From 5186e33c6d218e9003f3da20bedfa840c1765d27 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Tue, 3 Feb 2015 23:39:18 +0000 Subject: ebproof (3feb15) git-svn-id: svn://tug.org/texlive/trunk@36202 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/ebproof/README | 16 + Master/texmf-dist/doc/latex/ebproof/ebproof.pdf | Bin 0 -> 196387 bytes Master/texmf-dist/doc/latex/ebproof/ebproof.tex | 493 ++++++++++++++++++++++++ 3 files changed, 509 insertions(+) create mode 100644 Master/texmf-dist/doc/latex/ebproof/README create mode 100644 Master/texmf-dist/doc/latex/ebproof/ebproof.pdf create mode 100644 Master/texmf-dist/doc/latex/ebproof/ebproof.tex (limited to 'Master/texmf-dist/doc/latex/ebproof') diff --git a/Master/texmf-dist/doc/latex/ebproof/README b/Master/texmf-dist/doc/latex/ebproof/README new file mode 100644 index 00000000000..a64bac6f41f --- /dev/null +++ b/Master/texmf-dist/doc/latex/ebproof/README @@ -0,0 +1,16 @@ +The ebproofs package provides commands to typeset proof trees, in the style of +sequent calculus and related systems. The commands allow for writing +inferences with any number of premisses and alignment of successive formulas +on an arbitrary point. Various options allow complete control over spacing, +styles of inference rules, placement of labels, etc. + +The distribution includes the following files: + + - ebproof.sty : the package + - ebproof.pdf : the documentation + - ebproof.tex : the LaTeX source for the documentation + +The package requires pgfkeys (from TikZ/PGF) for the option system. + +This package is written by Emmanuel Beffara +It is subject to the LaTeX Project Public License. diff --git a/Master/texmf-dist/doc/latex/ebproof/ebproof.pdf b/Master/texmf-dist/doc/latex/ebproof/ebproof.pdf new file mode 100644 index 00000000000..e58d9616168 Binary files /dev/null and b/Master/texmf-dist/doc/latex/ebproof/ebproof.pdf differ diff --git a/Master/texmf-dist/doc/latex/ebproof/ebproof.tex b/Master/texmf-dist/doc/latex/ebproof/ebproof.tex new file mode 100644 index 00000000000..acb05d56759 --- /dev/null +++ b/Master/texmf-dist/doc/latex/ebproof/ebproof.tex @@ -0,0 +1,493 @@ +\documentclass{article} + +\DeclareRobustCommand\package[1]{\texttt{#1}} + +\title{The \package{ebproof} package} +\author{Emmanuel Beffara \\ \url{manu@beffara.org}} +\date{Version 1.0 \\ February 3, 2015} + +\usepackage{amssymb} +\usepackage{color} +\usepackage{fancyvrb} +\usepackage[a4paper]{geometry} +\usepackage[colorlinks=true,urlcolor=blue]{hyperref} +\usepackage{multicol} + +\usepackage{tikz} +\usetikzlibrary{decorations.pathmorphing} + +\usepackage{ebproof} + +\newcommand\lit[1]{\texttt{#1}} +\newcommand\cs[1]{\lit{\char`\\#1}} +\newcommand\env[1]{\lit{#1}} +\newcommand\opt[1]{\lit{#1}} +\newcommand\meta[1]{$\langle$\textit{#1}$\rangle$} +\newcommand\oarg[1]{\lit{[}\meta{#1}\lit{]}} +\newcommand\marg[1]{\lit{\{}\meta{#1}\lit{\}}} + +\newenvironment{csdoc}[1]{% + \smallbreak\noindent{#1}% + \begin{list}{}{% + \topsep=1ex% + }% + \item +}{% + \end{list}% +} + +\newenvironment{example}[1]{% + \def\exampleoptions{#1}% + \VerbatimOut{example.tex}}{% + \endVerbatimOut + \begin{center} + \begin{minipage}{.4\textwidth} + \input{example.tex} + \end{minipage}% + \begin{minipage}{.6\textwidth} + \small + \expandafter\VerbatimInput\expandafter[\exampleoptions]{example.tex} + \end{minipage}% + \end{center} +} + +\setcounter{tocdepth}{2} + +\begin{document} +\maketitle + +\begin{multicols}{2} + \tableofcontents +\end{multicols} + +\section{Introduction} + +The \env{ebproof} package provides commands to typeset proof trees, in the +style of sequent calculus and related systems: + +\begin{example}{gobble=2} + \begin{prooftree} + \Hypo{ \Gamma, A &\vdash B } + \Infer1[abs]{ \Gamma &\vdash A\to B } + \Hypo{ \Gamma \vdash A } + \Infer2[app]{ \Gamma \vdash B } + \end{prooftree} +\end{example} + +The structure is very much inspired by the +\href{http://math.ucsd.edu/~sbuss/ResearchWeb/bussproofs/}{\package{bussproofs}} +package, in particular for the postfix notation. +I actually wrote \package{ebproof} because there were some limitations in +\package{bussproofs} that I did not know how to lift, and also because I did +not like some choices in that package (and also because it was fun to write). + +\section{Environments} + +The package provides the \env{prooftree} environment, in a standard and +starred variants. + +\begin{csdoc}{ + \cs{begin}\lit{\{prooftree\}}\oarg{options} + \meta{statements} + \cs{end}\lit{\{prooftree\}}} + Typeset the proof tree desribed by the \meta{statements}, as described in + section~\ref{sec:statements}. + The \meta{options} provide default formatting options for the proof tree. + This environment can be used either in math mode or in text mode. + It produces a proof tree at the current position in the text flow. +\end{csdoc} + +\begin{csdoc}{ + \cs{begin}\lit{\{prooftree*\}}\oarg{options} + \meta{statements} + \cs{end}\lit{\{prooftree*\}}} + Typeset the proof centered on a line of its own; it is essentially + equivalent to wrapping the \env{prooftree} environment inside a \env{center} + environment. +\end{csdoc} + +\noindent +The starred version is used in situations when a single proof will be +displayed. +The non-starred version is useful in order to integrate the proof into some +larger structure, like two parts of a formula: + +\begin{example}{gobble=2} + \[ + \begin{prooftree} + \Hypo{ \vdash A } + \Hypo{ \vdash B } \Infer1{ \vdash B, C } + \Infer2{ \vdash A\wedge B, C } + \end{prooftree} + \quad \rightsquigarrow \quad + \begin{prooftree} + \Hypo{ \vdash A } \Hypo{ \vdash B } + \Infer2{ \vdash A\wedge B } + \Infer1{ \vdash A\wedge B, C } + \end{prooftree} + \] +\end{example} + +\section{Statements} +\label{sec:statements} + +Statements describes proofs in postfix notation: when typesetting a proof tree +whose last rule has, say, two premisses, you will first write statements for +the subtree of the first premiss, then statements for the subtree of the +second premiss, then a statement like \cs{Infer2}\{\meta{conclusion}\} to +build an inference with these two subtrees as premisses and the given text as +conclusion. + +Hence statements operate on a stack of proof trees. +At the beginning of a \lit{prooftree} environment, the stack is empty. +At the end, it must contain exactly one tree, which is the one that will be +printed. + +\subsection{Basic statements} + +The basic statements for building proofs are the following, where +\meta{options} stands for arbitrary options as described in +section~\ref{sec:options}. +\begin{csdoc}{\cs{Hypo}\oarg{options}\marg{text}} + Push a new proof tree consisting only in one conclusion line, with no + premiss and no line above, in other words a tree with only a leaf + (\cs{Hypo} stands for \emph{hypothesis}). +\end{csdoc} +\begin{csdoc}{\cs{Infer}\oarg{options}\marg{arity}\oarg{label}\marg{text}} + Build an inference step by taking some proof trees from the top of the + stack, assembling them with a rule joining their conclusions and putting a + new conclusion below. + The \meta{arity} is the number of sub-proofs, it may be any number + including 0 (in this case there will be a line above the conclusion but no + sub-proof). + If \meta{label} is present, it is used as the label on the right of the + inference line; it is equivalent to using the \opt{right label} option. +\end{csdoc} + +The \meta{text} in these statements is the contents of the conclusion at the +root of the tree that the statements create. +It is typeset in math mode by default but any kind of formatting can be used +instead, using the \opt{template} option. +The \meta{label} text is formatted in horizontal text mode by default. + +Each proof tree has a vertical axis, used for alignment of successive steps. +The position of the axis is deduced from the text of the conclusion at the +root of the tree: if \meta{text} contains the alignment character \verb|&| +then the axis is set at that position, otherwise the axis is set at the center +of the conclusion text. +The \cs{Infer} statement makes sure that the axis of the premiss is at the +same position as the axis of the conclusion. +If there are several premisses, it places the axis at the center between the +left of the leftmost conclusion and the right of the rightmost conclusion: + +\begin{example}{gobble=2} + \begin{prooftree} + \Hypo{ &\vdash A, B, C } + \Infer1{ A &\vdash B, C } + \Infer1{ A, B &\vdash C } + \Hypo{ D &\vdash E } + \Infer2{ A, B, D &\vdash C, E } + \Infer1{ A, B &\vdash C, D, E } + \Infer1{ A &\vdash B, C, D, E } + \end{prooftree} +\end{example} + +\subsection{Additional statements} + +The following additional statements may be used to affect the format of the +last proof tree on the stack: + +\begin{csdoc}{\cs{Ellipsis}\marg{label}\marg{text}} + Typeset vertical dots, with a label on the right, and a new conclusion. + No inference lines are inserted. + \begin{example}{gobble=4} + \begin{prooftree} + \Hypo{ \Gamma &\vdash A } + \Ellipsis{foo}{ \Gamma &\vdash A, B } + \end{prooftree} + \end{example} +\end{csdoc} + +\begin{csdoc}{\cs{Alter}\marg{code}} + Modify the proof with arbitrary commands, assuming that these commands do + not affect the size. + The \meta{code} is executed in an \cs{hbox} and is followed by the insertion + of the actual box with the current sub-proof. + It is mostly useful with \cs{color} commands: + \begin{example}{gobble=4} + \begin{prooftree} + \Hypo{ \Gamma, A &\vdash B } + \Infer1[abs]{ \Gamma &\vdash A\to B } + \Alter{\color{red}} + \Hypo{ \Gamma \vdash A } + \Infer2[app]{ \Gamma \vdash B } + \end{prooftree} + \end{example} +\end{csdoc} + +\begin{csdoc}{\cs{Delims}\marg{left}\marg{right}} + Put left and right delimiters around the whole sub-proof, without changing + the alignment (the spacing is affected by the delimiters, however). + The \meta{left} text must contain an opening occurrence of \cs{left} and the + \meta{right} text must contain a matching occurrence of \cs{right}. + For instance, \verb|\Delims{\left(}{\right)}| will put the + sub-proof between parentheses. + \begin{example}{gobble=4} + \begin{prooftree} + \Hypo{ A_1 \vee \cdots \vee A_n } + \Hypo{ [A_i] } + \Ellipsis{}{ B } + \Delims{ \left( }{ \right)_{1\leq i\leq n} } + \Infer2{ B } + \end{prooftree} + \end{example} +\end{csdoc} + +\section{Options} +\label{sec:options} + +The formatting of trees, conclusion texts and inference rules is affected by +options, specfied using the key-value system of PGF/TikZ, provided by the +\package{pgfkeys} package. +All options are in the \lit{/ebproof/} path in the key tree of +\package{pgfkeys}. +They can be set locally for a proof tree or for a single statement using +optional arguments in the associated commands. + +\begin{csdoc}{\cs{ebproofset}\marg{options}} + Set some options. + The options will apply in the current scope; using this in preamble will + effectively set options globally. + Specific options may also be specified for each proof tree and for each + statement in a proof tree, using optional arguments. +\end{csdoc} + +\subsection{General shape} + +The options in this section only make sense at the global level and at the +proof level. +Changing the proof style inside a \lit{proof} environment has undefined +behaviour. + +\begin{csdoc}{\opt{proof style=}\meta{name}} + Set the general shape for representing proofs. + The following styles are provided: + \begin{csdoc}{\lit{upwards}} + This is the default style. + Proof trees grow upwards, with conclusions below and premisses above. + \end{csdoc} + \begin{csdoc}{\lit{downwards}} + Proof trees grow downwards, with conclusions above and premisses below. + \begin{example}{gobble=4} + \begin{prooftree}[proof style=downwards] + \Hypo{ \Gamma, A &\vdash B } + \Infer1[abs]{ \Gamma &\vdash A\to B } + \Hypo{ \Gamma \vdash A } + \Infer2[app]{ \Gamma \vdash B } + \end{prooftree} + \end{example} + \end{csdoc} +\end{csdoc} + +In the optional argument of \lit{prooftree} environments, proof styles can +be specified directly, without prefixing the name by ``\lit{proof style=}''. +For instance, the first line of the example above could be written +\cs{begin}\lit{\{prooftree\}[downwards]} equivalently. + +\begin{csdoc}{\opt{center=}\meta{boolean}} + If set to \lit{true}, the tree produced by the \env{prooftree} environment + will be vertically centered around the text line. + If set to \lit{false}, the base line of the tree will be the base line of + the conclusion. + The default value is \lit{true}. + \begin{example}{gobble=4} + \begin{prooftree}[center=false] + \Infer0{ A \vdash A } + \end{prooftree} + \qquad + \begin{prooftree}[center=false] + \Hypo{ \Gamma, A \vdash B } + \Infer1{ \Gamma \vdash A \to B } + \end{prooftree} + \end{example} +\end{csdoc} + +\subsection{Spacing} + +\begin{csdoc}{\opt{separation=}\meta{dimension}} + The horizontal separation between sub-proofs in an inference. + The default value is \lit{1.5em}. + \begin{example}{gobble=4} + \begin{prooftree}[separation=0.5em] + \Hypo{ A } \Hypo{ B } \Infer2{ C } + \Hypo{ D } \Hypo{ E } \Hypo{ F } \Infer3{ G } + \Hypo{ H } \Infer[separation=3em]3{ K } + \end{prooftree} + \end{example} +\end{csdoc} + +\begin{csdoc}{\opt{rule margin=}\meta{dimension}} + The spacing above and below inference lines. + The default value is \lit{0.7ex}. + \begin{example}{gobble=4} + \begin{prooftree}[rule margin=2ex] + \Hypo{ \Gamma, A &\vdash B } + \Infer1[abs]{ \Gamma &\vdash A\to B } + \Hypo{ \Gamma \vdash A } + \Infer2[app]{ \Gamma \vdash B } + \end{prooftree} + \end{example} +\end{csdoc} + +\subsection{Shape of inference lines} + +\begin{csdoc}{\opt{rule style=}\meta{name}} + Set the shape of inference lines. + The following values are provided: + \begin{csdoc}{\opt{simple}} + A simple horizontal rule is drawn. + This is the default style. + \end{csdoc} + \begin{csdoc}{\opt{no rule}} + No inference line is drawn. + A single space of the length of \lit{rule margin} is inserted. + \end{csdoc} + \begin{csdoc}{\opt{double}} + A double line is drawn. + \end{csdoc} + \begin{csdoc}{\opt{dashed}} + A single dashed line is drawn. + \end{csdoc} + The precise rendering is influenced by parameters specified below. + Arbitrary new shapes can defined using the \lit{rule code} option described + afterwards. +\end{csdoc} + +In the optional argument of the \cs{Infer} statement, rule styles can be +specified directly, without prefixing the style name by ``\lit{rule style=}''. +For instance, \cs{Infer}\lit{[dashed]} is equivalent to +\cs{Infer}\lit{[rule style=dashed]}. + +\begin{example}{gobble=2} + \begin{prooftree} + \Hypo{ \Gamma &\vdash A \to B } + \Infer[no rule]1{ \Gamma &\vdash {!A} \multimap B } + \Hypo{ \Delta &\vdash A } + \Infer[rule thickness=2pt]1{ \Delta &\vdash {!A} } + \Infer0{ B \vdash B } + \Infer[dashed]2{ \Delta, {!A}\multimap B \vdash B } + \Infer2{ \Gamma, \Delta &\vdash B } + \Infer[double]1{ \Gamma \cup \Delta &\vdash B } + \end{prooftree} +\end{example} + +\begin{csdoc}{\opt{rule thickness=}\meta{dimension}} + The thickness of inference lines. + It is \lit{0.4pt} by default. +\end{csdoc} +\begin{csdoc}{\opt{rule separation=}\meta{dimension}} + The distance between the two lines in the \lit{double} rule style. + It is \lit{2pt} by default. +\end{csdoc} +\begin{csdoc}{\opt{rule dash length=}\meta{dimension}} + The length of dashes in the \lit{dashed} rule style. + It is \lit{0.2em} by default. +\end{csdoc} +\begin{csdoc}{\opt{rule dash space=}\meta{dimension}} + The space between dashes in the \lit{dashed} rule style. + It is \lit{0.3em} by default. +\end{csdoc} + +\begin{csdoc}{\opt{rule code=}\meta{code}} + This option is used to define an arbitrary shape for rules. + The \meta{code} is used to render the rule, it is executed in vertical mode + in a \cs{vbox} whose \cs{hsize} is set to the width of the rule. + Margins above and below are inserted automatically (they can be removed by + setting \lit{rule margin} to \lit{0pt}). + + \begin{example}{gobble=4} + \begin{prooftree}[rule code={\hbox{\tikz + \draw[decorate,decoration={snake,amplitude=.3ex}] + (0,0) -- (\hsize,0);}}] + \Hypo{ \Gamma &\vdash A } + \Infer1{ \Gamma &\vdash A, \ldots, A } + \Hypo{ \Delta, A, \ldots, A \vdash \Theta } + \Infer2{ \Gamma, \Delta \vdash \Theta } + \end{prooftree} + \end{example} + Note that this example requires the \package{tikz} package, with the + \package{decorations.pathmorphing} library for the \lit{snake} decoration. +\end{csdoc} + +The option \opt{rule code} is particularly useful in a ``styles'' in the sense of +\package{pgfkeys} as it allows to define new rule styles. +The allowed values for \opt{rule style} are actually defined this way. +The above example could be turned into a new rule style \lit{zigzag} with the +following command: +\begin{example}{gobble=2} + \ebproofset{ + rule style/zigzag/.style={rule code={\hbox{\tikz + \draw[decorate,decoration={snake,amplitude=.3ex}] + (0,0) -- (\hsize,0);}}}} + \begin{prooftree} + \Hypo{ \Gamma &\vdash A } + \Infer1{ \Gamma &\vdash A, \ldots, A } + \Hypo{ \Delta, A, \ldots, A \vdash \Theta } + \Infer[zigzag]2{ \Gamma, \Delta \vdash \Theta } + \end{prooftree} +\end{example} + +\subsection{Format of conclusions} + +\begin{csdoc}{% + \opt{template=}\meta{macro} \\ + \opt{left template=}\meta{macro} \\ + \opt{right template=}\meta{macro}} + Defines how conclusions are formatted. + The macros are arbitrary \TeX\ code, composed in horizontal mode, with the + macro argument \verb|#1| standing for the actual text passed to the + \cs{Hypo} and \cs{Infer} statements. + The \opt{template} value is used for conclusions with no alignment mark. + The \opt{left template} and \opt{right template} values are used on the left + and right side of the alignment mark when it is present. + The default value for \opt{template} is simply \verb|$#1$|, so that + conclusions are set in math mode. + The default values for \opt{left template} and \opt{right template} are + similar, with spacing assuming that a relation symbol is put near the + alignment mark, so that \verb|\Infer1{A &\vdash B}| is spaced correctly. + + \begin{example}{gobble=4} + \begin{prooftree}[template=(\textbf{#1})] + \Hypo{ foo } + \Hypo{ bar } + \Infer1{ baz } + \Infer2{ quux } + \end{prooftree} + \end{example} +\end{csdoc} + +\subsection{Format of labels} + +\begin{csdoc}{% + \opt{left label=}\meta{text} \\ + \opt{right label=}\meta{text}} + The text to use as the labels of the rules, on the left and on the right + of the inference line. + Using the second optional argument in \cs{Infer} is equivalent to setting + the \env{right label} option with the value of that argument. +\end{csdoc} +\begin{csdoc}{% + \opt{left label template=}\meta{macro} \\ + \opt{right label template=}\meta{macro}} + These macros are used to typeset the text of labels on the left and right of + inference lines. + The default values are \verb|#1| so that labels are set in plain text mode. +\end{csdoc} + +\begin{csdoc}{\opt{label separation=}\meta{dimension}} + The spacing between an inference lines and its labels. + The default value is \lit{0.5em}. +\end{csdoc} + + +\end{document} -- cgit v1.2.3