And once you understand the basics, you can move onto something more interesting like this self-compiling compiler:
http://homepage.ntlworld.com/edmund.grimley-evans/cc500/
This one is fun too, since it contains both a bytecode compiler and its interpreter VM:
https://github.com/rswier/c4
(Previously discussed on HN at https://news.ycombinator.com/item?id=8576068 and https://news.ycombinator.com/item?id=8558822 )
I think a Lisp compiler isn't quite as interesting for beginners as something that handles the more usual syntax with precedence etc., since it's so trivial that it leaves the "how does a 'real' compiler parse" question unanswered.
In that respect, I would suggest beginning with a simple recursive-descent parser that can handle the usual maths expressions - then extending it to e.g. all the operators in a C-like language is not a
Read the rest
huge leap (table-driven precedence-climbing can be derived from recursive descent and makes this much easier), and it also leads to the opportunity for a compiler that can parse and compile itself - unless you are also writing the compiler in Lisp.
The AST stuff can come later; with expressions, the parser can perform evaluation as it parses, which gives the opportunity to write a calculator. Generating an AST is just replacement of evaluation with creation of tree nodes.
IMHO "it can compile itself" (as well as other non-trivial programs) is a good goal, and really makes people pay attention because it dispels the notion that compilers are somehow "magic".