▁parameters ). ▁ ▁Conc ern ing ▁the ▁practical ity ▁of ▁using ▁either ▁the ▁Church ▁or ▁Scott ▁encoding ▁for ▁programming , ▁there ▁is ▁a ▁symmetric ▁trade - off : ▁Church - encoded ▁numer als ▁support ▁a ▁constant - time ▁addition ▁operation ▁and ▁have ▁no ▁better ▁than ▁a ▁linear - time ▁prede cess or ▁operation ; ▁Scott - encoded ▁numer als ▁support ▁a ▁constant - time ▁prede cess or ▁operation ▁and ▁have ▁no ▁better ▁than ▁a ▁linear - time ▁addition ▁operation . ▁ ▁Type ▁definitions ▁ ▁Church - encoded ▁data ▁and ▁operations ▁on ▁them ▁are ▁typ able ▁in ▁system ▁F , ▁but ▁Scott - encoded ▁data ▁and ▁operations ▁are ▁not ▁obviously ▁typ able ▁in ▁system ▁F . ▁Universal ▁as ▁well ▁as ▁recursive ▁types ▁appear ▁to ▁be ▁required ,. ▁As ▁strong ▁normal ization ▁does ▁not ▁hold ▁for ▁un rest rict ed ▁recursive ▁types ▁, ▁establish ing ▁term ination ▁of ▁programs ▁manip ulating ▁Scott - encoded ▁data ▁by ▁determ ining ▁well - ty ped ness ▁requires ▁the ▁type ▁system ▁provide ▁additional ▁restrictions ▁on ▁the ▁formation ▁of ▁recurs ively ▁typed ▁terms . ▁ ▁See ▁also ▁▁ ▁Church ▁encoding ▁ ▁System ▁F ▁ ▁L ambda ▁cube ▁ ▁Notes ▁ ▁References ▁Direct ly ▁Ref lect ive ▁Meta - Program ming ▁Tor ben ▁M og ensen ▁( 1 9 9 2 ). ▁E fficient ▁Self - Inter pret ation ▁in ▁L ambda ▁Calcul us . ▁ ▁Journal ▁of ▁Function al ▁Program ming . ▁ ▁Category : Lambda ▁calculus <0x0A> </s> ▁Gary ▁Str outs os ▁( born ▁July ▁ 1 9 ,