Editor for this issue: Richard John Harvey <richardlinguistlist.org>
CSLI Publications is pleased to announce the availability of: A PARADIGM FOR PROGRAM SEMANTICS: POWER STRUCTURES AND DUALITY: Chris Brink (University of Wollongong and Ingrid Rewitzky (University of Cape Town); Paper ISBN: 1575863448, $27.50, cloth ISBN: 1575863456, $67.50, 284 page CSLI Publications 2001. http://cslipublications.stanford.edu , email: pubscsli.stanford.edu. To order this book, contact The University of Chicago Press. Call their toll free order number 18006212736 (U.S. & Canada only) or order online at http://www.press.uchicago.edu/ (use the search feature to locate the book, then order). Book description: This book provides a synthesis of four versions of program semantics. In relational semantics a program is thought of as a binary inputoutput relation over some state space; in predicate transformer semantics a program is a mapping from predicates to predicates; in information systems (and Hoare logic) a program is considered as a relation between predicates; and in domain theory a program is a multifunction mapping states to sets of states. Brink and Rewitzky show, through an exhaustive case study analysis, that it is possible to do backandforth translation from any of these versions of program semantics from and to any of the others. They do so by invoking techniques from nonclassical logics, lattice theory, topology and the calculus of binary relations. At the heart of their method is the notion of a power construction along with an invocation of duality theory. A power construction lifts a given structure from its base set to its power set (the set of all its subsets); duality theory is then used to recapture the original structure from the lifted structure. Specifcally, the duality theory at work in this book is Priestley duality, which identifies certain topological spaces (Priestley spaces) as the duals of bounded distributive lattices. In the authors' version, relational Priestley spaces are the duals of bounded distributive lattices with operators. The importance of this book lies in its demonstration that, although there are many variations of each of the four versions of program semantics, in principle they may be thought of as intertranslatable.Mail to authorRespond to listRead more issuesLINGUIST home pageTop of issue

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