Object oriented programming, for example, doesn't let me have a variable hold half of one object and half of another or let the language derive the code that gave me that object at runtime, but object oriented + differentiable programming does. It's no less of a paradigm than logic, quantum, or probabilistic programming. If you want to, you can view differentiable programming as extending logic programming with a product and chain rule (+ some additional constraints) that allows (smooth, if you want it) interpolation between data and code.
That said, most discussion of differentiable programming is at the level of syntax sugar for reverse mode differentiation, so I can't blame you for that conclusion.
That said, most discussion of differentiable programming is at the level of syntax sugar for reverse mode differentiation, so I can't blame you for that conclusion.