If you're thinking of programming your DSP in a high-level language instead of assembler, that high-level language will almost certainly be a C-type language. It's unlikely to be standard C, however, ...

C is also a curious creature, in that it’s a high-level language (these are the easy ones to understand), but with low-level elements (so-called because they are “close to the metal”).

The HLA (High Level Assembly) language was developed as a tool to help teach assembly language programming and machine organization to University students at the University of California, Riverside.