Stack-oriented programming

Stack-oriented programming is a programming paradigm that relies on one or more stacks to manipulate data and/or pass parameters. Programming constructs in other programming languages need to be modified for use in a stack-oriented system. Most stack-oriented languages operate in postfix or Reverse Polish notation: arguments or parameters for a command are listed before that command. For example, postfix notation would be written 2, 3, multiply instead of multiply, 2, 3 (prefix or Polish notation), or 2 multiply 3 (infix notation). The programming languages Forth, Factor, RPL, PostScript, BibTeX style design language and many assembly languages fit this paradigm.

Stack-based algorithms manipulate data by popping data from and pushing data to the stack. Operators govern how the stack manipulates data. To emphasize the effect of a statement, a comment is often used showing the top of the stack before and after the statement; this is known as the stack effect diagram. Some stack-oriented languages may use multiple stacks for different purposes; for example, PostScript uses separate stacks for variables, dictionaries, procedures, some typical procedures, and control flow statements. Analysis of the language model allows expressions and programs to be interpreted simply.

PostScript is an example of a postfix stack-based language. An expression example in this language is 2 3 mul('mul' being the command for the multiplication operation). Calculating the expression involves understanding how stack orientation works.

Stack orientation can be presented as the following conveyor belt analogy. At the end of a conveyor belt (the input), plates marked 2, 3, and mul are placed in sequence. The plate at the end of the conveyor (2) can be taken, however other plates cannot be accessed until the plate at the end is removed. The plates can only be stored in a stack, and can only be added or removed from atop the stack, not from the middle or bottom. Blank plates (and a marker) can be supplied and plates can be permanently discarded.

Take plate 2 and put it on the stack, then take plate 3 and put it on the stack. Next, take the mul plate. This is an instruction to perform. Then, take the top two plates off the stack, multiply their labels (2 and 3), and write the result (6) on a new plate. Discard the two old plates (2 and 3) and the plate mul, and put the new plate on the stack. With no more plates remaining on the conveyor, the result of the calculation (6) is shown on the plate atop the stack.

This is a very simple calculation. What if a more complex calculation is needed, such as (2 + 3) × 11 + 1? If it is first written in postfix form, that is, 2 3 add 11 mul 1 add, the calculation can be performed in exactly the same manner and achieve the correct result. The steps of the calculation are shown in the table below. Each column shows an input element (the plate at the end of the conveyor), and the contents of the stack after processing that input.

After processing all the input, the stack contains 56, which is the answer.

From this, the following can be concluded: a stack-based programming language has only one way to handle data, by taking one piece of data from atop the stack, termed popping, and putting data back atop the stack, termed pushing. Any expression that can be written conventionally, or in another programming language, can be written in postfix (or prefix) form and thus be amenable to being interpreted by a stack-oriented language.