Almost all ARM processors are compatible... That's the reason the DS can run GBA but not original Gameboy (the original GB ran on a Zilog80 processor at 3mhz). The DS itself is Powered by an ARM9...
Actually: no.
The DS has two Arm CPUs one Arm9 @67mhz and one Arm7@33 mhz.
In DS games both cpus are used. In gba games the Arm7 gets locked at the 17mhz clockspeed of the original GBA and is running the games as it was the GBA itself.
However I don't know how compatible the different arm series are, the Arm7 is much slower than the Arm9 missing some nice instructions they added to the Arm9 series. But if the Arm9 was compatible with the Arm7 then I don't see the need for Nintendo to include the exact same cpu in the DS, that the GBA allready has