hw2: add big-step semantics

hw2/while-semantics.tex

@@ -20,7 +20,7 @@
 
 \author{
   CS 252: Advanced Programming Languages \\
-  Prof. Thomas H. Austin \\
+  Yuri Tatishchev \\
   San Jos\'{e} State University \\
   }
 \date{}
@@ -113,6 +113,17 @@ Both choices, however, would complicate our language needlessly.
 \section{YOUR ASSIGNMENT}
 \newcommand{\bstep}[4]{{#1},{#2} \Downarrow {#3},{#4}}
 
+% Format for a big-step evaluation rule.
+% #1 is the name of the rule.
+% #2 are the premises.  Leave blank if there are none.
+% #3 is the conclusion.
+\newcommand{\bsrule}[3]{
+  \rel{#1} &
+  \frac{\strut\begin{array}{@{}c@{}} #2 \end{array}}
+       {\strut\begin{array}{@{}c@{}} #3 \end{array}}
+   \\~\\
+}
+
 \noindent
 {\bf Part 1:}
 Rewrite the operational semantic rules for WHILE in \LaTeX\
@@ -288,5 +299,77 @@ Finally, implement the interpreter to match your semantics.
 \end{figure}
 
 
+\begin{figure}[H]\label{fig:bigstep}
+\caption{Big-step semantics for WHILE}
+{\bf Runtime Syntax:}
+\[
+\begin{array}{rclcl}
+  \sigma & \in & {Store} \quad  & = & \quad {variable} ~\rightarrow ~v \\
+  \\
+\end{array}
+\]
+{\bf Evaluation Rules:~~~ \fbox{$\bstep{e}{\sigma}{e'}{\sigma'}$}} \\
+\[
+\begin{array}{r@{\qquad\qquad}c}
+\bsrule{B-Value}{}{
+  \bstep{v}{\sigma}{v}{\sigma}
+}
+\bsrule{B-Var}{
+  x \in domain(\sigma) \qquad \sigma(x)=v
+}{
+  \bstep{x}{\sigma}{v}{\sigma}
+}
+\bsrule{B-Assign}{
+  \bstep{e}{\sigma}{v}{\sigma'}
+}{
+  \bstep{\assign{x}{e}}{\sigma}{v}{\sigma'[x:=v]}
+}
+\bsrule{B-Seq}{
+  \bstep{e_1}{\sigma}{v_1}{\sigma'} \\
+  \bstep{e_2}{\sigma'}{v_2}{\sigma''}
+}{
+  \bstep{e_1;e_2}{\sigma}{v_2}{\sigma''}
+}
+\bsrule{B-Op}{
+  \bstep{e_1}{\sigma}{v_1}{\sigma'} \\
+  \bstep{e_2}{\sigma'}{v_2}{\sigma''} \\
+  v = apply(op, v_1, v_2)
+}{
+  \bstep{e_1~op~e_2}{\sigma}{v}{\sigma''}
+}
+\bsrule{B-IfTrue}{
+  \bstep{e_1}{\sigma}{\true}{\sigma'} \\
+  \bstep{e_2}{\sigma'}{v}{\sigma''}
+}{
+  \bstep{\ife{e_1}{e_2}{e_3}}{\sigma}{v}{\sigma''}
+}
+\bsrule{B-IfFalse}{
+  \bstep{e_1}{\sigma}{\false}{\sigma'} \\
+  \bstep{e_3}{\sigma'}{v}{\sigma''}
+}{
+  \bstep{\ife{e_1}{e_2}{e_3}}{\sigma}{v}{\sigma''}
+}
+\bsrule{B-WhileTrue}{
+  \bstep{e_1}{\sigma}{\true}{\sigma'} \\
+  \bstep{e_2}{\sigma'}{v}{\sigma''}
+}{
+  \bstep{\whilee{e_1}{e_2}}{\sigma}{v}{\sigma''}
+}
+\bsrule{B-WhileFalse}{
+  \bstep{e_1}{\sigma}{\false}{\sigma'}
+}{
+  \bstep{\whilee{e_1}{e_2}}{\sigma}{\false}{\sigma'}
+}
+% \bsrule{B-While}{
+%   \bstep{e_1}{\sigma}{v_1}{\sigma'} \\
+%   \bstep{e_2}{\sigma'}{v_2}{\sigma''}
+% }{
+%   \bstep{\whilee{e_1}{e_2}}{\sigma}{\ife{v_1}{e_2;\whilee{e_1}{e_2}}{\false}}{\sigma''}
+% }
+\end{array}
+\]
+\end{figure}
+
+
 \end{document}