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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/perfectcut/perfectcut.tex |
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diff --git a/macros/latex/contrib/perfectcut/perfectcut.tex b/macros/latex/contrib/perfectcut/perfectcut.tex new file mode 100644 index 0000000000..23e637d51c --- /dev/null +++ b/macros/latex/contrib/perfectcut/perfectcut.tex @@ -0,0 +1,333 @@ +%%% perfectcut.sty documentation +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% +%%% Author: Guillaume Munch-Maccagnoni +%%% https://gitlab.com/gadmm/perfectcut +%%% +%%% This work may be distributed and/or modified under the conditions of +%%% the LaTeX Project Public License, either version 1.3 of this license +%%% or (at your option) any later version. Refer to the README file. +%%% +\documentclass[12pt,a4paper,british]{scrartcl} +\usepackage[T1]{fontenc} +\usepackage[latin9]{inputenc} +\setcounter{secnumdepth}{1} +\setcounter{tocdepth}{1} +\usepackage{babel} +\usepackage{array} +\usepackage{booktabs} +\usepackage{calc} +\usepackage{amsmath} +\usepackage[unicode=true]{hyperref} +\usepackage{perfectcut} +\usepackage{stix} +\renewcommand*\ttdefault{txtt} +\usepackage[oldstyle,lining,scale=0.97]{sourcesanspro} +\usepackage[protrusion=true,expansion=true,tracking=false,kerning=true,spacing=true]{microtype} + +\begin{document} +\global\long\def\cut#1#2{\perfectcut{#1}{#2}} + +\global\long\def\mt{\bar{\mu}} + + +\title{\texttt{perfectcut.sty} documentation} + +\author{\noindent {\large{}Guillaume Munch-Maccagnoni}\thanks{\protect\href{https://gitlab.com/gadmm/perfectcut}{https://gitlab.com/gadmm/perfectcut}}} + +\date{3rd September 2017} + +\maketitle + +\tableofcontents{} + +\section{Use} + +\paragraph{Original use} + +This package supplies the following commands: + +\begin{center} +\begin{tabular}{ll} +\toprule +Command & Produces\tabularnewline +\midrule +\texttt{\textbackslash perfectcut\{\#1\}\{\#2\}} & $\perfectcut{\#1}{\#2}$\tabularnewline +\texttt{\textbackslash perfectbra\{\#1\}} & $\perfectbra{\#1}$\tabularnewline +\texttt{\textbackslash perfectket\{\#1\}} & $\perfectket{\#1}$\tabularnewline +\bottomrule +\end{tabular}\quad{}% +\begin{tabular}{ll} +\toprule +Command & Produces\tabularnewline +\midrule +\texttt{\textbackslash perfectcase\{\#1\}} & $\perfectcase{\#1}{\#2}$\tabularnewline +\texttt{\textbackslash perfectbrackets\{\#1\}} & $\perfectbrackets{\#1}$\tabularnewline +\texttt{\textbackslash perfectparens\{\#1\}} & $\perfectparens{\#1}$\tabularnewline +\bottomrule +\end{tabular} +\par\end{center} + +The effect of these commands is to let the delimiters grow according +to the number of nested \texttt{\textbackslash perfect}\texttt{\emph{command}}s +(regardless of the size of contents). The package is originally intended +for solving a notational issue regarding the representation of abstract-machine-like +calculi in proof theory and computer science. + +\paragraph{General use} + +The package also defines \texttt{\textbackslash perfectunary} and +\texttt{\textbackslash perfectbinary} for defining custom delimiters +that behave similarly to the above ones. These commands should be +considered when facing the need of nested delimiters that consistently +grow regardless of the contents. (See ``Advanced Use''.) + +\section{Example} + + +\subsection{Using \texttt{perfectcut.sty}} + +\global\long\def\cut#1#2{\cutprimitive{#1}{#2}} + +\noindent \texttt{\footnotesize{}\textbackslash usepackage\{perfectcut\}}~\\ +\texttt{\footnotesize{}\textbackslash let\textbackslash cut\textbackslash perfectcut} + +\begin{center} +\fbox{\begin{minipage}[t]{0.8\columnwidth}% +The following states the idempotency of an adjunction: +\[ +\cut t{\mt x.\cut{\mu\alpha.\cut ue}{e'}}=\cut{\mu\alpha.\cut t{\mt x.\cut ue}}{e'} +\] + +The following states the commutativity of a strong monad: +\[ +\cut t{\mt x.\cut u{\mt y.\cut ve}}=\cut u{\mt y.\cut t{\mt x.\cut ve}} +\] +Using \texttt{\textbackslash underline} to mark redexes: +\begin{align*} + & \delta(V,x.y,x.y)\\ + & =\mu{\star}.\cut V{\perfectcase{\mt x.\underline{\cut y{\star}}}{\mt x.\underline{\cut y{\star}}}}\\ + & =\mu{\star}.\cut V{\underline{\perfectcase{\mt x.\cut{\iota_{1}(x)}{\mt z.\cut y{\star}}}{\mt x.\cut{\iota_{2}(x)}{\mt z.\cut y{\star}}}}}\\ + & =\mu{\star}.\cut V{\underline{\mt z.}\cut y{\star}}\\ + & =\mu{\star}.\cut y{\star}=y +\end{align*} + % +\end{minipage}} +\par\end{center} + +\subsection{Using \texttt{\textbackslash left}, \texttt{\textbackslash middle} +and \texttt{\textbackslash right} instead} + +\global\long\def\fakecut#1#2{\left\langle #1\middle|\mkern-2mu \middle|#2\right\rangle } + +\noindent \texttt{\footnotesize{}\textbackslash renewcommand\{\textbackslash cut\}{[}2{]}\{\textbackslash left\textbackslash langle +\#1\textbackslash middle|\textbackslash mkern-2mu\textbackslash middle|\#2\textbackslash right\textbackslash rangle\}} + +\begin{center} +\fbox{\parbox[t]{0.8\columnwidth}{% +The following states the idempotency of an adjunction: +\[ +\fakecut t{\mt x.\fakecut{\mu\alpha.\fakecut ue}{e'}}=\fakecut{\mu\alpha.\fakecut t{\mt x.\fakecut ue}}{e'} +\] + +The following states the commutativity of a strong monad: +\[ +\fakecut t{\mt x.\fakecut u{\mt y.\fakecut ve}}=\fakecut u{\mt y.\fakecut t{\mt x.\fakecut ve}} +\] + +Using \texttt{\textbackslash underline} to mark redexes: +\begin{align*} + & \delta(V,x.y,x.y)\\ + & =\mu{\star}.\fakecut V{\left[\mt x.\underline{\fakecut y{\star}}\middle|\mt x.\underline{\fakecut y{\star}}\right]}\\ + & =\mu{\star}.\fakecut V{\underline{\left[\mt x.\fakecut{\iota_{1}(x)}{\mt z.\fakecut y{\star}}\middle|\mt x.\fakecut{\iota_{2}(x)}{\mt z.\fakecut y{\star}}\right]}}\\ + & =\mu{\star}.\fakecut V{\underline{\mt z.}\fakecut y{\star}}\\ + & =\mu{\star}.\fakecut y{\star}=y +\end{align*} +% +}} +\par\end{center} + +As we can see, the legibility of the above rendering is hampered by +multiple issues: the delimiters grow inconsistently, vertical bars +have the wrong size, accents or underlines uselessly make the delimiters +grow, and the spacing could be improved. The package is designed to +fix these issues. + +\section{Advanced use} + +The package lets you define your own growing delimiters. Let us first +stress that the size of these delimiters is entirely determined by +the number of nestings and is insensitive to the size of the contents. +If you need the size of the contents to be taken into account then +it is probably sufficient to use \texttt{\textbackslash left} and +\texttt{\textbackslash right} while tweaking \texttt{\textbackslash delimitershortfall} +and \texttt{\textbackslash delimiterfactor}. + +\subsection{Example} + +The following displays a set $\{\#1\mid\#2\}$ with delimiters appropriately +sized if there are other \texttt{\textbackslash perfectcommands} +inside \texttt{\#1} and \texttt{\#2}.\medskip{} + +\texttt{\footnotesize{}\textbackslash def\textbackslash Set\#1\#2\{\textbackslash perfectbinary\{IncreaseHeight\}\textbackslash\{|\textbackslash\}\{\#1\textbackslash mathrel\{\}\}\{\textbackslash mathrel\{\}\#2\}\}}{\footnotesize\par} + +\texttt{\footnotesize{}\textbackslash{[}\textbackslash Set\{\textbackslash perfectparens\{a\}\}\{\textbackslash perfectparens\{b\}\}\textbackslash{]}}{\footnotesize\par} + +\def\Set#1#2{\perfectbinary{IncreaseHeight}\{|\}{#1\mathrel{}}{\mathrel{}#2}} + +\[ +\fbox{\ensuremath{\Set{\perfectparens{a}}{\perfectparens{b}}}} +\] + + +\subsection{Custom delimiters} +\begin{description} +\item [{\texttt{\textbackslash perfectunary\#1\#2\#3\#4}}] Displays \texttt{\#2} +\texttt{\#4} \texttt{\#3} where \texttt{\#2} and \texttt{\#3} are +delimiters. The delimiters grow according to \texttt{\#1} which must +be one of \texttt{IncreaseHeight}, \texttt{CurrentHeight}, or \texttt{CurrentHeightPlusOne}. +\item [{\texttt{\textbackslash perfectbinary\#1\#2\#3\#4\#5\#6}}] Displays +\texttt{\#2} \texttt{\#5} \texttt{\#3} \texttt{\#6} \texttt{\#4} where +\texttt{\#2}, \texttt{\#3} and \texttt{\#4} are delimiters. The delimiters +grow according to \texttt{\#1} which must be one of \texttt{IncreaseHeight}, +\texttt{CurrentHeight}, or \texttt{CurrentHeightPlusOne}. +\end{description} + +\subsection{Stock delimiters} + +The stock commands behave as follow: + +\begin{center} +\begin{tabular}{>{\raggedright}p{11em}lll} +\toprule +Command & Produces & Growth & Inserts skips\tabularnewline +\midrule +\texttt{\textbackslash perfectcut\{\#1\}\{\#2\}} & $\perfectcut{\#1}{\#2}$ & \texttt{IncreaseHeight} & Yes\tabularnewline +\texttt{\textbackslash perfectbra\{\#1\}} & $\perfectbra{\#1}$ & \texttt{IncreaseHeight} & Yes\tabularnewline +\texttt{\textbackslash perfectket\{\#1\}} & $\perfectket{\#1}$ & \texttt{IncreaseHeight} & Yes\tabularnewline +\texttt{\textbackslash perfectcase\{\#1\}} & $\perfectcase{\#1}{\#2}$ & \texttt{CurrentHeightPlusOne} & Yes\tabularnewline +\texttt{\textbackslash perfectbrackets\{\#1\}} & $\perfectbrackets{\#1}$ & \texttt{CurrentHeightPlusOne} & Only inside\tabularnewline +\texttt{\textbackslash perfectparens\{\#1\}} & $\perfectparens{\#1}$ & \texttt{CurrentHeight} & Only inside\tabularnewline +\texttt{\textbackslash perfectunary\{\#1\}}~\\ +\texttt{~\{\#2\}\{\#3\}\{\#4\}} & $\#2\,\#4\,\#3$ & \#1 & No\tabularnewline +\texttt{\textbackslash perfectbinary\{\#1\}}~\\ +\texttt{~\{\#2\}\{\#3\}\{\#4\}\{\#5\}\{\#6\}} & $\#2\,\#5\,\#3\,\#6\,\#4$ & \#1 & No\tabularnewline +\bottomrule +\end{tabular} +\par\end{center} + +\section{Options} + +\subsection{Option \texttt{mathstyle}} + +With this option, the command \texttt{\textbackslash currentmathstyle} +from the package \texttt{mathstyle} is used instead of the command +\texttt{\textbackslash ThisStyle} from the \texttt{scalerel} package. +The latter (default) uses \texttt{\textbackslash mathchoice}, and +in order to avoid an exponential time complexity in the number of +nestings, it is only called for the outermost command. Concretely, +with \texttt{mathstyle}, math style changes are taken into account +both inside and outside of \texttt{\textbackslash perfectcommands}, +whereas without it, changes in math style are not obeyed inside a +command. Moreover, using the \texttt{mathstyle} option speeds up compilation. +The downside of using \texttt{mathstyle} is that it redefines many +standard math commands, and is therefore a source of incompatibilities, +notably with \texttt{xypic}. + +\subsection{Option \texttt{realVert}} + +With the option \texttt{realVert}, the double bars are obtained with +the \texttt{\textbackslash Vert} command. But without it, two \texttt{\textbackslash vert} +symbols are used and their spacing is controlled with \texttt{\textbackslash cutinterbarskip}. +Also, if \texttt{realVert} is not activated, then a penalty (\texttt{binoppenalty}) +is added, such that $\cut{\mu\alpha.\cut ab}{\mt x.\cut cd}$ splits +across lines. + +\subsection{Option \texttt{fixxits}} + +For some reason that the author was unable to identify, the vertical +alignment is wrong with the Opentype XITS math font with XeTeX. The +option \texttt{fixxits} fixes this behaviour. + +\subsection{Customisation} + +The following mu-skips can be redefined in your preamble: + +\begin{center} +\begin{tabular}{ll} +\toprule +Command & Defines the spacing...\tabularnewline +\midrule +\texttt{\textbackslash cutbarskip=5.0mu plus 8mu minus 2.0mu} & around bars\tabularnewline +\texttt{\textbackslash cutangleskip=0.0mu plus 8mu minus 1.0mu} & around delimiters (inside)\tabularnewline +\texttt{\textbackslash cutangleouterskip=0.0mu plus 8mu minus 0mu} & around delimiters (outside)\tabularnewline +\texttt{\textbackslash cutinterbarskip=0.8mu plus 0mu minus 0mu} & between bars (excl. \texttt{realVert})\tabularnewline +\bottomrule +\end{tabular} +\par\end{center} + +\noindent (1 mu equals $1/18$ of an em in the current math font.) + +\section{Reimplementation of fixed-size delimiters} + +In addition, I provide the following corrections and generalisations +of \texttt{\textbackslash big},\texttt{\textbackslash bigg}, etc. +Why not using the latter? Because both the plain \TeX{} and the \texttt{amsmath} +versions can be incorrect when changing the math font, the font size, +the math style or \texttt{\textbackslash delimitershortfall}. Moreover, +Opentype math fonts sometimes offer more than five sizes. For this +package we need a robust solution. + +\begin{center} +\begin{tabular}{lll} +\toprule +Command & Example & \tabularnewline +\midrule +\multicolumn{3}{l}{\emph{\#1-th size of delimiter \#2}}\tabularnewline +\texttt{\textbackslash nthleft\{\#1\}\{\#2\} } & \texttt{\textbackslash nthleft\{2\}(} & $\nthleft{2}($\tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash nthmiddle\{\#1\}\{\#2\}} & \texttt{\textbackslash nthmiddle\{2\}\textbackslash Vert} & $\nthmiddle{2}\Vert$\tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash nthright\{\#1\}\{\#2\}} & \texttt{\textbackslash nthright\{2\})} & $\nthright{2})$\tabularnewline\addlinespace[0.1em] +\multicolumn{1}{l}{\emph{delimiter \#2 of height at least \#1}} & & \tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash lenleft\{\#1\}\{\#2\}} & \texttt{\textbackslash lenleft\{3.2mm\}{[}} & $\lenleft{3mm}[$\tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash lenmiddle\{\#1\}\{\#2\}} & \texttt{\textbackslash lenmiddle\{3.2mm\}|} & $\lenmiddle{3mm}|$\tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash lenright\{\#1\}\{\#2\}} & \texttt{\textbackslash lenright\{3.2mm\}{]}} & $\lenright{3mm}]$\tabularnewline\addlinespace[0.1em] +\multicolumn{3}{l}{\emph{delimiter \#2 of height exactly \#1 obtained by scaling the +above one}}\tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash reallenleft\{\#1\}\{\#2\}} & \texttt{\textbackslash reallenleft\{3.2mm\}{[}} & $\reallenleft{3mm}[$\tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash reallenmiddle\{\#1\}\{\#2\}} & \texttt{\textbackslash reallenmiddle\{3.2mm\}|} & $\reallenmiddle{3mm}|$\tabularnewline\addlinespace[0.1em] +\texttt{\textbackslash reallenright\{\#1\}\{\#2\}} & \texttt{\textbackslash reallenright\{3.2mm\}{]}} & $\reallenright{3mm}]$\tabularnewline +\bottomrule +\end{tabular} +\par\end{center} + +\subsection{Example with \texttt{\textbackslash nthleft}} + +\texttt{\footnotesize{}\textbackslash nrthleft0(\textbackslash nthleft1(\textbackslash nthleft2(\textbackslash nthleft3(\textbackslash nthleft4(\textbackslash nthleft5(\textbackslash nthleft6(}{\footnotesize\par} + +\[ +\nthleft0(\nthleft1(\nthleft2(\nthleft3(\nthleft4(\nthleft5(\nthleft6( +\] + + +\subsection{Example with \texttt{\textbackslash big},\texttt{\textbackslash Big},\texttt{\textbackslash bigg},\texttt{\textbackslash Bigg}} + +\texttt{\footnotesize{}(\textbackslash big(\textbackslash Big(\textbackslash bigg(\textbackslash Bigg(}{\footnotesize\par} + +\[ +(\big(\Big(\bigg(\Bigg( +\] +The above uses the \texttt{\textbackslash big} commands from the +\texttt{amsmath} package. The \texttt{amsmath} package corrects issues +with the original \TeX{} commands, but I could still notice inconsistencies, +such as \texttt{\textbackslash big} starting at size 2, under some +font combinations. \texttt{\textbackslash nthleft}, \texttt{\textbackslash nthright} +and \texttt{\textbackslash nthmiddle} are implemented in a more robust +way. + +\section{License} + +This work may be distributed and/or modified under the conditions +of the \LaTeX{} Project Public License, either version 1.3 of this +license or (at your option) any later version. Refer to the \texttt{README} +file. +\end{document} |