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: non-transitory computer readable memory; one or more hardware processors coupled to the non-transitory memory and configured to read instructions from the non-transitory memory to cause the numerical controller to perform operations comprising: outputting a second machining program obtained by applying coordinate system conversion processing to the first machining program; and outputting instruction data for specifying operation of the driving axes based on the second machining program, wherein the coordinate system conversion processing involves interchanging of an instruction based on a right-handed coordinate system and an instruction based on a left-handed coordinate system.