Write ‘3 4 + 5 *’ instead of ‘(3 + 4) × 5’ and you never need a parenthesis again. Reverse Polish Notation feeds a STACK: push numbers on; when an operator arrives, pop two, combine, push the result. It’s how HP calculators, PostScript, the JVM, and Forth actually compute. Slide to step through the evaluation and watch the stack rise and fall.
A stack machine evaluates Reverse Polish (postfix) Notation with no operator precedence and no parentheses: scan left to right, PUSH each operand, and on each operator POP the top two, apply it, and PUSH the result. ‘3 4 + 5 *’ → push 3, push 4, +→7, push 5, *→35. It is the execution model of Forth, PostScript, the Java Virtual Machine, and RPN calculators, and the target of the shunting-yard parse. A fail-loud self-check throws unless ‘3 4 + 5 *’ evaluates to 35 and ‘2 3 4 * +’ to 14. ◆ real computer architecture, node-verified.
Shown with a fixed expression and integer ops; the push/pop evaluation and precedence-free property are exact. Division-by-zero and malformed input are not handled in this demo.