Scheme_3_Higher_Order

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1、Lecturecontents•Inthislecturewewilllookat:•Formulatingabstractionswithhigher-orderprocedures(A&S1.3)–(proceduresasarguments:previouslecture)FormulatingAbstractionswithHigher–constructingproceduresusinglambdaOrderProcedures(part2)–proceduresasgeneralmethods–procedure

2、sasreturnedvaluesAbelson&Sussman&Sussmansections:1.3.2-4AdvancedProgrammingParadigmsAdvancedProgrammingParadigms©2002TheUniversityofAdelaide/1.0IntroScheme-3/Slide1©2002TheUniversityofAdelaide/1.0IntroScheme-3/Slide2ConstructingproceduresusinglambdaProceduredefiniti

3、on•Sofar,we’veuseddefinewhenwewantanewprocedure•Proceduredefinitionactuallyuseslambda–Cumbersomeifweusetheprocedureonlyasanargument(define(plus4x)(+x4))•Butproceduresarevalues–Wecanwriteexpressionsthatdenoteproceduresisequivalentto–Schemeprovidesthespecialformlambda

4、–Notationfromtheλ-calculus(defineplus4•Anexampleandhowtoreadit(lambda(x)(lambda(x)(+x4))(+x4))–theprocedureofanargumentxthataddsxand4–equivalenttoλx.x+4)•Generalformis•Schemetransformsthefirstformintothesecond(lambda())AdvancedProgrammingPar

5、adigmsAdvancedProgrammingParadigms©2002TheUniversityofAdelaide/1.0IntroScheme-3/Slide3©2002TheUniversityofAdelaide/1.0IntroScheme-3/Slide4Localvariables:let…let•Generalform•Localdefinitionsareusefultolimitthescopeof,forexample,temporary(let(()variables(<

6、var2>)•Schemeprovidesletforthispurpose(ex.adaptedfrombook)…(define(fxy)())(let((a5)(b(-1y))))•Issyntacticshorthandforthelambdaform(+(*x(squarea))((lambda(...)(*yb))(*ab)))…))•Notehowthebindingsareestablished,ands

7、cope–SimplifybyhandexpressionsinExercise1.34AdvancedProgrammingParadigmsAdvancedProgrammingParadigms©2002TheUniversityofAdelaide/1.0IntroScheme-3/Slide5©2002TheUniversityofAdelaide/1.0IntroScheme-3/Slide6Proceduresasgeneralmethods…half-interval•Thehalf-intervalmetho

8、d:–Findazerobylookinginsmallerandsmallerintervals•Wewrapitintoaprocedurethatsanity-checksarguments–Hereisaninterative,logarithmicprocedure