Compress pattern description for short paper

1 files changed, 16 insertions, 120 deletions

diff --git a/aied2018/aied2018_short.tex b/aied2018/aied2018_short.tex
index 1272be8..1a371fa 100644
--- a/aied2018/aied2018_short.tex
+++ b/aied2018/aied2018_short.tex
@@ -45,7 +45,7 @@
 
 \begin{abstract}
 % background / problem
-Writing programs is essential to learning programming. Most programming courses encourage students to practice with lab and homework assignments. By analyzing solutions to these exercises teachers can discover mistakes and concepts students are struggling with, and use that knowledge to improve the content and presentation of the course. Students however tend to submit many different programs even for simple exercises, making such analysis difficult.
+Writing programs is essential to learning programming. Most programming courses encourage students to practice with lab and homework assignments. By analyzing solutions to these exercises teachers can discover mistakes and concepts students are struggling with, and use that knowledge to improve the course. Students however tend to submit many different programs even for simple exercises, making such analysis difficult.
 % solution
 We propose using tree regular expressions to encode common patterns in programs. Based on these patterns we induce rules describing common approaches and mistakes for a given assignment. In this paper we present a case study of rule-based analysis for an introductory Python exercise. We show that our rules are easy to interpret, and can be learned from a relatively small set of programs.
 \\\\
@@ -56,17 +56,14 @@ We propose using tree regular expressions to encode common patterns in programs.
 
 Providing feedback to students is among the most time-consuming tasks when teaching programming. In large courses with hundreds of students, feedback is therefore often limited to automated program testing. While test cases can reliably determine whether a program is correct or not, they cannot easily be associated with specific errors in the code.
 
-Several attempts have been made to automatically discover commonalities in a set of programs~\cite{jin2012program,rivers2015data-driven,nguyen2014codewebs,hovemeyer2016control}. This would allow a teacher to annotate a representative subset of submissions with feedback messages, which could then be automatically propagated to similar programs. These techniques are used for instance by the OverCode tool to visualize variations in student programs~\cite{glassman2015overcode}.
+Several attempts have been made to automatically discover common errors in student programs~\cite{jin2012program,rivers2015data-driven,nguyen2014codewebs,hovemeyer2016control}. This would allow a teacher to annotate a representative subset of submissions with feedback messages, which could then be automatically propagated to similar programs. These techniques are used for instance by the OverCode tool to visualize variations in student programs~\cite{glassman2015overcode}.
 
-This paper presents a new language for describing patterns in student code. Our approach is based on \emph{tree regular expressions} (TREs) used in natural language processing~\cite{levy2006tregex}. TREs are similar to ordinary regular expressions: they allow us to specify important patterns in a program’s abstract syntax tree (AST) while disregarding irrelevant parts. We found that TREs are sufficiently expressive to represent various concepts and errors in novice programs.
-
-We have previously demonstrated this approach with Prolog programs~\cite{lazar2017automatic}. Here we refine the definition of AST patterns, and show that they can be applied to Python -- representing a different programming paradigm -- with only a few language-specific modifications. The exercises and the solutions were obtained from the online programming environment CodeQ\footnote{Available at \url{https://codeq.si}. Source under AGPL3+ at \url{https://codeq.si/code}.}. In the case study, we demonstrate that rules learned from such patterns can be easily interpreted.
+We use \emph{tree regular expressions} (TREs) to specify important patterns in a program’s abstract syntax tree (AST) while disregarding irrelevant parts.
+We have previously demonstrated this approach with Prolog programs~\cite{lazar2017automatic}. Here we refine the AST patterns and show that they can be applied to Python -- a different programming paradigm -- with only a few modifications.
 
 \section{AST patterns}
 
-We encode structural patterns in ASTs using tree regular expressions (TREs). An ordinary regular expression describes the set of strings matching certain constraints; similarly, a TRE describes the set of trees containing certain nodes and relations. Since TREs describe structure, they are themselves represented as trees. More specifically, both ASTs and TREs are ordered rooted trees.
-
-In this work we used TREs to encode (only) child and sibling relations in ASTs. We write them as S-expressions, such as \pattern{(a (b \textbf{\textasciicircum}~d~\textbf{.}~e~\$) c)}. This expression matches any tree satisfying the following constraints (see Fig.~\ref{fig:tre-example} for an example):
+We encode structural patterns in ASTs using tree regular expressions (TREs). In this work we consider (only) child and sibling relations in ASTs. We write them as S-expressions, such as \pattern{(a (b \textbf{\textasciicircum}~d~\textbf{.}~e~\$) c)}. This expression matches any tree satisfying the following constraints:
 
 \begin{itemize}
 	\item the root \pattern{a} has at least two children, \pattern{b} and \pattern{c}, adjacent and in that order; and
@@ -74,107 +71,18 @@ In this work we used TREs to encode (only) child and sibling relations in ASTs.
 \end{itemize}
 
 \noindent
-Analogous to ordinary regular expressions, caret (\texttt{\textbf{\textasciicircum}}) and dollar sign (\texttt{\$}) anchor a node to be respectively the first or last child of its parent. A period (\texttt{\textbf{.}}) is a wildcard that matches any node.
-
-\begin{figure}[tbp]
-	\centering
-	\begin{forest}
-		for tree={
-			font=\sf,
-			edge=darkgray,
-			l sep=0,
-			l=0.9cm,
-		}
-		[a,name=a
-		[f]
-		[b,name=b
-		[d,name=d] [g,name=g] [e,name=e]]
-		[c,name=c [j] [k]]
-		[h]
-		]
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (a) edge[transform canvas={xshift=0.8mm,yshift=-0.2mm}] (b);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (a) edge[transform canvas={xshift=-0.9mm,yshift=-0.3mm}] (c);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (b) edge[transform canvas={xshift=-1.1mm,yshift=0.2mm}] (d);
-		\draw[opacity=0] (b) -- node[anchor=east,thick,blue,opacity=1,font=\large] {\texttt{\textasciicircum}} (d);
-		\path[draw,thick,relative,blue,transform canvas={xshift=-0.7mm}] (b) -- ($ (b)!0.6!(g) $);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (b) edge[transform canvas={xshift=1.1mm,yshift=0.2mm}] (e);
-		\draw[opacity=0] (b) -- node[anchor=west,thick,blue,opacity=1,font=\scriptsize,transform canvas={xshift=0mm,yshift=1mm}] {\texttt{\$}} (e);
-	\end{forest}
-	\caption{A tree matching a pattern (blue arrows besides the edges). In the pattern, each arrow $x→y$ means that node $x$ has a child $y$. A shorter line without an arrowhead (e.g. \pattern{b}$\boldsymbol{-}$ \pattern{g}) indicates a wildcard, where the child can be any node. Anchors \texttt{\textbf{\textasciicircum}} and \texttt{\$} mean that the pattern will match only the first or last child.}
-	\label{fig:tre-example}
-\end{figure}
+As in ordinary regular expressions, caret (\texttt{\textbf{\textasciicircum}}) and dollar sign (\texttt{\$}) anchor a node to be respectively the first or last child, and a period (\texttt{\textbf{.}}) matches any node.
 
 With TREs we encode interesting patterns in a program while disregarding irrelevant parts. Take for example the following, nearly correct Python function that prints the divisors of its argument $n$:
 
 \begin{Verbatim}
-def divisors(n):
-for d in range(1, n):
-if n % d == 0:
-print(d)
+\red{\dashuline{\textbf{def}}} divisors(\blue{\underline{\textbf{n}}}):
+    \red{\dashuline{\textbf{for}}} d in range(1, \blue{\underline{\textbf{n}}}):
+        \red{\dashuline{\textbf{if}}} n % d == 0:
+            print(d)
 \end{Verbatim}
 
-Figure~\ref{fig:patterns-example} shows the simplified AST for this program, with two patterns overlaid. These patterns are represented by the S-expressions
-
-\begin{figure}[htb]
-	\centering
-	\begin{forest}
-		for tree={
-			font=\sf,
-			edge=darkgray,
-			l sep=0,
-			l=0.9cm,
-		}
-		[Function, name=def, draw,rectangle,red,dashed
-		[name, name=name1 [divisors, name=divisors, font=\bfseries\sffamily]]
-		[args, name=args1
-		[Var, name=args1-1, draw,rectangle,blue [n, font=\bfseries\sffamily, l=0.7cm]]]
-		[body, name=body1, before computing xy={s=2cm}
-		[For, name=for, l=1.2cm, draw,rectangle,red,dashed
-		[target
-		[Var, l=0.9cm [d, font=\bfseries\sffamily, l=0.7cm]]]
-		[iter, name=iter
-		[Call, name=call, l=0.9cm
-		[func, name=func, l=0.8cm [range, name=range, font=\bfseries\sffamily, l=0.7cm]]
-		[args, name=args2, l=0.8cm
-		[Num, name=args2-1, l=1cm [1, font=\bfseries\sffamily, l=0.7cm]]
-		[Var, name=args2-2, l=1cm,draw,rectangle,blue [n, font=\bfseries\sffamily, l=0.7cm]]]]]
-		[body, name=body2
-		[If, name=if, draw,rectangle,red,dashed
-		[test, l=0.7cm [Compare, l=0.8cm
-		[BinOp
-		[Var [n, font=\bfseries\sffamily, l=0.6cm]]
-		[\%, font=\bfseries\sffamily]
-		[Var [d, font=\bfseries\sffamily, l=0.6cm]]]
-		[{==}, font=\bfseries\sffamily, l=0.7cm]
-		[Num [0, font=\bfseries\sffamily, l=0.7cm]]]]
-		[body, l=0.7cm [Call, l=0.8cm
-		[func [print, font=\bfseries\sffamily, l=0.7cm]]
-		[args [Var, l=0.7cm [d, font=\bfseries\sffamily, l=0.6cm]]]]]]]]]]
-		% first pattern
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,red,dashed] (def) edge[transform canvas={xshift=1.1mm,yshift=0.2mm}] (body1);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,red,dashed] (body1) edge[transform canvas={xshift=0.8mm}] (for);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,red,dashed] (for) edge[transform canvas={xshift=1.1mm,yshift=0.5mm}] (body2);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,red,dashed] (body2) edge[transform canvas={xshift=0.8mm}] (if);
-		% second pattern
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (def) edge[transform canvas={xshift=-1.1mm,yshift=0.2mm}] (name1);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (def) edge[transform canvas={xshift=-0.8mm}] (args1);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (args1) edge[transform canvas={xshift=-0.8mm}] (args1-1);
-		\draw[opacity=0] (args1) -- node[anchor=east,thick,blue,opacity=1,font=\large] {\texttt{\textasciicircum}} (args1-1);
-		\draw[opacity=0] (args1) -- node[anchor=west,thick,blue,opacity=1,font=\scriptsize,transform canvas={xshift=-0.5mm,yshift=0.6mm}] {\texttt{\$}} (args1-1);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (def) edge[transform canvas={xshift=-1mm,yshift=-0.3mm}] (body1);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (body1) edge[transform canvas={xshift=-0.8mm}] (for);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (for) edge[transform canvas={xshift=1mm,yshift=-0.5mm}] (iter);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (iter) edge[transform canvas={xshift=0.8mm}] (call);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (call) edge[transform canvas={xshift=-1.2mm}] (func);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (call) edge[transform canvas={xshift=1.2mm}] (args2);
-		\path[draw,thick,relative,blue,transform canvas={xshift=-0.7mm}] (args2) -- ($ (args2)!0.55!(args2-1) $);
-		\draw[opacity=0] (args2) -- node[anchor=east,thick,blue,opacity=1,font=\large,transform canvas={xshift=0.6mm,yshift=0.4mm}] {\texttt{\textasciicircum}} (args2-1);
-		\path[-{Latex[length=1.5mm,width=1mm]},thick,relative,blue] (args2) edge[transform canvas={xshift=1mm}] (args2-2);
-		\draw[opacity=0] (args2) -- node[anchor=west,thick,blue,opacity=1,font=\scriptsize,transform canvas={xshift=0mm,yshift=1mm}] {\texttt{\$}} (args2-2);
-	\end{forest}
-	\caption{The AST for the \code{divisors} program with two patterns. Leaf nodes (in bold) correspond to terminals in the program, i.e. names and values. Dashed red arrows represent the pattern describing the control structure of the program. Solid blue arrows encode the incorrect second argument to the \code{range} function.}
-	\label{fig:patterns-example}
-\end{figure}
+The highlighted fragments correspond to the following two patterns:
 
 \begin{enumerate}
 	\item \pattern{(Function (body (For (body If))))} and
@@ -182,24 +90,12 @@ Figure~\ref{fig:patterns-example} shows the simplified AST for this program, wit
 	\item[] ~~~~\pattern{(body (For (iter (Call (func range) (args \textbf{\textasciicircum}~\textbf{.} Var \$))))))}.
 \end{enumerate}
 
-The first TRE encodes a single path in the AST and describes the program’s block structure: \textsf{Function}$\boldsymbol{-}$\textsf{For}$\boldsymbol{-}$\textsf{If}. The second TRE relates the argument in the definition of \code{divisors} with the last argument to \code{range} that provides the iterator in the for loop. Since S-expressions are not easy to read, we will instead represent TREs by highlighting relevant text in examples of matching programs:
-
-\begin{Verbatim}
-\red{\dashuline{\textbf{def}}} divisors(\blue{\underline{\textbf{n}}}):
-\red{\dashuline{\textbf{for}}} d in range(1, \blue{\underline{\textbf{n}}}):
-\red{\dashuline{\textbf{if}}} n % d == 0:
-print(d)
-\end{Verbatim}
-
+The first TRE encodes a single path in the AST and describes the program’s structure: \textsf{Function}$\boldsymbol{-}$\textsf{For}$\boldsymbol{-}$\textsf{If}. The second TRE relates the argument in the definition of \code{divisors} to the last argument to \code{range}.
 The second pattern shows a common mistake for this problem: \code{range(1,n)} will only generate values up to \code{n-1}, so \code{n} will not be printed as its own divisor. A correct pattern would include the binary operator \code{+} on the path to \code{n}, indicating a call to \code{range(1,n+1)}.
 
-\subsection{Constructing patterns}
-
-Patterns are extracted automatically from student programs. We first canonicalize each program~\cite{rivers2015data-driven} using code from ITAP\footnote{Available at \url{https://github.com/krivers/ITAP-django}.}. To construct TREs describing individual patterns, we select a subset of nodes in the AST, and walk the tree from each selected node to the root, including all nodes along those paths.
-
-Depending on node type we also include some nodes adjacent to such paths. For each comparison and unary/binary expression on the path we include the corresponding operator. For function definitions and calls we include the function name. Finally, in all argument lists we include the anchors (\textbf{\texttt{\textasciicircum}}~and~\code{\$}) and a wildcard (\textbf{\texttt{.}}) for each argument not on the path. This allows our TREs to discriminate between e.g. the first and second argument to a function.
+Patterns are extracted automatically from student programs. We first canonicalize each program~\cite{rivers2015data-driven} using code from ITAP\footnote{Available at \url{https://github.com/krivers/ITAP-django}.}. For each pattern we select a subset of nodes in the AST, then walk the tree from each selected node to the root and construct the TRE by including all nodes along those paths.
 
-While pattern extraction is completely automated, we have manually defined the kinds of node subsets that are selected. After analyzing solutions to several programming problems, we decided to use the following kinds of patterns. Figure~\ref{fig:patterns-example} shows two examples of the first two kinds of patterns.
+While pattern extraction is completely automated, we have manually defined the kinds of node subsets that are selected. After analyzing solutions to several programming problems, we decided to use the following kinds of patterns:
 
 \begin{enumerate}
 	\item
@@ -207,10 +103,10 @@ While pattern extraction is completely automated, we have manually defined the k
 	\item
 	For each control-flow node $n$ we construct a pattern from the set $\{n\}$; we do the same for each \textsf{Call} node representing a function call.
 	\item
-	For each expression (such as \code{(F-32)*5/9}) we select the different combinations of literal and variable nodes in the expression. In these patterns we include at most one node referring to a variable.
+	For each expression -- such as \code{(F-32)*5/9} -- we select the different combinations of literal and variable nodes in the expression. In these patterns we include at most one node referring to a variable.
 \end{enumerate}
 
-Note that in every constructed pattern, all \textsf{Var} nodes refer to the same variable. We found that patterns constructed from such nodesets are useful for discriminating between programs. As we show in Sect.~\ref{sec:interpreting-rules}, they are also easily interpreted in terms of bugs and strategies for a given problem.
+Note that in every constructed pattern, all \textsf{Var} nodes refer to the same variable. We found that patterns constructed from such nodesets are useful for discriminating between programs. As we show in the next section, they are also easily interpreted in terms of bugs and strategies for a given problem.
 
 \section{Interpreting learned rules: a case study}
 \label{sec:rules}