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Topology, Domain Theory and Theoretical Computer Science
, 1997
"... In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from ..."
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In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from concerns that semantics generates. Keywords: Domain theory, Scott topology, power domains, untyped lambda calculus Subject Classification: 06B35,06F30,18B30,68N15,68Q55 1 Introduction Topology has proved to be an essential tool for certain aspects of theoretical computer science. Conversely, the problems that arise in the computational setting have provided new and interesting stimuli for topology. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra. In this paper, we outline some of these interactions between topology and theoretical computer science, focusing on those aspects that have been mo...
Semantics for Finite Delay
 Theoretical Computer Science
, 1997
"... We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's antifoundation axiom and it is constructed along the lines of the antifounded model for SCCS given by Aczel. We revisit Acze ..."
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We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's antifoundation axiom and it is constructed along the lines of the antifounded model for SCCS given by Aczel. We revisit Aczel's semantics for SCCS where we prove a unique fixpoint theorem under the assumption of guarded recursion. Then we consider Milner's extension of SCCS to include a finite delay operator ". Working with fair bisimilarity we construct a fully abstract model, which is also fully abstract for fortification. We discuss the solution of recursive equations in the model. The paper is concluded with an investigation of the algebraic theory of fair bisimilarity. Keywords: fairness, antifoundation, finite delay, parallelism, fair bisimilarity, fortification. This paper was composed while I was unemployed and an unofficial visitor at the Department of Mathematics, University of Ioannina, Greece. My than...
A Fixpoint Approach to Finite Delay and Fairness
, 1998
"... We introduce a language SCCS oe with a restriction operation on recursion. This involves a relativization of processes to formal environments which can be seen as a simple typing of processes. The fragment SCCS ¯ of SCCS oe drops explicit typing by introducing both least and greatest fixpoint operat ..."
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We introduce a language SCCS oe with a restriction operation on recursion. This involves a relativization of processes to formal environments which can be seen as a simple typing of processes. The fragment SCCS ¯ of SCCS oe drops explicit typing by introducing both least and greatest fixpoint operators. SCCS ¯ is expressive enough so that both SCCS and the Finite Delay Calculus of Milner [21] can be regarded as subcalculi. The delay operators can be defined by "P := ¯x:1x + P and ffi P := x:1x+P . Syntactic full abstractness results are proven for fortification and fair bisimilarity. We propose a collection of algebraic laws and induction rules (which imply Milner's fixpoint rule in [21]) and prove the theory sound for fair bisimilarity and fortification. The theory is strong enough so that it can prove all the laws for the delay operators taken as axioms in the Finite Delay Calculus of Milner. Finally, we sketch a semantics for SCCS oe that is fully abstract for fair bisimilarity and...