Any Turing machine is a (computable) function; and https://www.sciencedirect.com/science/article/pii/S0885064X07000246 https://www.sciencedirect.com/science/art

Any Turing machine is a (computable) function; and https://www.sciencedirect.com/science/article/pii/S0885064X07000246 https://www.sciencedirect.com/science/article/pii/S0885064X0... shows any computable function can be computed by a GPAC. Therefore, if you take any universal Turing machine, there exists a GPAC that computes that Turing machine; and it is programmable because you can change the input it would give to the emulated Turing machine. Sure it's inefficient due to the two layers of emulation, but it shows it's possible.