Infix syntax with Unicode characters

Question

Tex (and XeLaTeX) use what I would call prefix syntax for user-defined macros. For example, the macro \newcommand{\identity}[1]{#1} is used with the variables prefixed by the macro: \identity{vars}. Some macros (is ^ a macro?) can also be used sandwiched between the variables: a^b. I would call that infix syntax.

How can I define my own infix macros using Unicode characters, say ♤ U+2660 or ⊗ or •? I want to be able to write {a+b}♤{c+d} and that should be interpreted as \mymacro{a+b}{c+d}.

This post says that new infix macros are impossible. What about defining ♤ as a different type of character. I do not know enough about changing the character classes (or types) but I know it is possible: the character @ works differently within a class file (.sty) than in a normal .tex file.

Answer 1

The question is tagged xetex which doesn't allow for infix operators. For future readers however an answer with LuaLaTeX. The idea is to write a line callback with a regular expression that substitutes an infix operator for a prefix macro.

Note that this approach is rather fragile as it does not allow for nested braces for example. This could be made more robust by actually processing tex tokens instead of a (problematic) catch-all regex, but just as a proof of concept.

\documentclass{article}
\usepackage{luacode}
\usepackage{fontspec}
\setmainfont{DejaVu Serif}
\begin{luacode}
    function translate(line)
        return string.gsub(line, "{(.*)}♤{(.*)}", "\\mymacro{%1}{%2}")
    end
    luatexbase.add_to_callback("process_input_buffer", translate, "infix")
\end{luacode}
\let\mymacro\frac
\begin{document}
See the following fraction: ${a+b}♤{c+d}$

Regular club: a ♤ b
\end{document}

Result:

Answer 2

What you call “infix macro” actually isn't. The behavior of ^ is hardwired in TeX (not the character itself, just any character with category code 7 would behave in exactly the same way); the same holds for _ (category code 8, actually).

There are “infix commands” such as \over or \overwithdelims, but they're not macros: they're unexpandable primitives.

The working of the above tokens is deeply based on TeX's math mode, where very different things happen with the input. Indeed, a math list is built by classifying the objects found as atoms of various types; an atom has three fields: the nucleus, the subscript and the superscript and each of these can itself be a math list.

How does \over work? First, we note that an “alone” { (one not used for delimiting arguments to macros) or \left start a new math list that will be later inserted in the outer math list.

Now, when TeX finds \over, it stores whatever it has found in the current math list (that might be the main math list), starts a new math list until coming to the matching } or \right (or the end of math mode) and then takes the two so built math lists and forms with them a Frac atom.

This cannot be reproduced via macros: it is a built in behavior (and one of the flaws of TeX, in my opinion).

How might your proposed ♤ operator determine what's the “left part” and “right part”? Something like \over can, because its behavior is built in in TeX which has specific processing rules for it.

---

Footnote. The peculiar syntax of \over is meant to reflect how fractions are read aloud. But what would be the meaning of “x plus one over x plus two”? Does it correspond to

\frac{x+1}{x+2}

or to

x+\frac{1}{x}+2

or to something else?

Answer 3

I write a package for this purpose. Currently the source code is at https://github.com/user202729/TeXlib (not yet published to CTAN); however unfortunately there's little to no documentation and as with most things implemented in TeX, it's slow.

\documentclass{article}
\usepackage{rewriterest}      % ← this package!
\usepackage{newunicodechar}   % pdflatex does not have spade suit

\newunicodechar{♤}{\ensuremath{\spadesuit}}

\begin{document}

\ExplSyntaxOn
\rewriterest:n {
    \regex_replace_all:nnN {
        (    \{ [^\{\}]* \}    )  % group 1: {...}, content does not contain any { or }
        ♤                         % the club
        (    \{ [^\{\}]* \}    )  % group 2: same as group 1
    } {
        \\frac   % we're doing textual substitution here, so no \c{frac}
            \1
            \2
    } \RWRbody
}
\ExplSyntaxOff

See the following fraction: ${a+b}♤{c+d}$

Regular club: a ♤ b
\end{document}

It works by capturing the content of the remaining part of the file, then do some regex substitution on it, then execute the result.