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Add first draft for semantics

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regnat 2017-03-28 17:39:08 +02:00
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commit b7e3fb43b7
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\documentclass{article}
\usepackage{fontspec}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
\usepackage{ amssymb }
%The \leftsquigarrow command
\makeatletter
\providecommand{\leftsquigarrow}{%
\mathrel{\mathpalette\reflect@squig\relax}%
}
\newcommand{\reflect@squig}[2]{%
\reflectbox{$\m@th#1\rightsquigarrow$}%
}
\makeatother
\usepackage{syntax}
\title{Nix simplified semantics}
\author{Théophane Hufschmitt}
\date{}
\newcommand{\assign}[2]{#1 := #2}
\newcommand{\subst} [3] {#3 [\assign{#1}{#2}]}
\newcommand{\substp} [3] {#3 [#1 \ensuremath{\leftsquigarrow} #2]}
\newcommand{\dstep} [2] {#1 \ensuremath{\rightarrow} #2}
\newcommand{\ndstep} [2] {#1 \ensuremath{\nrightarrow} #2}
\newcommand{\ndsteps} [2] {#1 \ensuremath{\nrightarrow^*} #2}
\newcommand{\dstepa} [3] {\dstep{#1}{&#2}~\emph{#3} \\}
\newcommand{\sone}{\ensuremath{s_1}}
\newcommand{\sn}{\ensuremath{s_n}}
\newcommand{\eone}{\ensuremath{e_1}}
\newcommand{\etwo}{\ensuremath{e_2}}
\newcommand{\en}{\ensuremath{e_n}}
\begin{document}
\maketitle{}
\begin{tabular}{rl}
\dstepa{\{ "s" = e; ... \}."s"}{e}{}
\dstepa{\{ "s" = e; ... \}."s" or e}{e}{}
\dstepa{e.a or e'}{e'}{if \ndsteps{e}{\{ "s" = e; ... \}}}
% TODO: complete
\dstepa{(p:e1) e2}{\substp{p}{e2}{e1}}{} % TODO: define the substitution
\dstepa{with \{ "\sone" = \eone; ...; "\sn"= \en; e \}}{%
e[\assign{\sone}{\eone}; ...; \assign{\sn}{\en}]
}{}
\dstepa{raise e}{$\bot$}{}
\dstepa{if true then \eone else \etwo}{\eone}{}
\dstepa{if false then \eone else \etwo}{\etwo}{}
\dstepa{let \sone = \eone; ...; \sn = \en; in e}{%
\parbox[t]{10cm}{e [ \\
\assign{\sone}{\subst{\sone}{let \sone = \eone; ...; \sn = \en; in \sone}{\eone}}; \\
...; \\
\assign{\sn}{\subst{\sn}{let \sone = \eone; ...; \sn = \en; in \sn}{\en}} \\
]}
}{}
\end{tabular}
\end{document}