subcategories  ...  cartesian closed subcategory of SABC; The compact elements of function spaces in the category SABC are also studied.  ...  Theorem 4.1 The category of dI-domains is the largest cartesian closed subcategory of ω-SABC. Next we show that the category SDABC is the largest cartesian closed subcategory of SABC.  ... 
doi:10.1016/j.entcs.2014.01.011 fatcat:27gq52katrg2jjcuunrgvnvjjq

The largest cartesian closed category of domains

Michael B. Smyth
1983 Theoretical Computer Science  
The importance of this is that it enables us to conclude that SFP is the largest category of domains that iq closed under the constructions of interest in semantics.  ...  In the final section we briefly consider how our results may need to be extended if our, admittedly rather restrictive, notion of 'category of domains' is relaxed in certain ways.  ...  Acknowledgment The author is grateful tcl Gordon Tlotkin, Dana Scott. Flynn Winskel and an anonymous referee for suggesting improvements and corrections to the wiginal version of this paper.  ... 
doi:10.1016/0304-3975(83)90095-6 fatcat:qi67gnfd2ng6tmgmia3mqqli6q

Weakly Distributive Domains [chapter]

Ying Jiang, Guo-Qiang Zhang
2007 Lecture Notes in Computer Science  
This accomplishes the first of a possible, two-step process in solving the problem raised in [1, 2] : whether the category of stable bifinite domains of Amadio-Droste-Göbel [1, 6] is the largest cartesian  ...  We introduce a new class of domains called weakly distributive domains and show that for these domains to be in a cartesian closed category using ω-algebraic meet-cpos, property MI ∞ must not be violated  ...  The existence of a variety of cartesian closed categories of domains motivated a systematic investigation of the question of "largest cartesian closed categories of domains", starting with the work of  ... 
doi:10.1007/978-3-540-73228-0_15 fatcat:xvl4t2mkbrff3dz7uqk5s5xne4

Book review

1999 Science of Computer Programming  
the largest cartesian closed subcategory of the category of algebraic dcpo's (with a countable basis) and some of its variants.  ...  of the theory developed in Chapter 2), and give rise to several cartesian closed categories of domains whose morphisms restrict Scott-continuous functions to match better the operational behavior of programs  ... 
doi:10.1016/s0167-6423(99)00032-5 fatcat:lkbeujvaxbbxjb2pg2cqlbvksq

On exponentiating exponentiation

Evelyn Nelson
1981 Journal of Pure and Applied Algebra  
One of the simplest examples of a Cartesian closed category which is not complete is the category FEns of finite sets; the last section investigates the Cartesian closedness of categories FEnsJ.  ...  each complete, Cartesian closed category K, the category of all K-valued sheaves on any topological space is also Cartesian closed.  ... 
doi:10.1016/0022-4049(81)90050-5 fatcat:a4vam3fykngtna22sv5ifcx74a

All cartesian closed categories of quasicontinuous domains consist of domains

Xiaodong Jia, Achim Jung, Hui Kou, Qingguo Li, Haoran Zhao
2015 Theoretical Computer Science  
In this paper we ask which cartesian closed full subcategories exist in qCONT, the category of all quasicontinuous domains and Scottcontinuous functions.  ...  Quasicontinuity is a generalisation of Scott's notion of continuous domain, introduced in the early 80s by Gierz, Lawson and Stralka.  ...  Acknowledgements The first author acknowledges support by the University of Birmingham  ... 
doi:10.1016/j.tcs.2015.05.014 fatcat:4q4huwdaafbepbdhmq4b3gmuk4

A Convenient Category of Domains

Ingo Battenfeld, Matthias Schröder, Alex Simpson
2007 Electronical Notes in Theoretical Computer Science  
Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations.  ...  We motivate and define a category of topological domains, whose objects are certain topological spaces, generalising the usual ω-continuous dcppos of domain theory.  ...  Acknowledgements We are happy to acknowledge the enormous influence Gordon Plotkin has had on the development of this research.  ... 
doi:10.1016/j.entcs.2007.02.004 fatcat:tfvmwjta3bghfip63xew2onqvi

Coherence and consistency in domains

Carl A. Gunter, Achim Jung
1990 Journal of Pure and Applied Algebra  
These form a Cartesian closed category which has fixed points for domain equations. It is shown that a 'universal domain' exists.  ...  Since the construction of this domain seems to be of general significance, a categorical treatment is provided and applied to other classes of domains.  ...  Cartesian closed subcategories: the category of Ldomains and the category of bifinite domains, which we now proceed to define.  ... 
doi:10.1016/0022-4049(90)90055-m fatcat:j5f7xcez3vgpvl2wd4ajy3wn5q

The versatile continuous order [chapter]

Jimmie D. Lawson
1988 Lecture Notes in Computer Science  
The earlier sections concentrate on the order-theoretic aspects of continuously ordered sets and then specifically of domains.  ...  The ideal completion can be characterized alternately as arising from the adjoint functor to the forgetful functor from the category of CPO's and continuous morphisms to the category of partially ordered  ...  Do the finitely continuous CPO's form the largest cartesian closed full subcategory contained in the category of continuous CPO's? Problem.  ... 
doi:10.1007/3-540-19020-1_7 fatcat:3llpijdzfnb3dnzo5znb5uh7eq

Compactly generated domain theory

INGO BATTENFELD, MATTHIAS SCHRÖDER, ALEX SIMPSON
2006 Mathematical Structures in Computer Science  
The category of such spaces enjoys the usual properties of categories of "predomains" in denotational semantics.  ...  We compare the standard domain-theoretic constructions of products and function spaces on dcpos with their compactly generated counterparts, showing that these agree in important cases though not in general  ...  We also thank the editors of this volume for their patience and encouragement.  ... 
doi:10.1017/s0960129506005202 fatcat:7mdv54evlramxmmf5a5goncsme

Comparing categories of domains [chapter]

Carl A. Gunter
1986 Lecture Notes in Computer Science  
We discuss some of the reasons for the proliferation of categories of domains suggested for the mathematical foundations of the Scott-Strachey theory of programming semantics.  ...  Five general conditions are presented which such a category should satisfy and they arc used to motivate a number of examples.  ...  I would like to thank the following people for suggestions and encouragement: Achim Jung, Gordon Plotkin, Pino Itosolini, Dana Scott, Rick Statman, Adrian Tang.  ... 
doi:10.1007/3-540-16816-8_27 fatcat:uz3bqcsf3ndvrcoswzle4y6o2e

A uniform approach to domain theory in realizability models

JOHN R. LONGLEY, ALEX K. SIMPSON
1997 Mathematical Structures in Computer Science  
One possibility is to cut down the category of topological spaces to a full subcategory that is cartesian closed.  ...  spaces) (Hyland 1979b); or the even larger category of quotients of exponentiable spaces considered in Day (1972) .  ...  We are especially grateful to Matthias Schröder for permission to include his proof of Theorem 3. We also acknowledge the use of Paul Taylor's diagram macros.  ... 
doi:10.1017/s0960129597002387 fatcat:j6roaodr2fgbzjrth4emkq5ctu

Topological and limit-space subcategories of countably-based equilogical spaces

MATÍAS MENNI, ALEX SIMPSON
2002 Mathematical Structures in Computer Science  
Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed-for example, the category of sequential spaces.  ...  There are two main approaches to obtaining "topological" cartesian-closed categories.  ...  We are especially grateful to Matthias Schröder for permission to include his proof of Theorem 3. We also acknowledge the use of Paul Taylor's diagram macros.  ... 
doi:10.1017/s0960129502003699 fatcat:tg66vh7on5amneyxftvenedxlu

A characterisation of the least-fixed-point operator by dinaturality

Alex K. Simpson
1993 Theoretical Computer Science  
., A characterisation of the least-fixed-point operator by dinaturality, Theoretical Computer Science 118 (1993) 301-314.  ...  (The category of countably based algebraic L-domains is not Cartesian-closed.201, and so the category ContL, of continuous L-domains, is Cartesian-closed. Theorem 5.1.  ...  D is an L-domain if, for every XED, the set Jx is a complete lattice under the induced ordering. AlgL, the category of algebraic L-domains, is Cartesian-closed [S].  ... 
doi:10.1016/0304-3975(93)90112-7 fatcat:whulglkzcvaoporhup5ptquvza
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