简介：Inthestudyofprocesscalculi,encodingbetweendifferentcalculiisaneffectivewaytocomparetheexpressivepowerofcalculiandcanshedlightontheessenceofwherethedifferencelies.ThomsenandSangiorgihaveworkedonthehigher-ordercalculi(higher-orderCalculusofCommunicatingSystems(CCS)andhigher-orderπ-calculus,respectively)andtheencodingfromandtofirst-orderπ-calculus.Howeverafullyabstractencodingoffirst-orderπ-calculuswithhigher-orderCCSisnotavailableup-today.Thisiswhatweintendtosettleinthispaper.Wefollowtheencodingstrategy,firstproposedbyThomsen,oftranslatingfirst-orderπ-calculusintoPlainCHOCS.Weshowthattheencodingstrategyisfullyabstractwithrespecttoearlybisimilarity(first-orderπ-calculus)andwiredbisimilarity(PlainCHOCS)(whichisabisimulationdefinedonwiredprocessesonlysendingandreceivingwires),thatisthecoreoftheencodingstrategy.Moreoverfromthefactthatthewiredbisimilarityiscontainedbythewell-establishedcontextbisimilarity,wesecurethesoundnessoftheencoding,withrespecttoearlybisimilarityandcontextbisimilarity.Weuseindextechniquetogetaroundallthetechnicaldetailstoreachthesemainresultsofthispaper.Finally,wemakesomediscussiononourworkandsuggestsomefuturework.