This immediately triggers the Liar's paradox [1].
Can a regular expression check its own validity?
How can you tell if it's lying?
Beware of bugs in the above code; I have only proved it correct, not tried it --Donald Knuth
Can a regular expression check its own validity?
How can you tell if it's lying?
Beware of bugs in the above code; I have only proved it correct, not tried it --Donald Knuth
FYI. I am just having some philosophical fun with GIGO.
Ultimately, computers are just instruments which amplify human intention, it's not the computers's job to be ultimate moral arbiter of our words.
Gödel's incompleteness theorem already tells us that a system cannot prove its own correctness.
The liar's knowledge is incomplete.
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
You can't codify moral judgments.
In the case at hand, correctness of the validator expression V clearly means "V determines well-formedness of any regular expressions" which is clearly not implied by "V is well-formed" (a much weaker statement because ".*" is well-formed but matches everything). Therefore, when applying V to itself, we only learn if a weak requirement for V's correctness holds.
Similar, perhaps, to validating whether a given number is a Gödel number of a well-formed logical statement rather than assessing the verity of the logical statement it encodes.
Also, I am not saying whether it is or is not possible to build such a regular expression. Rather, the question just doesn't tick the boxes of either, the Liar's Paradox, nor Gödel's Incompleteness result -- contrary to what was suggested. So you could still be right but for different reasons.
I am asking you to prove that. Constructively.
<syntax> ::= <rule> | <rule> <syntax>
<rule> ::= <opt-whitespace> "<" <rule-name> ">" <opt-whitespace> "::=" <opt-whitespace> <expression> <line-end>
<opt-whitespace> ::= " " <opt-whitespace> | ""
<expression> ::= <list> | <list> <opt-whitespace> "|" <opt-whitespace> <expression>
<line-end> ::= <opt-whitespace> <EOL> | <line-end> <line-end>
<list> ::= <term> | <term> <opt-whitespace> <list>
<term> ::= <literal> | "<" <rule-name> ">"
<literal> ::= '"' <text1> '"' | "'" <text2> "'"
<text1> ::= "" | <character1> <text1>
<text2> ::= '' | <character2> <text2>
<character> ::= <letter> | <digit> | <symbol>
<letter> ::= "A" | "B" | "C" | "D" | "E" | "F" | "G" | "H" | "I" | "J" | "K" | "L" | "M" | "N" | "O" | "P" | "Q" | "R" | "S" | "T" | "U" | "V" | "W" | "X" | "Y" | "Z" | "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"
<digit> ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
<symbol> ::= "|" | " " | "!" | "#" | "$" | "%" | "&" | "(" | ")" | "*" | "+" | "," | "-" | "." | "/" | ":" | ";" | ">" | "=" | "<" | "?" | "@" | "[" | "\" | "]" | "^" | "_" | "`" | "{" | "}" | "~"
<character1> ::= <character> | "'"
<character2> ::= <character> | '"'
<rule-name> ::= <letter> | <rule-name> <rule-char>
<rule-char> ::= <letter> | <digit> | "-"
The choice exists.
https://en.wikipedia.org/wiki/Total_functional_programming
Observe though that BNF is just a notation. Parsers for BNF are not implemented in BNF. Bison. Yacc.
All models are wrong - some are useful.