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authorKarl Berry <karl@freefriends.org>2015-02-03 23:39:18 +0000
committerKarl Berry <karl@freefriends.org>2015-02-03 23:39:18 +0000
commit5186e33c6d218e9003f3da20bedfa840c1765d27 (patch)
treefccf82dae9fd18882993ef75df511c43809c08c5 /Master/texmf-dist/tex/latex/ebproof
parentee0e64e16ff5d81050d780da9298fecd9eeae3b8 (diff)
ebproof (3feb15)
git-svn-id: svn://tug.org/texlive/trunk@36202 c570f23f-e606-0410-a88d-b1316a301751
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+% This package contains macros for typesetting proof trees.
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{ebproof}[2015/02/03 v1.0 EB's proof trees]
+
+% The |pgfkeys| package is used for the parameters in proof construction.
+% The |ifthen| package is used for some tests.
+
+\RequirePackage{pgfkeys}
+\RequirePackage{ifthen}
+
+%%% Registers and internal parameters
+
+\newbox\ebproof@leftbox
+\newbox\ebproof@rightbox
+\newif\ifebproof@updown \ebproof@updownfalse
+\newif\ifebproof@center \ebproof@centertrue
+
+\def\ebproof@template#1{$#1$}
+\def\ebproof@lefttemplate#1{$#1\mathrel{}$}
+\def\ebproof@righttemplate#1{$\mathrel{}#1$}
+\def\ebproof@leftlabeltemplate#1{#1}
+\def\ebproof@rightlabeltemplate#1{#1}
+\def\ebproof@setleftlabel{\setbox\ebproof@leftbox=\box\voidb@x}
+\def\ebproof@setrightlabel{\setbox\ebproof@rightbox=\box\voidb@x}
+
+%%% Parameters
+
+\def\ebproofset#1{\pgfqkeys{/ebproof}{#1}}
+
+\ebproofset{
+%
+% general shape
+%
+center/.is if=ebproof@center,
+proof style/.is choice,
+proof style/upwards/.code={\ebproof@updownfalse},
+proof style/downwards/.code={\ebproof@updowntrue},
+%
+% spacing
+%
+separation/.initial=1.5em,
+rule margin/.initial=.7ex,
+%
+% shape of inference lines
+%
+rule thickness/.initial=.4pt,
+rule separation/.initial=2pt,
+rule dash length/.initial=.2em,
+rule dash space/.initial=.3em,
+rule code/.initial=,
+%
+% templates
+%
+template/.code={\def\ebproof@template##1{#1}},
+left template/.code={\def\ebproof@lefttemplate##1{#1}},
+right template/.code={\def\ebproof@righttemplate##1{#1}},
+%
+% labels
+%
+left label/.code={%
+ \def\ebproof@setleftlabel{%
+ \setbox\ebproof@leftbox=\hbox{\ebproof@leftlabeltemplate{#1}}}},
+right label/.code={%
+ \def\ebproof@setrightlabel{%
+ \setbox\ebproof@rightbox=\hbox{\ebproof@rightlabeltemplate{#1}}}},
+left label template/.code={\def\ebproof@leftlabeltemplate##1{#1}},
+right label template/.code={\def\ebproof@rightlabeltemplate##1{#1}},
+label separation/.initial=0.5em,
+}
+
+% Rule styles
+
+\pgfqkeys{/ebproof/rule style}{
+.is choice,
+.search also=/ebproof,
+simple/.style={/ebproof/rule code={%
+ \hrule height \pgfkeysvalueof{/ebproof/rule thickness}\relax
+ }},
+%
+no rule/.style={/ebproof/rule code=},
+%
+double/.style={/ebproof/rule code={%
+ \hrule height \pgfkeysvalueof{/ebproof/rule thickness}
+ \kern\pgfkeysvalueof{/ebproof/rule separation}%
+ \hrule height \pgfkeysvalueof{/ebproof/rule thickness}
+ }},
+%
+dashed/.style={/ebproof/rule code={%
+ \hbox to \hsize{%
+ \@tempdima=\pgfkeysvalueof{/ebproof/rule dash space}%
+ \divide\@tempdima2%
+ \kern-\@tempdima%
+ \cleaders\hbox{%
+ \kern\@tempdima%
+ \vrule
+ height \pgfkeysvalueof{/ebproof/rule thickness}
+ width \pgfkeysvalueof{/ebproof/rule dash length}%
+ \kern\@tempdima
+ }\hfill
+ \kern-\@tempdima
+ }%
+ }},
+%
+simple % use the 'simple' rule style by default
+}
+
+%%% Storage
+
+% Proof trees are represented as a data structure that consists of the
+% following data:
+%
+% - box : the tree itself, as a box, with the base line on that of
+% the conclusion
+% - left : the distance from the left of the box to the left of the
+% conclusion
+% - right : the distance from the right of the box to the right of the
+% conclusion
+% - axis : the distance from the left of the box to the vertical axis
+% of the conclusion
+%
+% TeX does not actually provide data structures, so we have to encode things.
+% First we provide local allocators, for temporary allocation of registers in
+% a group. Dimensions are initialized to 0pt.
+
+\def\ebproof@localdimen#1{%
+ \advance\count11\@ne% \count11 is the number of the last allocated \dimen
+ \expandafter\dimendef\csname#1\endcsname=\count11%
+ \csname#1\endcsname=0pt\relax}
+
+% For boxes, the allocator must be used as
+%
+% \ebproof@localbox{NAME}=\hbox{...}
+%
+% in order to set the value of the box.
+
+\def\ebproof@localbox#1{%
+ \advance\count14\@ne% \count14 is the number of the last allocated \box
+ \expandafter\chardef\csname#1\endcsname\count14%
+ \setbox\csname#1\endcsname}
+
+% From this we deduce an allocator for data structures. This allocator
+% receives a base name |A| and defines the registers |\A@box|, |\A@left|,
+% |\A@right| and |\A@axis|. The macro is used like |\ebproof@localbox|, by
+% providing a value for the box.
+
+\def\ebproof@alloc#1{%
+ \ebproof@localdimen{#1@left}%
+ \ebproof@localdimen{#1@right}%
+ \ebproof@localdimen{#1@axis}%
+ \ebproof@localbox{#1@box}}
+
+% Logically, such structures are stored on a stack. However, TeX does not
+% provide data structures, so we encode them using what we actually have. A
+% stack for boxes is implemented using a global hbox |\ebproof@box@stack| that
+% contains all the boxes successively, and the |\lastbox| primitive allows us
+% to pop elements from there. A macro |\ebproof@stack| is used to store the
+% dimensions textually: the empty stack is an empty macro, and a non-empty
+% stack is represented as |{left}{right}{axis}{tail}|. We maintain a counter
+% |\ebproof@level| with the number of elements on the stack, for consistency
+% checks.
+
+\newcount\ebproof@level
+\newbox\ebproof@box@stack
+\newbox\ebproof@box@temp
+
+% Clear the stack.
+
+\def\ebproof@clear{%
+ \global\ebproof@level=0%
+ \global\setbox\ebproof@box@stack=\box\voidb@x%
+ \gdef\ebproof@stack{}}
+
+% Push an allocated structure (by name) on the stack.
+
+\def\ebproof@push#1{%
+ \global\advance\ebproof@level1\relax
+ \global\setbox\ebproof@box@stack=\hbox{%
+ \unhbox\ebproof@box@stack\copy\csname#1@box\endcsname}%
+ \xdef\ebproof@stack{%
+ {\the\csname#1@left\endcsname}%
+ {\the\csname#1@right\endcsname}%
+ {\the\csname#1@axis\endcsname}%
+ {\ebproof@stack}}}
+
+% Allocate a structure and pop its value from the top of the stack.
+
+\def\ebproof@pop#1{%
+ \ifnum\ebproof@level>0\relax
+ \global\advance\ebproof@level-1\relax
+ \global\setbox\ebproof@box@stack=\hbox{%
+ \unhbox\ebproof@box@stack
+ \global\setbox\ebproof@box@temp=\lastbox}%
+ \ebproof@alloc{#1}=\box\ebproof@box@temp%
+ \begingroup\def\pop##1##2##3##4{\endgroup%
+ \csname#1@left\endcsname=##1\relax
+ \csname#1@right\endcsname=##2\relax
+ \csname#1@axis\endcsname=##3\relax
+ \gdef\ebproof@stack{##4}}%
+ \expandafter\pop\ebproof@stack
+ \else
+ \PackageError{ebproof}{%
+ Missing premiss in a proof tree}{}%
+ \ebproof@alloc{#1}=\box\voidb@x%
+ \fi}
+
+
+%%% Making boxes
+
+% Push a box with the axis in the middle.
+
+\def\ebproof@pushsimple#1{%
+ \begingroup
+ \ebproof@alloc{A}=\hbox{#1}%
+ \A@axis=.5\wd\A@box
+ \ebproof@push{A}%
+ \endgroup}
+
+% Push a box made of two halves, with the axis between the halves.
+
+\def\ebproof@pushsplit#1#2{%
+ \begingroup
+ \ebproof@alloc{A}=\hbox{#1}%
+ \A@axis=\wd\A@box
+ \setbox\A@box=\hbox{\unhbox\A@box#2}%
+ \ebproof@push{A}%
+ \endgroup}
+
+% Join horizontally the two elements at the top of the stack.
+
+\def\ebproof@joinh{%
+ \begingroup
+ \ebproof@pop{A}%
+ \ebproof@pop{B}%
+ \ebproof@alloc{C}=\hbox{%
+ \box\B@box
+ \kern\pgfkeysvalueof{/ebproof/separation}%
+ \box\A@box}%
+ \C@left=\B@left
+ \C@right=\A@right
+ \C@axis=\wd\C@box
+ \advance\C@axis\B@left
+ \advance\C@axis-\A@right
+ \divide\C@axis2\relax
+ \ebproof@push{C}%
+ \endgroup}
+
+% An $n$-ary version of the horizontal join.
+
+\def\ebproof@joinh@multi#1{%
+ \begingroup
+ \countdef\c=1
+ \c=#1\relax%
+ \ifnum\c=0
+ \ebproof@alloc{X}=\hbox{}%
+ \ebproof@push{X}%
+ \else
+ \ebproof@joinh@loop
+ \fi
+ \endgroup}
+\def\ebproof@joinh@loop{%
+ \ifnum\c>1
+ \ebproof@joinh
+ \advance\c-1
+ \expandafter\ebproof@joinh@loop
+ \fi}
+
+% Append the last element to the right of the previous one, without changing
+% its alignment.
+
+\def\ebproof@joinright{%
+ \begingroup
+ \ebproof@pop{A}%
+ \ebproof@pop{B}%
+ \ebproof@alloc{C}=\hbox{%
+ \box\B@box
+ \kern\pgfkeysvalueof{/ebproof/separation}%
+ \copy\A@box}%
+ \C@left=\B@left
+ \C@right=\B@right
+ \advance\C@right\wd\A@box
+ \advance\C@right\pgfkeysvalueof{/ebproof/separation}%
+ \ebproof@push{C}%
+ \endgroup}
+
+% Join vertically the two elements at the top of the stack, with a horizontal
+% rule of the appropriate size.
+
+\def\ebproof@joinv{%
+ \begingroup
+ \ebproof@setleftlabel
+ \ebproof@setrightlabel
+ \ebproof@pop{A}%
+ \ebproof@pop{B}%
+ %
+ \ebproof@alloc{C}=\box\voidb@x%
+ \ebproof@localdimen{A@shift}%
+ \ebproof@localdimen{B@shift}%
+ \ebproof@localdimen{R@shift}%
+ \ebproof@localdimen{R@raise}%
+ \ebproof@localdimen{R@width}%
+ \ebproof@localdimen{C@width}%
+ \ebproof@localdimen{tmp}%
+ %
+ % The placement of the boxes and the axis of the result
+ \ifdim\A@axis>\B@axis
+ \A@shift=0pt%
+ \B@shift=\A@axis
+ \advance\B@shift-\B@axis
+ \C@axis=\A@axis
+ \else
+ \A@shift=\B@axis
+ \advance\A@shift-\A@axis
+ \B@shift=0pt%
+ \C@axis=\B@axis
+ \fi
+ % The paddings of the result
+ \C@left=\A@left
+ \advance\C@left\A@shift
+ \C@right=\A@right
+ \tmp=\wd\B@box
+ \advance\tmp\B@shift
+ \advance\tmp-\wd\A@box
+ \advance\tmp-\A@shift
+ \ifdim\tmp>0pt%
+ \C@width=\wd\B@box
+ \advance\C@width\B@shift
+ \advance\C@right\tmp
+ \else
+ \C@width=\wd\A@box
+ \advance\C@width\A@shift
+ \fi
+ % The position of the rule
+ \R@shift=\A@left
+ \advance\R@shift\A@shift
+ \tmp=\B@left
+ \advance\tmp\B@shift
+ \ifdim\R@shift>\tmp
+ \R@shift=\tmp
+ \fi
+ % The width of the rule
+ \R@width=\wd\A@box
+ \advance\R@width\A@shift
+ \advance\R@width-\A@right
+ \tmp=\wd\B@box
+ \advance\tmp\B@shift
+ \advance\tmp-\B@right
+ \ifdim\tmp>\R@width
+ \R@width=\tmp
+ \fi
+ \advance\R@width-\R@shift
+ % Make the rule box
+ \ebproof@localbox{R@box}=\vbox{%
+ \hsize=\R@width
+ \hrule width \R@width height 0pt\relax
+ \kern\pgfkeysvalueof{/ebproof/rule margin}%
+ \pgfkeysgetvalue{/ebproof/rule code}{\@rulecode}%
+ \ifx\@rulecode\@empty\else
+ \@rulecode
+ \unskip% so that only one margin is inserted if no rule is drawn
+ \kern\pgfkeysvalueof{/ebproof/rule margin}%
+ \fi
+ }%
+ % Shift things if the left box is wider than |\R@shift|
+ \ifvoid\ebproof@leftbox\else
+ \tmp=\wd\ebproof@leftbox
+ \advance\tmp\pgfkeysvalueof{/ebproof/label separation}
+ \ifdim\tmp>\R@shift
+ \advance\tmp-\R@shift
+ \advance\A@shift\tmp
+ \advance\B@shift\tmp
+ \advance\C@left\tmp
+ \advance\C@axis\tmp
+ \advance\C@width\tmp
+ \R@shift=0pt\relax
+ \else
+ \advance\R@shift-\tmp
+ \fi
+ \fi
+ % Compute how the rule box must be shifted so that labels are aligned
+ \ebproof@localbox{RC@box}=\hbox{$\vcenter{\copy\R@box}$}%
+ \R@raise=\ht\R@box
+ \advance\R@raise-\ht\RC@box
+ % Make the complete rule box
+ \setbox\RC@box=\hbox{%
+ \ifvoid\ebproof@leftbox\else
+ \copy\ebproof@leftbox
+ \kern\pgfkeysvalueof{/ebproof/label separation}
+ \fi
+ \box\RC@box
+ \ifvoid\ebproof@rightbox\else
+ \kern\pgfkeysvalueof{/ebproof/label separation}
+ \copy\ebproof@rightbox
+ \fi}
+ % Adapt the dimensions on the right if the total rule width is too large
+ \tmp=\wd\RC@box
+ \advance\tmp\R@shift
+ \ifdim\tmp>\C@width
+ \advance\tmp-\C@width
+ \advance\C@right\tmp
+ \fi
+ % Cancel the labels' height and depth
+ \setbox\RC@box=\hbox{\raise\R@raise\box\RC@box}
+ \ht\RC@box=\ht\R@box
+ \dp\RC@box=\dp\R@box
+ % Make the box
+ \ifebproof@updown
+ \setbox\C@box=\vtop{%
+ \moveright\A@shift\box\A@box
+ \hrule height 0pt
+ \moveright\R@shift\box\RC@box%
+ \hrule height 0pt
+ \moveright\B@shift\box\B@box}%
+ \else
+ \setbox\C@box=\vbox{%
+ \moveright\B@shift\box\B@box
+ \hrule height 0pt
+ \moveright\R@shift\box\RC@box%
+ \hrule height 0pt
+ \moveright\A@shift\box\A@box}%
+ \fi
+ \ebproof@push{C}%
+ \endgroup}
+
+%%% Modifying boxes
+
+% Alter a proof with a command that does not affect the size. Typically useful
+% with |\color| commands.
+
+\def\ebproof@alter#1{%
+ \begingroup
+ \ebproof@pop{A}%
+ \setbox\A@box=\hbox{{#1\box\A@box}}%
+ \ebproof@push{A}%
+ \endgroup}
+
+% Insert |\left| and |\right| delimiters without changing the alignment
+
+\def\ebproof@delims#1#2{%
+ \begingroup
+ \ebproof@pop{TREE}%
+ \ebproof@localbox{@SHIFTED}=%
+ \hbox{$\vcenter{\copy\TREE@box}$}%
+ \ebproof@localbox{@LEFT}=%
+ \hbox{$#1\vrule height \ht\@SHIFTED depth \dp\@SHIFTED width 0pt\right.$}%
+ \ebproof@localbox{@RIGHT}=%
+ \hbox{$\left.\vrule height \ht\@SHIFTED depth \dp\@SHIFTED width 0pt#2$}%
+ \ebproof@localdimen{dy}
+ \dy=\dp\@SHIFTED
+ \advance\dy-\dp\TREE@box
+ \ebproof@alloc{A}=%
+ \hbox{\raise\dy\hbox{\copy\@LEFT\box\@SHIFTED\copy\@RIGHT}}%
+ \A@left=\wd\@LEFT \advance\A@left\TREE@left
+ \A@right=\wd\@RIGHT \advance\A@right\TREE@right
+ \A@axis=\wd\@LEFT \advance\A@axis\TREE@axis
+ \ebproof@push{A}%
+ \endgroup}
+
+%%% High-level commands
+
+% Push a box with default formatting, using explicit alignment if the code
+% contains a |&| character
+
+\def\ebproof@hypo@parse#1&#2&#3\ebproof@hypo@stop{
+ \ifthenelse{\equal{#3}{}}%
+ {\ebproof@pushsimple{\ebproof@template{#1}}}%
+ {\ebproof@pushsplit
+ {\ebproof@lefttemplate{#1}}%
+ {\ebproof@righttemplate{#2}}}}
+
+\newcommand\ebproof@hypo[2][]{%
+ {\ebproofset{#1}\ebproof@hypo@parse#2&&\ebproof@hypo@stop}}
+
+% Build a n-ary rule
+
+\def\ebproof@infer{%
+ \@ifnextchar[{\ebproof@infer@}{\ebproof@infer@[]}}
+\def\ebproof@infer@[#1]#2{%
+ \@ifnextchar[{\ebproof@infer@@{#1}{#2}}{\ebproof@infer@@{#1}{#2}[]}}
+\def\ebproof@infer@@#1#2[#3]#4{{%
+ \pgfqkeys{/ebproof/rule style}{.search also=/ebproof,#1}%
+ \ebproof@joinh@multi{#2}%
+ \ebproof@hypo{#4}%
+ \ifthenelse{\equal{#3}{}}{}{\ebproofset{right label={#3}}}%
+ \ebproof@joinv}}
+
+% Ellipsis with vertical dots
+
+\def\ebproof@ellipsis#1#2{{%
+ \ebproofset{rule code=}%
+ \ebproof@pushsplit{}{%
+ \setbox0=\vbox{\kern1.2ex\hbox{\ignorespaces#1}\hrule height 0pt\kern1.2ex}%
+ \vbox to\ht0{\xleaders\vbox to .8ex{\vss\hbox{.}\vss}\vfill}%
+ \rlap{ \box0}}%
+ \ebproof@joinv
+ \ebproof@hypo{#2}%
+ \ebproof@joinv}}
+
+%%% Environment interface
+
+\ebproof@clear
+
+\def\ebproof@begin{%
+ \edef\ebproof@start@level{\the\ebproof@level}%
+ \setbox1=\vbox\bgroup
+ \let\Hypo=\ebproof@hypo
+ \let\Infer=\ebproof@infer
+ \let\Ellipsis=\ebproof@ellipsis
+ \let\Alter=\ebproof@alter
+ \let\Delims=\ebproof@delims}
+\def\ebproof@end{%
+ \egroup
+ \ebproof@pop{X}%
+ \ifnum\ebproof@level=\ebproof@start@level\else
+ \PackageError{ebproof}{Malformed proof tree}{%
+ Some hypotheses were declared but not used in this tree.}%
+ \fi
+ \ifebproof@center
+ \hbox{$\vcenter{\hbox{\box\X@box}}$}%
+ \else
+ \box\X@box
+ \fi
+ \global\setbox\ebproof@box@temp=\box1}
+
+\newenvironment{prooftree}[1][]{%
+ \pgfqkeys{/ebproof/proof style}{.search also=/ebproof,#1}%
+ \leavevmode\ebproof@begin
+}{%
+ \ebproof@end}
+
+\newenvironment{prooftree*}[1][]{%
+ \center
+ \pgfqkeys{/ebproof/proof style}{.search also=/ebproof,#1}%
+ \leavevmode\ebproof@begin
+}{%
+ \ebproof@end
+ \endcenter}