CODEWITHSUNDEEP
xmlhaskelltypescomputer-sciencedefinition
jjj
jjj

Reputation: 1109

Why use "or" instead of "xor" in definitions?

This might be a trivial question but I really can't find the answer anywhere. There is a convention in computer science which I find peculiar.

In haskell datatypes can be defined like this:

data Bool = False | True

In xml qualified names are defined like this:

QName   ::=   PrefixedName | UnprefixedName

There are probably more similar examples but this should suffice.

Usually it is well understood that | (pipe or bar) should be read as or. But this seems strange. A or B is true also when both A and B are true. While it makes sense in the first example (there is a possibility that something is True and False at the same time, but we implicitly assume the law of non-contradiction), it doesn't in the second: something is either a PrefixedName or an UnprefixedName it can't be both.

So why is this often put like this? Why not use exclusive or? Are there any non-conventional reasons?

Upvotes: 1

Views: 587

Answers (3)

chepner
chepner

Reputation: 532003

| has a long history of being used to separate items in a list of mutually exclusive choices:

  1. Regular expressions: a* | b* means a string can either be 0 or more as or 0 or more bs, but not both.

  2. Backus-Naur form for representing context-free grammars:

    Expr ::= Term | Expr AddOp Term

    in which an expression can either be a single term, or another expression combined with a term with an addition operator. (It cannot be both simultaneously.)

  3. Usage messages for command-line programs:

    git branch (-d | -D) [-r] <branchname>...

    Here the git branch command can take either the -d or the -D option, but not both in the same invocation.

The data statement in Haskell continues this tradition; it is unrelated to the use of | as a logical or bit-wise operator.

(If anything, it is possible that the use of | for bitwise OR was inspired by Backus-Naur form, in which case you could be asking why | is used for OR instead of XOR.)

Upvotes: 2

leftaroundabout
leftaroundabout

Reputation: 120741

This data X = A | B notation should not really be understood as a logical OR at all (though that corresponds quite well to the intuitive meaning). What it really means is that X is a sum type of A and B, i.e. a coproduct. Now, the product operation on booleans is in fact AND, and so the dual would quite naturally be OR.

Though then again, the sum operation on a vector space of booleans is actually XOR so we're turning circles a bit...

I just wouldn't read too much into this. | is simply a symbol; in C-like languages it happens to also mean bitwise OR, but the actual logical OR is generally denoted differently, be it || or ∨.

Upvotes: 8

Bartvbl
Bartvbl

Reputation: 2928

I think the meaning of "or" here is in a literal sense as opposed to a mathematical sense. Using the term "or" means that the value can have one value, or another. It is not an operator which aims to determine a truth value.

While it may not be entirely logical to use an "or" operator sign for this, it does a good enough job at getting the point across for a reader. This clarity is ultimately the thing a language is striving for. As long as a greater proportion of readers is capable of interpreting it as a "literal" usage as opposed to a "mathematical" operator usage, using or in a literal sense means you, as a language, are doing a better job at getting your point across, making the method superior to using something such as XOR.

Upvotes: 1

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