How to redefine infix (binary, relational) operator spacing so that precedence can be communicated visually?

Question

Assume we have an infix binary operator * with precedence level 0 (highest precedence), and another infix binary operator @, with precedence level 1 (lower than *). Also, assume we have two relational operators ~ (precedence level 2) and ~ (precedence level 3).

Note: the symbols I have chosen don't matter, I am trying to select arbitrary ones, because I might need to define arbitrary operators in my use case.

An expression involving these operators should look something like this:

a*b @ c*d ~ a*b || a*b ~ c @ d

The spaces in this expression match up with the precedence level (0 spaces for precedence level 0, and so on).

I'd like to do something similar in LaTeX by defining operators with a command that looks something like this:

\precedenceop{<relational or binary operator?>}{<precedence level>}{<symbol>}

I have learned today that:

• \medmuskip controls spacing for binary operators, \thickmuskip for relational operators

• I can use the xstring package to deal with conditional cases

So I envision that my command would look something like:

\usepackage{amsmath}
\usepackage{xstring}

\newcommand{\precedenceop}[3]{%
    \IfEqCase{#1}{%
        {rel}{<do stuff with \thickmuskip using #2 (the precedence level) and #3 (the symbol)>}%
        {bin}{<do stuff with \medmuskip using #2 (the precedence level) and #3 (the symbol)>}%
    }[\PackageError{tree}{Undefined option to tree: #1 (should be rel or bin)}{}]%
}

Another question I made attempted to go about the problem a different way, and had a suggested solution of manipulating the skips using something like:

\mspace{-\muexpr\medmuskip/2}
    <symbol, #3>
\mspace{-\muexpr\medmuskip/2}

But it would be nicer if the 2 in this solution could be replaced by some function of #2 (preferably, some type of multiplication, because then 0 would map to 0mu, 1 could map to 2mu, and 2 could map to 4mu, and so on).

Anyway, how should I make the pieces come together properly to do what I'd like?

Answer 1

\documentclass{article}




\newcommand\declareop[3]{%
\newcommand#1{%
\mskip\muexpr\medmuskip*#2\relax
{#3}%
\mskip\muexpr\medmuskip*#2\relax
}}

\declareop\mytimes{0}{*}
\declareop\myat{1}{@}
\declareop\mysim{2}{\sim}
\declareop\myor{3}{\|}

\begin{document}

\[
a\mytimes b
\myat
c\mytimes d
\mysim
a\mytimes b
\myor
a\mytimes b
\mysim
c\myat d
\]
\end{document}

this uses muskip expressions to multiply the base \medmuskip value by the precedence integer scaling the stretch and shrink by the same amount. The original symbol is surrounded by {} (as {#3} in the definition) so that it is converted to a mathord and loses any spacing rules that it would have by default, so just gets the space specified here.