main.tex 87.7 KB
 fpottier committed Mar 01, 2013 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 \def\true{true} \let\fpacm\true \documentclass[onecolumn,11pt,nocopyrightspace]{sigplanconf} \usepackage{amstext} \usepackage[OT1]{fontenc} \usepackage{graphicx} \usepackage[latin1]{inputenc} \usepackage{type1cm} \usepackage{xspace} \usepackage{mymacros} \usepackage{fppdf} \input{macros} \input{version} % TEMPORARY indiquer que le comportement par défaut (en l'absence % de --only-tokens ou --external-tokens) est d'engendrer la déf. % du type token % --------------------------------------------------------------------------------------------------------------------- % Headings. \title{\menhir Reference Manual\\\normalsize (version \menhirversion)} \begin{document} \authorinfo{François Pottier\and Yann Régis-Gianas} {INRIA} {\{Francois.Pottier, Yann.Regis-Gianas\}@inria.fr} \maketitle % --------------------------------------------------------------------------------------------------------------------- \clearpage \tableofcontents \clearpage % --------------------------------------------------------------------------------------------------------------------- \section{Foreword} \menhir is a parser generator. It turns high-level grammar specifications, decorated with semantic actions expressed in the \ocaml programming language~\cite{objective-caml}, into parsers, again expressed in \ocaml. It is based on Knuth's LR(1) parser construction technique~\cite{knuth-lr-65}. It is strongly inspired by its precursors: \yacc~\cite{johnson-yacc-79}, \texttt{ML-Yacc}~\cite{tarditi-appel-00}, and \ocamlyacc~\cite{objective-caml}, but offers a large number of minor and major improvements that make it a more modern tool. This brief reference manual explains how to use \menhir. It does not attempt to explain context-free grammars, parsing, or the LR technique. Readers who have never used a parser generator are encouraged to read about these ideas first~\cite{aho-86,appel-tiger-98,hopcroft-motwani-ullman-00}. They are also invited to have a look at the \distrib{demos} directory in \menhir's distribution. At this stage, potential users should be warned about two facts. First, \menhir's feature set is not stable. There is a tension between preserving a measure of compatibility with \ocamlyacc, on the one hand, and introducing new ideas, on the other hand. Some aspects of the tool, such as the error handling and recovery mechanism, are still potentially subject to incompatible changes. Second, the present release is \emph{beta}-quality. There is much room for improvement in the tool and in this reference manual. Bug reports and suggestions are welcome! % --------------------------------------------------------------------------------------------------------------------- \section{Usage} \menhir is invoked as follows: \begin{quote} \cmenhir \nt{option} \ldots \nt{option} \nt{filename} \ldots \nt{filename} \end{quote} Each of the file names must end with \texttt{.mly} and denotes a partial grammar specification. These partial grammar specifications are joined (\sref{sec:split}) to form a single, self-contained grammar specification, which is then processed. A number of optional command line switches allow controlling many aspects of the process. \docswitch{\obase \nt{basename}} This switch controls the base name of the \ml and \mli files that are produced. That is, the tool will produce files named \nt{basename}\texttt{.ml} and \nt{basename}\texttt{.mli}. Note that \nt{basename} can contain occurrences of the \texttt{/} character, so it really specifies a path and a base name. When only one \nt{filename} is provided on the command line, the default \nt{basename} is obtained by depriving \nt{filename} of its final \texttt{.mly} suffix. When multiple file names are provided on the command line, no default base name exists, so that the \obase switch \emph{must} be used. \docswitch{\ocomment} This switch causes a few comments to be inserted into the \ocaml code that is written to the \ml file. \docswitch{\odepend} This switch causes \menhir to generate dependency information for use in conjunction with \make. When invoked in this mode, \menhir does not generate a parser. Instead, it examines the grammar specification and prints a list of prerequisites for the targets \nt{basename}\texttt{.cm[oix]}, \nt{basename}\texttt{.ml}, and \nt{basename}\texttt{.mli}. This list is intended to be textually included within a \Makefile. It is important to note that \nt{basename}\texttt{.ml} and \nt{basename}\texttt{.mli} can have \texttt{.cm[iox]} prerequisites. This is because, when the \oinfer switch is used, \menhir infers types by invoking \ocamlc, and \ocamlc itself requires the \ocaml modules that the grammar specification depends upon to have been compiled first. The file \distrib{demos/Makefile.shared} helps exploit the \odepend switch. When in \odepend mode, \menhir computes dependencies by invoking \ocamldep. The command that is used to run \ocamldep is controlled by the \oocamldep switch. \docswitch{\odump} This switch causes a description of the automaton to be written to the file \nt{basename}\automaton. \docswitch{\oerrorrecovery} This switch causes error recovery code to be generated. Error recovery, also known as re-synchronization, consists in dropping tokens off the input stream, after an error has been detected, until a token that can be shifted in the current state is found. This behavior is made optional because it is seldom exploited and requires extra code in the parser. See also \sref{sec:errors}. \docswitch{\oexplain} This switch causes conflict explanations to be written to the file \nt{basename}\conflicts. See also \sref{sec:conflicts}. \docswitch{\oexternaltokens \nt{T}} This switch causes the definition of the \token type to be omitted in \nt{basename}\texttt{.ml} and \nt{basename}\texttt{.mli}. Instead, the generated parser relies on the type $T$\texttt{.}\token, where $T$ is an \ocaml module name. It is up to the user to define module $T$ and to make sure that it exports a suitable \token type. Module $T$ can be hand-written. It can also be automatically generated out of a grammar specification using the \oonlytokens switch.  fpottier committed Mar 02, 2013 132 133 134 135 \docswitch{\ofixedexc} This switch causes the exception \texttt{Error} to be declared equal to \texttt{Parsing.Parse\_error}. This helps increase Menhir's compatibility with \ocamlyacc. There is otherwise no reason to use it.  fpottier committed Mar 01, 2013 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 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1894 1895 1896 1897 1898 1899 1900 \docswitch{\ograph} This switch causes a description of the grammar's dependency graph to be written to the file \nt{basename}\dott. The graph's vertices are the grammar's nonterminal symbols. There is a directed edge from vertex $A$ to vertex $B$ if the definition of $A$ refers to $B$. The file is in a format that is suitable for processing by the \emph{graphviz} toolkit. \docswitch{\oinfer} This switch causes the semantic actions to be checked for type consistency \emph{before} the parser is generated. This is done by invoking the \ocaml compiler. Use of \oinfer is \textbf{strongly recommended}, because it helps obtain consistent, well-located type error messages, especially when advanced features such as \menhir's standard library or \dinline keyword are exploited. One downside of \oinfer is that the \ocaml compiler usually needs to consult a few \texttt{.cm[iox]} files. This means that these files must have been created first, requiring \Makefile changes and use of the \odepend switch. The file \distrib{demos/Makefile.shared} suggests how to deal with this difficulty. Another option is to avoid \make altogether and use \ocamlbuild, which has built-in knowledge of \menhir. % There is a slight catch with \oinfer. The types inferred by \ocamlc are valid % in the toplevel context, but can change meaning when inserted into a local % context. \docswitch{\ointerpret} This switch causes \menhir to act as an interpreter, rather than as a compiler. No \ocaml code is generated. Instead, \menhir reads sentences off the standard input channel, parses them, and displays outcomes. For more information, see \sref{sec:interpret}. \docswitch{\ointerpretshowcst} This switch, used in conjunction with \ointerpret, causes \menhir to display a concrete syntax tree when a sentence is successfully parsed. For more information, see \sref{sec:interpret}. \docswitch{\ologautomaton \nt{level}} When \nt{level} is nonzero, this switch causes some information about the automaton to be logged to the standard error channel. \docswitch{\ologcode \nt{level}} When \nt{level} is nonzero, this switch causes some information about the generated \ocaml code to be logged to the standard error channel. \docswitch{\ologgrammar \nt{level}} When \nt{level} is nonzero, this switch causes some information about the grammar to be logged to the standard error channel. When \nt{level} is 2, the \emph{nullable}, \emph{FIRST}, and \emph{FOLLOW} tables are displayed. \docswitch{\onoinline} This switch causes all \dinline keywords in the grammar specification to be ignored. This is especially useful in order to understand whether these keywords help solve any conflicts. \docswitch{\onostdlib} This switch causes the standard library \emph{not} to be implicitly joined with the grammar specifications whose names are explicitly provided on the command line. \docswitch{\oocamlc \nt{command}} This switch controls how \ocamlc is invoked (when \oinfer is used). It allows setting both the name of the executable and the command line options that are passed to it. \docswitch{\oocamldep \nt{command}} This switch controls how \ocamldep is invoked (when \odepend is used). It allows setting both the name of the executable and the command line options that are passed to it. \docswitch{\oonlypreprocess} This switch causes the grammar specifications to be transformed up to the point where the automaton's construction can begin. The grammar specifications whose names are provided on the command line are joined (\sref{sec:split}); all parameterized nonterminal symbols are expanded away (\sref{sec:templates}); type inference is performed, if \oinfer is enabled; all nonterminal symbols marked \dinline are expanded away (\sref{sec:inline}). This yields a single, monolithic grammar specification, which is printed on the standard output channel. \docswitch{\oonlytokens} This switch causes the \dtoken declarations in the grammar specification to be translated into a definition of the \token type, which is written to the files \nt{basename}\texttt{.ml} and \nt{basename}\texttt{.mli}. No code is generated. This is useful when a single set of tokens is to be shared between several parsers. The directory \distrib{demos/calc-two} contains a demo that illustrates the use of this switch. \docswitch{\orawdepend} This switch is analogous to \odepend, except that \ocamldep's output is not postprocessed by \menhir; it is echoed without change. This switch is \emph{not} suitable for direct use with \make; it is intended for use with \omake, which performs its own postprocessing. \docswitch{\ostrict} This switch causes several warnings about the grammar and about the automaton to be considered errors. This includes warnings about useless precedence declarations, non-terminal symbols that produce the empty language, unreachable non-terminal symbols, productions that are never reduced, conflicts that are not resolved by precedence declarations, and end-of-stream conflicts. \docswitch{\osuggestcomp} This switch causes \menhir to print a set of suggested compilation flags, and exit. These flags are intended to be passed to the \ocaml compilers (\ocamlc or \ocamlopt) when compiling and linking the parser generated by \menhir. What are these flags? In the absence of the \otable switch, they are empty. When \otable is set, these flags ensure that \menhirlib is visible to the \ocaml compiler. If the support library \menhirlib was installed via \ocamlfind, a \texttt{-package} directive is issued; otherwise, a \texttt{-I} directive is used. The file \distrib{demos/Makefile.shared} shows how to exploit the \texttt{--suggest-*} switches. \docswitch{\osuggestlinkb} This switch causes \menhir to print a set of suggested link flags, and exit. These flags are intended to be passed to \texttt{ocamlc} when producing a bytecode executable. What are these flags? In the absence of the \otable switch, they are empty. When \otable is set, these flags ensure that \menhirlib is linked in. If the support library \menhirlib was installed via \ocamlfind, a \texttt{-linkpkg} directive is issued; otherwise, the object file \texttt{menhirLib.cmo} is named. The file \distrib{demos/Makefile.shared} shows how to exploit the \texttt{--suggest-*} switches. \docswitch{\osuggestlinko} This switch causes \menhir to print a set of suggested link flags, and exit. These flags are intended to be passed to \texttt{ocamlopt} when producing a native code executable. What are these flags? In the absence of the \otable switch, they are empty. When \otable is set, these flags ensure that \menhirlib is linked in. If the support library \menhirlib was installed via \ocamlfind, a \texttt{-linkpkg} directive is issued; otherwise, the object file \texttt{menhirLib.cmx} is named. The file \distrib{demos/Makefile.shared} shows how to exploit the \texttt{--suggest-*} switches. \docswitch{\ostdlib \nt{directory}} This switch controls the directory where the standard library is found. It allows overriding the default directory that is set at installation time. The trailing \texttt{/} character is optional. \docswitch{\otable} This switch causes \menhir to use its table-based back-end, as opposed to its (default) code-based back-end. When \otable is used, \menhir produces significantly more compact, slightly slower parsers. The table-based back-end produces rather compact tables, which are analogous to those produced by \yacc, \bison, or \ocamlyacc. These tables are not quite stand-alone: they are exploited by an interpreter, which is shipped as part of the support library \menhirlib. For this reason, when \otable is used, \menhirlib must be made visible to the \ocaml compilers, and must be linked into your executable program. The \texttt{--suggest-*} switches, described above, help do this. The code-based back-end compiles the LR automaton directly into a nest of mutually recursive \ocaml functions. In that case, \menhirlib is not required. \docswitch{\otimings} This switch causes internal timing information to be sent to the standard error channel. \docswitch{\otrace} This switch causes tracing code to be inserted into the generated parser, so that, when the parser is run, its actions are logged to the standard error channel. This is analogous to \texttt{ocamlrun}'s \texttt{p=1} parameter, except this switch must be enabled at compile time: one cannot selectively enable or disable tracing at runtime. \docswitch{\oversion} This switch causes \menhir to print its own version number and exit. % --------------------------------------------------------------------------------------------------------------------- \section{Lexical conventions} The semicolon character (\kw{;}) is treated as insignificant, just like white space. Thus, rules and producers (for instance) can be separated with semicolons if it is thought that this improves readability. They can be omitted otherwise. Identifiers (\nt{id}) coincide with \ocaml identifiers, except they are not allowed to contain the quote (\kw{'}) character. Following \ocaml, identifiers that begin with a lowercase letter (\nt{lid}) or with an uppercase letter (\nt{uid}) are distinguished. Comments are C-style (surrounded with \kw{/*} and \kw{*/}, cannot be nested), C++-style (announced by \kw{/$\!$/} and extending until the end of the line), or \ocaml-style (surrounded with \kw{(*} and \kw{*)}, can be nested). Of course, inside \ocaml code, only \ocaml-style comments are allowed. \ocaml type expressions are surrounded with \kangle{and}. Within such expressions, all references to type constructors (other than the built-in \textit{list}, \textit{option}, etc.) must be fully qualified. % --------------------------------------------------------------------------------------------------------------------- \section{Syntax of grammar specifications} \begin{figure} \begin{center} \begin{tabular}{r@{}c@{}l} \nt{specification} \is \sepspacelist{\nt{declaration}} \percentpercent \sepspacelist{\nt{rule}} \optional{\percentpercent \textit{Objective Caml code}} \\ \nt{declaration} \is \dheader{\textit{Objective Caml code}} \\ && \dparameter \ocamlparam \\ && \dtoken \optional{\ocamltype} \sepspacelist{\nt{uid}} \\ && \dnonassoc \sepspacelist{\nt{uid}} \\ && \dleft \sepspacelist{\nt{uid}} \\ && \dright \sepspacelist{\nt{uid}} \\ && \dtype \ocamltype \sepspacelist{\nt{lid}} \\ && \dstart \optional{\ocamltype} \sepspacelist{\nt{lid}} \\ \nt{rule} \is \optional{\dpublic} \optional{\dinline} \nt{lid} \optional{\dlpar\sepcommalist{\nt{id}}\drpar} \deuxpoints \optional{\barre} \seplist{\ \barre}{\nt{group}} \\ \nt{group} \is \seplist{\ \barre}{\nt{production}} \daction \optional {\dprec \nt{id}} \\ \nt{production} \is \sepspacelist{\nt{producer}} \optional {\dprec \nt{id}} \\ \nt{producer} \is \optional{\nt{lid} \dequal} \nt{actual} \\ \nt{actual} \is \nt{id} \optional{\dlpar\sepcommalist{\nt{actual}}\drpar} \optional{\dquestion \barre \dplus \barre \dstar} \\ \end{tabular} \end{center} \caption{Syntax of grammar specifications} \label{fig:syntax} \end{figure} The syntax of grammar specifications appears in \fref{fig:syntax}. (For compatibility with \ocamlyacc, some specifications that do not fully adhere to this syntax are also accepted.) \subsection{Declarations} A specification file begins with a sequence of declarations, ended by a mandatory \percentpercent keyword. \subsubsection{Headers} A header is a piece of \ocaml code, surrounded with \dheader{and}. It is copied verbatim at the beginning of the \ml file. It typically contains \ocaml \kw{open} directives and function definitions for use by the semantic actions. If a single grammar specification file contains multiple headers, their order is preserved. However, when two headers originate in distinct grammar specification files, the order in which they are copied to the \ml file is unspecified. \subsubsection{Parameters} A declaration of the form: \begin{quote} \dparameter \ocamlparam \end{quote} causes the entire parser to become parameterized over the \ocaml module \nt{uid}, that is, to become an \ocaml functor. If a single specification file contains multiple \dparameter declarations, their order is preserved, so that the module name \nt{uid} introduced by one declaration is effectively in scope in the declarations that follow. When two \dparameter declarations originate in distinct grammar specification files, the order in which they are processed is unspecified. Last, \dparameter declarations take effect before \dheader{$\ldots$}, \dtoken, \dtype, or \dstart declarations are considered, so that the module name \nt{uid} introduced by a \dparameter declaration is effectively in scope in \emph{all} \dheader{$\ldots$}, \dtoken, \dtype, or \dstart declarations, regardless of whether they precede or follow the \dparameter declaration. This means, in particular, that the side effects of an \ocaml header are observed only when the functor is applied, not when it is defined. \subsubsection{Tokens} A declaration of the form: \begin{quote} \dtoken \optional{\ocamltype} $\nt{uid}_1, \ldots, \nt{uid}_n$ \end{quote} defines the identifiers $\nt{uid}_1, \ldots, \nt{uid}_n$ as tokens, that is, as terminal symbols in the grammar specification and as data constructors in the \textit{token} type. If an \ocaml type $t$ is present, then these tokens are considered to carry a semantic value of type $t$, otherwise they are considered to carry no semantic value. \subsubsection{Priority and associativity} \label{sec:assoc} A declaration of one of the following forms: \begin{quote} \dnonassoc $\nt{uid}_1 \ldots \nt{uid}_n$ \\ \dleft $\nt{uid}_1 \ldots \nt{uid}_n$ \\ \dright $\nt{uid}_1 \ldots \nt{uid}_n$ \end{quote} attributes both a \emph{priority level} and an \emph{associativity status} to the symbols $\nt{uid}_1, \ldots, \nt{uid}_n$. The priority level assigned to $\nt{uid}_1, \ldots, \nt{uid}_n$ is not defined explicitly: instead, it is defined to be higher than the priority level assigned by the previous \dnonassoc, \dleft, or \dright declaration, and lower than that assigned by the next \dnonassoc, \dleft, or \dright declaration. The symbols $\nt{uid}_1, \ldots, \nt{uid}_n$ can be tokens (defined elsewhere by a \dtoken declaration) or dummies (not defined anywhere). Both can be referred to as part of \dprec annotations. Associativity status and priority levels allow shift/reduce conflicts to be silently resolved (\sref{sec:conflicts}). \subsubsection{Types} A declaration of the form: \begin{quote} \dtype \ocamltype $\nt{lid}_1 \ldots \nt{lid}_n$ \end{quote} assigns an \ocaml type to each of the nonterminal symbols $\nt{lid}_1, \ldots, \nt{lid}_n$. For start symbols, providing an \ocaml type is mandatory, but is usually done as part of the \dstart declaration. For other symbols, it is optional. Providing type information can improve the quality of \ocaml's type error messages. \subsubsection{Start symbols} A declaration of the form: \begin{quote} \dstart \optional{\ocamltype} $\nt{lid}_1 \ldots \nt{lid}_n$ \end{quote} declares the nonterminal symbols $\nt{lid}_1, \ldots, \nt{lid}_n$ to be start symbols. Each such symbol must be assigned an \ocaml type either as part of the \dstart declaration or via separate \dtype declarations. Each of $\nt{lid}_1, \ldots, \nt{lid}_n$ becomes the name of a function whose signature is published in the \mli file and that can be used to invoke the parser. \subsection{Rules} Following the mandatory \percentpercent keyword, a sequence of rules is expected. Each rule defines a nonterminal symbol~\nt{id}. In its simplest form, a rule begins with \nt{id}, followed by a colon character (\deuxpoints), and continues with a sequence of production groups (\sref{sec:productiongroups}). Each production group is preceded with a vertical bar character (\barre); the very first bar is optional. The meaning of the bar is choice: the nonterminal symbol \nt{id} develops to either of the production groups. We defer explanations of the keyword \dpublic (\sref{sec:split}), of the keyword \dinline (\sref{sec:inline}), and of the optional formal parameters $\dlpar\sepcommalist{\nt{id}}\drpar$ (\sref{sec:templates}). \subsubsection{Production groups} \label{sec:productiongroups} In its simplest form, a production group consists of a single production (\sref{sec:productions}), followed by an \ocaml semantic action (\sref{sec:actions}) and an optional \dprec annotation (\sref{sec:prec}). A production specifies a sequence of terminal and nonterminal symbols that should be recognized, and optionally binds identifiers to their semantic values. \paragraph{Semantic actions} \label{sec:actions} A semantic action is a piece of \ocaml code that is executed in order to assign a semantic value to the nonterminal symbol with which this production group is associated. A semantic action can refer to the (already computed) semantic values of the terminal or nonterminal symbols that appear in the production via the semantic value identifiers bound by the production. For compatibility with \ocamlyacc, semantic actions can also refer to these semantic values via positional keywords of the form \kw{\$1}, \kw{\$2}, etc.\ This style is discouraged. \paragraph{\dprec annotations} \label{sec:prec} An annotation of the form \dprec \nt{uid} indicates that the precedence level of the production group is the level assigned to the symbol \nt{uid} via a previous \dnonassoc, \dleft, or \dright declaration (\sref{sec:assoc}). In the absence of a \dprec annotation, the precedence level assigned to each production is the level assigned to the rightmost terminal symbol that appears in it. It is undefined if the rightmost terminal symbol has an undefined precedence level or if the production mentions no terminal symbols at all. The precedence level assigned to a production is used when resolving shift/reduce conflicts (\sref{sec:conflicts}). \paragraph{Multiple productions in a group} If multiple productions are present in a single group, then the semantic action and precedence annotation are shared between them. This short-hand effectively allows several productions to share a semantic action and precedence annotation without requiring textual duplication. It is legal only when every production binds exactly the same set of semantic value identifiers and when no positional semantic value keywords (\kw{\$1}, etc.) are used. \subsubsection{Productions} \label{sec:productions} A production is a sequence of producers (\sref{sec:producers}), optionally followed by a \dprec annotation (\sref{sec:prec}). If a precedence annotation is present, it applies to this production alone, not to other productions in the production group. It is illegal for a production and its production group to both carry \dprec annotations. \subsubsection{Producers} \label{sec:producers} A producer is an actual (\sref{sec:actual}), optionally preceded with a binding of a semantic value identifier, of the form \nt{lid} \dequal. The actual specifies which construction should be recognized and how a semantic value should be computed for that construction. The identifier \nt{lid}, if present, becomes bound to that semantic value in the semantic action that follows. Otherwise, the semantic value can be referred to via a positional keyword (\kw{\$1}, etc.). \subsubsection{Actuals} \label{sec:actual} In its simplest form, an actual simply consists of a terminal or nonterminal symbol. The optional actual parameters $\dlpar\sepcommalist{\nt{actual}}\drpar$ and the optional modifier (\dquestion, \dplus, or \dstar) are explained further on (see \sref{sec:templates} and \fref{fig:sugar}). \section{Advanced features} \subsection{Splitting specifications over multiple files} \label{sec:split} \paragraph{Modules} Grammar specifications can be split over multiple files. When \menhir is invoked with multiple argument file names, it considers each of these files as a \emph{partial} grammar specification, and \emph{joins} these partial specifications in order to obtain a single, complete specification. This feature is intended to promote a form a modularity. It is hoped that, by splitting large grammar specifications into several modules'', they can be made more manageable. It is also hoped that this mechanism, in conjunction with parameterization (\sref{sec:templates}), will promote sharing and reuse. It should be noted, however, that this is only a weak form of modularity. Indeed, partial specifications cannot be independently processed (say, checked for conflicts). It is necessary to first join them, so as to form a complete grammar specification, before any kind of grammar analysis can be done. This mechanism is, in fact, how \menhir's standard library (\sref{sec:library}) is made available: even though its name does not appear on the command line, it is automatically joined with the user's explicitly-provided grammar specifications, making the standard library's definitions globally visible. A partial grammar specification, or module, contains declarations and rules, just like a complete one: there is no visible difference. Of course, it can consist of only declarations, or only rules, if the user so chooses. (Don't forget the mandatory \percentpercent keyword that separates declarations and rules. It must be present, even if one of the two sections is empty.) \paragraph{Private and public nonterminal symbols} It should be noted that joining is \emph{not} a purely textual process. If two modules happen to define a nonterminal symbol by the same name, then it is considered, by default, that this is an accidental name clash. In that case, each of the two nonterminal symbols is silently renamed so as to avoid the clash. In other words, by default, a nonterminal symbol defined in module $A$ is considered \emph{private}, and cannot be defined again, or referred to, in module $B$. Naturally, it is sometimes desirable to define a nonterminal symbol $N$ in module $A$ and to refer to it in module $B$. This is permitted if $N$ is public, that is, if either its definition carries the keyword \dpublic or $N$ is declared to be a start symbol. A public nonterminal symbol is never renamed, so it can be referred to by modules other than its defining module. In fact, it is even permitted to split the definition of a public nonterminal symbol over multiple modules. That is, a public nonterminal symbol $N$ can have multiple definitions in distinct modules. When the modules are joined, the definitions are joined as well, using the choice (\barre) operator. This feature allows splitting a grammar specification in a manner that is independent of the grammar's structure. For instance, in the grammar of a programming language, the definition of the nonterminal symbol \nt{expression} could be split into multiple modules, where one module groups the expression forms that have to do with arithmetic, one module groups those that concern function definitions and function calls, one module groups those that concern object definitions and method calls, and so on. \paragraph{Tokens aside} Another use of modularity consists in placing all \dtoken declarations in one module, and the actual grammar specification in another module. The module that contains the token definitions can then be shared, making it easier to define multiple parsers that accept the same type of tokens. (On this topic, see \distrib{demos/calc-two}.) \subsection{Parameterizing rules} \label{sec:templates} A rule (that is, the definition of a nonterminal symbol) can be parameterized over an arbitrary number of symbols, which are referred to as formal parameters. \paragraph{Example} For instance, here is the definition of the parameterized nonterminal symbol \nt{option}, taken from the standard library (\sref{sec:library}): % \begin{quote} \begin{tabular}{l} \dpublic \basic{option}(\basic{X}): \newprod \dpaction{\basic{None}} \newprod \basic{x} = \basic{X} \dpaction{\basic{Some} \basic{x}} \end{tabular} \end{quote} % This definition states that \nt{option}(\basic{X}) expands to either the empty string, producing the semantic value \basic{None}, or to the string \basic{X}, producing the semantic value {\basic{Some}~\basic{x}}, where \basic{x} is the semantic value of \basic{X}. In this definition, the symbol \basic{X} is abstract: it stands for an arbitrary terminal or nonterminal symbol. The definition is made public, so \nt{option} can be referred to within client modules. A client that wishes to use \nt{option} simply refers to it, together with an actual parameter -- a symbol that is intended to replace \basic{X}. For instance, here is how one might define a sequence of declarations, preceded with optional commas: % \begin{quote} \begin{tabular}{l} \nt{declarations}: \newprod \dpaction{[]} \newprod \basic{ds} = \nt{declarations}; \nt{option}(\basic{COMMA}); \basic{d} = \nt{declaration} \dpaction{ \basic{d} :: \basic{ds} } \end{tabular} \end{quote} % This definition states that \nt{declarations} expands either to the empty string or to \nt{declarations} followed by an optional comma followed by \nt{declaration}. (Here, \basic{COMMA} is presumably a terminal symbol.) When this rule is encountered, the definition of \nt{option} is instantiated: that is, a copy of the definition, where \basic{COMMA} replaces \basic{X}, is produced. Things behave exactly as if one had written: \begin{quote} \begin{tabular}{l} \basic{optional\_comma}: \newprod \dpaction{\basic{None}} \newprod \basic{x} = \basic{COMMA} \dpaction{\basic{Some} \basic{x}} \\ \nt{declarations}: \newprod \dpaction{[]} \newprod \basic{ds} = \nt{declarations}; \nt{optional\_comma}; \basic{d} = \nt{declaration} \dpaction{ \basic{d} :: \basic{ds} } \end{tabular} \end{quote} % Note that, even though \basic{COMMA} presumably has been declared as a token with no semantic value, writing \basic{x}~=~\basic{COMMA} is legal, and binds \basic{x} to the unit value. This design choice ensures that the definition of \nt{option} makes sense regardless of the nature of \basic{X}: that is, \basic{X} can be instantiated with a terminal symbol, with or without a semantic value, or with a nonterminal symbol. \paragraph{Parameterization in general} In general, the definition of a nonterminal symbol $N$ can be parameterized with an arbitrary number of formal parameters. When $N$ is referred to within a production, it must be applied to the same number of actuals. In general, an actual is: % \begin{itemize} \item either a single symbol, which can be a terminal symbol, a nonterminal symbol, or a formal parameter; \item or an application of such a symbol to a number of actuals. \end{itemize} For instance, here is a rule whose single production consists of a single producer, which contains several, nested actuals. (This example is discussed again in \sref{sec:library}.) % \begin{quote} \begin{tabular}{l} \nt{plist}(\nt{X}): \newprod \basic{xs} = \nt{loption}(% \nt{delimited}(% \basic{LPAREN}, \nt{separated\_nonempty\_list}(\basic{COMMA}, \basic{X}), \basic{RPAREN}% )% ) \dpaction{\basic{xs}} \end{tabular} \end{quote} \begin{figure} \begin{center} \begin{tabular}{r@{\hskip 2mm}c@{\hskip 2mm}l} \nt{actual}\dquestion & is syntactic sugar for & \nt{option}(\nt{actual}) \\ \nt{actual}\dplus & is syntactic sugar for & \nt{nonempty\_list}(\nt{actual}) \\ \nt{actual}\dstar & is syntactic sugar for & \nt{list}(\nt{actual}) \end{tabular} \end{center} \caption{Syntactic sugar for simulating regular expressions} \label{fig:sugar} \end{figure} % Applications of the parameterized nonterminal symbols \nt{option}, \nt{nonempty\_list}, and \nt{list}, which are defined in the standard library (\sref{sec:library}), can be written using a familiar, regular-expression like syntax (\fref{fig:sugar}). \paragraph{Higher-order parameters} A formal parameter can itself expect parameters. For instance, here is a rule that defines the syntax of procedures in an imaginary programming language: % \begin{quote} \begin{tabular}{l} \nt{procedure}(\nt{list}): \newprod \basic{PROCEDURE} \basic{ID} \nt{list}(\nt{formal}) \nt{SEMICOLON} \nt{block} \nt{SEMICOLON} \dpaction{$\ldots$} \end{tabular} \end{quote} % This rule states that the token \basic{ID}, which represents the name of the procedure, should be followed with a list of formal parameters. (The definitions of the nonterminal symbols \nt{formal} and \nt{block} are not shown.) However, because \nt{list} is a formal parameter, as opposed to a concrete nonterminal symbol defined elsewhere, this definition does not specify how the list is laid out: which token, if any, is used to separate, or terminate, list elements? is the list allowed to be empty? and so on. A more concrete notion of procedure is obtained by instantiating the formal parameter \nt{list}: for instance, \nt{procedure}(\nt{plist}), where \nt{plist} is the parameterized nonterminal symbol defined earlier, is a valid application. \paragraph{Consistency} Definitions and uses of parameterized nonterminal symbols are checked for consistency before they are expanded away. In short, it is checked that, wherever a nonterminal symbol is used, it is supplied with actual arguments in appropriate number and of appropriate nature. This guarantees that expansion of parameterized definitions terminates and produces a well-formed grammar as its outcome. \subsection{Inlining} \label{sec:inline} It is well-known that the following grammar of arithmetic expressions does not work as expected: that is, in spite of the priority declarations, it has shift/reduce conflicts. % \begin{quote} \begin{tabular}{l} \dtoken \kangle{\basic{int}} \basic{INT} \\ \dtoken \basic{PLUS} \basic{TIMES} \\ \dleft \basic{PLUS} \\ \dleft \basic{TIMES} \\ \\ \percentpercent \\ \\ \nt{expression}: \newprod \basic{i} = \basic{INT} \dpaction{\basic{i}} \newprod \basic{e} = \nt{expression}; \basic{o} = \nt{op}; \basic{f} = \nt{expression} \dpaction{\basic{o} \basic{e} \basic{f}} \\ \nt{op}: \newprod \basic{PLUS} \dpaction{( + )} \newprod \basic{TIMES} \dpaction{( * )} \end{tabular} \end{quote} % The trouble is, the precedence level of the production \nt{expression} $\rightarrow$ \nt{expression} \nt{op} \nt{expression} is undefined, and there is no sensible way of defining it via a \dprec declaration, since the desired level really depends upon the symbol that was recognized by \nt{op}: was it \basic{PLUS} or \basic{TIMES}? The standard workaround is to abandon the definition of \nt{op} as a separate nonterminal symbol, and to inline its definition into the definition of \nt{expression}, like this: % \begin{quote} \begin{tabular}{l} \nt{expression}: \newprod \basic{i} = \basic{INT} \dpaction{\basic{i}} \newprod \basic{e} = \nt{expression}; \basic{PLUS}; \basic{f} = \nt{expression} \dpaction{\basic{e} + \basic{f}} \newprod \basic{e} = \nt{expression}; \basic{TIMES}; \basic{f} = \nt{expression} \dpaction{\basic{e} * \basic{f}} \end{tabular} \end{quote} % This avoids the shift/reduce conflict, but gives up some of the original specification's structure, which, in realistic situations, can be damageable. Fortunately, \menhir offers a way of avoiding the conflict without manually transforming the grammar, by declaring that the nonterminal symbol \nt{op} should be inlined: % \begin{quote} \begin{tabular}{l} \nt{expression}: \newprod \basic{i} = \basic{INT} \dpaction{\basic{i}} \newprod \basic{e} = \nt{expression}; \basic{o} = \nt{op}; \basic{f} = \nt{expression} \dpaction{\basic{o} \basic{e} \basic{f}} \\ \dinline \nt{op}: \newprod \basic{PLUS} \dpaction{( + )} \newprod \basic{TIMES} \dpaction{( * )} \end{tabular} \end{quote} % The \dinline keyword causes all references to \nt{op} to be replaced with its definition. In this example, the definition of \nt{op} involves two productions, one that develops to \basic{PLUS} and one that expands to \basic{TIMES}, so every production that refers to \nt{op} is effectively turned into two productions, one that refers to \basic{PLUS} and one that refers to \basic{TIMES}. After inlining, \nt{op} disappears and \nt{expression} has three productions: that is, the result of inlining is exactly the manual workaround shown above. In some situations, inlining can also help recover a slight efficiency margin. For instance, the definition: % \begin{quote} \begin{tabular}{l} \dinline \nt{plist}(\nt{X}): \newprod \basic{xs} = \nt{loption}(% \nt{delimited}(% \basic{LPAREN}, \nt{separated\_nonempty\_list}(\basic{COMMA}, \basic{X}), \basic{RPAREN}% )% ) \dpaction{\basic{xs}} \end{tabular} \end{quote} % effectively makes \nt{plist}(\nt{X}) an alias for the right-hand side \nt{loption}($\ldots$). Without the \dinline keyword, the language recognized by the grammar would be the same, but the LR automaton would probably have one more state and would perform one more reduction at run time. \subsection{The standard library} \label{sec:library} \begin{figure} \begin{center} \begin{tabular}{lp{51mm}ll} Name & Recognizes & Produces & Comment \\ \hline\\ \nt{option}(\nt{X}) & $\epsilon$ \barre \nt{X} & $\alpha$ \basic{option}, if \nt{X} : $\alpha$ \\ \nt{ioption}(\nt{X}) & $\epsilon$ \barre \nt{X} & $\alpha$ \basic{option}, if \nt{X} : $\alpha$ & (inlined) \\ \nt{boption}(\nt{X}) & $\epsilon$ \barre \nt{X} & \basic{bool} \\ \nt{loption}(\nt{X}) & $\epsilon$ \barre \nt{X} & $\alpha$ \basic{list}, if \nt{X} : $\alpha$ \nt{list} \\ \\ \nt{pair}(\nt{X}, \nt{Y}) & \nt{X} \nt{Y} & $\alpha\times\beta$, if \nt{X} : $\alpha$ and \nt{Y} : $\beta$ \\ \nt{separated\_pair}(\nt{X}, \nt{sep}, \nt{Y}) & \nt{X} \nt{sep} \nt{Y} & $\alpha\times\beta$, if \nt{X} : $\alpha$ and \nt{Y} : $\beta$ \\ \nt{preceded}(\nt{opening}, \nt{X}) & \nt{opening} \nt{X} & $\alpha$, if \nt{X} : $\alpha$ \\ \nt{terminated}(\nt{X}, \nt{closing}) & \nt{X} \nt{closing} & $\alpha$, if \nt{X} : $\alpha$ \\ \nt{delimited}(\nt{opening}, \nt{X}, \nt{closing}) & \nt{opening} \nt{X} \nt{closing} & $\alpha$, if \nt{X} : $\alpha$ \\ \\ \nt{list}(\nt{X}) & a possibly empty sequence of \nt{X}'s & $\alpha$ \basic{list}, if \nt{X} : $\alpha$ \\ \nt{nonempty\_list}(\nt{X}) & a nonempty sequence of \nt{X}'s & $\alpha$ \basic{list}, if \nt{X} : $\alpha$ \\ \nt{separated\_list}(\nt{sep}, \nt{X}) & a possibly empty sequence of \nt{X}'s separated with \nt{sep}'s & $\alpha$ \basic{list}, if \nt{X} : $\alpha$ \\ \nt{separated\_nonempty\_list}(\nt{sep}, \nt{X}) & a nonempty sequence of \nt{X}'s separated with \nt{sep}'s & $\alpha$ \basic{list}, if \nt{X} : $\alpha$ \\ \end{tabular} \end{center} \caption{Summary of the standard library} \label{fig:standard} \end{figure} Once equipped with a rudimentary module system (\sref{sec:split}), parameterization (\sref{sec:templates}), and inlining (\sref{sec:inline}), it is straightforward to propose a collection of commonly used definitions, such as options, sequences, lists, and so on. This \emph{standard library} is joined, by default, with every grammar specification. A summary of the nonterminal symbols offered by the standard library appears in \fref{fig:standard}. See also the short-hands documented in \fref{fig:sugar}. By relying on the standard library, a client module can concisely define more elaborate notions. For instance, the following rule: % \begin{quote} \begin{tabular}{l} \dinline \nt{plist}(\nt{X}): \newprod \basic{xs} = \nt{loption}(% \nt{delimited}(% \basic{LPAREN}, \nt{separated\_nonempty\_list}(\basic{COMMA}, \basic{X}), \basic{RPAREN}% )% ) \dpaction{\basic{xs}} \end{tabular} \end{quote} % causes \nt{plist}(\nt{X}) to recognize a list of \nt{X}'s, where the empty list is represented by the empty string, and a non-empty list is delimited with parentheses and comma-separated. % --------------------------------------------------------------------------------------------------------------------- \section{Conflicts} \label{sec:conflicts} When a shift/reduce or reduce/reduce conflict is detected, it is classified as either benign, if it can be resolved by consulting user-supplied precedence declarations, or severe, if it cannot. Benign conflicts are not reported. Severe conflicts are reported and, if the \oexplain switch is on, explained. \subsection{When is a conflict benign?} A shift/reduce conflict involves a single token (the one that one might wish to shift) and one or more productions (those that one might wish to reduce). When such a conflict is detected, the precedence level (\sref{sec:assoc}, \sref{sec:prec}) of these entities are looked up and compared as follows: \begin{enumerate} \item if only one production is involved, and if it has higher priority than the token, then the conflict is resolved in favor of reduction. \item if only one production is involved, and if it has the same priority as the token, then the associativity status of the token is looked up: \begin{enumerate} \item if the token was declared nonassociative, then the conflict is resolved in favor of neither action, that is, a syntax error will be signaled if this token shows up when this production is about to be reduced; \item if the token was declared left-associative, then the conflict is resolved in favor of reduction; \item if the token was declared right-associative, then the conflict is resolved in favor of shifting. \end{enumerate} \item \label{multiway} if multiple productions are involved, and if, considered one by one, they all cause the conflict to be resolved in the same way (that is, either in favor in shifting, or in favor of neither), then the conflict is resolved in that way. \end{enumerate} In either of these cases, the conflict is considered benign. Otherwise, it is considered severe. Note that a reduce/reduce conflict is always considered severe, unless it happens to be subsumed by a benign multi-way shift/reduce conflict (item~\ref{multiway} above). \subsection{How are severe conflicts explained?} When the \odump switch is on, a description of the automaton is written to the \automaton file. Severe conflicts are shown as part of this description. Fortunately, there is also a way of understanding conflicts in terms of the grammar, rather than in terms of the automaton. When the \oexplain switch is on, a textual explanation is written to the \conflicts file. \emph{Not all conflicts are explained} in this file: instead, \emph{only one conflict per automaton state is explained}. This is done partly in the interest of brevity, but also because Pager's algorithm can create artificial conflicts in a state that already contains a true LR(1) conflict; thus, one cannot hope in general to explain all of the conflicts that appear in the automaton. As a result of this policy, once all conflicts explained in the \conflicts file have been fixed, one might need to run \menhir again to produce yet more conflict explanations. \begin{figure} \begin{quote} \begin{tabular}{l} \dtoken \basic{IF THEN ELSE} \\ \dstart \kangle{\basic{expression}} \nt{expression} \\ \\ \percentpercent \\ \\ \nt{expression}: \newprod $\ldots$ \newprod \basic{IF b} = \nt{expression} \basic{THEN e} = \nt{expression} \dpaction{$\ldots$} \newprod \basic{IF b} = \nt{expression} \basic{THEN e} = \nt{expression} \basic{ELSE f} = \nt{expression} \dpaction{$\ldots$} \newprod $\ldots$ \end{tabular} \end{quote} \caption{Basic example of a shift/reduce conflict} \label{fig:basicshiftreduce} \end{figure} \paragraph{How the conflict state is reached} \fref{fig:basicshiftreduce} shows a grammar specification with a typical shift/reduce conflict. % When this specification is analyzed, the conflict is detected, and an explanation is written to the \conflicts file. The explanation first indicates in which state the conflict lies by showing how that state is reached. Here, it is reached after recognizing the following string of terminal and nonterminal symbols---the \emph{conflict string}: % \begin{quote} \basic{IF expression THEN IF expression THEN expression} \end{quote} Allowing the conflict string to contain both nonterminal and terminal symbols usually makes it shorter and more readable. If desired, a conflict string composed purely of terminal symbols could be obtained by replacing each occurrence of a nonterminal symbol $N$ with an arbitrary $N$-sentence. The conflict string can be thought of as a path that leads from one of the automaton's start states to the conflict state. When multiple such paths exist, the one that is displayed is chosen shortest. Nevertheless, it may sometimes be quite long. In that case, artificially (and temporarily) declaring some existing nonterminal symbols to be start symbols has the effect of adding new start states to the automaton and can help produce shorter conflict strings. Here, \nt{expression} was declared to be a start symbol, which is why the conflict string is quite short. In addition to the conflict string, the \conflicts file also states that the \emph{conflict token} is \basic{ELSE}. That is, when the automaton has recognized the conflict string and when the lookahead token (the next token on the input stream) is \basic{ELSE}, a conflict arises. A conflict corresponds to a choice: the automaton is faced with several possible actions, and does not know which one should be taken. This indicates that the grammar is not LR(1). The grammar may or may not be inherently ambiguous. In our example, the conflict string and the conflict token are enough to understand why there is a conflict: when two \basic{IF} constructs are nested, it is ambiguous which of the two constructs the \basic{ELSE} branch should be associated with. Nevertheless, the \conflicts file provides further information: it explicitly shows that there exists a conflict, by proving that two distinct actions are possible. Here, one of these actions consists in \emph{shifting}, while the other consists in \emph{reducing}: this is a \emph{shift/reduce} conflict. A \emph{proof} takes the form of a \emph{partial derivation tree} whose \emph{fringe} begins with the conflict string, followed by the conflict token. A derivation tree is a tree whose nodes are labeled with symbols. The root node carries a start symbol. A node that carries a terminal symbol is considered a leaf, and has no children. A node that carries a nonterminal symbol $N$ either is considered a leaf, and has no children; or is not considered a leaf, and has $n$ children, where $n\geq 0$, labeled $\nt{x}_1,\ldots,\nt{x}_n$, where $N \rightarrow \nt{x}_1,\ldots,\nt{x}_n$ is a production. The fringe of a partial derivation tree is the string of terminal and nonterminal symbols carried by the tree's leaves. A string of terminal and nonterminal symbols that is the fringe of some partial derivation tree is a \emph{sentential form}. \paragraph{Why shifting is legal} \begin{figure} \vspace{5mm} \begin{center} \hskip -3mm\includegraphics{tree1} \end{center} \caption{A partial derivation tree that justifies shifting} \label{fig:shifting:tree} \end{figure} \begin{figure} \begin{center} \begin{tabbing} \= \nt{expression} \\ \> \basic{IF} \nt{expression} \basic{THEN} \= \nt{expression} \\ \> \> \basic{IF} \nt{expression} \basic{THEN} \basic{expression} . \basic{ELSE} \nt{expression} \end{tabbing} \end{center} \caption{A textual version of the tree in \fref{fig:shifting:tree}} \label{fig:shifting:text} \end{figure} In our example, the proof that shifting is possible is the derivation tree shown in Figures~\ref{fig:shifting:tree} and~\ref{fig:shifting:text}. At the root of the tree is the grammar's start symbol, \nt{expression}. This symbol develops into the string \nt{IF expression THEN expression}, which forms the tree's second level. The second occurrence of \nt{expression} in that string develops into \nt{IF expression THEN expression ELSE expression}, which forms the tree's last level. The tree's fringe, a sentential form, is the string \nt{IF expression THEN IF expression THEN expression ELSE expression}. As announced earlier, it begins with the conflict string \nt{IF expression THEN IF expression THEN expression}, followed with the conflict token \nt{ELSE}. In \fref{fig:shifting:text}, the end of the conflict string is materialized with a dot. Note that this dot does not occupy the rightmost position in the tree's last level. In other words, the conflict token (\basic{ELSE}) itself occurs on the tree's last level. In practical terms, this means that, after the automaton has recognized the conflict string and peeked at the conflict token, it makes sense for it to \emph{shift} that token. \paragraph{Why reducing is legal} \begin{figure} \vspace{5mm} \begin{center} \hskip -3mm\includegraphics{tree2} \end{center} \caption{A partial derivation tree that justifies reducing} \label{fig:reducing:tree} \end{figure} \begin{figure} \begin{center} \begin{tabbing} \= \nt{expression} \\ \> \basic{IF} \nt{expression} \basic{THEN} \= \nt{expression} \basic{ELSE} \nt{expression} \sidecomment{lookahead token appears} \\ \> \> \basic{IF} \nt{expression} \basic{THEN} \basic{expression} . \end{tabbing} \end{center} \caption{A textual version of the tree in \fref{fig:reducing:tree}} \label{fig:reducing:text} \end{figure} In our example, the proof that shifting is possible is the derivation tree shown in Figures~\ref{fig:reducing:tree} and~\ref{fig:reducing:text}. Again, the sentential form found at the fringe of the tree begins with the conflict string, followed with the conflict token. Again, in \fref{fig:reducing:text}, the end of the conflict string is materialized with a dot. Note that, this time, the dot occupies the rightmost position in the tree's last level. In other words, the conflict token (\basic{ELSE}) appeared on an earlier level (here, on the second level). This fact is emphasized by the comment \inlinesidecomment{lookahead token appears} found at the second level. In practical terms, this means that, after the automaton has recognized the conflict string and peeked at the conflict token, it makes sense for it to \emph{reduce} the production that corresponds to the tree's last level---here, the production is \nt{expression} $\rightarrow$ \basic{IF} \nt{expression} \basic{THEN} \basic{expression}. \paragraph{An example of a more complex derivation tree} Figures~\ref{fig:xreducing:tree} and~\ref{fig:xreducing:text} show a partial derivation tree that justifies reduction in a more complex situation. (This derivation tree is relative to a grammar that is not shown.) Here, the conflict string is \basic{DATA UIDENT EQUALS UIDENT}; the conflict token is \basic{LIDENT}. It is quite clear that the fringe of the tree begins with the conflict string. However, in this case, the fringe does not explicitly exhibit the conflict token. Let us examine the tree more closely and answer the question: following \basic{UIDENT}, what's the next terminal symbol on the fringe? \begin{figure} \vspace{5mm} \begin{center} \hskip -3mm\includegraphics{tree3} \end{center} \caption{A partial derivation tree that justifies reducing} \label{fig:xreducing:tree} \end{figure} \begin{figure} \begin{center} \begin{tabbing} \= \nt{decls} \\ \> \nt{decl} \nt{opt\_semi} \nt{decls} \sidecomment{lookahead token appears because \nt{opt\_semi} can vanish and \nt{decls} can begin with \basic{LIDENT}} \\ \> \basic{DATA UIDENT} \basic{EQUALS} \= \nt{tycon\_expr} \sidecomment{lookahead token is inherited} \\ \> \> \nt{tycon\_item} \sidecomment{lookahead token is inherited} \\ \> \> \basic{UIDENT} \= \nt{opt\_type\_exprs} \sidecomment{lookahead token is inherited} \\ \> \> \> . \end{tabbing} \end{center} \caption{A textual version of the tree in \fref{fig:xreducing:tree}} \label{fig:xreducing:text} \end{figure} First, note that \nt{opt\_type\_exprs} is \emph{not} a leaf node, even though it has no children. The grammar contains the production $\nt{opt\_type\_exprs} \rightarrow \epsilon$: the nonterminal symbol \nt{opt\_type\_exprs} develops to the empty string. (This is made clear in \fref{fig:xreducing:text}, where a single dot appears immediately below \nt{opt\_type\_exprs}.) Thus, \nt{opt\_type\_exprs} is not part of the fringe. Next, note that \nt{opt\_type\_exprs} is the rightmost symbol within its level. Thus, in order to find the next symbol on the fringe, we have to look up one level. This is the meaning of the comment \inlinesidecomment{lookahead token is inherited}. Similarly, \nt{tycon\_item} and \nt{tycon\_expr} appear rightmost within their level, so we again have to look further up. This brings us back to the tree's second level. There, \nt{decl} is \emph{not} the rightmost symbol: next to it, we find \nt{opt\_semi} and \nt{decls}. Does this mean that \nt{opt\_semi} is the next symbol on the fringe? Yes and no. \nt{opt\_semi} is a \emph{nonterminal} symbol, but we are really interested in finding out what the next \emph{terminal} symbol on the fringe could be. The partial derivation tree shown in Figures~\ref{fig:xreducing:tree} and~\ref{fig:xreducing:text} does not explicitly answer this question. In order to answer it, we need to know more about \nt{opt\_semi} and \nt{decls}. Here, \nt{opt\_semi} stands (as one might have guessed) for an optional semicolon, so the grammar contains a production $\nt{opt\_semi} \rightarrow \epsilon$. This is indicated by the comment \inlinesidecomment{\nt{opt\_semi} can vanish}. (Nonterminal symbols that generate $\epsilon$ are also said to be \emph{nullable}.) Thus, one could choose to turn this partial derivation tree into a larger one by developing \nt{opt\_semi} into $\epsilon$, making it a non-leaf node. That would yield a new partial derivation tree where the next symbol on the fringe, following \basic{UIDENT}, is \nt{decls}. Now, what about \nt{decls}? Again, it is a \emph{nonterminal} symbol, and we are really interested in finding out what the next \emph{terminal} symbol on the fringe could be. Again, we need to imagine how this partial derivation tree could be turned into a larger one by developing \nt{decls}. Here, the grammar happens to contain a production of the form $\nt{decls} \rightarrow \basic{LIDENT} \ldots$ This is indicated by the comment \inlinesidecomment{\nt{decls} can begin with \basic{LIDENT}}. Thus, by developing \nt{decls}, it is possible to construct a partial derivation tree where the next symbol on the fringe, following \basic{UIDENT}, is \basic{LIDENT}. This is precisely the conflict token. To sum up, there exists a partial derivation tree whose fringe begins the conflict string, followed with the conflict token. Furthermore, in that derivation tree, the dot occupies the rightmost position in the last level. As in our previous example, this means that, after the automaton has recognized the conflict string and peeked at the conflict token, it makes sense for it to \emph{reduce} the production that corresponds to the tree's last level---here, the production is $\nt{opt\_type\_exprs} \rightarrow \epsilon$. \paragraph{Greatest common factor among derivation trees} Understanding conflicts requires comparing two (or more) derivation trees. It is frequent for these trees to exhibit a common factor, that is, to exhibit identical structure near the top of the tree, and to differ only below a specific node. Manual identification of that node can be tedious, so \menhir performs this work automatically. When explaining a $n$-way conflict, it first displays the greatest common factor of the $n$ derivation trees. A question mark symbol $\basic{(?)}$ is used to identify the node where the trees begin to differ. Then, \menhir displays each of the $n$ derivation trees, \emph{without their common factor} -- that is, it displays $n$ sub-trees that actually begin to differ at the root. This should make visual comparisons significantly easier. \subsection{How are severe conflicts resolved in the end?} It is unspecified how severe conflicts are resolved. \menhir attempts to mimic \ocamlyacc's specification, that is, to resolve shift/reduce conflicts in favor of shifting, and to resolve reduce/reduce conflicts in favor of the production that textually appears earliest in the grammar specification. However, this specification is inconsistent in case of three-way conflicts, that is, conflicts that simultaneously involve a shift action and several reduction actions. Furthermore, textual precedence can be undefined when the grammar specification is split over multiple modules. In short, \menhir's philosophy is that \begin{center} severe conflicts should not be tolerated, \end{center} so you should not care how they are resolved. % If a shift/reduce conflict is resolved in favor of reduction, then there can % exist words of terminal symbols that are accepted by the canonical LR(1) % automaton without traversing any conflict state and which are rejected by our % automaton (constructed by Pager's method followed by conflict % resolution). Same problem when a shift/reduce conflict is resolved in favor of % neither action (via \dnonassoc) or when a reduce/reduce conflict is resolved % arbitrarily. \subsection{End-of-stream conflicts} \label{sec:eos} \menhir's treatment of the end of the token stream is (believed to be) fully compatible with \ocamlyacc's. Yet, \menhir attempts to be more user-friendly by warning about a class of so-called end-of-stream conflicts''. \paragraph{How the end of stream is handled} In many textbooks on parsing, it is assumed that the lexical analyzer, which produces the token stream, produces a special token, written \eos, to signal that the end of the token stream has been reached. A parser generator can take advantage of this by transforming the grammar: for each start symbol $\nt{S}$ in the original grammar, a new start symbol $\nt{S'}$ is defined, together with the production $S'\rightarrow S\eos$. The symbol $S$ is no longer a start symbol in the new grammar. This means that the parser will accept a sentence derived from $S$ only if it is immediately followed by the end of the token stream. This approach has the advantage of simplicity. However, \ocamlyacc and \menhir do not follow it, for several reasons. Perhaps the most convincing one is that it is not flexible enough: sometimes, it is desirable to recognize a sentence derived from $S$, \emph{without} requiring that it be followed by the end of the token stream: this is the case, for instance, when reading commands, one by one, on the standard input channel. In that case, there is no end of stream: the token stream is conceptually infinite. Furthermore, after a command has been recognized, we do \emph{not} wish to examine the next token, because doing so might cause the program to block, waiting for more input. In short, \ocamlyacc and \menhir's approach is to recognize a sentence derived from $S$ and to \emph{not look}, if possible, at what follows. However, this is possible only if the definition of $S$ is such that the end of an $S$-sentence is identifiable without knowledge of the lookahead token. When the definition of $S$ does not satisfy this criterion, and \emph{end-of-stream conflict} arises: after a potential $S$-sentence has been read, there can be a tension between consulting the next token, in order to determine whether the sentence is continued, and \emph{not} consulting the next token, because the sentence might be over and whatever follows should not be read. \menhir warns about end-of-stream conflicts, whereas \ocamlyacc does not. \paragraph{A definition of end-of-stream conflicts} Technically, \menhir proceeds as follows. A \eos symbol is introduced. It is, however, only a \emph{pseudo-}token: it is never produced by the lexical analyzer. For each start symbol $\nt{S}$ in the original grammar, a new start symbol $\nt{S'}$ is defined, together with the production $S'\rightarrow S$. The corresponding start state of the LR(1) automaton is composed of the LR(1) item $S' \rightarrow . \;S\; [\eos]$. That is, the pseudo-token \eos initially appears in the lookahead set, indicating that we expect to be done after recognizing an $S$-sentence. During the construction of the LR(1) automaton, this lookahead set is inherited by other items, with the effect that, in the end, the automaton has: \begin{itemize} \item \emph{shift} actions only on physical tokens; and \item \emph{reduce} actions either on physical tokens or on the pseudo-token \eos. \end{itemize} A state of the automaton has a reduce action on \eos if, in that state, an $S$-sentence has been read, so that the job is potentially finished. A state has a shift or reduce action on a physical token if, in that state, more tokens potentially need to be read before an $S$-sentence is recognized. If a state has a reduce action on \eos, then that action should be taken \emph{without} requesting the next token from the lexical analyzer. On the other hand, if a state has a shift or reduce action on a physical token, then the lookahead token \emph{must} be consulted in order to determine if that action should be taken. \begin{figure}[p] \begin{quote} \begin{tabular}{l} \dtoken \kangle{\basic{int}} \basic{INT} \\ \dtoken \basic{PLUS TIMES} \\ \dleft PLUS \\ \dleft TIMES \\ \dstart \kangle{\basic{int}} \nt{expr} \\ \percentpercent \\ \nt{expr}: \newprod \basic{i} = \basic{INT} \dpaction{\basic{i}} \newprod \basic{e1} = \nt{expr} \basic{PLUS} \basic{e2} = \nt{expr} \dpaction{\basic{e1 + e2}} \newprod \basic{e1} = \nt{expr} \basic{TIMES} \basic{e2} = \nt{expr} \dpaction{\basic{e1 * e2}} \end{tabular} \end{quote} \caption{Basic example of an end-of-stream conflict} \label{fig:basiceos} \end{figure} \begin{figure}[p] \begin{verbatim} State 6: expr -> expr . PLUS expr [ # TIMES PLUS ] expr -> expr PLUS expr . [ # TIMES PLUS ] expr -> expr . TIMES expr [ # TIMES PLUS ] -- On TIMES shift to state 3 -- On # PLUS reduce production expr -> expr PLUS expr State 4: expr -> expr . PLUS expr [ # TIMES PLUS ] expr -> expr . TIMES expr [ # TIMES PLUS ] expr -> expr TIMES expr . [ # TIMES PLUS ] -- On # TIMES PLUS reduce production expr -> expr TIMES expr State 2: expr' -> expr . [ # ] expr -> expr . PLUS expr [ # TIMES PLUS ] expr -> expr . TIMES expr [ # TIMES PLUS ] -- On TIMES shift to state 3 -- On PLUS shift to state 5 -- On # accept expr \end{verbatim} \caption{Part of an LR automaton for the grammar in \fref{fig:basiceos}} \label{fig:basiceosdump} \end{figure} \begin{figure}[p] \begin{quote} \begin{tabular}{l} \ldots \\ \dtoken \basic{END} \\ \dstart \kangle{\basic{int}} \nt{main} \hskip 1cm \textit{// instead of \nt{expr}} \\ \percentpercent \\ \nt{main}: \newprod \basic{e} = \nt{expr} \basic{END} \dpaction{\basic{e}} \\ \nt{expr}: \newprod \ldots \end{tabular} \end{quote} \caption{Fixing the grammar specification in \fref{fig:basiceos}} \label{fig:basiceos:sol} \end{figure} An end-of-stream conflict arises when a state has distinct actions on \eos and on at least one physical token. In short, this means that the end of an $S$-sentence cannot be unambiguously identified without examining one extra token. \menhir's default behavior, in that case, is to suppress the action on \eos, so that more input is \emph{always} requested. \paragraph{Example} \fref{fig:basiceos} shows a grammar that has end-of-stream conflicts. When this grammar is processed, \menhir warns about these conflicts, and further warns that \nt{expr} is never accepted. Let us explain. Part of the corresponding automaton, as described in the \conflicts file, is shown in \fref{fig:basiceosdump}. Explanations at the end of the \conflicts file (not shown) point out that states 6 and 2 have an end-of-stream conflict. Indeed, both states have distinct actions on \eos and on the physical token \basic{TIMES}. % It is interesting to note that, even though state 4 has actions on \eos and on physical tokens, it does not have an end-of-stream conflict. This is because the action taken in state 4 is always to reduce the production $\nt{expr} \rightarrow \nt{expr}$ \basic{TIMES} \nt{expr}, regardless of the lookahead token. By default, \menhir produces a parser where end-of-stream conflicts are resolved in favor of looking ahead: that is, the problematic reduce actions on \eos are suppressed. This means, in particular, that the \emph{accept} action in state 2, which corresponds to reducing the production $\nt{expr} \rightarrow \nt{expr'}$, is suppressed. This explains why the symbol \nt{expr} is never accepted: because expressions do not have an unambiguous end marker, the parser will always request one more token and will never stop. In order to avoid this end-of-stream conflict, the standard solution is to introduce a new token, say \basic{END}, and to use it as an end marker for expressions. The \basic{END} token could be generated by the lexical analyzer when it encounters the actual end of stream, or it could correspond to a piece of concrete syntax, say, a line feed character, a semicolon, or an \texttt{end} keyword. The solution is shown in \fref{fig:basiceos:sol}. % --------------------------------------------------------------------------------------------------------------------- \section{Positions} \label{sec:positions} When an \ocamllex-generated lexical analyzer produces a token, it updates two fields, named \verb+lex_start_p+ and \verb+lex_curr_p+, in its environment record, whose type is \verb+Lexing.lexbuf+. Each of these fields holds a value of type \verb+Lexing.position+. Together, they represent the token's start and end positions within the text that is being scanned. A position consists mainly of an offset (the position's \verb+pos_cnum+ field), but also holds information about the current file name, the current line number, and the current offset within the current line. (Not all \ocamllex-generated analyzers keep this extra information up to date. This must be explicitly programmed by the author of the lexical analyzer.) \begin{figure} \begin{center} \begin{tabular}{lp{9cm}} \verb+$startpos+ & start position of the sentence derived out of the production that is being reduced \\ \verb+$endpos+ & end position of the sentence derived out of the production that is being reduced \\ \verb+$startpos(+ \verb+$+\nt{i} \barre \nt{id} \verb+)+ & start position of the sentence derived out of the symbol whose semantic value is referred to as \verb+$+\nt{i} or \nt{id} \\ \verb+$endpos(+ \verb+$+\nt{i} \barre \nt{id} \verb+)+ & end position of the sentence derived out of the symbol whose semantic value is referred to as \verb+$+\nt{i} or \nt{id} \\ \verb+$startofs+ & start offset of the sentence derived out of the production that is being reduced \\ \verb+$endofs+ & end offset of the sentence derived out of the production that is being reduced \\ \verb+$startofs(+ \verb+$+\nt{i} \barre \nt{id} \verb+)+ & start offset of the sentence derived out of the symbol whose semantic value is referred to as \verb+$+\nt{i} or \nt{id} \\ \verb+$endofs(+ \verb+$+\nt{i} \barre \nt{id} \verb+)+ & end offset of the sentence derived out of the symbol whose semantic value is referred to as \verb+$+\nt{i} or \nt{id} \\ \end{tabular} \end{center} \caption{Position-related keywords} \label{fig:pos} \end{figure} This mechanism allows associating pairs of positions with terminal symbols. If desired, \menhir automatically extends it to nonterminal symbols as well. That is, it offers a mechanism for associating pairs of positions with terminal or nonterminal symbols. This is done by making a set of keywords, documented in \fref{fig:pos}, available to semantic actions. Note that these keywords are \emph{not} available elsewhere---in particular, not within \ocaml headers. Note also that \ocaml's standard library module \texttt{Parsing} is deprecated. The functions that it offers \emph{can} be called, but will return dummy positions. % --------------------------------------------------------------------------------------------------------------------- \section{Error handling and recovery} \label{sec:errors} \paragraph{Error handling} \menhir's error handling and recovery is inspired by that of \yacc and \ocamlyacc, but is not identical. A special \error token is made available for use within productions. The LR automaton is constructed exactly as if \error was a regular terminal symbol. However, \error is never produced by the lexical analyzer. Instead, when an error is detected, the current lookahead token is discarded and replaced with the \error token, which becomes the current lookahead token. At this point, the parser enters \emph{error handling} mode. In error handling mode, automaton states are popped off the automaton's stack until a state that can \emph{act} on \error is found. This includes \emph{both} shift \emph{and} reduce actions. (\yacc and \ocamlyacc do not trigger reduce actions on \error. It is somewhat unclear why this is so.) When a state that can reduce on \error is found, reduction is performed. Since the lookahead token is still \error, the automaton remains in error handling mode. When a state that can shift on \error is found, the \error token is shifted. At this point, the parser either enters \emph{error recovery} mode, if the \oerrorrecovery switch was enabled at compile time, or returns to normal mode. When no state that can act on \error is found on the automaton's stack, the parser stops and raises the exception \texttt{Error}. This exception carries no information. The position of the error can be obtained by reading the lexical analyzer's environment record. \paragraph{Error recovery} Error recovery mode is entered immediately after an \error token was successfully shifted, and only if \menhir's \oerrorrecovery switch was enabled when the parser was produced. In error recovery mode, tokens are repeatedly taken off the input stream and discarded until an acceptable token is found. A token is acceptable if the current state has an action on that token. When an acceptable token is found, the parser returns to normal mode and the action takes place. Error recovery is also known as \emph{re-synchronization}. Error recovery mode is peculiar, in that it can cause non-termination if the token stream is infinite. In practice, token streams often \emph{are} infinite, due to an \ocamllex peculiarity: every \ocamllex-generated analyzer that maps the \kw{eof} pattern to an \basic{EOF} token will produce an infinite stream of \basic{EOF} tokens, even if the underlying text that is being scanned is finite. In order to address this issue, \menhir attributes special meaning to the token named \basic{EOF}, if there is one in the grammar specification, when \oerrorrecovery is enabled. It checks that every automaton state that can be reached when in error recovery mode accepts this token, and issues a warning otherwise. This ensures that the parser always terminates. \paragraph{Error-related keywords} A couple of error-related keywords are made available to semantic actions. When the \verb+$syntaxerror+ keyword is evaluated, evaluation of the semantic action is aborted, so that the current reduction is abandoned; the current lookahead token is discarded and replaced with the \error token; and error handling mode is entered. Note that there is no mechanism for inserting an \error token \emph{in front of} the current lookahead token, even though this might also be desirable. It is unclear whether this keyword is useful; it might be suppressed in the future. The \verb+$previouserror+ keyword evaluates to an integer value, and indicates how many tokens were successfully shifted since the last \error token was shifted. This allows heuristics such as \textit{when a new error is detected, do not display a new error message unless the previous error is ancient enough''} to be implemented if and where desired. \paragraph{When are errors detected?} An error is detected when the current state of the automaton has no action on the current lookahead token. Thus, understanding exactly when errors are detected requires understanding how the automaton is constructed. \menhir's construction technique is \emph{not} Knuth's canonical LR(1) technique~\cite{knuth-lr-65}, which is too expensive to be practical. Instead, \menhir \emph{merges} states~\cite{pager-77} and introduces so-called \emph{default reductions}. Both techniques can \emph{defer} error detection by allowing extra reductions to take place before an error is detected. All LALR(1) parser generators exhibit the same problem. % --------------------------------------------------------------------------------------------------------------------- \section{Using \menhir as an interpreter} \label{sec:interpret} When \ointerpret is set, \menhir no longer behaves as a compiler. Instead, it acts as an interpreter. That is, it repeatedly: \begin{itemize} \item reads a sentence off the standard input channel; \item parses this sentence, according to the grammar; \item displays an outcome. \end{itemize} This process stops when the end of the input channel is reached. \subsection{Sentences} \label{sec:sentences} The syntax of sentences is as follows: \begin{center} \begin{tabular}{r@{}c@{}l} \nt{sentence} \is \optional{\nt{lid}\,\deuxpoints} \sepspacelist{\nt{uid}} \,\dnewline \end{tabular} \end{center} Less formally, a sentence is a sequence of zero or more terminal symbols (\nt{uid}'s), separated with whitespace, terminated with a newline character, and optionally preceded with a non-terminal start symbol (\nt{lid}). This non-terminal symbol can be omitted if, and only if, the grammar only has one start symbol. For instance, here are four valid sentences for the grammar of arithmetic expressions found in the directory \distrib{demos/calc}: % \begin{verbatim} main: INT PLUS INT EOL INT PLUS INT INT PLUS PLUS INT EOL INT PLUS PLUS \end{verbatim} % In the first sentence, the start symbol \texttt{main} was explicitly specified. In the other sentences, it was omitted, which is permitted, because this grammar has no start symbol other than \texttt{main}. The first sentence is a stream of four terminal symbols, namely \texttt{INT}, \texttt{PLUS}, \texttt{INT}, and \texttt{EOL}. These terminal symbols must be provided under their symbolic names. Writing, say, \texttt{12+32\textbackslash n}'' instead of \texttt{INT PLUS INT EOL} is not permitted. \menhir would not be able to make sense of such a concrete notation, since it does not have a lexer for it. % On pourrait documenter le fait qu'une phrase finie est transformée par Menhir % en un flot de tokens potentiellement infinie, avec un suffixe infini EOF ... % Mais c'est un hack, qui pourrait changer à l'avenir. \subsection{Outcomes} \label{sec:outcomes} As soon as \menhir is able to read a complete sentence off the standard input channel (that is, as soon as it finds the newline character that ends the sentence), it parses the sentence according to whichever grammar was specified on the command line, and displays an outcome. An outcome is one of the following: \begin{itemize} \item \texttt{ACCEPT}: a prefix of the sentence was successfully parsed; a parser generated by \menhir would successfully stop and produce a semantic value; \item \texttt{OVERSHOOT}: the end of the sentence was reached before it could be accepted; a parser generated by \menhir would request a non-existent next token'' from the lexer, causing it to fail or block; \item \texttt{REJECT}: the sentence was not accepted; a parser generated by \menhir would raise the exception \texttt{Error}. \end{itemize} When \ointerpretshowcst is set, each \texttt{ACCEPT} outcome is followed with a concrete syntax tree. A concrete syntax tree is either a leaf or a node. A leaf is either a terminal symbol or \error. A node is annotated with a non-terminal symbol, and carries a sequence of immediate descendants that correspond to a valid expansion of this non-terminal symbol. \menhir's notation for concrete syntax trees is as follows: \begin{center} \begin{tabular}{r@{}c@{}l} \nt{cst} \is \nt{uid} \\ && \error \\ && \texttt{[} \nt{lid}\,\deuxpoints \sepspacelist{\nt{cst}} \texttt{]} \end{tabular} \end{center} % This notation is not quite unambiguous (it is ambiguous if several % productions are identical). For instance, if one wished to parse the example sentences of \sref{sec:sentences} using the grammar of arithmetic expressions in \distrib{demos/calc}, one could invoke \menhir as follows: \begin{verbatim} $menhir --interpret --interpret-show-cst demos/calc/parser.mly main: INT PLUS INT EOL ACCEPT [main: [expr: [expr: INT] PLUS [expr: INT]] EOL] INT PLUS INT OVERSHOOT INT PLUS PLUS INT EOL REJECT INT PLUS PLUS REJECT \end{verbatim} (Here, \menhir's input---the sentences provided by the user on the standard input channel--- is shown intermixed with \menhir's output---the outcomes printed by \menhir on the standard output channel.) The first sentence is valid, and accepted; a concrete syntax tree is displayed. The second sentence is incomplete, because the grammar specifies that a valid expansion of \texttt{main} ends with the terminal symbol \texttt{EOL}; hence, the outcome is \texttt{OVERSHOOT}. The third sentence is invalid, because of the repeated occurrence of the terminal symbol \texttt{PLUS}; the outcome is \texttt{REJECT}. The fourth sentence, a prefix of the third one, is rejected for the same reason. \subsection{Remarks} Using \menhir as an interpreter offers an easy way of debugging your grammar. For instance, if one wished to check that addition is considered left-associative, as requested by the \dleft directive found in the file \distrib{demos/calc/parser.mly}, one could submit the following sentence: \begin{verbatim}$ ./menhir --interpret --interpret-show-cst ../demos/calc/parser.mly INT PLUS INT PLUS INT EOL ACCEPT [main: [expr: [expr: [expr: INT] PLUS [expr: INT]] PLUS [expr: INT]] EOL ] \end{verbatim} The concrete syntax tree displayed by \menhir is skewed towards the left, as desired. The switches \ointerpret and \otrace can be used in conjunction. When \otrace is set, the interpreter logs its actions to the standard error channel. % --------------------------------------------------------------------------------------------------------------------- \section{A comparison with \ocamlyacc} Here is an incomplete list of the differences between \ocamlyacc and \menhir. The list is roughly sorted by decreasing order of importance. \begin{itemize} \item \menhir allows the definition of a nonterminal symbol to be parameterized by other (terminal or nonterminal) symbols (\sref{sec:templates}). Furthermore, it offers a library of standard parameterized definitions (\sref{sec:library}), including options, sequences, and lists. It offers some support for EBNF syntax, via the \dquestion, \dplus, and \dstar modifiers. \item \ocamlyacc only accepts LALR(1) grammars. \menhir accepts LR(1) grammars, thus avoiding certain artificial conflicts. \item \menhir's \dinline keyword (\sref{sec:inline}) helps avoid or resolve some LR(1) conflicts without artificial modification of the grammar. \item \menhir explains conflicts (\sref{sec:conflicts}) in terms of the grammar, not just in terms of the automaton. \menhir's explanations are believed to be understandable by mere humans. \item \menhir offers an interpreter (\sref{sec:interpret}) that helps debug grammars interactively. \item \menhir allows grammar specifications to be split over multiple files (\sref{sec:split}). It also allows several grammars to share a single set of tokens. \item \menhir produces reentrant parsers. \item \menhir is able to produce parsers that are parameterized by \ocaml modules. \item \ocamlyacc requires semantic values to be referred to via keywords: \verb+$1+, \verb+$2+, and so on. \menhir allows semantic values to be explicitly named. \item \menhir warns about end-of-stream conflicts (\sref{sec:eos}), whereas \ocamlyacc does not. \menhir warns about productions that are never reduced, whereas, at least in some cases, \ocamlyacc does not. \item \menhir offers an option to typecheck semantic actions \emph{before} a parser is generated: see \oinfer. \item \ocamlyacc produces tables that are interpreted by a piece of C code, requiring semantic actions to be encapsulated as \ocaml closures and invoked by C code. \menhir offers a choice between producing tables and producing code. In either case, no C code is involved. \item \menhir makes \ocaml's standard library module \texttt{Parsing} entirely obsolete. Access to locations is now via keywords (\sref{sec:positions}). Uses of \verb+raise Parse_error+ within semantic actions are deprecated. The function \verb+parse_error+ is deprecated. They are replaced with keywords (\sref{sec:errors}). \item \menhir's error handling and error recovery mechanisms (\sref{sec:errors}) are inspired by \ocamlyacc's, but are not guaranteed to be fully compatible. Error recovery, also known as re-synchronization, is now optional. \item The way in which severe conflicts (\sref{sec:conflicts}) are resolved is not guaranteed to be fully compatible with \ocamlyacc. \item \menhir warns about unused \dtoken, \dnonassoc, \dleft, and \dright declarations. It also warns about \dprec annotations that do not help resolve a conflict. \item \menhir accepts \ocaml-style comments. \item \menhir allows \dstart and \dtype declarations to be condensed. \item \menhir allows two (or more) productions to share a single semantic action. \item \menhir produces better error messages when a semantic action contains ill-balanced parentheses. % \item \ocamlyacc allows nonterminal start symbols to start with an uppercase % letter, and produces invalid \ocaml code in that case. \menhir disallows this. \item \ocamlyacc ignores semicolons and commas everywhere. \menhir also ignores semicolons everywhere, but treats commas as significant. Commas are optional within \dtoken declarations. % \item \ocamlyacc ignores multiple definitions of a token, even when two of them are at % different types. \menhir rejects this. \item \ocamlyacc allows \dtype declarations to refer to terminal or non-terminal symbols, whereas \menhir requires them to refer to non-terminal symbols. Types can be assigned to terminal symbols with a \dtoken declaration. \end{itemize} % --------------------------------------------------------------------------------------------------------------------- \section{Questions and Answers} \question{Turning on \oinfer broke my \Makefile! What should I do?} Look at \distrib{demos/Makefile.shared}. It is meant to be re-used without change. If it does not suit your needs, you can copy parts of it into your own \Makefile, or submit suggestions for improvement. \question{I am unable to write a correct \Makefile for \menhir, and so are you.} True enough. Have a look at \ocamlbuild. It has built-in compilation rules for \ocaml and \menhir. Maybe that will help. \question{\menhir reports \emph{more} shift/reduce conflicts than \ocamlyacc! How come?} \ocamlyacc sometimes merges two states of the automaton that \menhir considers distinct. This happens when the grammar is not LALR(1). If these two states happen to contain a shift/reduce conflict, then \menhir reports two conflicts, while \ocamlyacc only reports one. Of course, the two conflicts are very similar, so fixing one will usually fix the other as well. \question{I do not use \ocamllex. Is there an API that does not involve lexing buffers?} Like \ocamlyacc, \menhir produces parsers whose API is intended for use with \ocamllex. However, it is possible to convert them, after the fact, to a simpler, revised API. In the revised API, there are no lexing buffers, and a lexer is just a function from unit to tokens. Converters are provided within \menhirlibconvert. This can be useful, for instance, for users of \texttt{ulex}, the Unicode lexer generator. % --------------------------------------------------------------------------------------------------------------------- \section{Technical background} After experimenting with Knuth's canonical LR(1) technique~\cite{knuth-lr-65}, we found that it \emph{really} is not practical, even on today's computers. For this reason, \menhir implements a slightly modified version of Pager's algorithm~\cite{pager-77}, which merges states on the fly if it can be proved that no reduce/reduce conflicts will arise as a consequence of this decision. This is how \menhir avoids the so-called \emph{mysterious} conflicts created by LALR(1) parser generators~\cite[section 5.7]{bison}. \menhir's algorithm for explaining conflicts is inspired by DeRemer and Pennello's~\cite{deremer-pennello-82} and adapted for use with Pager's construction technique. By default, \menhir produces code, as opposed to tables. This approach has been explored before~\cite{bhamidipaty-proebsting-98,horspool-faster-90}. \menhir performs some static analysis of the automaton in order to produce more compact code. When asked to produce tables, \menhir performs compression via first-fit row displacement, as described by Tarjan and Yao~\cite{tarjan-yao-79}. Double displacement is not used. The action table is made sparse by factoring out an error matrix, as suggested by Dencker, Dürre, and Heuft~\cite{dencker-84}. The type-theoretic tricks that triggered our interest in LR parsers~\cite{pottier-regis-gianas-typed-lr} are not implemented in \menhir, because the \ocaml compiler does not currently offer generalized algebraic data types (GADTs). % --------------------------------------------------------------------------------------------------------------------- \section{Acknowledgements} \menhir's interpreter (\ointerpret) and table-based back-end (\otable) were implemented by Guillaume Bau, Raja Boujbel, and François Pottier. The project was generously funded by Jane Street Capital, LLC through the OCaml Summer Project'' initiative. % --------------------------------------------------------------------------------------------------------------------- % Bibliography. \bibliographystyle{plain} \bibliography{english} \end{document}