I wrote a sample precedence-climbing expression parser. I wrote it for Patrick Dubroy’s excellent small website for small programs, which uses docco to pull out code comments into a side pane next to the code and make everything look pretty.
My implementation is a tokenizer and parser for simple math expressions and function calls in under 200 SLOC. It builds an “AST” in the form of nested Python lists that kind of look like S-expressions (but you could also make classes for AST nodes if you like).
>>> tokenize("1+2*3")
[1, '+', 2, '*', 3]
>>> parse(_)
['+', 1, ['*', 2, 3]]
>>>
It also comes with tests. It works standalone or can be used as the “simple expression parser” component of a larger recursive descent parser (that handles function definitions, variable binding, etc).
See also Parsing to IR and lvalues which takes this approach but builds an SSA based IR instead of an AST.