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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 461 (20 self)
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Least fixpoints as meanings of recursive definitions.
Inheritance As Implicit Coercion
 Information and Computation
, 1991
"... . We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. ..."
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Cited by 116 (3 self)
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. We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. Our goal is to interpret inheritances in Fun via coercion functions which are definable in the target of the translation. Existing techniques in the theory of semantic domains can be then used to interpret the extended polymorphic lambda calculus, thus providing many models for the original language. This technique makes it possible to model a rich type discipline which includes parametric polymorphism and recursive types as well as inheritance. A central difficulty in providing interpretations for explicit type disciplines featuring inheritance in the sense discussed in this paper arises from the fact that programs can typecheck in more than one way. Since interpretations follow the type...
On functors expressible in the polymorphic typed lambda calculus
 Logical Foundations of Functional Programming
, 1990
"... This is a preprint of a paper that has been submitted to Information and Computation. ..."
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Cited by 16 (1 self)
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This is a preprint of a paper that has been submitted to Information and Computation.
Coherence and Consistency in Domains
 IN THIRD ANNUAL SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 1990
"... Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The goal of this paper is to explore the possibility of using a different conditionthat of coherencewhich has its origins in topology and log ..."
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Cited by 8 (4 self)
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Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The goal of this paper is to explore the possibility of using a different conditionthat of coherencewhich has its origins in topology and logic. In particular, we concentrate on those posets whose principal ideals are algebraic lattices and whose topologies are coherent. 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. Universal domains constructed in this fashion enjoy an additional property: they are saturated. We show that there is exactly one such domain in each of the classes under consideration.
Disjunctive Systems and LDomains
 Proceedings of the 19th International Colloquium on Automata, Languages, and Programming (ICALP’92
, 1992
"... . Disjunctive systems are a representation of Ldomains. They use sequents of the form X ` Y , with X finite and Y pairwise disjoint. We show that for any disjunctive system, its elements ordered by inclusion form an Ldomain. On the other hand, via the notion of stable neighborhoods, every Ldomain ..."
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. Disjunctive systems are a representation of Ldomains. They use sequents of the form X ` Y , with X finite and Y pairwise disjoint. We show that for any disjunctive system, its elements ordered by inclusion form an Ldomain. On the other hand, via the notion of stable neighborhoods, every Ldomain can be represented as a disjunctive system. More generally, we have a categorical equivalence between the category of disjunctive systems and the category of Ldomains. A natural classification of domains is obtained in terms of the style of the entailment: when jXj = 2 and jY j = 0 disjunctive systems determine coherent spaces; when jY j 1 they represent Scott domains; when either jXj = 1 or jY j = 0 the associated cpos are distributive Scott domains; and finally, without any restriction, disjunctive systems give rise to Ldomains. 1 Introduction Discovered by Coquand [Co90] and Jung [Ju90] independently, Ldomains form one of the maximal cartesian closed categories of algebraic cpos. Tog...
The Classification of Continuous Domains (Extended Abstract)
"... Achim Jung y Technische Hochschule Darmstadt and Imperial College of Science and Technology, London Abstract The longstanding problem of finding the maximal cartesian closed categories of continuous domains is solved. The solution requires the definition of a new class of continuous domains, cal ..."
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Achim Jung y Technische Hochschule Darmstadt and Imperial College of Science and Technology, London Abstract The longstanding problem of finding the maximal cartesian closed categories of continuous domains is solved. The solution requires the definition of a new class of continuous domains, called FSdomains, which contains all retracts of SFPobjects. The properties of FSdomains are discussed in some detail. Keywords: continuous domains, SFPobjects, Lawsontopology, Smyth's Theorem, FSdomains, Ldomains 1 Introduction The first spaces suitable for the interpretation of programming language constructs were continuous lattices discovered by Dana Scott in the late sixties. Continuous lattices turned out to have numerous connections to other fields of mathematics such as algebra, topology, and convex analysis. An indication of this is the voluminous Bibliography of Continuous Lattices contained in [4]. In Computer Science, however, it was soon recognized that the subclass of al...
PseudoRetract Functors for Local Lattices and Bifinite LDomains
"... Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of Ldomains, has been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, ..."
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Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of Ldomains, has been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, and then this operator is extended to a functor from posets with embeddingprojection pairs to local lattices with embeddingprojection pairs. The result of applying this functor to a local lattice yields a local lattice isomorphic to the rst; this functor is a pseudoretract. Using the functor into local lattices, a continuous pseudoretraction functor from ωbifinite posets to ωbifinite Ldomains can be constructed. Such a functor takes a universal domain for the ωbifinite posets to a universal domain for the ωbifinite Ldomains. Moreover, the existence of such a functor implies that, from the existence of a saturated universal domain for the ωalgebraic bifinites, we can conclude...
A Logical Approach to Stable Domains
, 2006
"... Building on earlier work by GuoQiang Zhang on disjunctive information systems, and by Thomas Ehrhard, Pasquale Malacaria, and the first author on stable Stone duality, we develop a framework of disjunctive propositional logic in which theories correspond to algebraic Ldomains. Disjunctions in the ..."
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Building on earlier work by GuoQiang Zhang on disjunctive information systems, and by Thomas Ehrhard, Pasquale Malacaria, and the first author on stable Stone duality, we develop a framework of disjunctive propositional logic in which theories correspond to algebraic Ldomains. Disjunctions in the logic can be indexed by arbitrary sets (as in geometric logic) but must be provably disjoint. This raises several technical issues which have to be addressed before clean notions of axiom system and theory can be defined. We show soundness and completeness of the proof system with respect to distributive disjunctive semilattices, and prove that every such semilattice arises as the Lindenbaum algebra of a disjunctive theory. Via stable Stone duality, we show how to use disjunctive propositional logic for a logical description of algebraic Ldomains.