lambda-fp
摘要:1Lambda-CalculusandFunctionalProgrammingJonathanP.SeldinDepartmentofMathematicsConcordiaUniversityMontréal,Québec,Canadaseldin@alcor.concordia.caThelambda-calculusisaformalismforrepresentingfunctions.Bythesecondhalfofthenineteenthcentury,theconceptoffunctionasusedinmathematicshadreachedthepointatwhichthestandardnotationhadbecomeambiguous.Forexample,considertheoperatorPdefinedonrealfunctionsasfollows:P[f(x)]=WhatisP[f(x+1)]?f(x)–f(0)xf′(0)forx0forx=0Toseethatthisisambiguous,letf(x)=x2.Thenifg(x)=f(x+1),x+2.Butifh(x)=P[f(x)]=x,thenh(x+1)=x+1P[g(x)].P[g(x)]=P[x2+2x+1]=Thisambiguityhasactuallyledtoanerrorinthepublishedliterature;seethediscussionin(CurryandFeys1958pp.81—82).Astheab
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