Results 11  20
of
20
Integration in real PCF
 Information and Computation
, 1996
"... Real PCF is an extension of the programming language PCF with a data type for real numbers. Although a Real PCF definable real number cannot be computed in finitely many steps, it is possible to compute an arbitrarily small rational interval containing the real number in a sufficiently large number ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Real PCF is an extension of the programming language PCF with a data type for real numbers. Although a Real PCF definable real number cannot be computed in finitely many steps, it is possible to compute an arbitrarily small rational interval containing the real number in a sufficiently large number of steps. Based on a domaintheoretic approach to integration, we show how to define integration in Real PCF. We propose two approaches to integration in Real PCF. One consists in adding integration as primitive. The other consists in adding a primitive for function maximization and then recursively defining integration from maximization. In both cases we have a computational adequacy theorem for the corresponding extension of Real PCF. Moreover, based on previous work on Real PCF definability, we show that Real PCF extended with the maximization operator is universal. 1
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 ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
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...
Data refinement, call by value, and higher order programs. unpublished draft
 Formal Aspects of Computing
, 1995
"... higher types, lax exponent. Abstract. 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 ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
higher types, lax exponent. Abstract. 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. 1.
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 Hoare, Smyth and Plotk ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
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.
On the CompactRegular Coreflection of a Stably Compact Locale
"... 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 the category of compact regular locales and con ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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 the category of compact regular locales and continuous maps as a coreflective subcategory of the category of stably compact locales and perfect maps, and the category of Stone locales and continuous maps as a coreflective subcategory of the category of spectral locales and spectral maps. We relate our patch construction to Banaschewski and Brummer's construction of the dual equivalence of the category of stably compact locales and perfect maps with the category of compact regular biframes and biframe homomorphisms. Keywords: Frame of nuclei, Scott continuous nuclei, patch topology, stably locally compact locales, perfect maps, compact regular locales. AMS Classification: 06A15, 06B35, 06D20, 06E15, 54C10, 54D45, 54F05. 1 Introduction ...
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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 ...
Metric Predicate Transformers: Towards a Notion of Refinement for Concurrency
, 1994
"... For two parallel languages with recursion a compositional weakest precondition semantics is given using two new metric resumption domains. The underlying domains are characterized by domain equations involving functors that deliver `observable' and `safety' predicate transformers. Further a refineme ..."
Abstract
 Add to MetaCart
For two parallel languages with recursion a compositional weakest precondition semantics is given using two new metric resumption domains. The underlying domains are characterized by domain equations involving functors that deliver `observable' and `safety' predicate transformers. Further a refinement relation is defined for this domains and illustrated by rules dealing with concurrent composition. It turns out, by extending the classical duality of predicate vs. state transformers, that the weakest precondition semantics for the parallel languages is isomorphic to the standard metric state transformers semantics. Moreover, the proposed refinement relation on the predicate transformer domain will correspond to the familiar notion of simulation in the state transformer domain. Contents 1 Introduction 1 2 Mathematical Preliminaries 3 3 Four Languages with Recursion 5 4 Domains for Predicate Transformers 8 5 Predicate Transformer Semantics 14 6 Refinement, Simulation and State Transforme...
MFPS XV Preliminary Version On the compactregular coreflection of a stably compact locale
"... 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 ..."
Abstract
 Add to MetaCart
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