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paper: tweak font sizes harder using anyfont; lmodern
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artagnon committed Nov 19, 2023
1 parent 2aae42e commit 0bb6de9
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4 changes: 1 addition & 3 deletions paper/msc.cls
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\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{CUP-MSC-LaTeX-V1}[2018/08/09 v1.0 CUP MSC LaTeX document class]
\ProvidesClass{msc}[2018/08/09 v1.0 CUP MSC LaTeX document class]
%
\newif\ifOA\global\OAfalse%
\newif\iflsans\global\lsansfalse
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Standard Packages

\usepackage{etex}
\usepackage{amsthm}
\usepackage{soul}
\usepackage{calc}
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%
\def\endash{--}
%
%\RequirePackage{CUP-XML-Inputs}%

\ifonline
\usepackage{hyperref}%
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11 changes: 6 additions & 5 deletions paper/paper.tex
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\documentclass{msc}

\usepackage{amsmath, amssymb, mathrsfs, wasysym, tikz, tikz-cd, mathpazo, xargs, environ, multirow, float, tabularx, caption, bookmark, booktabs, makecell, colortbl, minted, art.cls/colorpal, art.cls/ct, art.cls/sset, art.cls/lim, art.cls/joinargs}

\usepackage{amsmath, amssymb, mathrsfs, wasysym, tikz, tikz-cd, lmodern, mathpazo, t1enc, anyfontsize, xargs, environ, multirow, float, tabularx, caption, bookmark, booktabs, makecell, colortbl, minted, art.cls/colorpal, art.cls/ct, art.cls/sset, art.cls/lim, art.cls/joinargs}
\usepackage[prefix=bonak]{art.cls/xkeymask}

% Use the patterns library to draw the cubes figure
\usetikzlibrary{patterns}

% Magic with xkeyval to go over the 9-argument limit of LaTeX
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% The eqntable environment
\newcolumntype{Y}{>{\centering\arraybackslash}X}
\NewEnviron{eqntable}[1]{
\scriptsize
\begin{tabularx}{0.93\linewidth}{
\fontsize{7.2}{9}\selectfont
\begin{tabularx}{0.94\linewidth}{
@{}
>{$}l<{$}
>{$}c<{$}
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\ldots
\end{align*}

In there, the process of construction of the type of $X_1$ from that of $X_0$, and from the type of $X_2$ to that of $X_1$, and so on, is similar to iteratively applying a binary parametricity translation. The binary parametricity which we consider is composed with the diagonal on types and interprets a type $A$ by a family $A_\kstar$ over $A \times A$, what can be seen as a graph whose vertices are in $A$. To each type constructor is thus associated the construction of a graph. To start with, the type of types $\U$ is interpreted as the family of type of families ${\U}_\kstar$, which takes $A_L$ and $A_R$ in $\U$ and returns the type $A_L \times A_R \rightarrow \U$ of families over $A_L$ and $A_R$. Also, for $A$ interpreted by $A_\kstar$ and $B$ interpreted by $B_\kstar$, a dependent function type $\Pi a: A.\, B$ is interpreted as the graph $(\Pi a: A.\, B)_\kstar$ that takes two functions $f_L$ and $f_R$ of type $\Pi a: A.\, B$, and expresses that these functions map related arguments in $A$ to related arguments in $B$:
In there, the process of construction of the type of $X_1$ from that of $X_0$, and from the type of $X_2$ to that of $X_1$, and so on, is similar to iteratively applying a binary parametricity translation. The binary parametricity which we consider interprets a type $A$ by a family $A_\kstar$ over $A \times A$, what can be seen as a graph whose vertices are in $A$. To each type constructor is thus associated the construction of a graph. To start with, the type of types $\U$ is interpreted as the family of type of families ${\U}_\kstar$, which takes $A_L$ and $A_R$ in $\U$ and returns the type $A_L \times A_R \rightarrow \U$ of families over $A_L$ and $A_R$. Also, for $A$ interpreted by $A_\kstar$ and $B$ interpreted by $B_\kstar$, a dependent function type $\Pi a: A.\, B$ is interpreted as the graph $(\Pi a: A.\, B)_\kstar$ that takes two functions $f_L$ and $f_R$ of type $\Pi a: A.\, B$, and expresses that these functions map related arguments in $A$ to related arguments in $B$:
\begin{align*}
(\Pi a: A.\, B)_\kstar(f_L,f_R) \; \defeq \; \Pi (a_L,a_R): (A \times A).\, (A_\kstar(a_L,a_R)\,\rightarrow B_\kstar(f_L(a_L),f_R(a_R)))
\end{align*}
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