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During a meeting in Toronto last winter, Mike Jenkins, Bob Bernecky and I were discussing how the two existing theories on arrays influenced or were in fluenced by programming languages and systems. More's Army Theory was the basis for NIAL and APL2 and Mullin's A Mathematics of A rmys(MOA) , is being used as an algebra of arrays in functional and A-calculus based pro gramming languages. MOA was influenced by Iverson's initial and extended algebra, the foundations for APL and J respectively. We discussed that there is a lot of interest in the Computer Science and Engineering communities concerning formal methods for languages that could support massively parallel operations in scientific com...
This book discusses issues concerning functional programming, logic programming, and integration of the two. The topics include language design, formal semantics, compilation techniques, program transformation, programming methods, integration of programming paradigms, constraint solving, and concurrency. Contents:Mathematica as a Rewrite Language (B Buchberger)Strong Completeness of a Lazy Conditional Narrowing Calculus (M Hamada & A Middeldorp)The Design and Implementation of Mondrian (E Meijer et al)A Functional Perspective of Array Primitives (T-R Chuang)Curry — A Truly Functional Logic Language (M Hanus)On the Inference of Structured Recursive Effects with Subtyping (M Debbabi et al)T...
Is Nine-Men Morris, in the hands of perfect players, a win for white or for black - or a draw? Can king, rook, and knight always defeat king and two knights in chess? What can Go players learn from economists? What are nimbers, tinies, switches and minies? This book deals with combinatorial games, that is, games not involving chance or hidden information. Their study is at once old and young: though some games, such as chess, have been analyzed for centuries, the first full analysis of a nontrivial combinatorial game (Nim) only appeared in 1902. The first part of this book will be accessible to anyone, regardless of background: it contains introductory expositions, reports of unusual tournaments, and a fascinating article by John H. Conway on the possibly everlasting contest between an angel and a devil. For those who want to delve more deeply, the book also contains combinatorial studies of chess and Go; reports on computer advances such as the solution of Nine-Men Morris and Pentominoes; and theoretical approaches to such problems as games with many players. If you have read and enjoyed Martin Gardner, or if you like to learn and analyze new games, this book is for you.
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Mathematics of Computing -- Parallelism.