[mhh__]

I can't think of any reason to contradict that as a abstract description of a compiler, although the standard - Practical? - definition of a compiler is probably the more useful of the two.

Graph rewriting is probably a little bit niche, e.g. AFAIK most compilers don't describe what they do as graph rewriting. Perhaps because many compilers do a lot of their work on linear data structures (which are part of a larger graph) like Basic Blocks.