Anintroductiontodependenttypes,demonstratingthemostbeautifulaspects,onestepatatime.Aprogram'stypedescribesitsbehavior.Dependenttypesareafirst-classpartofalanguage,andaremuchmorepowerfulthanotherkindsoftypes;usingjustonelanguagefortypesandprogramsallowsprogramdescriptionstobea