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Convex powerdomains I

Karel Hrbacek
1987 Information and Computation  
A crucial role in singling out cpo's of particular interest to the theory of domains is played by the next definition. Let (D, 6 ) be a cpo.  ...  CONTINUOUS FUNCTIONS Domains required by denotational semantics are often obtained as solutions of domain equations, i.e., equations of the form D 2 T(D), where T is some functor in the category of domains  ... 
doi:10.1016/0890-5401(87)90021-6 fatcat:o77u7acbdfhlbbtirev72qcghi

Page 7818 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
It is shown that the set of ideals of any solution to this domain equation is a reflexive domain.  ...  Gianfranco Mascari (Rome) 97m:68132 68Q55 03B70 Ciobanu, Gabriel (R-IASIFI; lasi) The reflexive domain of cpo’s ideals. (English summary) Acta Cybernet. 12 (1996), no. 3, 249-260.  ... 

Topology, domain theory and theoretical computer science

Michael W. Mislove
1998 Topology and its Applications  
In this paper, we survey the use of order-theoretic topology in theoretical computer science, with an emphasis on applications of domain theory.  ...  Our focus is on the applications of domain-theoretic methods in programming language semantics, and on problems of potential interest to topologists that stem from concerns that semantics generates. 0  ...  Acknowledgements This paper arose from a series of lectures the author delivered at the Summer Topology Conference held in Portland, Maine in August, 1995.  ... 
doi:10.1016/s0166-8641(97)00222-8 fatcat:53vlsbi555cl7bt2rz3ly5twh4

An algebraic approach to the interpretation of recursive types [chapter]

Felice Cardone
1992 Lecture Notes in Computer Science  
We present an algebraic framework for the interpretation of type systems including type recursion, where types are interpreted as partial equivalence relations over a Scott domain.  ...  The existence of type interpretations follows from the initiality, in the class of iterative algebras, of the algebra of regular infinite trees obtained by infinitely unfolding recursive types.  ...  Jan Willem Klop brought to my attention the close similarity between cpo's with a notion of approximation and the projection spaces of [14] , [18] .  ... 
doi:10.1007/3-540-55251-0_4 fatcat:nzn7wp54kfbufd36yfrekioaoi

Atomicity, coherence of information, and point-free structures

Basil A. Karádais
2016 Annals of Pure and Applied Logic  
We prove basic facts about the properties of atomicity and coherence for Scott information systems, and we establish direct connections between coherent information systems and well-known point-free structures  ...  Acknowledgments The questions answered in this work occurred to the author at the Third Workshop in Formal Topology in Padua, May 2007, organized by Elena Paccagnella, Silvia  ...  objects of the domain are then recovered as ideals.  ... 
doi:10.1016/j.apal.2016.04.012 fatcat:kiuenaulbrch7izuw3ftzmflqu

Semantic Domains and Denotational Semantics

Carl A. Gunter, Peter D. Mosses, Dana S. Scott
1989 DAIMI Report Series  
The first, Semantic Domains, was written by Gunter and Scott. It is concerned with the theory of domains of denotations. The second, Denotational Semantics, was written by Mosses.  ...  The main idea of Denotational Semantics is that each phrase of the described language is given a denotation: a mathematical object that represents the contribution of the phrase to the meaning of any program  ...  Notice that the domain F is reflexive: it is isomorphic to a domain that (essentially) includes a domain of functions from F.  ... 
doi:10.7146/dpb.v18i276.7630 fatcat:i27j4middfapxjlvuuiyjwf4ma

Continuity spaces: Reconciling domains and metric spaces

Bob Flagg, Ralph Kopperman
1997 Theoretical Computer Science  
We use continuity spaces, a common refinement of posets and metric spaces, to develop a general theory of semantic domains which includes metric spaces and domains of cpo's as special cases and provides  ...  We show that the category of symmetrically compact V-continuity spaces with continuous maps has many of the key properties required of a category of domains and that it captures, in a natural way, the  ...  the manuscript and Jimmie Lawson and Horst Herrlich for helping us understand the issue of Cartesian closedness for categories of <domains.  ... 
doi:10.1016/s0304-3975(97)00236-3 fatcat:qm4kami47zdvzoalvb4germkpu

Sequentiality and Piecewise-affinity in Segments of Real-PCF

Amin Farjudian
2004 Electronical Notes in Theoretical Computer Science  
One of the key -and most controversial -constants is parallel-if (pif I ), the existence of which causes a serious inefficiency in the language leading to RPCF being impractical.  ...  While search is being undertaken to replace pif I with a more efficient operator, one needs to be assured of the segment of RPCF without pif I being sequential.  ...  Acknowledgement Achim Jung -my supervisor -suggested the problem of sequentiality of wRPCF and the definition of the generalized Vuillemin-sequentiality, i.e. Definition 2.4, page 26.  ... 
doi:10.1016/j.entcs.2004.08.002 fatcat:kqv3mhh6dzhshimladtzqa436y

Mathematics of Domains [article]

Michael A. Bukatin
2015 arXiv   pre-print
Do subdomains of a given domain A form a domain? B. Which retractions are finitary? C. What is the essence of generalizations of information systems based on non-reflexive logics?  ...  Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types.  ...  and general version of a subdomain definition in the framework of domains as abstract cpo's.  ... 
arXiv:1512.03868v1 fatcat:suopli6v3zelrgoqgnvdrqjurm

Recursive domain equations for concrete data structures

Manfred Droste
1989 Information and Computation  
In the theory of denotational semantics of programming languages, we study event structures which combine features of Scott's information systems and Kahn and Plotkin's concrete data structures and model  ...  We show that a simple approximation concept for event structures allows us to obtain straightforward solutions of recursive domain equations for event domains.  ...  Hence one applies a categorical version of the usual Knaster-Tarski theorem for cpo's and obtains solutions of domain equations only up to isomorphism.  ... 
doi:10.1016/0890-5401(89)90065-5 fatcat:2ruohpgndjfv5cejstx2dwpxie

Relating total and partial correctness interpretations of non-deterministic programs

Carl A. Gunter
1990 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '90  
It is shown that the mixed powerdomain has many pleasing domain-theoretic and algebraic properties.  ...  The purpose of this paper is to discuss the relationship between the interpretations of non-deterministic programs using the upper (total correctness) powerdomain on the one hand and the lower (partial  ...  The research on this paper was supported in part by U.S. Army Research Office Grant DAAG29-84-K-0061 and ONR contract number NOOO14-88-K-0557.  ... 
doi:10.1145/96709.96741 dblp:conf/popl/Gunter90 fatcat:6e5wxbtaqnbtzdvzupmwqablgq

Retraction map categories and their applications to the construction of lambda calculus models

Hirofumi Yokouchi
1986 Information and Control  
R is the category whose objects are ideals of (IC], ~<) and whose arrows are ideals of (C, E_), where ~< is the partial order relation in R and ~ is the partial order relation defined by f E g iff dom(  ...  Moreover when E and R satisfy a particular condition, E(C, R) has a reflexive object.  ...  The domain and the codomain of F are defined by dora(F) = {dom(f) l f EF} cod(F) = {cod(f)[feF}. (Note that dom(F) and cod(F) are ideals of (ICI, ~) from the definition of ~_.  ... 
doi:10.1016/s0019-9958(86)80017-1 fatcat:bc6oin52kvgufd6p626st6i6ce

Lecture notes on the lambda calculus [article]

Peter Selinger
2013 arXiv   pre-print
This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013.  ...  Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization  ...  Berry and others developed a theory of "stable domain theory", which is based on cpo's with a additional properties intended to capture sequentiality.  ... 
arXiv:0804.3434v2 fatcat:4pubrmtokjfldcs4autyp5k6ty

Information systems for continuous posets

Steven Vickers
1993 Theoretical Computer Science  
A frequent choice is to use Scott domains (bounded complete algebraic cpo's).  ...  The information systems are crucial when one comes to solving domain equations [20, 141, essentially because a colimit of a chain of domains (obtained by iterating the constructor in the domain equation  ...  Function spccces A crucial part of information system theory for domains is the treatment of function spaces.  ... 
doi:10.1016/0304-3975(93)90072-2 fatcat:4aeiicta2bc25cz7ptp3ixi7qa

Recursion over realizability structures

Roberto M. Amadio
1991 Information and Computation  
Realizability structures play a major role in the metamathematics of intuitionistic systems and they are a basic tool in the extraction of the computational content of constructive proofs.  ...  for the study of programming languages.  ...  Continuous discussions with him and other attendants of our "internal seminar" in Pisa provided the cultural humus for the growth of this work.  ... 
doi:10.1016/0890-5401(91)90074-c fatcat:qqvu3anxabekjef36d332f7qzy
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