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Lower Bag Domains
 FUNDAMENTA INFORMATICAE
, 1995
"... Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains c ..."
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Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains can be described concretely as bags. For continuous domains, initial and final lower bag domains coincide. They are continuous again and can be described via a basis which is constructed from a basis of the argument domain. The lower bag domain construction preserves algebraicity and the properties I and M, but does not preserve bounded completeness, property L, or bifiniteness.
Induction and recursion on the partial real line with applications to Real PCF
 Theoretical Computer Science
, 1997
"... The partial real line is an extension of the Euclidean real line with partial real numbers, which has been used to model exact real number computation in the programming language Real PCF. We introduce induction principles and recursion schemes for the partial unit interval, which allow us to verify ..."
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Cited by 5 (1 self)
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The partial real line is an extension of the Euclidean real line with partial real numbers, which has been used to model exact real number computation in the programming language Real PCF. We introduce induction principles and recursion schemes for the partial unit interval, which allow us to verify that Real PCF programs meet their specification. They resemble the socalled Peano axioms for natural numbers. The theory is based on a domainequationlike presentation of the partial unit interval. The principles are applied to show that Real PCF is universal in the sense that all computable elements of its universe of discourse are definable. These elements include higherorder functions such as integration operators. Keywords: Induction, coinduction, exact real number computation, domain theory, Real PCF, universality. Introduction The partial real line is the domain of compact real intervals ordered by reverse inclusion [28,21]. The idea is that singleton intervals represent total rea...
An Upper Power Domain Construction in terms of Strongly Compact Sets
 MFPS '91. LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... A novel upper power domain construction is defined by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of st ..."
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Cited by 4 (3 self)
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A novel upper power domain construction is defined by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of stronger properties than compactness would, e.g. an intrinsic universal property of the upper power construction, and its commutation with the lower construction.
Isomorphisms between Predicate and State Transformers
 In Proc., MFCS '93, Springer LNCS 711
, 1993
"... We study the relation between state transformers based on directed complete partial orders and predicate transformers. Concepts like `predicate', `liveness', `safety' and `predicate transformers' are formulated in a topological setting. We treat state transformers based on the Ho ..."
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We study the relation between state transformers based on directed complete partial orders and predicate transformers. Concepts like `predicate', `liveness', `safety' and `predicate transformers' are formulated in a topological setting. We treat state transformers based on the Hoare, Smyth and Plotkin powerdomains and consider continuous, monotonic and unrestricted functions. We relate the transformers by isomorphisms thereby extending and completing earlier results and giving a complete picture of all the relationships.
Data refinement, call by value, and higher order programs
, 2003
"... Using 2categorical laws of algorithmic refinement, we show soundness of data refinement for stored programs and hence for higher order procedures with value/result parameters. The refinement laws hold in a model that slightly generalizes the standard predicate transformer semantics for the usual ..."
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Cited by 4 (2 self)
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Using 2categorical laws of algorithmic refinement, we show soundness of data refinement for stored programs and hence for higher order procedures with value/result parameters. The refinement laws hold in a model that slightly generalizes the standard predicate transformer semantics for the usual imperative programming constructs including prescriptions.
On the compactregular coreflection of a stably compact locale
 MFPS XV PRELIMINARY VERSION
"... A nucleus on a frame is a finitemeet preserving closure operator. The nuclei on a frame form themselves a frame, with the Scott continuous nuclei as a subframe. We refer to this subframe as the patch frame. We show that the patch construction exhibits ..."
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Cited by 3 (2 self)
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A nucleus on a frame is a finitemeet preserving closure operator. The nuclei on a frame form themselves a frame, with the Scott continuous nuclei as a subframe. We refer to this subframe as the patch frame. We show that the patch construction exhibits
Relating State Transformation Semantics and Predicate Transformer Semantics for Parallel Programs
, 1993
"... A state transformation semantics and a predicate transformer semantics for programs built from atomic actions, sequential composition, nondeterministic choice, parallel composition, atomisation, and recursion are presented. Both semantic models are derived from some SOSstyle labelled transition sys ..."
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A state transformation semantics and a predicate transformer semantics for programs built from atomic actions, sequential composition, nondeterministic choice, parallel composition, atomisation, and recursion are presented. Both semantic models are derived from some SOSstyle labelled transition system. The state transformation semantics and the predicate transformer semantics are shown to be isomorphic extending results of Plotkin and Best. AMS Subject Classification (1991): 68Q55 CR Subject Classification (1991): D.3.1, F.3.2 Keywords & Phrases: state transformation, predicate transformer, isomorphism, labelled transition system, parallelism Note: This work was partially supported by the Netherlands Nationale Faciliteit Informatica programme, project Research and Education in Concurrent Systems (REX).
Hierarchical Reasoning in Probabilistic CSP
, 1996
"... Probabilistic CSP extends the language of CSP with an operator for probabilistic choice. However reasoning about an intricate combination of nondeterminism, communication and probabilistic behaviour can be complicated. In standard CSP such complication is overcome (when possible) by use of hierarchi ..."
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Probabilistic CSP extends the language of CSP with an operator for probabilistic choice. However reasoning about an intricate combination of nondeterminism, communication and probabilistic behaviour can be complicated. In standard CSP such complication is overcome (when possible) by use of hierarchical reasoning. In this paper we provide a foundation for lifting such reasoning to the probabilistic setting. First we formalise the common observation that the standard models of CSP (traces, refusals and refusals/divergences) form a hierarchy, by showing that they are linked by embeddingprojection pairs. Such structure underlies hierarchical reasoning in which complex process behaviour is reasoned about in terms of its simpler projections. Then we show how that hierarchy can be extended to a corresponding hierarchy between the probabilistic models, by using each of those three models of standard CSP as a basis for a probabilistic extension. Finally we show that there is a projection from ...