In the grammar , no logical formula is a proper initial segment of another. A recursive parser reads one variable, or a negation followed by one formula, or a parenthesized pair of formulas separated by implication. Structural induction shows that this parser consumes precisely one whole formula. Its deterministic stopping position proves prefix-freeness. Consequently any formula substring in a valid formula coincides with the formula of a syntax subtree.

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  1. Unique readability theorem
  2. Syntax tree of a formula
  3. Abstract syntax tree
  4. Programming language
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