Rotating symbols in LaTeX

Linear logic uses an unusual symbol, an ampersand rotated 180 degrees, for multiplicative disjunction.

The symbol is U+214B in Unicode.

I was looking into how to produce this character in LaTeX when I found that the package `cmll` has two commands that produce this character, one semantic and one descriptive: `\parr` and `\invamp` [1].

This got me to wondering how you might create a symbol like the one above if there wasn’t one built into a package. You can do that by using the `graphicx` package and the `\rotatebox` command. Here’s how you could roll your own par operator:

`    \rotatebox[origin=c]{180}{\&}`

There’s a backslash in front of the & because it’s a special character in LaTeX. If you wanted to rotate a K, for example, there would be no need for a backslash.

The `\rotatebox` command can rotate any number of degrees, and so you could rotate an ampersand 30° with

`    \rotatebox[origin=c]{30}{\&}`

to produce a tilted ampersand.

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[1] The name `\parr` comes from the fact that the operator is sometimes pronounced “par” in linear logic. (It’s not simply `\par` because LaTeX already has a command `\par` for inserting a paragraph break.)

The name `\invamp` is short for “inverse ampersand.” Note however that the symbol is not an inverted ampersand in the sense of being a reflection; it is an ampersand rotated 180°.