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Advanced Functional Programming: Third International School, AFP'98, Braga, Portugal, September 1219, 1998, Revised Lectures (L,Used
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Inthisvolumeyouwill?ndthelecturenotescorrespondingtothepres rd tationsgivenatthe3 summerschoolonAdvancedFunctionalProgramming, heldinBraga, PortugalfromSeptember1219,1998. ThisschoolwasprecededbyearlieronesinB?astad(1995, Sweden, LNCS925) andOlympia, WA(1996, USA, LNCS1129). Thegoalofthisseriesofschoolsis tobringrecentdevelopmentsintheareaoffunctionalprogrammingtoalarge groupofstudents. Thenotesarepublishedinordertoenableindividuals, small studygroups, andlecturerstobecomeacquaintedwithrecentworkinthefast developingareaoffunctionalprogramming. Whatmadethisschoolparticularlyinterestingwasthefactthatalllectures introducedusefulsoftware, thatwasusedbythestudentsintheclassestoget handsonexperiencewiththesubjectstaught. Weurgereadersofthisvolumeto downloadthelatestversionofthissoftwarefromtheInternetandtrytodothe exercisesfromthetextthemselves;theproofoftheprogramisinthetyping. The?rstlecture, onSortingMorphisms, servesasagentleintroductiontothe thingstocome. Ifyouhavealwaysbeenafraidoftheword"morphism", andyou havebeenwonderingwhatcatamorphisms, anamorphisms, hylomorphims, and paramorphimswereabout, thisisthepapertoread?rst;youwilldiscoverthat theyaremerelynamesforrecursionpatternsthatoccuroverandoveragainwhen writingfunctionalprograms. Thealgorithmsinthepaperareallaboutsorting, andsinceyouarelikelytoknowthosealgorithmsbyheartalready, seeingthem structuredandanalyzedinanovelwayshouldserveasamotivationtoreadon tothesecondlecture. Thesecondlecture, onGenericProgramming, isalmostabookinabook. ThenotescanbeseenastheculminatingpointoftheSTOPproject, sponsored bytheDutchgovernmentattheendofthe80'sandthebeginningofthe90's. Its overallgoalwasthedevelopmentofacalculationalwayofderivingprograms. The projecthasprovideddeeperinsightintorealfunctionalprogrammingandinto thetheorybehindmanythingscommonlywrittenbyfunctionalprogrammers. Oneofthemainachievementsoftheprojecthasbeentomakepeopleaware ofthefactthatmanyalgorithmscanbedescribedinadataindependentway. ThePolyPsystemintroducedinthesenotesisoneofthetranslationstothe Haskellworldofthistheoreticalunderpinning. Thethirdlecture, onGenericProgramTransformation, canalsobeseenas anapplicationofthetheoryintroducedinlecturetwo. Manye?ciencyimproving programtransformationscanbeperformedinamechanicalway, andthesewould nothavebeenpossiblewithoutinsightintothecorrectnessofsuchtransfor tionsgainedinthelectureonGenericProgramming. Thefourthlecture, onDesigningandImplementingCombinatorLanguages, introducesaneasytowriteformalismforwritingdownthecatamorphismsint ducedinearlierchapters. Itisshownhowquitecomplicatedcatamorphisms, that at?rstsightseemratherforbiddingbymakingextensiveuseofhigherorderdo VI Preface mains, canactuallybedevelopedinastepwisefashion, usinganattributegr marview;itisfurthermoreshownhowtorelatethiswayofprogrammingwith conceptsfromtheobjectorientedworldthusmakingclearwhatthestrengths andweaknessesofeachworldare. The?fthlecture, titledUsingMetaML: AStagedProgrammingLanguage, introducestheconceptofpartialevaluation. Itservesasanotherinstanceof thequestfor"themostgenericofwritingprogramsatthelowestcost". The stagingtechniquesshowhowcoststhatwereintroducedbyaddingextralevels ofabstraction, maybemovedfromruntimetocompiletime. Ithasbeencommonknowledgetousersofmodernfunctionallanguagesthat thetypesystemcanbeagreathelpinshorteningprogramsandreducingerrors. Intheextremeonemightseeatypeasapredicatecapturingtheproperties ofanyexpressionwiththattype. InthesixthlectureonCayenneSpiceup yourProgrammingwithDependentTypesitisshowninwhatdirectionfunct
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