How to center an \inference* rule from mathpartir properly

Question

Continuing http://tex.stackexchange.com/a/656192, how to center the inference rules carrying names or side conditions in the scope of \[…\] in narrow columns? For example,

\documentclass[twocolumn]{article}
\pagestyle{empty}
\usepackage{mathpartir}
\begin{document}
\noindent A sentence introducing the first rule, which has a name and protrudes to the left:
\[%\quad\ \,\qquad%%% Ad-hoc, manually added space would mitigate the problem.
  \inferrule*[Left=RULE\_NAME,Right=.]%
  {\mathrm{an\ extensive\ list\ of\ antecedences}}%
  {\mathrm{an\ extensive\ consequent}}
\]%
\noindent A long, extensive, lengthy, and boring text explaining the first rule in detail.\par

\noindent A sentence introducing the second rule, which has a side condition and protrudes to the right:
\[
  \inferrule*[Right=a\ side\ condition.]%
  {\mathrm{an\ extensive\ list\ of\ antecedences}}%
  {\mathrm{an\ extensive\ consequent}}
  %\qquad\qquad\qquad\qquad%%% Ad-hoc, manually added space would mitigate the problem.
\]%
\noindent A long, extensive, lengthy, and boring text explaining the second rule in detail.

\noindent A sentence introducing the third rule, which has both a name and a side condition and is not centered:
\[
  \inferrule*[Left=RULE,Right=formula.]%
  {\mathrm{an\ extensive\ list\ of\ antecedences}}%
  {\mathrm{an\ extensive\ consequent}}
  %%% Here, some unknown amount of space should be added so that the rule is really centered.
\]%
\noindent A long, extensive, lengthy, and boring text explaining the third rule in detail.
\end{document}

compiled by latex or pdflatex yields an output in which the inference rules with names and conditions are not centered:

Sometimes they even stick out to the margins although there would be space if the whole rule together with the name and side condition were centered.

Any way to center the rule including the stuff to its left and right?

PS. It turned out that this semantics of Left and Right is by design, as explained in the documentation of mathpartir. Not a bug.

Answer 1

The inferences are centered, but without taking into account the side material.

You can use LEFT and RIGHT instead, but you need to explicitly tell that the material is in text mode.

\documentclass[twocolumn]{article}
\usepackage{mathpartir}

\makeatletter
% fix a long standing bug
\define@key {mprset}{style}[1]{\def\TirNameStyle{#1}}
\makeatother

\begin{document}

\noindent A sentence introducing the first rule, which has a name and protrudes to the left:
\[
  \inferrule*[Left=RULE\_NAME,Right=.]
  {\textrm{an extensive list of antecedences}}
  {\textrm{an extensive consequent}}
\]
A long, extensive, lengthy, and boring text explaining the first rule in detail.
\[
  \inferrule*[LEFT=\textrm{RULE\_NAME },Right=.]
  {\textrm{an extensive list of antecedences}}
  {\textrm{an extensive consequent}}
\]
A sentence introducing the third rule, which has both a name and a side 
condition and is not centered:
\[
  \inferrule*[LEFT=\textrm{RULE },RIGHT=\textrm{ formula.}]
  {\textrm{an extensive list of antecedences}}
  {\textrm{an extensive consequent}}
  %%% Here, some unknown amount of space should be added so that the rule is really centered.
\]
A long, extensive, lengthy, and boring text explaining the third rule in detail.

\end{document}

A different approach could be to define new keys Left* and Right* that do the same as Left and Right but not with zero width boxes.

\documentclass[twocolumn]{article}
\usepackage{mathpartir}

\makeatletter
% fix a long standing bug
\define@key {mprset}{style}[1]{\def\TirNameStyle{#1}}
% define new keys Right* and Left*
\define@key {mpr}{Left*}{\hbox{$\LeftTirName {#1}\;$}}
\define@key {mpr}{Right*}
  {\setbox \mpr@right \hbox {\unhbox \mpr@right $\;\RightTirName {#1}$}}
\makeatother

\begin{document}

\noindent A sentence introducing the first rule, which has a name and protrudes to the left:
\[
  \inferrule*[Left=RULE\_NAME,Right=.]
  {\textrm{an extensive list of antecedences}}
  {\textrm{an extensive consequent}}
\]
A long, extensive, lengthy, and boring text explaining the first rule in detail.
\[
  \inferrule*[Left*=RULE\_NAME,Right=.]
  {\textrm{an extensive list of antecedences}}
  {\textrm{an extensive consequent}}
\]
A sentence introducing the third rule, which has both a name and a side 
condition and is not centered:
\[
  \inferrule*[Left*=RULE,Right*=formula.]
  {\textrm{an extensive list of antecedences}}
  {\textrm{an extensive consequent}}
  %%% Here, some unknown amount of space should be added so that the rule is really centered.
\]
A long, extensive, lengthy, and boring text explaining the third rule in detail.

\end{document}

Answer 2

Not a bug: Left means “Put label l on the left of the rule […] but as if label l had zero width.” Similar for Right.

As for the minimal example at hand, left and right would do the job (but just for the minimal example):

\documentclass[twocolumn]{article}
\pagestyle{empty}
\usepackage{mathpartir}
\begin{document}
\noindent A sentence introducing the first rule, which has a name and protrudes to the left:
\[
  \inferrule*[left=RULE\_NAME,right=.]%
  {\mathrm{an\ extensive\ list\ of\ antecedences}}%
  {\mathrm{an\ extensive\ consequent}}
\]%
\noindent A long, extensive, lengthy, and boring text explaining the first rule in detail.\par

\noindent A sentence introducing the second rule, which has a side condition and protrudes to the right:
\[
  \inferrule*[right=a\ side\ condition.]%
  {\mathrm{an\ extensive\ list\ of\ antecedences}}%
  {\mathrm{an\ extensive\ consequent}}
  %\qquad\qquad\qquad\qquad%%% Ad-hoc, manually added space would mitigate the problem.
\]%
\noindent A long, extensive, lengthy, and boring text explaining the second rule in detail.

\noindent A sentence introducing the third rule, which has both a name and a side condition and is not centered:
\[
  \inferrule*[left=RULE,right=formula.]%
  {\mathrm{an\ extensive\ list\ of\ antecedences}}%
  {\mathrm{an\ extensive\ consequent}}
  %%% Here, some unknown amount of space should be added so that the rule is really centered.
\]%
\noindent A long, extensive, lengthy, and boring text explaining the third rule in detail.
\end{document}

Notice, however, that the text to the left is normal size (as in the OP), and the text to the right is in small capitals (as in the OP). Not sure whether this is intended.