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1、AnAlgebraofDesignPatternsHongZhuandIanBayleyOxfordBrookesUniversityInapattern-orientedsoftwaredesignprocess,designdecisionsaremadebyselectingandinstanti-atingappropriatepatterns,andcomposingthemtogether.Inourpreviouswork,weenabledthesedecisionstobeformalisedbyde ningasetofoperatorson
2、patternswithwhichinstantiationsandcompositionscanberepresented.Inthispaper,weinvestigatethealgebraicpropertiesoftheseoperators.Weprovideandproveacompletesetofalgebraiclawssothatequivalencebetweenpatternexpressionscanbeproven.Furthermore,wede neanalways-terminatingnormalisationofpatte
3、rnexpressionstoacanonicalform,whichisuniquemoduloequivalencein rst-orderlogic.Byacasestudy,thepattern-orienteddesignofanextensiblerequest-handlingframework,wedemonstratetwopracticalapplicationsofthealgebraicframework.Firstly,wecanprovethecorrectnessofa nisheddesignwithrespecttothedes
4、igndecisionsmadeandtheformalspeci cationofthepatterns.Secondly,wecanevenderivethedesignfromthesecomponents.CategoriesandSubjectDescriptors:D.2.2[SoftwareEngineering]:DesignToolsandTechniques—Object-orienteddesignmethods;D.2.10[Software]:Design—MethodologiesGeneralTerms:DesignAddition
5、alKeyWordsandPhrases:DesignPatterns,Formalmethod,Softwaredesignmethod-ology,Patterncomposition,Algebra,Equationalreasoning1.INTRODUCTIONDesignpatternsarecodifiedreusablesolutionstorecurringdesignproblems[Gammaetal.1995;Aluretal.2003].Inthepasttwodecades,muchresearchonsoftwaredesignpat
6、ternshavebeenreportedintheliterature.Manysuchpatternshavebeenidentified,documented,catalogued[Gammaetal.1995;Aluretal.2003;Grand2002b;1999;2002a;Fowler2003;HohpeandWoolf2004;Buschmannetal.2007b;Voelteretal.2004;Schumacheretal.2005;Steel2005;DiPippoandGill2005;Douglass2002;Hanmer2007],
7、andformallyspecified[Alencaretal.1996;Mikkonen1998;Taibietal.2003;Gasparisetal.2008;BayleyandZhu2010b].Numeroussoftwaretoolshavebeendevelopedfordetectingpat-ternsinreverseengineeringandinstantiatingpatternsforsoftwaredesign[Niereetal.2002;HouandHoover2006;NijaShiandOlsson2006;Blewitte
8、tal.2005;Map
