main.tex 178 KB
 fpottier committed Mar 01, 2013 1 2 \def\true{true} \let\fpacm\true  POTTIER Francois committed Jan 05, 2017 3 \documentclass[onecolumn,11pt,nocopyrightspace,preprint]{sigplanconf}  fpottier committed Mar 01, 2013 4 \usepackage{amstext}  fpottier committed Mar 02, 2013 5 \usepackage[T1]{fontenc}  POTTIER Francois committed Jan 06, 2017 6 \usepackage[utf8]{inputenc}  POTTIER Francois committed Dec 29, 2014 7 \usepackage{moreverb}  fpottier committed Mar 02, 2013 8 \usepackage{tikz}  fpottier committed Mar 01, 2013 9 10 \usepackage{xspace} \usepackage{mymacros}  fpottier committed Mar 02, 2013 11 \def\fppdf{true}  fpottier committed Mar 01, 2013 12 13 14 \usepackage{fppdf} \input{macros} \input{version}  POTTIER Francois committed Jan 05, 2017 15 16 17 18 % Let Menhir's version number appear at the bottom right of every page. \makeatletter \def\@formatyear{\menhirversion} \makeatother  fpottier committed Mar 01, 2013 19   POTTIER Francois committed Apr 06, 2017 20 21 % ------------------------------------------------------------------------------  fpottier committed Mar 01, 2013 22 23 24 25 26 27 % Headings. \title{\menhir Reference Manual\\\normalsize (version \menhirversion)} \begin{document}  POTTIER Francois committed Jan 06, 2017 28 \authorinfo{François Pottier\and Yann Régis-Gianas}  fpottier committed Mar 01, 2013 29 30 31 32 33  {INRIA} {\{Francois.Pottier, Yann.Regis-Gianas\}@inria.fr} \maketitle  POTTIER Francois committed Apr 06, 2017 34 % ------------------------------------------------------------------------------  fpottier committed Mar 01, 2013 35 36 37 38 39  \clearpage \tableofcontents \clearpage  POTTIER Francois committed Apr 06, 2017 40 % ------------------------------------------------------------------------------  fpottier committed Mar 01, 2013 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  \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.  POTTIER Francois committed Oct 27, 2015 60 Potential users of \menhir should be warned that \menhir's feature set is not  POTTIER Francois committed Dec 02, 2014 61 62 63 64 65 66 67 68 69 70 completely 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 mechanism, are still potentially subject to incompatible changes: for instance, in the future, the current error handling mechanism (which is based on the \error token, see \sref{sec:errors}) could be removed and replaced with an entirely different mechanism. There is room for improvement in the tool and in this reference manual. Bug reports and suggestions are welcome!  fpottier committed Mar 01, 2013 71   POTTIER Francois committed Apr 06, 2017 72 % ------------------------------------------------------------------------------  fpottier committed Mar 01, 2013 73 74 75 76 77 78 79  \section{Usage} \menhir is invoked as follows: \begin{quote} \cmenhir \nt{option} \ldots \nt{option} \nt{filename} \ldots \nt{filename} \end{quote}  POTTIER Francois committed Apr 06, 2017 80 81 Each of the file names must end with \mly (unless \ocoq is used, in which case it must end with \vy) and denotes a partial  fpottier committed Mar 01, 2013 82 83 grammar specification. These partial grammar specifications are joined (\sref{sec:split}) to form a single, self-contained grammar specification,  POTTIER Francois committed Apr 06, 2017 84 which is then processed. The following optional command line switches allow  fpottier committed Mar 01, 2013 85 86 87 88 89 90 91 92 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  POTTIER Francois committed Apr 06, 2017 93 depriving \nt{filename} of its final \mly suffix. When multiple file  fpottier committed Mar 01, 2013 94 95 96 names are provided on the command line, no default base name exists, so that the \obase switch \emph{must} be used.  POTTIER Francois committed Apr 06, 2017 97 98 99 100 \docswitch{\ocmly} This switch causes Menhir to produce a \cmly file in addition to its normal operation. This file contains a (binary-form) representation of the grammar and automaton (see \sref{sec:sdk}).  fpottier committed Mar 01, 2013 101 102 103 \docswitch{\ocomment} This switch causes a few comments to be inserted into the \ocaml code that is written to the \ml file.  POTTIER Francois committed Oct 27, 2015 104 105 106 107 108 109 \docswitch{\ocompareerrors \nt{filename1} \ocompareerrors \nt{filename2}} Two such switches must always be used in conjunction so as to specify the names of two \messages files, \nt{filename1} and \nt{filename2}. Each file is read and internally translated to a mapping of states to messages. \menhir then checks that the left-hand mapping is a subset of the right-hand mapping. This feature is typically used in conjunction with \olisterrors to check that \nt{filename2}  POTTIER Francois committed Oct 27, 2015 110 is complete (that is, covers all states where an error can occur).  POTTIER Francois committed Oct 27, 2015 111 112 113 114 115 116 117 118 119 For more information, see \sref{sec:errors:new}. \docswitch{\ocompileerrors \nt{filename}} This switch causes \menhir to read the file \nt{filename}, which must obey the \messages file format, and to compile it to an OCaml function that maps a state number to a message. The OCaml code is sent to the standard output channel. At the same time, \menhir checks that the collection of input sentences in the file \nt{filename} is correct and irredundant. For more information, see \sref{sec:errors:new}.  POTTIER Francois committed Dec 18, 2014 120 121 \docswitch{\ocoq} This switch causes \menhir to produce Coq code. See \sref{sec:coq}.  POTTIER Francois committed Dec 22, 2014 122 \docswitch{\ocoqnoactions} (Used in conjunction with \ocoq.) This switch  POTTIER Francois committed Apr 06, 2017 123 causes the semantic actions present in the \vy file to be ignored and  POTTIER Francois committed Dec 22, 2014 124 replaced with \verb+tt+, the unique inhabitant of Coq's \verb+unit+ type. This  POTTIER Francois committed Oct 27, 2015 125 feature can be used to test the Coq back-end with a standard grammar, that is, a  POTTIER Francois committed Dec 22, 2014 126 grammar that contains \ocaml semantic actions. Just rename the file from  POTTIER Francois committed Apr 06, 2017 127 \mly to \vy and set this switch.  POTTIER Francois committed Dec 22, 2014 128 129 130 131 132 133 134 135 136  \docswitch{\ocoqnocomplete} (Used in conjunction with \ocoq.) This switch disables the generation of the proof of completeness of the parser (\sref{sec:coq}). This can be necessary because the proof of completeness is possible only if the grammar has no conflict (not even a benign one, in the sense of \sref{sec:conflicts:benign}). This can be desirable also because, for a complex grammar, completeness may require a heavy certificate and its validation by Coq may take time.  fpottier committed Mar 01, 2013 137 138 139 \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  POTTIER Francois committed Dec 29, 2014 140 list of prerequisites for the targets \nt{basename}\texttt{.cm[iox]},  fpottier committed Mar 01, 2013 141 142 143 144 145 146 \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  POTTIER Francois committed Feb 09, 2015 147 148 149 compiled first. % The file \distrib{demos/obsolete/Makefile.shared} exploits the \odepend switch. An end user who uses \ocamlbuild does not need this switch.  fpottier committed Mar 01, 2013 150 151 152 153 154 155 156 157  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.  POTTIER Francois committed Jun 05, 2016 158 \docswitch{\oechoerrors \nt{filename}} This switch causes \menhir to  POTTIER Francois committed Oct 27, 2015 159 160 161 162 read the \messages file \nt{filename} and to produce on the standard output channel just the input sentences. (That is, all messages, blank lines, and comments are filtered out.) For more information, see \sref{sec:errors:new}.  fpottier committed Mar 01, 2013 163 164 165 166 167 168 169 170 171 172 173 \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 174 \docswitch{\ofixedexc} This switch causes the exception \texttt{Error} to be  fpottier committed Mar 02, 2013 175 176 internally defined as a synonym for \texttt{Parsing.Parse\_error}. This means that an exception handler that catches \texttt{Parsing.Parse\_error} will also  POTTIER Francois committed Oct 27, 2015 177 catch the generated parser's \texttt{Error}. This helps increase \menhir's  fpottier committed Mar 02, 2013 178 compatibility with \ocamlyacc. There is otherwise no reason to use this switch.  fpottier committed Mar 02, 2013 179   fpottier committed Mar 01, 2013 180 181 182 183 184 185 \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.  POTTIER Francois committed Jul 20, 2015 186 187 188 189 190 191 192 \docswitch{\oignoreone \nt{symbol}} This switch suppresses the warning that is normally emitted when \menhir finds that the terminal symbol \nt{symbol} is unused. \docswitch{\oignoreall} This switch suppresses all of the warnings that are normally emitted when \menhir finds that some terminal symbols are unused.  fpottier committed Mar 01, 2013 193 194 195 196 197 198 199 200 \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  POTTIER Francois committed Feb 09, 2015 201 use of the \odepend switch. The file \distrib{demos/obsolete/Makefile.shared} suggests  fpottier committed Mar 02, 2013 202 203 how to deal with this difficulty. A better option is to avoid \make altogether and use \ocamlbuild, which has built-in knowledge of \menhir. Using  POTTIER Francois committed Feb 09, 2015 204 \ocamlbuild is \textbf{strongly recommended}!  fpottier committed Mar 01, 2013 205 206 207 208 209  % 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.  POTTIER Francois committed Aug 27, 2015 210 211 212 213 214 215 \docswitch{\oinspection} This switch requires \otable. It causes \menhir to generate not only the monolithic and incremental APIs (\sref{sec:monolithic}, \sref{sec:incremental}), but also the inspection API (\sref{sec:inspection}). Activating this switch causes a few more tables to be produced, resulting in somewhat larger code size.  fpottier committed Mar 01, 2013 216 217 218 \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  POTTIER Francois committed Oct 27, 2015 219 220 221 222 223 224 225 outcomes. This switch can be usefully combined with \otrace. For more information, see \sref{sec:interpret}. \docswitch{\ointerpreterror} This switch is analogous to \ointerpret, except \menhir expects every sentence to cause an error on its last token, and displays information about the state in which the error is detected, in the \messages file format. For more information, see \sref{sec:errors:new}.  fpottier committed Mar 01, 2013 226 227 228 229 230  \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}.  POTTIER Francois committed Oct 27, 2015 231 232 233 234 \docswitch{\olisterrors} This switch causes \menhir to produce (on the standard output channel) a complete list of input sentences that cause an error, in the \messages file format. For more information, see \sref{sec:errors:new}.  fpottier committed Mar 01, 2013 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 \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.  POTTIER Francois committed Jan 01, 2017 252 253 \docswitch{\onostdlib} This switch instructs Menhir to \emph{not} use its standard library (\sref{sec:library}).  fpottier committed Mar 01, 2013 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  \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  POTTIER Francois committed Feb 09, 2015 281 282 283 284 285 change. This switch is not suitable for direct use with \make; it is intended for use with \omake or \ocamlbuild, which perform their own postprocessing. An end user who uses \ocamlbuild does not need to mention this switch: \ocamlbuild uses it automatically.  fpottier committed Mar 01, 2013 286   POTTIER Francois committed Jan 01, 2017 287 288 289 290 291 \docswitch{\ostdlib \nt{directory}} This switch controls the directory where the standard library (\sref{sec:library}) is found. It takes precedence over both the installation-time directory and the directory that may be specified via the environment variable \verb+$MENHIR_STDLIB+.  fpottier committed Mar 01, 2013 292 293 294 295 296 297 298 299 300 301 302 303 304 305 \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  POTTIER Francois committed Feb 09, 2015 306 307 308 issued; otherwise, a \texttt{-I} directive is used. % The file \distrib{demos/obsolete/Makefile.shared} shows how to exploit % the \texttt{--suggest-*} switches.  fpottier committed Mar 01, 2013 309 310 311 312 313 314 315  \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;  POTTIER Francois committed Feb 09, 2015 316 317 318 otherwise, the object file \texttt{menhirLib.cmo} is named. % The file \distrib{demos/obsolete/Makefile.shared} shows how to exploit % the \texttt{--suggest-*} switches.  fpottier committed Mar 01, 2013 319 320 321 322 323 324 325  \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  POTTIER Francois committed Feb 09, 2015 326 327 328 issued; otherwise, the object file \texttt{menhirLib.cmx} is named. % The file \distrib{demos/obsolete/Makefile.shared} shows how to exploit % the \texttt{--suggest-*} switches.  fpottier committed Mar 01, 2013 329   POTTIER Francois committed Oct 30, 2015 330 331 332 333 334 \docswitch{\osuggestmenhirlib} This switch causes \menhir to print (the absolute path of) the directory where \menhirlib was installed. If \menhirlib was installed via \ocamlfind, this is equivalent to calling \texttt{ocamlfind query menhirLib}.  POTTIER Francois committed Dec 30, 2015 335 336 337 338 \docswitch{\osuggestocamlfind} This switch causes \menhir to print a Boolean value (i.e., either \texttt{true} or \texttt{false}), which indicates whether \menhirlib was installed via \ocamlfind.  fpottier committed Mar 01, 2013 339 340 \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  POTTIER Francois committed Dec 13, 2014 341 342 used, \menhir produces significantly more compact and somewhat slower parsers. See \sref{sec:qa} for a speed comparison.  fpottier committed Mar 01, 2013 343 344 345 346 347 348 349 350 351 352 353 354  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.  POTTIER Francois committed Aug 27, 2015 355 356 357 The incremental API (\sref{sec:incremental}) and the inspection API (\sref{sec:inspection}) are made available only by the table-based back-end.  fpottier committed Mar 01, 2013 358 359 360 361 362 363 364 365 366 \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.  POTTIER Francois committed Jun 05, 2016 367 \docswitch{\oupdateerrors \nt{filename}} This switch causes \menhir to  POTTIER Francois committed Oct 27, 2015 368 369 370 371 372 read the \messages file \nt{filename} and to produce on the standard output channel a new \messages file that is identical, except the auto-generated comments have been re-generated. For more information, see \sref{sec:errors:new}.  fpottier committed Mar 01, 2013 373 374 375 \docswitch{\oversion} This switch causes \menhir to print its own version number and exit.  POTTIER Francois committed Apr 06, 2017 376 % ------------------------------------------------------------------------------  fpottier committed Mar 01, 2013 377 378 379 380 381  \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  POTTIER Francois committed Dec 29, 2014 382 semicolons if it is thought that this improves readability. Semicolons can be  fpottier committed Mar 01, 2013 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 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.  POTTIER Francois committed Apr 06, 2017 399 % ------------------------------------------------------------------------------  fpottier committed Mar 01, 2013 400 401 402 403 404 405 406 407 408 409 410  \section{Syntax of grammar specifications} \begin{figure} \begin{center} \begin{tabular}{r@{}c@{}l} \nt{specification} \is \sepspacelist{\nt{declaration}} \percentpercent \sepspacelist{\nt{rule}}  POTTIER Francois committed Dec 29, 2014 411  \optional{\percentpercent \textit{OCaml code}} \\  fpottier committed Mar 01, 2013 412 413  \nt{declaration} \is  POTTIER Francois committed Dec 29, 2014 414  \dheader{\textit{OCaml code}} \\  fpottier committed Mar 01, 2013 415 416 417 418 419 420 421 && \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}} \\  POTTIER Francois committed Oct 27, 2015 422 && \donerrorreduce \sepspacelist{\nt{lid}} \\  fpottier committed Mar 01, 2013 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442  \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  POTTIER Francois committed Feb 11, 2015 443 444  \nt{id} \optional{\dlpar\sepcommalist{\nt{actual}}\drpar} \\ && \nt{actual} \optional{\dquestion \barre \dplus \barre \dstar} \\  POTTIER Francois committed Feb 15, 2015 445 && \seplist{\ \barre}{\nt{group}} % not really allowed everywhere  fpottier committed Mar 01, 2013 446 447 448 449 450 451 452 453 454  \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  POTTIER Francois committed Apr 06, 2017 455 456 457 this syntax are also accepted.) Attributes are not documented in \fref{fig:syntax}: see \sref{sec:attributes}.  fpottier committed Mar 01, 2013 458 459  \subsection{Declarations}  POTTIER Francois committed Apr 06, 2017 460 \label{sec:decls}  fpottier committed Mar 01, 2013 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475  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}  POTTIER Francois committed Dec 19, 2014 476 \label{sec:parameter}  fpottier committed Mar 01, 2013 477 478 479 480 481 482  A declaration of the form: \begin{quote} \dparameter \ocamlparam \end{quote} causes the entire parser to become parameterized over the \ocaml module  POTTIER Francois committed Jan 14, 2015 483 484 485 486 \nt{uid}, that is, to become an \ocaml functor. The directory \distrib{demos/calc-param} contains a demo that illustrates the use of this switch. If a single specification file  fpottier committed Mar 01, 2013 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 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$\end{quote}  POTTIER Francois committed Apr 06, 2017 520 assigns both a \emph{priority level} and an \emph{associativity status} to  fpottier committed Mar 01, 2013 521 522 523 524 525 526 527 528 529 530 531 the symbols$\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$can be tokens (defined elsewhere by a \dtoken declaration) or dummies (not defined anywhere). Both can be referred to as part of \dprec annotations. Associativity status and priority levels allow shift/reduce conflicts to be silently resolved (\sref{sec:conflicts}). \subsubsection{Types}  POTTIER Francois committed Dec 19, 2014 532 \label{sec:type}  fpottier committed Mar 01, 2013 533 534 535 536 537 538 539 540 541  A declaration of the form: \begin{quote} \dtype \ocamltype$\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$. For start symbols, providing an \ocaml type is mandatory, but is usually done as part of the \dstart declaration. For other symbols, it is optional. Providing type information can improve the quality of \ocaml's type error messages.  POTTIER Francois committed Oct 27, 2015 542 543 544 545 546 547 % TEMPORARY type information can be mandatory in --coq mode; document? A \dtype declaration may concern not only a nonterminal symbol, such as, say, \texttt{expression}, but also a fully applied parameterized nonterminal symbol, such as \texttt{list(expression)} or \texttt{separated\_list(COMMA, option(expression))}.  fpottier committed Mar 01, 2013 548 549  \subsubsection{Start symbols}  POTTIER Francois committed Dec 19, 2014 550 \label{sec:start}  fpottier committed Mar 01, 2013 551 552 553 554 555 556 557 558 559 560 561 562  A declaration of the form: \begin{quote} \dstart \optional{\ocamltype}$\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$becomes the name of a function whose signature is published in the \mli file and that can be used to invoke the parser.  POTTIER Francois committed Oct 27, 2015 563 564 565 566 567 568 569 570 571 \subsubsection{Extra reductions on error} \label{sec:onerrorreduce} A declaration of the form: \begin{quote} \donerrorreduce$\nt{lid}_1 \ldots \nt{lid}_n$\end{quote} marks the nonterminal symbols$\nt{lid}_1, \ldots, \nt{lid}_n$as potentially eligible for reduction when an invalid token is found.  POTTIER Francois committed Aug 08, 2016 572 573 This may cause one or more extra reduction steps to be performed before the error is detected.  POTTIER Francois committed Oct 27, 2015 574 575 576 577 578  More precisely, this declaration affects the automaton as follows. Let us say that a production$\nt{lid} \rightarrow \ldots$is reducible on error'' if its left-hand symbol~\nt{lid} appears in a \donerrorreduce declaration. After the automaton has been constructed and after any conflicts have been resolved,  POTTIER Francois committed Aug 08, 2016 579 580 581 582 583 584 585 586 587 in every state~$s$, the following algorithm is applied: \begin{enumerate} \item Construct the set of all productions that are ready to be reduced in state~$s$and are reducible on error; \item Test if one of them, say$p$, has higher on-error-reduce-priority'' than every other production in this set; \item If so, in state~$s$, replace every error action with a reduction of the production~$p$. (In other words, for every terminal symbol~$t$, if the action table  POTTIER Francois committed Oct 27, 2015 588 says: in state~$s$, when the next input symbol is~$t$, fail'', then this  POTTIER Francois committed Aug 08, 2016 589 590 591 entry is replaced with: in state~$s$, when the next input symbol is~$t$, reduce production~$p$''.) \end{enumerate}  POTTIER Francois committed Oct 27, 2015 592   POTTIER Francois committed Aug 08, 2016 593 594 If step 3 above is executed in state~$s$, then an error can never be detected in state~$s$, since all error actions in state~$s$are replaced with reduce  POTTIER Francois committed Oct 27, 2015 595 596 597 598 actions. Error detection is deferred: at least one reduction takes place before the error is detected. It is a spurious'' reduction: in a canonical LR(1) automaton, it would not take place.  POTTIER Francois committed Oct 28, 2015 599 600 601 602 603 604 An \donerrorreduce declaration does not affect the language that is accepted by the automaton. It does not affect the location where an error is detected. It is used to control in which state an error is detected. If used wisely, it can make errors easier to report, because they are detected in a state for which it is easier to write an accurate diagnostic message (\sref{sec:errors:diagnostics}).  POTTIER Francois committed Oct 27, 2015 605 606 607 608 609 610 611 612 613  % This may make the tables bigger (but I have no statistics). % This makes LRijkstra significantly slower. Like a \dtype declaration, an \donerrorreduce declaration may concern not only a nonterminal symbol, such as, say, \texttt{expression}, but also a fully applied parameterized nonterminal symbol, such as \texttt{list(expression)} or \texttt{separated\_list(COMMA, option(expression))}.  POTTIER Francois committed Aug 08, 2016 614 615 616 617 618 619 620 621 622 The on-error-reduce-priority'' of a production is that of its left-hand symbol. The on-error-reduce-priority'' of a nonterminal symbol is determined implicitly by the order of \donerrorreduce declarations. In the declaration$\donerrorreduce\;\nt{lid}_1 \ldots \nt{lid}_n$, the symbols$\nt{lid}_1, \ldots, \nt{lid}_n$have the same on-error-reduce-priority''. They have higher on-error-reduce-priority'' than the symbols listed in previous \donerrorreduce declarations, and lower on-error-reduce-priority'' than those listed in later \donerrorreduce declarations.  fpottier committed Mar 01, 2013 623 624 625 \subsection{Rules} Following the mandatory \percentpercent keyword, a sequence of rules is  POTTIER Francois committed Sep 11, 2015 626 627 628 629 630 631 632 633 expected. Each rule defines a nonterminal symbol~\nt{id}. % (It is recommended that the name of a nonterminal symbol begin with a lowercase letter, so it falls in the category \nt{lid}. This is in fact mandatory for the start symbols.) In its simplest form, a rule begins with the nonterminal symbol \nt{id}, followed by a colon character (\deuxpoints),  fpottier committed Mar 01, 2013 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 and continues with a sequence of production groups (\sref{sec:productiongroups}). Each production group is preceded with a vertical bar character (\barre); the very first bar is optional. The meaning of the bar is choice: the nonterminal symbol \nt{id} develops to either of the production groups. We defer explanations of the keyword \dpublic (\sref{sec:split}), of the keyword \dinline (\sref{sec:inline}), and of the optional formal parameters$\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  659 660 661 662 production via the semantic value identifiers bound by the production. For compatibility with \ocamlyacc, semantic actions can also refer to unnamed semantic values via positional keywords of the form  Yann Régis-Gianas committed Jul 06, 2015 663 664 \kw{\$1}, \kw{\$2}, etc.\ This style is discouraged. Furthermore, as a positional keyword of the form \kw{\$i} is internally rewritten as  POTTIER Francois committed Sep 20, 2015 665 \nt{\_i}, the user should not use identifiers of the form \nt{\_i}.  fpottier committed Mar 01, 2013 666 667 668 669  \paragraph{\dprec annotations} \label{sec:prec}  POTTIER Francois committed Sep 11, 2015 670 671 An annotation of the form \dprec \nt{id} indicates that the precedence level of the production group is the level assigned to the symbol \nt{id} via a  fpottier committed Mar 01, 2013 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 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}  POTTIER Francois committed Feb 15, 2015 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 In its simplest form, an actual is just a terminal or nonterminal symbol $\nt{id}$. If it is a parameterized non-terminal symbol (see \sref{sec:templates}), then it should be applied: $\nt{id}\dlpar\sepcommalist{\nt{actual}}\drpar$. An actual may be followed with a modifier (\dquestion, \dplus, or \dstar). This is explained further on (see \sref{sec:templates} and \fref{fig:sugar}). An actual may also be an anonymous rule''. In that case, one writes just the rule's right-hand side, which takes the form $\seplist{\ \barre\ }{\nt{group}}$. (This form is allowed only as an argument in an application.) This form is expanded on the fly to a definition of a fresh non-terminal symbol, which is declared \dinline. For instance, providing an anonymous rule as an argument to \nt{list}: \begin{quote} \begin{tabular}{l} \nt{list} \dlpar \basic{e} = \nt{expression}; \basic{SEMICOLON} \dpaction{\basic{e}} \drpar \end{tabular} \end{quote} is equivalent to writing this: \begin{quote} \begin{tabular}{l} \nt{list} \dlpar \nt{expression\_SEMICOLON} \drpar \end{tabular} \end{quote} where the non-terminal symbol \nt{expression\_SEMICOLON} is chosen fresh and is defined as follows: \begin{quote} \begin{tabular}{l} \dinline \nt{expression\_SEMICOLON}: \newprod \basic{e} = \nt{expression}; \basic{SEMICOLON} \dpaction{\basic{e}} \end{tabular} \end{quote}  fpottier committed Mar 01, 2013 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796  \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.  797 798 799 800 801 In fact, it is permitted to split the definition of a \emph{public} nonterminal symbol, over multiple modules and/or within a single module. That is, a public nonterminal symbol $N$ can have multiple definitions, within one module and/or in distinct modules. All of these definitions are joined using the choice (\barre) operator. This  fpottier committed Mar 01, 2013 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 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.  POTTIER Francois committed Nov 06, 2015 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 The \dinline keyword does not affect the computation of positions (\sref{sec:positions}). The same positions are computed, regardless of where \dinline keywords are placed. If the semantic actions have side effects, the \dinline keyword \emph{can} affect the order in which these side effects take place. In the example of \nt{op} and \nt{expression} above, if for some reason the semantic action associated with \nt{op} has a side effect (such as updating a global variable, or printing a message), then, by inlining \nt{op}, we delay this side effect, which takes place \emph{after} the second operand has been recognized, whereas in the absence of inlining it takes place as soon as the operator has been recognized.  POTTIER Francois committed Jan 06, 2017 1079 1080 % Du coup, ça change l'ordre des effets, dans cet exemple, de infixe % à postfixe.  POTTIER Francois committed Nov 06, 2015 1081   fpottier committed Mar 01, 2013 1082 1083 1084 1085 1086 \subsection{The standard library} \label{sec:library} \begin{figure} \begin{center}  POTTIER Francois committed Dec 29, 2014 1087 \begin{tabular}{lp{51mm}l@{}l}  fpottier committed Mar 01, 2013 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 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.  POTTIER Francois committed Jan 01, 2017 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 The standard library is stored in a file named \texttt{standard.mly}, which is installed at the same time as Menhir. By default, Menhir attempts to find this file in the directory where this file was installed. This can be overridden by setting the environment variable \verb+$MENHIR_STDLIB+. If defined, this variable should contain the path of the directory where \texttt{standard.mly} is stored. (This path may end with a \texttt{/} character.) This can be overridden also via the command line switch \ostdlib. % The command line switch \onostdlib instructs Menhir to \emph{not} load the standard library.  POTTIER Francois committed Apr 06, 2017 1165 % ------------------------------------------------------------------------------  fpottier committed Mar 01, 2013 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175  \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?}  POTTIER Francois committed Dec 22, 2014 1176 \label{sec:conflicts:benign}  fpottier committed Mar 01, 2013 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306  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}  fpottier committed Mar 02, 2013 1307 \mycommonbaseline  fpottier committed Mar 01, 2013 1308 \begin{center}  fpottier committed Mar 02, 2013 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 \begin{tikzpicture}[level distance=12mm] \node { \nt{expression} } child { node {\basic{IF}} } child { node {\nt{expression}} } child { node {\basic{THEN}} } child { node {\nt{expression}} child { node {\basic{IF}} } child { node {\nt{expression}} } child { node {\basic{THEN}} } child { node {\nt{expression}} } child { node {\basic{ELSE}} } child { node {\nt{expression}} } } ; \end{tikzpicture}  fpottier committed Mar 01, 2013 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 \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}  fpottier committed Mar 02, 2013 1364 \mycommonbaseline  fpottier committed Mar 01, 2013 1365 \begin{center}  fpottier committed Mar 02, 2013 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 \begin{tikzpicture}[level distance=12mm] \node { \nt{expression} } child { node {\basic{IF}} } child { node {\nt{expression}} } child { node {\basic{THEN}} } child { node {\nt{expression}} child { node {\basic{IF}} } child { node {\nt{expression}} } child { node {\basic{THEN}} } child { node {\nt{expression}} } } child { node {\basic{ELSE}} } child { node {\nt{expression}} } ; \end{tikzpicture}  fpottier committed Mar 01, 2013 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 \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}  fpottier committed Mar 02, 2013 1428 \mycommonbaseline  fpottier committed Mar 01, 2013 1429 \begin{center}  fpottier committed Mar 02, 2013 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 \begin{tikzpicture}[level distance=12mm,level 1/.style={sibling distance=18mm}, level 2/.style={sibling distance=18mm}, level 4/.style={sibling distance=24mm}]] \node { \nt{decls} } child { node {\nt{decl}} child { node {\basic{DATA}} } child { node {\basic{UIDENT}} } child { node {\basic{EQUALS}} } child { node {\nt{tycon\_expr}} child { node {\nt{tycon\_item}} child { node {\basic{UIDENT}} } child { node {\nt{opt\_type\_exprs}} child { node {} edge from parent [dashed] } } } } } child { node {\nt{opt\_semi}} } child { node {\nt{decls}} }  POTTIER Francois committed Jun 05, 2016 1449 ;  fpottier committed Mar 02, 2013 1450 \end{tikzpicture}  fpottier committed Mar 01, 2013 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 \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$This is indicated by the comment \inlinesidecomment{\nt{decls} can begin with \basic{LIDENT}}. Thus, by developing \nt{decls}, it is possible to construct a partial derivation tree where the next symbol on the fringe, following \basic{UIDENT}, is \basic{LIDENT}. This is precisely the conflict token. To sum up, there exists a partial derivation tree whose  POTTIER Francois committed Jun 05, 2016 1519 fringe begins with the conflict string, followed with the conflict token.  fpottier committed Mar 01, 2013 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 Furthermore, in that derivation tree, the dot occupies the rightmost position in the last level. As in our previous example, this means that, after the automaton has recognized the conflict string and peeked at the conflict token, it makes sense for it to \emph{reduce} the production that corresponds to the tree's last level---here, the production is$\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''.  POTTIER Francois committed Jan 06, 2017 1572 1573 % TEMPORARY il faut noter que \menhir n'est pas conforme à ocamlyacc en % présence de conflits end-of-stream; apparemment il part dans le mur  POTTIER Francois committed May 01, 2015 1574 % en exigeant toujours le token suivant, alors que ocamlyacc est capable  POTTIER Francois committed Jan 06, 2017 1575 % de s'arrêter (comment?); cf. problème de S. Hinderer (avril 2015).  POTTIER Francois committed May 01, 2015 1576   fpottier committed Mar 01, 2013 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 \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  POTTIER Francois committed Jun 05, 2016 1662 -- On # PL