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One common way for a compiler for a high-level language to generate machine language instructions to evaluate arithmetic or boolean expressions, involves a conversion of the expression from infix to postfix.

One common way for a compiler for a high-level language to generate machine language instructions to evaluate arithmetic or Boolean expressions, involves a conversion of the expression from infix to postfix. Typically, the compiler does no require a fully parenthesized expression as input, but instead has a table of priorities which indicate the order in which operators will be applied within a pair of parentheses (the operator with highest priority is evaluated first). For example, consider a compiler with the following set of priorities: Operator Priority unary, unary and or Then the expression: will be evaluated as: A (B C)) (DE)) (A C) and its postfix form would be