▁the ▁original ▁non - generic ▁container ▁type ▁family ▁( list , ▁tree ▁etc .) ▁applied ▁to ▁unit . ▁ ▁One ▁of ▁the ▁main ▁motiv ations ▁for ▁introdu cing ▁the ▁notion ▁of ▁containers ▁is ▁to ▁support ▁generic ▁programming ▁in ▁a ▁depend ently ▁typed ▁setting . ▁ ▁C ategor ical ▁aspects ▁▁ ▁The ▁extension ▁of ▁a ▁container ▁is ▁an ▁end of un ctor . ▁It ▁takes ▁a ▁function ▁g ▁to ▁ ▁This ▁is ▁equivalent ▁to ▁the ▁familiar ▁map ▁g ▁in ▁the ▁case ▁of ▁lists , ▁and ▁does ▁something ▁similar ▁for ▁other ▁containers . ▁ ▁Index ed ▁containers ▁▁ ▁Index ed ▁containers ▁( also ▁known ▁as ▁dependent ▁polynomial ▁fun ctors ) ▁are ▁a ▁general isation ▁of ▁containers , ▁which ▁can ▁represent ▁a ▁wider ▁class ▁of ▁types , ▁such ▁as ▁vectors ▁( s ized ▁lists ). ▁ ▁The ▁element ▁type ▁( called ▁the ▁input ▁type ) ▁is ▁indexed ▁by ▁shape ▁and ▁position , ▁so ▁it ▁can ▁vary ▁by ▁shape ▁and ▁position , ▁and ▁the ▁extension ▁( called ▁the ▁output ▁type ) ▁is ▁also ▁indexed ▁by ▁shape . ▁ ▁See ▁also ▁▁ ▁Container ▁( abstract ▁data ▁type ) ▁ ▁Pol ynomial ▁fun ctor ▁( type ▁theory ) ▁ ▁References ▁ ▁External ▁links ▁Container ▁Types ▁blog ▁ ▁Category : Type ▁theory <0x0A> </s> ▁K atal in ▁K á ro ly i ▁is ▁a ▁Hung arian ▁mez zo - s op rano , ▁noted ▁for ▁singing ▁in ▁Bar o que ▁opera , ▁particularly ▁those ▁directed ▁by ▁William ▁Christ ie . ▁K á ro ly i ▁has ▁made ▁a ▁number ▁of