1. A numerical controller that controls a machine tool having a plurality of driving axes based on a first machining program, the numerical controller comprising: a coordinate system conversion unit that outputs a second machining program obtained by applying coordinate system conversion processing to the first machining program; and an instruction analysis unit that outputs instruction data for specifying operation of the driving axes based on the second machining program, wherein the coordinate system conversion processing applied by the coordinate system conversion unit involves interchanging of an instruction based on a right-handed coordinate system and an instruction based on a left-handed coordinate system.