Nemhauser and Trick presented the problem of finding a timetable for the 1997/98 Atlantic Coast Conference (ACC) in basketball. Their solution, found with a combination of integer programming and exhaustive enumeration, was accepted by the ACC. Finite-domain constraint programming is another programming technique that can be used for solving combinatorial search problems such as sports tournament scheduling. This paper presents a solution of round robin tournament planning based on finite-domain constraint programming. The approach yields a dramatic performance improvement, which makes an integrated interactive software solution feasible.
Oz is a multiparadigm language that supports logic programming as one of its major paradigms. A multiparadigm language is designed to support different programming paradigms (logic, functional, constraint, object-oriented, sequential, concurrent, etc.) with equal ease. This article has two goals: to give a tutorial of logic programming in Oz and to show how logic programming fits naturally into the wider context of multiparadigm programming. Our experience shows that there are two classes of problems, which we call algorithmic and search problems, for which logic programming can help formulate practical solutions. Algorithmic problems have known efficient algorithms. Search problems do not have known efficient algorithms but can be solved with search. The Oz support for logic programming targets these two problem classes specifically, using the concepts needed for each. This is in contrast to the Prolog approach, which targets both classes with one set of concepts, which results in less than optimal support for each class. We give examples that can be run interactively on the Mozart system, which implements Oz. To explain the essential difference between algorithmic and search programs, we define the Oz execution model. This model subsumes both concurrent logic programming (committed-choice-style) and search-based logic programming (Prolog-style). Furthermore, as consequences of its multiparadigm nature, the model supports new abilities such as first-class top levels, deep * This article is a much-extended version of the tutorial talk "Logic Programming in Oz withMozart" given at the International Conference on Logic Programming, Las Cruces, New Mexico, Nov. 1999. Some knowledge of traditional logic programming (with Prolog or concurrent logic languages) is assumed. guards, active objects, and sophisticated control of the search process. Instead of Horn clause syntax, Oz has a simple, fully compositional, higher-order syntax that accommodates the abilities of the language. We give a brief history of Oz that traces the development of its main ideas and we summarize the lessons learned from this work. Finally, we give many entry points into the Oz literature.
St.uhlsat.zf' nh a uswf' g 3 , 0-6600 S a arbrii cken , Germ a ny E-m a il : {s m o lka. hf. nz. wU f' rt.z} @dfki .uni-sh .d l' Abstl'act Oz is a n f' Xl)f' rill lf' nt.al hig hf' r-o rdf'r concurrf' nt. cons t.r a int. p rogrammin g syst.f' m IInd f' r df'w lop lll f' nt. a t, DFKI. It. cOl llhin es id f'as fr o lll log ic a nd con curre nt. prog ra mmill g in a s impl f' yf' t. f'xpl't~ss iv l' la ng ll a gl'. Fro lll logic prog ra lllluin g Oz inh f' rit.s log ic vari a bll's a nd logi c d at.a st.rur.t.llI'f'S, whi ch prov idf' fo r a progr a mmiu g s t.y lf' wllf' re pa rt.i a l info l'lw\,t.i o n a ho llt. tl lf' va lllf's of va ri a bl f's is imp mw d concurrf' nt.I y a nd in Cl'f'll w nt.ally. A now l ff'a t.lIl'f' of Oz is t.h a t. it. accommo d a t.es h ig hf' r-ordf' r p rogra mmin g wit.h o ut. sacr ificin g t.h a t. d pll o t.at.i o n a nd equ a lit.y of va ri a hlf's cu I' capt.llrf' d hy first.-ord f' r logic. All o t.h e r Ile w fl'at. llrp of O z is cons t.r a int. commtlllicat.ion , a nf' W fo rm of asyn chro no us communi cat.i o n I'x plo it.in g log ic vari a bl l's. COlls t.r a int. co mmuni cat.i o n a vo id s t.h p p ro hl pm s o f st. rl'am commllni cat.io n , Ut I' convent.io ll a l commllni cat.i o ll m echanism Pll1pl oyed in CO Il CIIITI' Il t. log ic p rog ra mming. Cons t.r a int. comllllllli cat.i o n call I)f' Sf'f' 1l as prov idill g a minim a l fo rlll o f st. a t.1' full y comp a t.ihll' wit.h log ic d a t. a s t.nt c.t. ures. Basl'd o n cons t.r a int. communi cat.i o n a nd high er-order p rog ra mllling, Oz readily s upp o rt.s a va riet.y of o hj l'd-orient.Pd progra mmillg st.yl l's incllldillg mlllt.iplf' inherit.a ll cl'.
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