The character "|" has been introduced in computers in the language NPL at IBM in December 1964 as a notation for bitwise OR, replacing ".OR.", which had been used by IBM in its previous programming language, "FORTRAN IV" (OR was between dots to distinguish it from identifiers, marking it as an operator).

The next year the experimental NPL (New Programming Language) has been rebranded as PL/I and it has become a commercial product of IBM.

Following PL/I, other programming languages have begun to use "&" and "|" for AND and OR, including the B language, the predecessor of C.

The pipe and its notation have been introduced in the Third Edition of UNIX (based on a proposal made by M. D. McIlroy), in 1972, so after the language B had been used for a few years and before the development of C. The oldest documentation about pipes that I have seen is in "UNIX Programmer's Manual Third Edition" from February 1973.

Before NPL, the vertical bar had already been used in the Backus-Naur notation introduced in the report about ALGOL 60 as a separator between alternatives in the description of the grammar of the language, so with a meaning somewhat similar to OR.

>as a notation for bitwise OR, replacing ".OR.", which had been used by IBM in its previous programming language, "FORTRAN IV".

Untrue: ".OR." in FORTRAN meant ordinary OR, not bitwise OR. I don't remember ever seeing bitwise OR or AND or XOR in FORTRAN IV.

That is right, but I did not want to provide too many details that did not belong to the topic.

FORTRAN IV did not have bit strings, it had only Boolean values ("LOGICAL").

Therefore all the logical operators could be applied only to Boolean operands, giving a Boolean result.

The same was true for all earlier high-level programming languages.

The language NPL, renamed PL/I in 1965, has been the first high-level programming language that has introduced bit string values, so the AND, OR and NOT operators could operate on bit strings, not only on single Boolean values.

If PL/I would have remained restricted to the smaller character set accepted by FORTRAN IV in source texts, they would have retained the FORTRAN IV operators ".NOT.", ".AND.", ".OR.", extending their meaning as bit string operators.

However IBM has decided to extend the character set, which has allowed the use of dedicated symbols for the logical operators and also for other operators that previously had to use keywords, like the relational operators, and also for new operators introduced by PL/I, like the concatenation operator.

I think the math usage was first. i.e. absolute value: |x|

The language APL\360 of IBM (August 1968) and the other APL dialects that have followed it have used a single "|" as a monadic prefix operator that computes the absolute value and also as a dyadic infix operator that computes the remainder of the division (but with the operand order reversed in comparison with the language C, which is usually much more convenient, especially in APL, where this order avoids the need for parentheses in most cases).

Not to get all semiotic about it, but |x| notation is a pair of vertical lines. I'm sure that someone has written a calculator program where two 0x7D characters bracketing a symbol means absolute value, but if I've ever seen it, I can't recall.

Although 0x7D is overly specific, since if a sibling comment is correct (I have no reason to think otherwise), | for bitwise OR originates in PL/1, where it would have been encoded in EBCDIC, which codes it as 0x4F.

I'm not really disagreeing with you, the |abs| notation is quite a bit older than computers, just musing on what should count as the first use of "|". I'm inclined to say that it should go to the first use of an encoding of "|", not to the similarly-appearing pen and paper notation, and definitely not the first use of ASCII "|" aka 0x7D in a programming language. But I don't think there's a right answer here, it's a matter of taste.

Because one could argue back to the Roman numeral I, if one were determined to do so: when written sans serif, it's just a vertical line, after all. Somehow, abs notation and "first use of an encoded vertical bar" both seem reasonable, while the Roman numeral and specifically-ASCII don't, but I doubt I can unpack that intuition in any detail.