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intensional-syntax.tex 1.52 KiB
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  • \documentclass{article}
    \usepackage{amssymb}
    \usepackage{amsmath}
    \usepackage{amsthm}
    \usepackage{tikz-cd}
    \usepackage{mathpartir}
    \usepackage{stmaryrd}
    \usepackage{parskip}
    \usepackage{tikz-cd}
    
    \newtheorem{theorem}{Theorem}[section]
    \newtheorem{nonnum-theorem}{Theorem}[section]
    \newtheorem{corollary}{Corollary}[section]
    \newtheorem{definition}{Definition}[section]
    \newtheorem{lemma}{Lemma}[section]
    
    \newcommand{\later}{{\vartriangleright\hspace{-2px}}}
    \newcommand{\nxt}{\texttt{next}}
    
    \newcommand{\calS}{\mathcal{S}}
    \newcommand{\gfix}{\texttt{gfix}}
    
    \newcommand{\calU}{\mathcal{U}}
    \newcommand{\laterhat}{\widehat{\later}}
    \newcommand{\El}{\mathsf{El}}
    
    \newcommand{\lift}{L_\mho}
    \newcommand{\lifthat}{\widehat{L_\mho}}
    
    \newcommand{\To}{\Rightarrow}
    \newcommand{\calC}{\mathcal{C}}
    \newcommand{\Set}{\texttt{Set}}
    \newcommand{\Yo}{\mathsf{Yo}}
    \newcommand{\Hom}{\mathsf{Hom}}
    
    \newcommand{\inl}{\texttt{inl}}
    \newcommand{\inr}{\texttt{inr}}
    \newcommand{\alt}{\,|\,}
    
    \begin{document}
    
    \title{Intensional Syntax}
    \author{Max S. New and Eric Giovannini}
    
    \maketitle
    
    \begin{mathpar}
      \begin{array}{rcl}
        \textrm{Value Types} & ::= & \mathbb N \alt D \alt A \rightharpoonup A'\alt \later A\\
        \textrm{Comp Types} & ::= & \mathcal L A
      \end{array}
    \end{mathpar}
    
    What are the rules for $\later$?
    
    \begin{mathpar}
      \inferrule
      {\Gamma \vdash V : A}
      {\Gamma \vdash \nxt\, V : \later A}
    
      \inferrule
      {}
      {\Gamma \vdash \theta : \later A \rightharpoonup A}
    
      \theta(\nxt x) = \theta(y); \texttt{ret}\, x
    \end{mathpar}
    
    \end{document}