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°.