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Terminal Metric Spaces of Finitely Branching and Image Finite Linear processes
, 1997
"... Wellknown metric spaces for modelling finitely branching and image finite systems are shown to be (the carrier of) terminal coalgebras. Introduction In the area of metric semantics, various metric structures have been proposed to model a wide spectrum of programming notions (see, e.g., [BV96]). In ..."
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Wellknown metric spaces for modelling finitely branching and image finite systems are shown to be (the carrier of) terminal coalgebras. Introduction In the area of metric semantics, various metric structures have been proposed to model a wide spectrum of programming notions (see, e.g., [BV96]). In this paper, we focus on metric structures for modelling nondeterministic systems which may give rise to both terminating and nonterminating computations. The systems we have in mind are labelled transition systems [Kel76]. A large variety of programming notions can be modelled by means of these systems (see, e.g., [Plo81]). The models we consider are linear (cf. [Pnu85]). In these models, the locations in a computation where a nondeterministic choice is made are not visible. These linear models are usually contrasted with branching models (cf. [Gla90]). In those models, the positions in the computation where a nondeterministic choice is made are administrated. Typical examples of linear me...
Towards a Denotational Semantics for Concurrent State Transformers
, 1995
"... Concurrent state transformers are an extension of state transformers investigated by Launchbury, Peyton Jones, Wadler, and others by concurrency primitives. A denotational semantics for state transformers executing in parallel is deøned using standard domain theoretic techniques. Using the semantics ..."
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Concurrent state transformers are an extension of state transformers investigated by Launchbury, Peyton Jones, Wadler, and others by concurrency primitives. A denotational semantics for state transformers executing in parallel is deøned using standard domain theoretic techniques. Using the semantics it is proved that concurrent state transformers still form a monad and that the concurrent semantics is a proper extension of the sequential one. Finally, we show that an important property of the øxpointing state transformer is also preserved. 1. Introduction In a recent sequence of papers, Launchbury, Peyton Jones, and Wadler 19;20;13;8;9 have introduced the concept of state transformers into purely functional programming languages. State transformers integrate I/O and computations on mutable variables without compromising referential transparency. The key is to use an abstract datatype of computations (a monad) with an explicit operator for sequential composition. Thus the program u...