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Paradigm | Imperative, structured |
---|---|

Designed by | Corrado Böhm |

First appeared | 1964 |

Typing discipline | untyped |

Dialects | |

Brainfuck | |

Influenced | |

Brainfuck |

**P′′** (P double prime^{[1]}) is a primitive computer programming language created by Corrado Böhm^{[2]}^{[3]} in 1964 to describe a family of Turing machines.

(hereinafter written **P′′**) is formally defined as a set of words on the four-instruction alphabet , as follows:

- and are words in P′′.
- If and are words in P′′, then is a word in P′′.
- If is a word in P′′, then is a word in P′′.
- Only words derivable from the previous three rules are words in P′′.

- is the tape-alphabet of a Turing machine with left-infinite tape, being the
*blank*symbol, equivalent to . - All instructions in P′′ are permutations of the set of all possible tape configurations; that is, all possible configurations of both the contents of the tape and the position of the tape-head.
- is a predicate saying that the current symbol is not . It is not an instruction and is not used in programs, but is instead used to help define the language.
- means move the tape-head rightward one cell (if possible).
- means replace the current symbol with , and then move the tape-head leftward one cell.
- means the function composition . In other words, the instruction is performed before .
- means iterate in a while loop, with the condition .

- P′′ was the first "GOTO-less" imperative structured programming language to be proven Turing-complete
^{[2]}^{[3]} - The Brainfuck language (apart from its I/O commands) is a minor informal variation of P′′. Böhm gives explicit P′′ programs for each of a set of basic functions sufficient to compute any computable function, using only , and the four words where with denoting the th iterate of , and . These are the equivalents of the six respective Brainfuck commands [, ], +, -, <, >. Note that since , incrementing the current symbol times will wrap around so that the result is to "decrement" the symbol in the current cell by one ().

Böhm^{[2]} gives the following program to compute the predecessor (*x*-1) of an integer *x* > 0:

which translates directly to the equivalent Brainfuck program:

```
>[>]<[−[<[<]]−<]>+
```

The program expects an integer to be represented in *bijective base-k* notation, with encoding the digits respectively, and to have before and after the digit-string. (E.g., in bijective base-2, the number eight would be encoded as , because 8 in bijective base-2 is 112.) At the beginning and end of the computation, the tape-head is on the preceding the digit-string.

**^**https://github.com/Pbtflakes/pdbl- ^
^{a}^{b}^{c}Böhm, C.: "On a family of Turing machines and the related programming language", ICC Bull. 3, 185-194, July 1964. - ^
^{a}^{b}Böhm, C. and Jacopini, G.: "Flow diagrams, Turing machines and languages with only two formation rules", CACM 9(5), 1966. (Note: This is the most-cited paper on the structured program theorem.)

: Demonstrating the iterative 99 Bottles of Beer song construed in 337568**P′′**Online interpreter**P′′**instructions.

**By:** Wikipedia.org

**Edited:** 2021-06-18 18:16:01

**Source:** Wikipedia.org