Polish notation
[9] Heinrich Behmann, editor in 1924 of the article of Moses Schönfinkel,[10] already had the idea of eliminating parentheses in logic formulas.For instance, the expression that would be written in conventional infix notation as can be written in Polish notation as Assuming a given arity of all involved operators (here the "−" denotes the binary operation of subtraction, not the unary function of sign-change), any well-formed prefix representation is unambiguous, and brackets within the prefix expression are unnecessary.In the conventional infix notation, parentheses are required to override the standard precedence rules, since, referring to the above example, moving them or removing them changes the meaning and the result of the expression.When starting at the right, the pushing of tokens is performed similarly, just the evaluation is triggered by an operator, finding the appropriate number of operands that fits its arity already at the stacktop.Now the leftmost token of a valid prefix expression must be an operator, fitting to the number of operands in the stack, which again yields the result.As can be seen from the description, a push-down store with no capability of arbitrary stack inspection suffices to implement this parsing.Bocheński introduced a system of Polish notation that names all 16 binary connectives of classical propositional logic.Prefix notation has seen wide application in Lisp S-expressions, where the parentheses are required since the operators in the language are themselves data (first-class functions).