Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!uunet!kddlab!icot32!nttlab!hirose!peach!tatsuta
From: tatsuta@sato.riec.tohoku.ac.jp (Makoto Tatsuta)
Newsgroups: comp.text.tex
Subject: proof figure macros
Message-ID: <TATSUTA.90Dec20184306@jupiter.sato.riec.tohoku.ac.jp>
Date: 20 Dec 90 09:43:06 GMT
Sender: news@peach.riec.tohoku.ac.jp
Distribution: comp
Organization: Research Institute of Electrical Communication, Tohoku University
Lines: 430

I have made LaTeX macros to write proof figures often used in
Mathematical Logic easily and beautifully.

proof.sty	definitions of the macros
proofeg.tex	examples

The usage is commented in the head of proof.sty. The output of
proofeg.tex will also explain how to use the macros.

I have been using these macros since I wrote them 3 years ago.  Many
people told me that they were very convenient and it encouraged me to
post them here.

Remark that a large proof figure often requires bigLaTeX instead of
usual LaTeX because of its capacity.

			Makoto Tatsuta
			(tatsuta@riec.tohoku.ac.jp)
			Tohoku University

------------------------------ CUT HERE ------------------------------
#! /bin/sh
# This is a shell archive, meaning:
# 1. Remove everything above the #! /bin/sh line.
# 2. Save the resulting text in a file.
# 3. Execute the file with /bin/sh (not csh) to create:
#	proof.sty
#	proofeg.tex
# This archive created: Sat Oct 13 15:43:27 1990
export PATH; PATH=/bin:/usr/bin:$PATH
if test -f 'proof.sty'
then
	echo shar: "will not over-write existing file 'proof.sty'"
else
cat << \SHAR_EOF > 'proof.sty'
%	proof.sty	(Proof Figure Macros)
%
% 	version 1.0
%	October 13, 1990
% 	Copyright (C) 1990 Makoto Tatsuta (tatsuta@riec.tohoku.ac.jp)
% 
% This program is free software; you can redistribute it or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either versions 1, or (at your option)
% any later version.
% 
% This program is distributed in the hope that it will be useful
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
%	Usage:
%		In \documentstyle, specify an optional style `proof', say,
%			\documentstyle[proof]{article}.
%
%	The following macros are available:
%
%	In all the following macros, all the arguments such as
%	<Lowers> and <Uppers> are processed in math mode.
%
%	\infer<Lower><Uppers>
%		draws an inference.
%
%		Use & in <Uppers> to delimit upper formulae.
%		<Uppers> consists more than 0 formulae.
%
%		\infer returns \hbox{ ... } or \vbox{ ... } and
%		sets \@LeftOffset and \@RightOffset globally.
%
%	\infer[<Label>]<Lower><Uppers>
%		draws an inference labeled with <Label>.
%
%	\infer*<Lower><Uppers>
%		draws a many step deduction.
%
%	\infer*[<Label>]<Lower><Uppers>
%		draws a many step deduction labeled with <Label>.
%
%	\deduce<Lower><Uppers>
%		draws an inference without a rule.
%
%	\deduce[<Proof>]<Lower><Uppers>
%		draws a many step deduction with a proof name.
%
%	Example:
%		If you want to write
%       	       	    B C
%		 	   -----
%		       A     D
%		      ----------
%			  E
%	use
%		\infer{E}{
%			A
%			&
%			\infer{D}{B & C}
%		}
%

%	Style Parameters

\newdimen\inferLineSkip		\inferLineSkip=2pt
\newdimen\inferLabelSkip	\inferLabelSkip=5pt
\def\inferTabSkip{\quad}

%	Variables

\newdimen\@LeftOffset	% global
\newdimen\@RightOffset	% global
\newdimen\@SavedLeftOffset	% safe from users

\newdimen\UpperWidth
\newdimen\LowerWidth
\newdimen\LowerHeight
\newdimen\UpperLeftOffset
\newdimen\UpperRightOffset
\newdimen\UpperCenter
\newdimen\LowerCenter
\newdimen\UpperAdjust
\newdimen\RuleAdjust
\newdimen\LowerAdjust
\newdimen\RuleWidth
\newdimen\HLabelAdjust
\newdimen\VLabelAdjust
\newdimen\WidthAdjust

\newbox\@UpperPart
\newbox\@LowerPart
\newbox\@LabelPart
\newbox\ResultBox

%	Flags

\newif\if@inferRule	% whether \@infer draws a rule.
\newif\if@ReturnLeftOffset	% whether \@infer returns \@LeftOffset.
\newif\if@MathSaved	% whether inner math mode where \infer or
			% \deduce appears.

%	Special Fonts

\def\DeduceSym{\vtop{\baselineskip4\p@ \lineskiplimit\z@
    \vbox{\hbox{.}\hbox{.}\hbox{.}}\hbox{.}}}

%	Math Save Macros
%
%	\@SaveMath is called in the very begining of toplevel macros
%	which are \infer and \deduce.
%	\@RestoreMath is called in the very last before toplevel macros end.
%	Remark \infer and \deduce ends calling \@infer.

\def\@SaveMath{\@MathSavedfalse \ifmmode \ifinner
	\relax $\relax \@MathSavedtrue \fi\fi }

\def\@RestoreMath{\if@MathSaved \relax $\relax\fi }

%	Macros

\def\@ifEmpty#1#2#3{\def\@tempa{\@empty}\def\@tempb{#1}\relax
	\ifx \@tempa \@tempb #2\else #3\fi }

\def\infer{\@SaveMath \@ifnextchar *{\@inferSteps}{\@inferOneStep}}

\def\@inferOneStep{\@inferRuletrue
	\@ifnextchar [{\@infer}{\@infer[\@empty]}}

\def\@inferSteps*{\@ifnextchar [{\@@inferSteps}{\@@inferSteps[\@empty]}}

\def\@@inferSteps[#1]{\@deduce{#1}[\DeduceSym]}

\def\deduce{\@SaveMath \@ifnextchar [{\@deduce{\@empty}}
	{\@inferRulefalse \@infer[\@empty]}}

%	\@deduce<Proof Label>[<Proof>]<Lower><Uppers>

\def\@deduce#1[#2]#3#4{\@inferRulefalse
	\@infer[\@empty]{#3}{\@SaveMath \@infer[{#1}]{#2}{#4}}}

%	\@infer[<Label>]<Lower><Uppers>
%		If \@inferRuletrue, draws a rule and <Label> is right to
%		a rule.
%		Otherwise, draws no rule and <Label> is right to <Lower>.

\def\@infer[#1]#2#3{\relax
% Get parameters
	\if@ReturnLeftOffset \else \@SavedLeftOffset=\@LeftOffset \fi
	\setbox\@LabelPart=\hbox{$#1$}\relax
	\setbox\@LowerPart=\hbox{$#2$}\relax
%
	\global\@LeftOffset=0pt
	\setbox\@UpperPart=\vbox{\tabskip=0pt \halign{\relax
		\global\@RightOffset=0pt \@ReturnLeftOffsettrue $##$&&
		\inferTabSkip
		\global\@RightOffset=0pt \@ReturnLeftOffsetfalse $##$\cr
		#3\cr}}\relax
%			Here is a little trick.
%			\@ReturnLeftOffsettrue(false) influences on \infer or
%			\deduce placed in ## locally
%			because of \@SaveMath and \@RestoreMath.
	\UpperLeftOffset=\@LeftOffset
	\UpperRightOffset=\@RightOffset
% Calculate Adjustments
	\LowerWidth=\wd\@LowerPart
	\LowerHeight=\ht\@LowerPart
	\LowerCenter=0.5\LowerWidth
%
	\UpperWidth=\wd\@UpperPart \advance\UpperWidth by -\UpperLeftOffset
	\advance\UpperWidth by -\UpperRightOffset
	\UpperCenter=\UpperLeftOffset
	\advance\UpperCenter by 0.5\UpperWidth
%
	\ifdim \UpperWidth > \LowerWidth
		% \UpperCenter > \LowerCenter
	\UpperAdjust=0pt
	\RuleAdjust=\UpperLeftOffset
	\LowerAdjust=\UpperCenter \advance\LowerAdjust by -\LowerCenter
	\RuleWidth=\UpperWidth
	\global\@LeftOffset=\LowerAdjust
%
	\else	% \UpperWidth <= \LowerWidth
	\ifdim \UpperCenter > \LowerCenter
%
	\UpperAdjust=0pt
	\RuleAdjust=\UpperCenter \advance\RuleAdjust by -\LowerCenter
	\LowerAdjust=\RuleAdjust
	\RuleWidth=\LowerWidth
	\global\@LeftOffset=\LowerAdjust
%
	\else	% \UpperWidth <= \LowerWidth
		% \UpperCenter <= \LowerCenter
%
	\UpperAdjust=\LowerCenter \advance\UpperAdjust by -\UpperCenter
	\RuleAdjust=0pt
	\LowerAdjust=0pt
	\RuleWidth=\LowerWidth
	\global\@LeftOffset=0pt
%
	\fi\fi
% Make a box
	\if@inferRule
%
	\setbox\ResultBox=\vbox{
		\moveright \UpperAdjust \box\@UpperPart
		\nointerlineskip \kern\inferLineSkip
		\moveright \RuleAdjust \vbox{\hrule width\RuleWidth}\relax
		\nointerlineskip \kern\inferLineSkip
		\moveright \LowerAdjust \box\@LowerPart }\relax
%
	\@ifEmpty{#1}{}{\relax
%
	\HLabelAdjust=\wd\ResultBox	\advance\HLabelAdjust by -\RuleAdjust
	\advance\HLabelAdjust by -\RuleWidth
	\WidthAdjust=\HLabelAdjust
	\advance\WidthAdjust by -\inferLabelSkip
	\advance\WidthAdjust by -\wd\@LabelPart
	\ifdim \WidthAdjust < 0pt \WidthAdjust=0pt \fi
%
	\VLabelAdjust=\dp\@LabelPart
	\advance\VLabelAdjust by -\ht\@LabelPart
	\VLabelAdjust=0.5\VLabelAdjust	\advance\VLabelAdjust by \LowerHeight
	\advance\VLabelAdjust by \inferLineSkip
%
	\setbox\ResultBox=\hbox{\box\ResultBox
		\kern -\HLabelAdjust \kern\inferLabelSkip
		\raise\VLabelAdjust \box\@LabelPart \kern\WidthAdjust}\relax
%
	}\relax % end @ifEmpty
%
	\else % \@inferRulefalse
%
	\setbox\ResultBox=\vbox{
		\moveright \UpperAdjust \box\@UpperPart
		\nointerlineskip \kern\inferLineSkip
		\moveright \LowerAdjust \hbox{\unhbox\@LowerPart
			\@ifEmpty{#1}{}{\relax
			\kern\inferLabelSkip \unhbox\@LabelPart}}}\relax
	\fi
%
	\global\@RightOffset=\wd\ResultBox
	\global\advance\@RightOffset by -\@LeftOffset
	\global\advance\@RightOffset by -\LowerWidth
	\if@ReturnLeftOffset \else \global\@LeftOffset=\@SavedLeftOffset \fi
%
	\box\ResultBox
	\@RestoreMath
}
SHAR_EOF
fi
if test -f 'proofeg.tex'
then
	echo shar: "will not over-write existing file 'proofeg.tex'"
else
cat << \SHAR_EOF > 'proofeg.tex'
%	proofeg.tex	(Examples for proof.sty)
%
%		on Oct 13, 1990
%		by Makoto Tatsuta
%
%	I hope you can learn how to use proof figure macros easily
%	by these examples.

\def\imp{\to}
\def\land{\mathbin\&}

\documentstyle[proof]{article}

\begin{document}
\section*{Examples of proof.sty}

\verb|\infer| draws beautiful proof figures easily:

\noindent (1)
$$
\infer{A}{
	\infer{B}{
		B11\land B12\land B13
		&
		B21\land B22\land B23
	}
	&
	C
}
$$

\noindent (2)
$$
\infer{A1\land A2\land A3\land A4\land A5\land A6}{
	\infer{B}{
		B11\land B12\land B13
		&
		B21\land B22\land B23
	}
	&
	C
}
$$

\noindent (3)
$$
\infer{A1\land A2\land A3\land A4\land A5\land A6}{
	C
	&
	\infer{B}{
		B11\land B12\land B13
		&
		B21\land B22\land B23
	}
}
$$

You can use also some variations:

\noindent (4)
$$
\infer[(1)]{A}{
	\infer*{B}{
		B11\land B12\land B13
		&
		B21\land B22\land B23
	}
	&
	C
}
$$

\noindent (5)
$$
\infer*[(1)]{A1\land A2\land A3\land A4\land A5\land A6}{
	\deduce[{\displaystyle \sum}]{B}{
		B11\land B12\land B13
		&
		B21\land B22\land B23
	}
	&
	\deduce{C}{(2)}
}
$$

Here are more practical examples:

\noindent (6)
$$
\infer[(\land I)]{A \land B}{A & B}
\qquad
\infer[(\land E_l)]A{A\land B}
\qquad
\infer[(\land E_r)]B{A\land B}
$$

$$
\infer[(\imp I)]{A \imp B}{
	\infer*{B}{[A]}
}
\qquad
\infer[(\imp E)]{B}{
	A \imp B
	&
	A
}
$$

Some techniques:
Use \verb|\vcenter| for an equation of proofs.

\noindent (7)
$$
\pi = \vcenter{
\infer{E}{
	A
	&
	\infer{D}{B & C}
}
}
$$

Use \verb|\kern| to adjust the form of a proof.

\noindent (8)
$$
\infer{E}{
	A
	&
	\infer{D}{B & C} \kern 0.5cm
}
$$

\end{document}
SHAR_EOF
fi
exit 0
#	End of shell archive