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\chapter{The Diderot Language}
\label{chap:lang}

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\section{Global declarations}

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\section{Actor definitions}

\subsection{Actor state}

\subsection{The update method}

\subsection{The stabilize method}

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\section{Initialization}

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\section{Statements}

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\section{Expressions}

\subsection{Conditional expressions}
There are three conditional expression forms in Diderot:
\emph{if-else} expressions, \emph{or-else} expressions, and \emph{and-also}
expressions.
The syntax of these is given by the following grammar fragment:
\begin{Grammar}
  \ExprRULES{}
  \TestExprRULES{}
  \AndExprRULES{}
\end{Grammar}%

\subsubsection{If-else expressions}
The if-else expression has the following typing rule:
\begin{displaymath}
  \infer{
      \HasTy{\ENV}{e_1\;\mkw{if}\;e_2\;\mkw{else}\;e_3}{\tau}
    }{
      \HasTy{\ENV}{e_1}{\tau} \quad
      \HasTy{\ENV}{e_2}{\TYbool} \quad
      \HasTy{\ENV}{e_3}{\tau} \quad
  }
\end{displaymath}%
Its semantics are that it evaluates $e_2$ first.
If the value is true, then it evaluate $e_1$, otherwise it evaluates $e_3$.

\subsubsection{Or-else expressions}
\begin{displaymath}
  \infer{
      \HasTy{\ENV}{e_1\;\mkw{||}\;e_2}{\TYbool}
    }{
      \HasTy{\ENV}{e_1}{\TYbool} \quad
      \HasTy{\ENV}{e_2}{\TYbool}
  }
\end{displaymath}%
The or-else form is derived from the if-else form as follows:
\begin{displaymath}
  e_1\;\mkw{||}\;e_2 \quad \equiv \quad \mkw{true}\;\mkw{if}\;e_1\;\mkw{else}\;e_2
\end{displaymath}%

\subsubsection{If-else expressions}
\begin{displaymath}
  \infer{
      \HasTy{\ENV}{e_1\;\mkw{\&\&}\;e_2}{\TYbool}
    }{
      \HasTy{\ENV}{e_1}{\TYbool} \quad
      \HasTy{\ENV}{e_2}{\TYbool}
  }
\end{displaymath}%
The and-also form is derived from the if-else form as follows:
\begin{displaymath}
  e_1\;\mkw{\&\&}\;e_2 \quad \equiv \quad e_2\;\mkw{if}\;e_1\;\mkw{else}\;\mkw{false}
\end{displaymath}%

\subsection{Binary expressions}
\begin{Grammar}
  \CmpExprRULES{}
  \AddExprRULES{}
  \MulExprRULES{}
  \CmpOpRULES{}
  \AddOpRULES{}
  \MulOpRULES{}
\end{Grammar}%

\subsection{Field-probe expressions}
\begin{Grammar}
  \ProbeExprRULES{}
\end{Grammar}%

\subsection{Unary expressions}
\begin{Grammar}
  \PrefixExprRULES{}
\end{Grammar}%

\subsection{Tensor-slice expressions}
\begin{Grammar}
  \SliceExprRULES{}
  \IndexRULES{}
\end{Grammar}%

\subsection{Atomic expressions}
\begin{Grammar}
  \AtomExpRULES{}
  \ArgumentsRULES{}
\end{Grammar}%