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The problem was found when printing an expression like parser.suite("3*4").tolist(),
then modifying the string, and feeding the outcome back to Python. It is not a serious problem that this works for every possible Python code - it is just confusing to get a SyntaxError when there is no syntax error in the input.
BTW, I believe the parser is *not* recursive on the C stack; I could not find any sign of recursion inside Parser/parser.c. Most likely, the crash you got when increasing the parser stack size comes from Python/compile.c; the com_* functions are recursive on the C stack. It would be possible to remove the recursion here as well (using an explicit stack that lives on the heap); that would require a larger rewrite of compile.c, though.