@"Expecting vpa() to return anything other than sym (or sometimes, symfun) is a substantial misunderstanding of the Symbolic Toolbox...."
I see, the "vpa" is actually a factory function, generating the instances of "sym" class. I stand corrected, "sym.diff" is the full name of the function.
However, these technical details of SMT implementation have nothing to do with the point we are discussing. We discuss the semantics of the functions in SMT. In other words, what the SMT functions do (or should do) with the input arguments. The type they return is just a technicality in this context.
The SMT does much more than pure symbolic operations. Many functions in SMT apply numerical algorithms (using extended precision) to compute the output results. For example, take a look on EIG:
Same for SVD, or other cases where result cannot be computed analytically or arbitrary-precision plays an important role.
(Of course the functions still return result of type "sym", but the result itself was computed numerically. I hope this distinction is clear.)
This is exactly the case with "diff". Extended precision is important for computing numerical derivatives/differences accurately, since it is a highly ill-conditioned problem (e.g. same as eigenvalues). Therefore it is quite natural to expect the "sym.diff" to have this functionality.
Besides, the original meaning of "diff" stands the same since the MATLAB inception - computing differences and numeric derivatives. It is not clear why SMT developers decided to change its semantics in SMT. They could've just introduced the new function for symbolic derivatives, as @Paul said. Ambiguity would be avoided.
Here is simple example for illustration:
1.752670342542888271728211766393
0.8398632587280311835223044391663
-0.18794383321803341008176836388774
Similarly, I expect the "sym.diff" to provide the analogous functionality of built-in "diff" and to work as "sym.eig" above - compute result numerically using extended precision. But instead we see:
