P′′

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: 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

(E.g., in bijective base-2, the number eight would be encoded as

, because 8 in base-2 is 1000, reverse the digits, and add one to each of them.)

At the beginning and end of the computation, the tape-head is on the

preceding the digit-string.