I am actively opposed to this design for a first compiler. There is no need for a lexer with a recursive descent parser. Register allocation is also an unnecessary distraction. It is better for a first compiler to compile to a higher level language in which neither register assignment nor memory management are necessary.

Optimizing compilers are suboptimal in that they waste enormous amount of time optimizing code that can't or needn't be optimized and even where the optimizations are helpful, they are opaque and at risk of unexpectedly regressing both due to small changes at the source code level or changes in the compiler optimizer, both of which are quite insidious.

If instead of optimizing compilers, we had languages that allowed for seamless interop between low level and high level functions, then perhaps an llm becomes the optimizer (or you can invoke the compiler to optimize a specific function by source level rewrite). The benefit of this compared to a traditional optimizing compiler is that the optimization is done once per function and never repeated (until prompted) and the implementation is human readable and not buried in a binary. Moreover, and perhaps even more importantly, by not doing optimizations in the compiler, compilation times can be much faster, easily 100-1000x than state of the art optimizing compiler, while generating equivalent or even better runtime performance. As it has been said: premature optimization is the root of all evil.

The academic literature on register allocation is scary.

First is presented a linear time optimal algorithm for graph coloring then it is claimed better can be done by a O(N^2) algorithm that uses a heuristic.

I do believe the dragon book got caught with the emperor's new register allocator and the literature hasn't really recovered yet.

Looks like there is quite a bit of overlap with regards to the optimizing parts between these two courses. I guess it's switching from the dragon book to academic papers that makes it advanced.