Even somewhat complicated arithmetic will become a constant if possible.
That's one of the simplest optimisations to implement even in a toy compiler, can be done at the asme time as parsing, and comes practically "for free" --- if all operands of an operator are constant, perform the operation and replace the operator and its operands with the constant result; and repeat this recursively.
Everything else is done based on pattern-matching the AST and performing the appropriate transformations.
Hm, last time I wrote a constant elimination I did so in the optimizer pass over the AST (as part of a lecture, we built a custom C frontend for LLVM and added some optimization passes). What you describe replaces e.g. "x = 3 + 4;", but you get that for free once your optimizer is able to replace more complicated things (e.g. "a = 3; b = 4; x = a + b;").
Also, your parser becomes more complicated; when writing a toy compiler, I think having a clean parser is worth a lot.
That's one of the simplest optimisations to implement even in a toy compiler, can be done at the asme time as parsing, and comes practically "for free" --- if all operands of an operator are constant, perform the operation and replace the operator and its operands with the constant result; and repeat this recursively.
Everything else is done based on pattern-matching the AST and performing the appropriate transformations.