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Domain Theory in Logical Form
 Annals of Pure and Applied Logic
, 1991
"... The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and system ..."
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Cited by 235 (10 self)
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The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of properties of processes). Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme:
Power Domain Constructions
 SCIENCE OF COMPUTER PROGRAMMING
, 1998
"... The variety of power domain constructions proposed in the literature is put into a general algebraic framework. Power constructions are considered algebras on a higher level: for every ground domain, there is a power domain whose algebraic structure is specified by means of axioms concerning the alg ..."
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Cited by 23 (9 self)
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The variety of power domain constructions proposed in the literature is put into a general algebraic framework. Power constructions are considered algebras on a higher level: for every ground domain, there is a power domain whose algebraic structure is specified by means of axioms concerning the algebraic properties of the basic operations empty set, union, singleton, and extension of functions. A host of derived operations is introduced and investigated algebraically. Every power construction is shown to be equipped with a characteristic semiring such that the resulting power domains become semiring modules. Power homomorphisms are introduced as a means to relate different power constructions. They also allow to define the notion of initial and final constructions for a fixed characteristic semiring. Such initial and final constructions are shown to exist for every semiring, and their basic properties are derived. Finally, the known power constructions are put into the general framewo...
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.
ICategories as a framework for solving domain equations
, 1993
"... An abstract notion of category of information systems or Icategory is introduced as a generalisation of Scott's wellknown category of information systems. As in the theory of partial orders, Icategories can be complete or !algebraic, and it is shown that !algebraic Icategories can be obt ..."
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Cited by 7 (1 self)
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An abstract notion of category of information systems or Icategory is introduced as a generalisation of Scott's wellknown category of information systems. As in the theory of partial orders, Icategories can be complete or !algebraic, and it is shown that !algebraic Icategories can be obtained from a certain completion of countable Icategories. The proposed axioms for a complete Icategory introduce a global partial order on the morphisms of the category, making them a cpo. An initial algebra theorem for a class of functors continuous on the cpo of morphisms is proved, thus giving canonical solution of domain equations; an effective version of these results for !algebraic Icategories is also provided. Some basic examples of Icategories representing the categories of sets, Boolean algebras, Scott domains and continuous Scott domains are constructed. 1 Introduction A distinctive feature of information systems representing Scott domains, as expressed in [Sco82, LW84], is that th...
HOLCF ’11: A Definitional Domain Theory for Verifying Functional Programs
, 2012
"... HOLCF is an interactive theorem proving system that uses the mathematics of domain theory to reason about programs written in functional programming languages. This thesis introduces HOLCF ’11, a thoroughly revised and extended version of HOLCF that advances the state of the art in program verificat ..."
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Cited by 3 (2 self)
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HOLCF is an interactive theorem proving system that uses the mathematics of domain theory to reason about programs written in functional programming languages. This thesis introduces HOLCF ’11, a thoroughly revised and extended version of HOLCF that advances the state of the art in program verification: HOLCF ’11 can reason about many program definitions that are beyond the scope of other formal proof tools, while providing a high degree of proof automation. The soundness of the system is ensured by adhering to a definitional approach: New constants and types are defined in terms of previous concepts, without introducing new axioms. Major features of HOLCF ’11 include two highlevel definition packages: the Fixrec package for defining recursive functions, and the Domain package for defining recursive datatypes. Each of these uses the domaintheoretic concept of least fixed points to translate usersupplied recursive specifications into safe lowlevel definitions. Together, these tools make it easy for users to translate a wide variety of functional programs into the formalism of HOLCF. Theorems generated by the tools also make it easy for users to reason about their programs, with a very high level of confidence in the soundness of the results. As a case study, we present a fully mechanized verification of a model of concurrency based on powerdomains. The formalization depends on many features unique to HOLCF ’11, and is the first verification of such a model in a formal proof tool. ii ACKNOWLEDGMENTS I would like to thank my advisor, John Matthews, for having continued to devote so much time to working with me, even as a parttime professor; and for motivating me to keep studying domain theory (and enjoying it!) these past years. iii
Universal QuasiPrime Algebraic Domains
 Theoretical Computer Science
, 1994
"... This paper demonstrates the existence of a ..."
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"... this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be found at the ENTCS Macro Home Page. Almost every domain is universal ..."
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this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be found at the ENTCS Macro Home Page. Almost every domain is universal
Stable Power Domains
, 1998
"... In the category of stable dcpo's, free constructions w.r.t. algebraic theories exist. From this, we obtain various stable power domain constructions. After handling their properties in general, we concentrate on the stable Plotkin power construction. For continuous ground domains, it is explici ..."
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In the category of stable dcpo's, free constructions w.r.t. algebraic theories exist. From this, we obtain various stable power domain constructions. After handling their properties in general, we concentrate on the stable Plotkin power construction. For continuous ground domains, it is explicitly described in terms of saturated compact sets. In case of algebraic ground domains, this description is isomorphic to Buneman's lossless power domains.
Full Abstraction and Expressive Completeness for FP
"... ion and Expressive Completeness for FP Joseph Y. Halpern Edward L. Wimmers IBM Almaden Research Center San Jose, CA 95120 email: halpern@ibm.com, wimmers@ibm.com Abstract: We consider issues related to the expressive power of the programming language FP. In particular, we consider whether a number ..."
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ion and Expressive Completeness for FP Joseph Y. Halpern Edward L. Wimmers IBM Almaden Research Center San Jose, CA 95120 email: halpern@ibm.com, wimmers@ibm.com Abstract: We consider issues related to the expressive power of the programming language FP. In particular, we consider whether a number of variants of FP are fully abstract and expressively complete. For example, we show that a version of FP with only onesided sequences behave similarly to PCF in that the addition of parallel or is sufficient to make it fully abstract. However, the addition of parallel or to FP (with its twosided infinite sequences) is not sufficient to achieve full abstraction. By considering these and other variants, we obtain a better understanding of what is required of a language and semantics in order to guarantee full abstraction and expressive completeness. This is an expanded version of a paper that appears in the Proceedings of the Second IEEE Symposium on Logic in Computer Science, 1987. It ...