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I've looked carefully at both the parser and the lexer. It's a long
while since I've used either of these tools, but I can find no reference
to anything that does arithmetic. The only instance of plus signs that I
can find are in the regular expressions and in the C code. There appears
to be no provision to recognise a "$((" - the parser seems to expect
only a variable name (with or without enclosing braces). "$[" is used
for arrays in bash - in any case the lexer doesn't recognise it.