manuscript. The lack of a standardized f o r m a t and typeface makes the book appear to be disorganized when, in fact, it is not. Another, and much m o r e serious problem, is the absence of an index which greatly diminishes the book's usefulness as a reference work. The final difficulty is the price. An advertisement in a recent issue of Communications of the A CM (Dec. 1986, p. A-14) listed the retail price as $39.50 (U.S.) which translates into o v e r $50.00 (Canadian) and effectively prices it out of the reach of many students. The British Computer Society o u g h t to consider more economical methods of disseminating conference proceedings in order to bring them within the budgets of more potential readers. Can the distinct strengths of logic p r o g r a m m i n g and functional p r o g r a m m i n g be c o m b i n e d into a unified c o m putational model? How can logic languages be extended to include functions and equations? The fourteen papers in this collection address these issues t o g e t h e r with their underlying t h e o r y and semantics. The purpose of the book is to assemble some of the more promising ideas for the growth and d e v e l o p m e n t of logic programming, and the editors are to be c o m m e n d e d for putting t o g e t h e r a w e l l - f o c u s e d and w e l l - o r g a n i z e d collection. Although most of the ideas presented here have been published elsewhere, their juxtaposition in a single v o l u m e make this a valuable resource for researchers interested in this area. The text w o u l d also be a good choice for a graduate course in logic p r o g r a m m i n g or p r o g r a m m i n g languages, and several of the papers would be suitable as supplemental readings for an u n d e r graduate p r o g r a m m i n g language course. Comparison of the selections reveals some c o m m o n themes. Every paper describes some sort of hybrid language that combines the desirable characteristics of logic and functional languages. Several of the articles explore mechanisms for incorporating functions and equations into logic programming. Most of these involve s o m e means of augmenting unification to p e r m i t terms that do not unify in the conventional m a n n e r to be reduced to equals. Other approaches start from a functional language and e x tend it with some sort of unification mechanism. Source code listings are provided for several of the hybrid models. The contributions are grouped into six sections: * setting the stage * unification and functional p r o g r a m m i n g * s y m m e t r i c combinations * p r o g r a m m i n g with equality * augmented unification * semantic foundations The first t w o articles are g o o d choices for "setting the stage." U. Reddy's "On the Relationship b e t w e e n Logic and Functional Languages" outlines the main differences b e t w e e n logic and functional languages in terms of his "theory of directionality." Functional programs are d i r e c tional, since t h e y make an explicit distinction b e t w e e n input and o u t p u t parameters. Logic programs are n o n directional, which makes t h e m m o r e expressive but harder to understand; f o r example, a single relation, such as PROLOG's append relation, cab be used in several different "modes." Reddy develops a notation for introducing d i r e c t i o n a l i t y into logic languages and shows that the resulting programs are equivalent to f i r s t - o r d e r functional programs. In "The Unification of Functional and Logic Languages," J. Darlington, A.J. Field, and H. Pull further delineate the c o m p a r a t i v e strengths of the t w o language styles: the simplicity and h i g h e r - o r d e r of functional n o t a tion versus the expressive p o w e r of m u l t i - m o d e relations and s o - c a l l e d "logical variables" - - i.e., t h o s e that contain free occurences of variables - - of logic languages. They present an extended functional language (HOPE with unification) designed to capture the expressiveness of logic p r o g r a m m i n g while retaining much of the underlying simplicity of the functional model. The three articles in the section on "unification and functional p r o g r a m m i n g " explore various ways of c o m b i n ing functions and unification. Abramson's HASL language adopts o n e - w a y unification - - only f o r m a l parameter e x pressions may contain variables - - as the primary binding mechanism for an underlying functional model. He Combinatorics, Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability B. Bollobas ISBN 0 521 337038 Cambridge University Press Reviewed by: W. Marek This is an advanced m o n o g r a p h in Combinatorics dealing with what quite often is called "Hungarian" c o m binatorics; hypergraphs, set systems, etc. Presently, the connections of this part of Combinatorics to Artificial Intelligence and Databases are rather loose, the only a p plication that comes to mind are topics related to cyclic and acyclic databases. Hence we should pose to o u r selves the following question: is it w o r t h it (from the professional point of view, of course) to read such books at all and is it w o r t h it, in particular, to review them in a specialized bulletin like SIGART news? Generally the a n s w e r to both questions is, in the opinion of this reviewer, negative. Let us point out h o w e v e r that the combinatorics treated in Bollobas b o o k is very interesting and sometimes stunning in it,,; beauty. I wish programs (like AM, Eurisco, etc.) w e r e a~le to produce such estetic results. For a , m o m e n t , though, we have no hope of b u i l d ing programs mimicking inventiveness of mathematicians and, finally I do not expect to see such programs written during my lifespan. Coming back to the reviewed book, one finds there a w e a l t h of results concerning so called hypergraphs (i.e. set systems). Anyone w h o is interested in "marriage problems" and its variants, Steiner triple system, LYM i n equality, Helly Families and even infinite Ramsey t h e o r y (including Mathias results on Ellentuck Topology) will find there are extensive and well presented information. All chapters are well e n d o w e d with revealing and rather d i f ficult exercises (we believe that a n y o n e able to solve half of t h e m would be able to get an NSF grant in combinatorics). Summing up - this t y p e of b o o k is a rare guest in our bulletin and let it stay this way. LOGIC PROGRAMMING: FUNCTIONS, RELATIONS AND EQUATIONS edited by D o u g D e G r o o t and Gary Lindstrom Prentice-Hall Englewood Cliffs, N e w Jersey 07632 Reviewed by: Ralph Morelli Engineering and C o m p u t e r Science Trinity College Hartford, CT 06106 203-527-3151 Bitnet: RAM@TRINCC SIGART Newsletter, July 198"7, Number 101 Page 14

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