Changeset becba789 for doc/aaron_comp_II/comp_II.tex

Timestamp:

Aug 2, 2016, 6:40:20 PM (9 years ago)

Author:

Rob Schluntz <rschlunt@…>

Branches:

ADT, aaron-thesis, arm-eh, ast-experimental, cleanup-dtors, ctor, deferred_resn, demangler, enum, forall-pointer-decay, jacob/cs343-translation, jenkins-sandbox, master, memory, new-ast, new-ast-unique-expr, new-env, no_list, persistent-indexer, pthread-emulation, qualifiedEnum, resolv-new, with_gc

Children:

8a443f4, 9799ec8

Parents:

e4957e7 (diff), 155cce0f (diff)
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Message:

Merge branch 'master' of plg.uwaterloo.ca:/u/cforall/software/cfa/cfa-cc

File:

• doc/aaron_comp_II/comp_II.tex (modified) (11 diffs)

doc/aaron_comp_II/comp_II.tex

@@ -43 +43 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\title{\Huge
-\vspace*{1in}
-Efficient Type Resolution in \CFA \\
-\vspace*{0.25in}
-\huge
-PhD Comprehensive II Research Proposal
+\title{
+\Huge \vspace*{1in} Efficient Type Resolution in \CFA \\
+\huge \vspace*{0.25in} PhD Comprehensive II Research Proposal
 \vspace*{1in}
 }
 
-\author{\huge
-\vspace*{0.1in}
-Aaron Moss \\
+\author{
+\huge Aaron Moss \\
+\Large \vspace*{0.1in} \texttt{a3moss@uwaterloo.ca} \\
 \Large Cheriton School of Computer Science \\
 \Large University of Waterloo
@@ -88 +85 @@
 
 \CFA\footnote{Pronounced ``C-for-all'', and written \CFA, CFA, or \CFL.} is an evolutionary modernization of the C programming language currently being designed and built at the University of Waterloo by a team led by Peter Buhr. 
-Features added to C by \CFA include name overloading, user-defined operators, parametric-polymorphic routines, and type constructors and destructors, among others. 
-These features make \CFA significantly more powerful and expressive than C, but impose a significant compile-time cost to implement, particularly in the expression resolver, which must evaluate the typing rules of a much more complex type system. 
+\CFA adds multiple features to C, including name overloading, user-defined operators, parametric-polymorphic routines, and type constructors and destructors, among others. 
+These features make \CFA significantly more powerful and expressive than C, but impose a significant compile-time cost to support, particularly in the expression resolver, which must evaluate the typing rules of a much more complex type system. 
 The primary goal of this proposed research project is to develop a sufficiently performant expression resolution algorithm, experimentally validate its performance, and integrate it into \Index*{CFA-CC}, the \CFA reference compiler.
 Secondary goals of this project include the development of various new language features for \CFA; parametric-polymorphic (``generic'') types have already been designed and implemented, and reference types and user-defined conversions are under design consideration. 
-The experimental performance-testing architecture for resolution algorithms will also be used to determine the compile-time cost of adding such new features to the \CFA type system.
+The experimental performance-testing architecture for resolution algorithms will also be used to determine the compile-time cost of adding such new features to the \CFA type system. 
+More broadly, this research should provide valuable data for implementers of compilers for other programming languages with similarly powerful static type systems.
 
 \section{\CFA}
@@ -101 +99 @@
 \subsection{Polymorphic Functions}
 The most significant feature \CFA adds is parametric-polymorphic functions. 
-Such functions are written using a ©forall© clause, the feature that gave the language its name:
+Such functions are written using a ©forall© clause (which gives the language its name):
 \begin{lstlisting}
 forall(otype T)
@@ -129 +127 @@
 
 Monomorphic specializations of polymorphic functions can themselves be used to satisfy type assertions. 
-For instance, ©twice© could have been define as below, using the \CFA syntax for operator overloading:
+For instance, ©twice© could have been defined as below, using the \CFA syntax for operator overloading:
 \begin{lstlisting}
 forall(otype S | { S ?+?(S, S); })
@@ -135 +133 @@
 \end{lstlisting} 
 This version of ©twice© will work for any type ©S© that has an addition operator defined for it, and it could have been used to satisfy the type assertion on ©four_times©. 
-The compiler accomplishes this by creating a wrapper function calling ©twice // (2)© with ©S© bound to ©double©, then providing this wrapper function to ©four_times©\footnote{©twice // (2)© could have had a type parameter named ©T©; \CFA specifies a renaming the type parameters, which would avoid the name conflict with the parameter ©T© of ©four_times©.}. 
+The compiler accomplishes this by creating a wrapper function calling ©twice // (2)© with ©S© bound to ©double©, then providing this wrapper function to ©four_times©\footnote{©twice // (2)© could also have had a type parameter named ©T©; \CFA specifies renaming of the type parameters, which would avoid the name conflict with the type variable ©T© of ©four_times©.}. 
 
 Finding appropriate functions to satisfy type assertions is essentially a recursive case of expression resolution, as it takes a name (that of the type assertion) and attempts to match it to a suitable declaration in the current scope. 
 If a polymorphic function can be used to satisfy one of its own type assertions, this recursion may not terminate, as it is possible that function will be examined as a candidate for its own type assertion unboundedly repeatedly. 
 To avoid infinite loops, the current \Index*{CFA-CC} compiler imposes a fixed limit on the possible depth of recursion, similar to that employed by most \Index*[C++]{\CC} compilers for template expansion; this restriction means that there are some semantically well-typed expressions which cannot be resolved by {CFA-CC}. 
-One area of potential improvement this project proposes to investigate is the possibility of using the compiler's knowledge of the current set of declarations to make a more precise judgement of when further type assertion satisfaction recursion will not produce a well-typed expression.
+One area of potential improvement this project proposes to investigate is the possibility of using the compiler's knowledge of the current set of declarations to more precicely determine when further type assertion satisfaction recursion will not produce a well-typed expression.
 
 \subsection{Name Overloading}
@@ -171 +169 @@
 Such a conversion system should be simple for user programmers to utilize, and fit naturally with the existing design of implicit conversions in C; ideally it would also be sufficiently powerful to encode C's usual arithmetic conversions itself, so that \CFA only has one set of rules for conversions. 
 
-Glen Ditchfield \textbf{TODO CITE} has laid out a framework for using polymorphic conversion constructor functions to create a directed acyclic graph (DAG) of conversions. 
+Ditchfield\cite{Ditchfield:conversions} has laid out a framework for using polymorphic conversion constructor functions to create a directed acyclic graph (DAG) of conversions. 
 A monomorphic variant of these functions can be used to mark a conversion arc in the DAG as only usable as the final step in a conversion. 
 With these two types of conversion arcs, separate DAGs can be created for the safe and the unsafe conversions, and conversion cost can be represented as path length through the DAG. 
@@ -210 +208 @@
 \CFA adds \emph{tuple types} to C, a facility for referring to multiple values with a single identifier. 
 A variable may name a tuple, and a function may return one. 
-Particularly relevantly for resolution, a tuple may be automatically \emph{destructured} into a list of values, as in the ©swap© function below:
+Particularly relevantly for resolution, a tuple may be implicitly \emph{destructured} into a list of values, as in the call to ©swap© below:
 \begin{lstlisting}
 [char, char] x = [ '!', '?' ];
@@ -218 +216 @@
 
 x = swap( x ); // destructure [char, char] x into two elements of parameter list
-// ^ can't use int x for parameter, not enough arguments to swap
+// can't use int x for parameter, not enough arguments to swap
 \end{lstlisting}
 Tuple destructuring means that the mapping from the position of a subexpression in the argument list to the position of a paramter in the function declaration is not straightforward, as some arguments may be expandable to different numbers of parameters, like ©x© above.
@@ -245 +243 @@
 
 \section{Expression Resolution}
-% TODO cite Baker, Cormack, etc.
-
+The expression resolution problem is essentially to determine an optimal matching between some combination of argument interpretations and the parameter list of some overloaded instance of a function; the argument interpretations are produced by recursive invocations of expression resolution, where the base case is zero-argument functions (which are, for purposes of this discussion, semantically equivalent to named variables or constant literal expressions). 
+Assuming that the matching between a function's parameter list and a combination of argument interpretations can be done in $O(p^k)$ time, where $p$ is the number of parameters and $k$ is some positive number, if there are $O(i)$ valid interpretations for each subexpression, there will be $O(i)$ candidate functions and $O(i^p)$ possible argument combinations for each expression, so a single recursive call to expression resolution will take $O(i^{p+1} \cdot p^k)$ time if it compares all combinations. 
+Given this bound, resolution of a single top-level expression tree of depth $d$ takes $O(i^{p+1} \cdot p^{k \cdot d})$ time\footnote{The call tree will have leaves at depth $O(d)$, and each internal node will have $O(p)$ fan-out, producing $O(p^d)$ total recursive calls.}.
+Expression resolution is somewhat unavoidably exponential in $p$, the number of function parameters, and $d$, the depth of the expression tree, but these values are fixed by the user programmer, and generally bounded by reasonably small constants. 
+$k$, on the other hand, is mostly dependent on the representation of types in the system and the efficiency of type assertion checking; if a candidate argument combination can be compared to a function parameter list in linear time in the length of the list (\ie $k = 1$), then the $p^{k \cdot d}$ term is linear in the input size of the source code for the expression, otherwise the resolution algorithm will exibit sub-linear performance scaling on code containing more-deeply nested expressions.
+The number of valid interpretations of any subexpression, $i$, is bounded by the number of types in the system, which is possibly infinite, though practical resolution algorithms for \CFA must be able to place some finite bound on $i$, possibly at the expense of type system completeness. 
+
+The research goal of this project is to develop a performant expression resolver for \CFA; this analysis suggests two primary areas of investigation to accomplish that end. 
+The first is efficient argument-parameter matching; Bilson\cite{Bilson03} mentions significant optimization opportunities available in the current literature to improve on the existing {CFA-CC} compiler.
+%TODO: look up and lit review 
+The second, and likely more fruitful, area of investigation is heuristics and algorithmic approaches to reduce the number of argument interpretations considered in the common case; given the large ($p+1$) exponent on number of interpretations considered in the runtime analysis, even small reductions here could have a significant effect on overall resolver runtime. 
+The discussion below presents a number of largely orthagonal axes for expression resolution algorithm design to be investigated, noting prior work where applicable. 
+
+\subsection{Argument-Parameter Matching}
+The first axis we consider is argument-parameter matching --- whether the type matching for a candidate function to a set of candidate arguments is directed by the argument types or the parameter types. 
+
+\subsubsection{Argument-directed (``Bottom-up'')}
+Baker's algorithm for expression resolution\cite{Baker82} pre-computes argument candidates, from the leaves of the expression tree up.
+For each candidate function, Baker attempts to match argument types to parameter types in sequence, failing if any parameter cannot be matched.
+
+Bilson\cite{Bilson03} similarly pre-computes argument candidates in the original \CFA compiler, but then explicitly enumerates all possible argument combinations for a multi-parameter function; these argument combinations are matched to the parameter types of the candidate function as a unit rather than individual arguments.
+This is less efficient than Baker's approach, as the same argument may be compared to the same parameter many times, but allows a more straightforward handling of polymorphic type binding and multiple return types.
+It is possible the efficiency losses here relative to Baker could be significantly reduced by application of memoization to the argument-parameter type comparisons.
+
+\subsubsection{Parameter-directed (``Top-down'')}
+Unlike Baker and Bilson, Cormack's algorithm\cite{Cormack81} requests argument candidates which match the type of each parameter of each candidate function, from the top-level expression down; memoization of these requests is presented as an optimization.
+As presented, this algorithm requires the result of the expression to have a known type, though an algorithm based on Cormack's could reasonably request a candidate set of any return type, though such a set may be quite large.
+
+\subsubsection{Hybrid}
+This proposal includes the investigation of hybrid top-down/bottom-up argument-parameter matching.
+A reasonable hybrid approach might be to take a top-down approach when the expression to be matched is known to have a fixed type, and a bottom-up approach in untyped contexts.
+This may include switches from one type to another at different levels of the expression tree, for instance:
+\begin{lstlisting}
+forall(otype T)
+int f(T x);  // (1)
+
+void* f(char y);  // (2)
+
+int x = f( f( '!' ) );
+\end{lstlisting}
+Here, the outer call to ©f© must have a return type that is (implicitly convertable to) ©int©, so a top-down approach could be used to select \textit{(1)} as the proper interpretation of ©f©. \textit{(1)}'s parameter ©x© here, however, is an unbound type variable, and can thus take a value of any complete type, providing no guidance for the choice of candidate for the inner ©f©. The leaf expression ©'!'©, however, gives us a zero-cost interpretation of the inner ©f© as \textit{(2)}, providing a minimal-cost expression resolution where ©T© is bound to ©void*©.
+
+Deciding when to switch between bottom-up and top-down resolution in a hybrid algorithm is a necessarily heuristic process, and though finding good heuristics for it is an open question, one reasonable approach might be to switch from top-down to bottom-up when the number of candidate functions exceeds some threshold.
+
+\subsection{Implicit Conversion Application}
+Baker's\cite{Baker82} and Cormack's\cite{Cormack81} algorithms do not account for implicit conversions\footnote{Baker does briefly comment on an approach for handling implicit conversions.}; both assume that there is at most one valid interpretation of a given expression for each distinct type.
+Integrating implicit conversion handling into their algorithms provides some choice of implementation approach. 
+
+\subsubsection{On Parameters}
+Bilson\cite{Bilson03} did account for implicit conversions in his algorithm, but it is not clear his approach is optimal. 
+His algorithm integrates checking for valid implicit conversions into the argument-parameter matching step, essentially trading more expensive matching for a smaller number of argument interpretations. 
+This approach may result in the same subexpression being checked for a type match with the same type multiple times, though again memoization may mitigate this cost, and this approach will not generate implicit conversions that are not useful to match the containing function. 
+
+\subsubsection{On Arguments}
+Another approach would be to generate a set of possible implicit conversions for each set of interpretations of a given argument. 
+This would have the benefit of detecting ambiguous interpretations of arguments at the level of the argument rather than its containing call, would also never find more than one interpretation of the argument with a given type, and would re-use calculation of implicit conversions between function candidates. 
+On the other hand, this approach may unncessarily generate argument interpretations that will never match a parameter, wasting work.
+
+\subsection{Candidate Set Generation}
+Cormack\cite{Cormack81}, Baker\cite{Baker82} \& Bilson\cite{Bilson03} all generate the complete set of candidate argument interpretations before attempting to match the containing function call expression. 
+However, given that the top-level expression interpretation that is ultimately chosen will be the minimal-cost valid interpretation, any consideration of non-minimal-cost interpretations is in some sense wasted work.
+If we assume that user programmers will generally write function calls with relatively low-cost interpretations, a possible work-saving heuristic is to generate only the lowest-cost argument interpretations first, attempt to find a valid top-level interpretation using them, and only if that fails generate the higher-cost argument interpretations.
+
+\subsubsection{Eager}
+Within the eager approach taken by Cormack, Baker \& Bilson, there are still variants to explore. 
+Cormack \& Baker do not account for implict conversions, and thus do not account for the possibility of multiple valid interpretations with distinct costs; Bilson, on the other hand, sorts the list of interpretations to aid in finding minimal-cost interpretations. 
+Sorting the lists of argument or function call interpretations by cost at some point during resolution may provide useful opportunities to short-circuit expression evaluation when a minimal-cost interpretation is found, though it is not clear if this short-circuiting behaviour would justify the cost of the sort.
+
+\subsubsection{Lazy}
+In the presence of implicit conversions, many argument interpretations may match a given parameter by application of an appropriate implicit conversion. 
+However, if user programmers actually use relatively few implicit conversions, then the ``on arguments'' approach to implicit conversions will generate a large number of high-cost interpretations which may never be used. 
+The essence of the lazy approach to candidate set generation is to wrap the matching algorithm into the element generator of a lazy list type, only generating as few elements at a time as possible to ensure that the next-smallest-cost interpretation has been generated. 
+Assuming that argument interpretations are provided to the parameter matching algorithm in sorted order, a sorted list of function call interpretations can be produced by generating combinations of arguments sorted by total cost\footnote{The author has developed a lazy $n$-way combination generation algorithm that can perform this task.}, then generating function call interpretations in the order suggested by this list. 
+Note that the function call interpretation chosen may have costs of its own, for instance polymorphic type binding, so in some cases a number of argument combinations (any combination whose marginal cost does not exceed the cost of the function call interpretation itself) may need to be considered to determine the next-smallest-cost function call interpretation.
+Ideally, this candidate generation approach will lead to very few unused candidates being generated (in the expected case where the user programmer has, in fact, provided a validly-typable program), but this research project will need to determine whether or not the overheads of lazy generation exceed the benefit produced from considering fewer interpretations.
+
+\subsubsection{Stepwise Lazy}
+As a compromise between the trade-offs of the eager and lazy approaches, it would also be interesting to investigate a ``stepwise lazy'' approach, where all the interpretations for some ``step'' are eagerly generated, then the interpretations in the later steps are only generated on demand. 
+Under this approach the \CFA resolver could, for instance, try expression interpretations in the following order:
+\begin{enumerate}
+\item Interpretations with no polymorphic type binding or implicit conversions.
+\item Interpretations containing no polymorphic type binding and at least one safe implicit conversion.
+\item Interpretations containing polymorphic type binding, but only safe implicit conversions.
+\item Interpretations containing at least one unsafe implicit conversion.
+\end{enumerate} 
+If a valid expression interpretation is found in one step, it is guaranteed to be lower-cost than any interpretation in a later step (by the structure of \CFA interpretation costs), so no step after the first one where a valid interpretation can be found need be considered.
+This may save significant amounts of work, especially given that the first steps avoid potentially expensive handling of implicit conversions and type assertion satisfaction entirely.
+
+%\subsection{Parameter-Directed}
+%\textbf{TODO: Richard's algorithm isn't Baker (Cormack?), disentangle from this section \ldots}. 
+%The expression resolution algorithm used by the existing iteration of {CFA-CC} is based on Baker's\cite{Baker82} algorithm for overload resolution in Ada. 
+%The essential idea of this algorithm is to first find the possible interpretations of the most deeply nested subexpressions, then to use these interpretations to recursively generate valid interpretations of their superexpressions. 
+%To simplify matters, the only expressions considered in this discussion of the algorithm are function application and literal expressions; other expression types can generally be considered to be variants of one of these for the purposes of the resolver, \eg variables are essentially zero-argument functions. 
+%If we consider expressions as graph nodes with arcs connecting them to their subexpressions, these expressions form a DAG, generated by the algorithm from the bottom up.
+%Literal expressions are represented by leaf nodes, annotated with the type of the expression, while a function application will have a reference to the function declaration chosen, as well as arcs to the interpretation nodes for its argument expressions; functions are annotated with their return type (or types, in the case of multiple return values).
+%
+%\textbf{TODO: Figure}
+%
+%Baker's algorithm was designed to account for name overloading; Richard Bilson\cite{Bilson03} extended this algorithm to also handle polymorphic functions, implicit conversions \& multiple return types when designing the original \CFA compiler. 
+%The core of the algorithm is a function which Baker refers to as $gen\_calls$. 
+%$gen\_calls$ takes as arguments the name of a function $f$ and a list containing the set of possible subexpression interpretations $S_j$ for each argument of the function and returns a set of possible interpretations of calling that function on those arguments. 
+%The subexpression interpretations are generally either singleton sets generated by the single valid interpretation of a literal expression, or the results of a previous call to $gen\_calls$. 
+%If there are no valid interpretations of an expression, the set returned by $gen\_calls$ will be empty, at which point resolution can cease, since each subexpression must have at least one valid interpretation to produce an interpretation of the whole expression. 
+%On the other hand, if for some type $T$ there is more than one valid interpretation of an expression with type $T$, all interpretations of that expression with type $T$ can be collapsed into a single \emph{ambiguous expression} of type $T$, since the only way to disambiguate expressions is by their return types. 
+%If a subexpression interpretation is ambiguous, than any expression interpretation containing it will also be ambiguous. 
+%In the variant of this algorithm including implicit conversions, the interpretation of an expression as type $T$ is ambiguous only if there is more than one \emph{minimal-cost} interpretation of the expression as type $T$, as cheaper expressions are always chosen in preference to more expensive ones.
+%
+%Given this description of the behaviour of $gen\_calls$, its implementation is quite straightforward: for each function declaration $f_i$ matching the name of the function, consider each of the parameter types $p_j$ of $f_i$, attempting to match the type of an element of $S_j$ to $p_j$ (this may include checking of implicit conversions).
+%If no such element can be found, there is no valid interpretation of the expression using $f_i$, while if more than one such (minimal-cost) element is found than an ambiguous interpretation with the result type of $f_i$ is produced. 
+%In the \CFA variant, which includes polymorphic functions, it is possible that a single polymorphic function definition $f_i$ can produce multiple valid interpretations by different choices of type variable bindings; these interpretations are unambiguous so long as the return type of $f_i$ is different for each type binding. 
+%If all the parameters $p_j$ of $f_i$ can be uniquely matched to a candidate interpretation, then a valid interpretation based on $f_i$ and those $p_j$ is produced. 
+%$gen\_calls$ collects the produced interpretations for each $f_i$ and returns them; a top level expression is invalid if this list is empty, ambiguous if there is more than one (minimal-cost) result, or if this single result is ambiguous, and valid otherwise.
+%
+%In this implementation, resolution of a single top-level expression takes time $O(\ldots)$, where \ldots. \textbf{TODO:} \textit{Look at 2.3.1 in Richard's thesis when working out complexity; I think he does get the Baker algorithm wrong on combinations though, maybe\ldots}
+%
+%\textbf{TODO: Basic Lit Review} \textit{Look at 2.4 in Richard's thesis for any possible more-recent citations of Baker\ldots} \textit{Look back at Baker's related work for other papers that look similar to what you're doing, then check their citations as well\ldots} \textit{Look at Richard's citations in 2.3.2 w.r.t. type data structures\ldots}
+%\textit{CormackWright90 seems to describe a solution for the same problem, mostly focused on how to find the implicit parameters}
+
+\section{Proposal}
+Baker\cite{Baker82} discussed various expression resolution algorithms that could handle name overloading, but left experimental comparison of those algorithms to future work; Bilson\cite{Bilson03} described one extension of Baker's algorithm to handle implicit conversions, but did not fully explore the space of algorithmic approaches to handle both overloaded names and implicit conversions. 
+This project is intended to experimentally test a number of expression resolution algorithms which are powerful enough to handle the \CFA type system, including both name overloading and implicit conversions. 
+This comparison will close Baker's open research question, as well as potentially improving on Bilson's \CFA compiler.
+
+Rather than testing all of these algorithms in-place in the \CFA compiler, a resolver prototype will be developed which acts on a simplified input language encapsulating the essential details of the \CFA type system\footnote{Note that this simplified input language is not required to be a usable programming language.}. 
+Multiple variants of this resolver prototype will be implemented, each encapsulating a different expression resolution variant, sharing as much code as feasible. 
+These variants will be instrumented to test runtime performance, and run on a variety of input files; the input files may be generated programmatically or from exisiting code in \CFA or similar languages.
+These experimental results will allow the research team to determine the algorithm likely to be most performant in practical use, and replace {CFA-CC}'s existing expression resolver with that code. 
+The experimental results will also provide some empirical sense of the compile-time cost of various language features by comparing the results of the most performant resolver variant that supports the feature with the most performant resolver variant that doesn't, a useful capability to guide language design.
+
+This proposed project should provide valuable data on how to implement a performant compiler for modern programming languages such as \CFA with powerful static type systems, specifically targeting the feature interaction between name overloading and implicit conversions.
+
+\appendix
 \section{Completion Timeline}
 The following is a preliminary estimate of the time necessary to complete the major components of this research project:
@@ -252 +380 @@
 \begin{tabular}{ | r @{--} l | p{4in} | }
 \hline       May 2015 & April 2016   & Project familiarization and generic types design \& implementation. \\
-\hline       May 2016 & April 2017   & Design \& implement prototype resolver and run performance experiments. \\
+\hline       May 2016 & April 2017   & Design \& implement resolver prototype and run performance experiments. \\
 \hline       May 2017 & August 2017  & Integrate new language features and best-performing resolver prototype into {CFA-CC}. \\
 \hline September 2017 & January 2018 & Thesis writing \& defense. \\
@@ -259 +387 @@
 \end{center}
 
-\section{Conclusion}
-
-\newpage
-
+\addcontentsline{toc}{section}{\refname}
 \bibliographystyle{plain}
 \bibliography{cfa}
 
-
-\addcontentsline{toc}{section}{\indexname} % add index name to table of contents
-\begin{theindex}
-Italic page numbers give the location of the main entry for the referenced term.
-Plain page numbers denote uses of the indexed term.
-Entries for grammar non-terminals are italicized.
-A typewriter font is used for grammar terminals and program identifiers.
-\indexspace
-\input{comp_II.ind}
-\end{theindex}
+%\addcontentsline{toc}{section}{\indexname} % add index name to table of contents
+%\begin{theindex}
+%Italic page numbers give the location of the main entry for the referenced term.
+%Plain page numbers denote uses of the indexed term.
+%Entries for grammar non-terminals are italicized.
+%A typewriter font is used for grammar terminals and program identifiers.
+%\indexspace
+%\input{comp_II.ind}
+%\end{theindex}
 
 \end{document}