Didier Rémy(Version 1.2.0, last modified 20/12/2005) 
Abstract: This package provides macros for displaying lists of formulas that are typeset in mixed horizontal and vertical modes. The package is twofolded.The first part is an environment
mathpar
that generalizes the math display mode to allow several formulas on the same line, and several lines in the same display. The arrangement of the sequence of formulas into lines is automatic depending on the line width and on a minimum interformula space and line width alike words in a paragraphs (in centerline mode). A typical application is displaying a set of type inference rules.The second par is a macro
inferrule
to typeset inference rules themselves. Here again, both premises and conclusions are presented as list of formulas that should be displayed in almost the same way, except that the width is not fixed in advance; and the inference rule should use no more width than necessary so that other inference rules are given a chance to appear on the same line.Although
mathpar
andinferrule
look similar in their specification, and are often used in combination, they are in fact completely different in their implementations.
Mathpartir is Copyright (C) 2001, 2002 INRIA. Mathpartir has been developed by Didier Rémy. Mathpartir is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. See the GNU General Public License for more details (http://pauillac.inria.fr/~remy/license/GPL). Mathpartir is distributed in the hope that it will be useful, but without any warranty.
The mathpar environment is a “paragraph mode for formulas”. It allows to typeset long list of formulas putting as many as possible on the same line:

Formulas are separated by \and
(or equivalently by a blank line).
To enforce a vertical break it sufficies to replace \and
by
\\
.
The implementation of mathpar
entirely relies on the paragraph mode
for text. It starts a new paragraph, and a math formula within a paragraph,
after adjusting the spacing and penalties for breaks. Then, it simply binds
\and
to something like \goodbreak
.
The inferrule macro is designed to typeset inference rules. It should only^{1} be used in math mode (or display math mode).
The basic use of the rule is
\inferrule {one \\ two \\ three \\ or \\ more \\ premisses} {and \\ any \\ number \\ of \\ conclusions \\ as \\ well}
This is the rendering on a large page

However, the same formula on a narrower page will automatically be typsetted like that:

An inference rule is mainly composed of a premisse and a conclusion.
The premisse and the conclusions are both list of formulas where the
elements are separated by \\
.
Note the dissymetry between typesetting of the premisses and of conclusions where lines closer to the center are fit first.
A newline can be forced by adding an empty line \\\\
\inferrule
{aa \\\\ bb}
{dd \\ ee \\ ff} 

Single rules are the default mode. Rules are aligned on their fraction bar, as illustrated below:


If the premise or the conclusion is empty, then the fraction bar is not typeset and the premise or the conclusion is centered:

Use use { }
instead of {}
to get an axiom for instance:

The macro \inferrule
acceps a label as optional argument, which will
be typeset on the top left corner of the rule:
\inferrule [yop]
{aa \\ bb}
{cc} 

See section 3 for changing typesetting of labels. A label can also be placed next to the rule directly, since the rule is centered:
\inferrule
{aa \\ bb}
{cc}
\quad (\textsc {Yop}) 

By default, lines are centerred in inference rules.
However, this can be changed by either \mprset{flushleft}
or \mprset{center}
. For instance,
$$\mprset{flushleft}
\inferrule
{a \\ bbb \\\\ ccc \\ dd}
{dd \\ ee \\ ff}$$ 

Note that lines are aligned independently in the premisse and the conclusion, which are both themselves centered. In particular, left alignment will not affect a singleline premisse or conclusion.
One may wish to change use rules for rewriting rule or implications, etc. There is a generic way of definition new rules by providing three parts: a tail, a body, and a head. The rule will then be built by joining all three components in this order and filling the body with leaders to extend as much as necessary. Here are examples
$$\mprset{fraction={===}}
\inferrule {a \\ bbb} {cc}$$ 
 
$$\mprset
{fraction={\models=\Rightarrow}}
\inferrule {a \\ bbb} {cc}$$ 

The height and depth of the body are used to adjust vertical space. One, may “smash” the body to reduce the vertical space
$$\mprset
{fraction={%
{\scriptstyle\vdash}%
{\smash}%
{\rightarrow\!\!}%
}}
\inferrule {a \\ bbb} {cc}\,\,$$ 
 
$$\mprset {fraction={\cdot\cdots\cdot}}
\inferrule {a \\ bbb} {cc}$$ 

Since vertical skip does not take header and footer into account, which is usually better but sometimes odd, this can be adjusted explicitly:
$$\mprset
{fraction={=/},
fractionaboveskip=0.6ex,
fractionbelowskip=0.4ex}
\inferrule
{a \\ bbb_{\downarrow}}
{cc^{\T\uparrow}}$$ 

Finally, it is also possible to provide its own definition of fraction by
\def \Over #1#2{\hbox{$#1 \over #2$}}
$$\mprset{myfraction=\Over}
\inferrule {a \\ bbb} {cc}$$ 

(default value is 2em).
$$\mprset {sep=6em} \inferrule {a \\ bbb} {cc}$$
a bbb cc
Although you probably do not want to do that, you may still use tabular or minipages inside inference rules, but between braces, as follows:

To help writing cascades of rules forming a derivation tree, inference rules can also be aligned on their bottom line. For this, we use the starversion:

The star version can also take an optional argument,
but with a different semantics. The optional argument is parsed by the
keyval
package, so as to offer a set of recordlike options:

Here is an example of a complex derivation:

and its code
The main macro in the implementation of inference rules is the one that
either premises and conclusions. The macros uses two boxregisters one
hbox
for typesetting each line and one vbox
for collecting
lines. The premise appears as a list with
\\
as separator. Each element is considered in turn typeset in a
hbox
in display math mode. Its width is compare to the space left on
the current line. If the box would not fit, the current horizontal line is
transferred to the vertical box and emptied. Then, the current formula can
safely be added to the horizontal line (if it does not fit, nothing can be
done). When moved to the vertical list, lines are aligned on their center
(as if their leftpart was a left overlapped). At the end the vbox is
readjusted on the right.
This description works for conclusions. For premises, the elements must be processes in reverse order and the vertical list is simply built upside down.
The package also defines \infer
as a shortcut for \inferrule
but only if it is not previously defined.
The package uses \TirName
and \RefTirName
to typeset labels,
which can safely be redefined by the user. The former is used for defining
occurrences (ie. in rule \inferrule
) while the latter is used
for referencing (ie. in the starversion).
The vertical space in mathpar
is adjusted by
\MathparLineskip
. To restore the normal paragraph parameters in mathpar
mode (for instance for some inner paragraph), use the command
\MathparNormalpar
.
The environment uses \MathparBindings
to
rebind \\
, and
, and \par
. You can redefine thus command
to change the default bindings or add your own.
See the source of this documentation —the file mathpartir.tex
—
for full examples.
The package also redefines \hva
to do nothing in mathpar
environment and nor in inference rules.
In HeVeA, \and
will always produce a vertical break in mathpar
environment; to obtain a horizontal break, use \hva \and
instead.
Conversely, \\
will always produce a horizontal break in type
inference rules; to obtain a vertical break, use \hva \\
instead.
For instance, by default the following code,
which typesets in T_{E}X as follows,


would appear as follows with the compatible H_{E}V_{E}A mode:


To obtain (almost) the same rendering as in T_{E}X, it could be typed as
Actually, it would be typeset and follows with the compatible H_{E}V_{E}A mode:


This document was translated from L^{A}T_{E}X by H_{E}V_{E}A.