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data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%AC%D8%B2%DB%8C%D9%87%E2%80%8C%DA%A9%D9%86%D9%86%D8%AF%D9%87_%D8%A7%D9%84%E2%80%8C%D8%A2%D8%B1_%D8%B3%D8%A7%D8%AF%D9%87" title="تجزیه‌کننده ال‌آر ساده – Persian" lang="fa" hreflang="fa" data-title="تجزیه‌کننده ال‌آر ساده" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Analyseur_SLR" title="Analyseur SLR – French" lang="fr" hreflang="fr" data-title="Analyseur SLR" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Parser_SLR" title="Parser SLR – Italian" lang="it" hreflang="it" data-title="Parser SLR" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8D%98%E7%B4%94LR%E6%B3%95" title="単純LR法 – Japanese" lang="ja" hreflang="ja" data-title="単純LR法" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Simpel_LR-parser" title="Simpel LR-parser – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Simpel LR-parser" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Parser_SLR" title="Parser SLR – 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srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Simple_LR_parser" title="Special:EditPage/Simple LR parser">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Simple+LR+parser%22">"Simple LR parser"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Simple+LR+parser%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Simple+LR+parser%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Simple+LR+parser%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Simple+LR+parser%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Simple+LR+parser%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">November 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Computer_science" title="Computer science">computer science</a>, a <b>Simple LR</b> or <b>SLR parser</b> is a type of <a href="/wiki/LR_parser" title="LR parser">LR parser</a> with small <a href="/wiki/LR_parser#Constructing_LR(0)_parsing_tables" title="LR parser">parse tables</a> and a relatively simple parser generator algorithm. As with other types of LR(1) parser, an SLR parser is quite efficient at finding the single correct <a href="/wiki/Bottom-up_parsing" title="Bottom-up parsing">bottom-up parse</a> in a single left-to-right scan over the input stream, without guesswork or backtracking. The parser is mechanically generated from a formal grammar for the language. </p><p>SLR and the more general methods <a href="/wiki/LALR_parser" title="LALR parser">LALR parser</a> and <a href="/wiki/Canonical_LR_parser" title="Canonical LR parser">Canonical LR parser</a> have identical methods and similar tables at parse time; they differ only in the mathematical grammar analysis algorithms used by the parser generator tool. SLR and LALR generators create tables of identical size and identical parser states. SLR generators accept fewer grammars than LALR generators like <a href="/wiki/Yacc" title="Yacc">yacc</a> and <a href="/wiki/GNU_bison" class="mw-redirect" title="GNU bison">Bison</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2024)">citation needed</span></a></i>]</sup> Many computer languages don't readily fit the restrictions of SLR, as is. Bending the language's natural grammar into <a href="/wiki/SLR_grammar" title="SLR grammar">SLR grammar</a> form requires more compromises and grammar hackery. So LALR generators have become much more widely used than SLR generators, despite being somewhat more complicated tools. SLR methods remain a useful learning step in college classes on compiler theory.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2024)">citation needed</span></a></i>]</sup> </p><p>SLR and LALR were both developed by <a href="/w/index.php?title=Frank_DeRemer&action=edit&redlink=1" class="new" title="Frank DeRemer (page does not exist)">Frank DeRemer</a> as the first practical uses of <a href="/wiki/Donald_Knuth" title="Donald Knuth">Donald Knuth</a>'s LR parser theory.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The tables created for real grammars by full LR methods were impractically large, larger than most computer memories of that decade, with 100 times or more parser states than the SLR and LALR methods.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Lookahead_sets">Lookahead sets</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Simple_LR_parser&action=edit&section=1" title="Edit section: Lookahead sets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To understand the differences between SLR and LALR, it is important to understand their many similarities and how they both make shift-reduce decisions. (See the article <a href="/wiki/LR_parser" title="LR parser">LR parser</a> now for that background, up through the section on reductions' <b>lookahead sets</b>.) </p><p>The one difference between SLR and LALR is how their generators calculate the lookahead sets of input symbols that should appear next, whenever some completed <a href="/wiki/Formal_grammar#The_syntax_of_grammars" title="Formal grammar">production rule</a> is found and reduced. </p><p>SLR generators calculate that lookahead by an easy approximation method based directly on the grammar, ignoring the details of individual parser states and transitions. This ignores the particular context of the current parser state. If some nonterminal symbol <i>S</i> is used in several places in the grammar, SLR treats those places in the same single way rather than handling them individually. The SLR generator works out <code>Follow(S)</code>, the set of all terminal symbols which can immediately follow some occurrence of <i>S</i>. In the parse table, each reduction to <i>S</i> uses Follow(S) as its LR(1) lookahead set. Such follow sets are also used by generators for LL top-down parsers. A grammar that has no shift/reduce or reduce/reduce conflicts when using follow sets is called an <a href="/wiki/SLR_grammar" title="SLR grammar">SLR grammar</a>. <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2024)">citation needed</span></a></i>]</sup> </p><p>LALR generators calculate lookahead sets by a more precise method based on exploring the graph of parser states and their transitions. This method considers the particular context of the current parser state. It customizes the handling of each grammar occurrence of some nonterminal S. See article <a href="/wiki/LALR_parser" title="LALR parser">LALR parser</a> for further details of this calculation. The lookahead sets calculated by LALR generators are a subset of (and hence better than) the approximate sets calculated by SLR generators. If a grammar has table conflicts when using SLR follow sets, but is conflict-free when using LALR follow sets, it is called a LALR grammar. <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2024)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Simple_LR_parser&action=edit&section=2" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A grammar that can be parsed by an SLR parser but not by an LR(0) parser is the following: </p> <dl><dd>(0) S → E</dd> <dd>(1) E → 1 E</dd> <dd>(2) E → 1</dd></dl> <p>Constructing the action and goto table as is done for LR(0) parsers would give the following item sets and tables: </p> <dl><dt>Item set 0</dt> <dd>S → • E</dd> <dd>+ E → • 1 E</dd> <dd>+ E → • 1</dd></dl> <dl><dt>Item set 1</dt> <dd>E → 1 • E</dd> <dd>E → 1 •</dd> <dd>+ E → • 1 E</dd> <dd>+ E → • 1</dd></dl> <dl><dt>Item set 2</dt> <dd>S → E •</dd></dl> <dl><dt>Item set 3</dt> <dd>E → 1 E •</dd></dl> <p>The action and goto tables: </p> <table class="wikitable"> <tbody><tr align="center"> <th></th> <th colspan="2"><i>action</i></th> <th><i>goto</i> </th></tr> <tr align="center"> <th><i>state</i> </th> <th>1</th> <th>$</th> <th>E </th></tr> <tr align="center"> <th>0 </th> <td>s1</td> <td></td> <td>2 </td></tr> <tr align="center"> <th>1 </th> <td>s1/r2</td> <td>r2</td> <td>3 </td></tr> <tr align="center"> <th>2 </th> <td></td> <td>acc</td> <td> </td></tr> <tr align="center"> <th>3 </th> <td>r1</td> <td>r1</td> <td> </td></tr></tbody></table> <p>As can be observed there is a shift-reduce conflict for state 1 and terminal '1'. This occurs because, when the action table for an LR(0) parser is created, reduce actions are inserted on a per-row basis. However, by using a follow set, reduce actions can be added with finer granularity. The follow set for this grammar: </p> <table class="wikitable"> <tbody><tr align="center"> <th>symbol </th> <td>S</td> <td>E</td> <td>1 </td></tr> <tr align="center"> <th>following </th> <td>$</td> <td>$</td> <td>1,$ </td></tr></tbody></table> <p>A reduce only needs to be added to a particular action column if that action is in the follow set associated with that reduce. This algorithm describes whether a reduce action must be added to an action column: </p> <pre>function mustBeAdded(reduceAction, action) { ruleNumber = reduceAction.value; ruleSymbol = rules[ruleNumber].leftHandSide; return (action in followSet(ruleSymbol)) } </pre> <p>for example, <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">mustBeAdded(r2, "1")</code> is false, because the left hand side of rule 2 is "E", and 1 is not in E's follow set. Contrariwise, <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">mustBeAdded(r2, "$")</code> is true, because "$" is in E's follow set. </p><p>By using mustBeAdded on each reduce action in the action table, the result is a conflict-free action table: </p> <table class="wikitable"> <tbody><tr align="center"> <th></th> <th colspan="2"><i>action</i></th> <th><i>goto</i> </th></tr> <tr align="center"> <th><i>state</i> </th> <th>1</th> <th>$</th> <th>E </th></tr> <tr align="center"> <th>0 </th> <td>s1</td> <td></td> <td>2 </td></tr> <tr align="center"> <th>1 </th> <td>s1</td> <td>r2</td> <td>3 </td></tr> <tr align="center"> <th>2 </th> <td></td> <td>acc</td> <td> </td></tr> <tr align="center"> <th>3 </th> <td></td> <td>r1</td> <td> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Simple_LR_parser&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/LR_parser" title="LR parser">LR parser</a></li> <li><a href="/wiki/LL_parser" title="LL parser">LL parser</a></li> <li><a href="/wiki/LALR_parser" title="LALR parser">LALR parser</a></li> <li><a href="/wiki/SLR_grammar" title="SLR grammar">SLR grammar</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Simple_LR_parser&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist 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href="https://wiki.eecs.yorku.ca/course_archive/2013-14/W/6339/_media/lrk.pdf">https://wiki.eecs.yorku.ca/course_archive/2013-14/W/6339/_media/lrk.pdf</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external free" href="https://www.seas.upenn.edu/~cis5110/notes/cis511-sl9.pdf">https://www.seas.upenn.edu/~cis5110/notes/cis511-sl9.pdf</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFChapman1987" class="citation book cs1">Chapman, Nigel P. (17 December 1987). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nEA9AAAAIAAJ&pg=PA87"><i>LR Parsing: Theory and Practice</i></a>. 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title="Recursive descent parser">Recursive descent</a> <ul><li><a href="/wiki/Tail_recursive_parser" title="Tail recursive parser">Tail recursive</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bottom-up_parsing" title="Bottom-up parsing">Bottom-up</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Precedence <ul><li><a href="/wiki/Simple_precedence_parser" title="Simple precedence parser">Simple</a></li> <li><a href="/wiki/Operator-precedence_parser" title="Operator-precedence parser">Operator</a> <ul><li><a href="/wiki/Shunting_yard_algorithm" title="Shunting yard algorithm">Shunting-yard</a></li></ul></li></ul></li> <li><a href="/wiki/LR_parser" title="LR parser">LR</a> <ul><li><a class="mw-selflink selflink">Simple</a></li> <li><a href="/wiki/LALR_parser" title="LALR parser">Look-ahead</a></li> <li><a href="/wiki/Canonical_LR_parser" title="Canonical LR parser">Canonical</a></li> <li><a href="/wiki/GLR_parser" title="GLR parser">Generalized</a></li></ul></li> <li><a href="/wiki/CYK_algorithm" title="CYK algorithm">CYK</a></li> <li><a href="/wiki/Recursive_ascent_parser" title="Recursive ascent parser">Recursive ascent</a></li> <li><a href="/wiki/Shift-reduce_parser" title="Shift-reduce parser">Shift-reduce</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mixed, other</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Parser_combinator" title="Parser combinator">Combinator</a></li> <li><a href="/wiki/Chart_parser" title="Chart parser">Chart</a> <ul><li><a href="/wiki/Left_corner_parser" title="Left corner parser">Left corner</a></li></ul></li> <li>Statistical</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Parsing_expression_grammar" title="Parsing expression grammar">PEG</a></li> <li><a href="/wiki/Definite_clause_grammar" title="Definite clause grammar">Definite clause grammar</a></li> <li><a href="/wiki/Deterministic_parsing" title="Deterministic parsing">Deterministic parsing</a></li> <li><a href="/wiki/Dynamic_programming" title="Dynamic programming">Dynamic programming</a></li> <li><a href="/wiki/Memoization" title="Memoization">Memoization</a></li> <li><a href="/wiki/Compiler-compiler" title="Compiler-compiler">Parser generator</a> <ul><li><a href="/wiki/LALR_parser_generator" title="LALR parser generator">LALR</a></li></ul></li> <li><a href="/wiki/Parse_tree" title="Parse tree">Parse tree</a></li> <li><a href="/wiki/Abstract_syntax_tree" title="Abstract syntax tree">AST</a></li> <li><a href="/wiki/Scannerless_parsing" title="Scannerless parsing">Scannerless parsing</a></li> <li><a href="/wiki/History_of_compiler_construction" title="History of compiler construction">History of compiler construction</a></li> <li><a href="/wiki/Comparison_of_parser_generators" title="Comparison of parser generators">Comparison of parser generators</a></li> <li><a href="/wiki/Operator-precedence_grammar" title="Operator-precedence grammar">Operator-precedence grammar</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Simple_LR_parser&oldid=1257076853">https://en.wikipedia.org/w/index.php?title=Simple_LR_parser&oldid=1257076853</a>"</div></div> <div id="catlinks" class="catlinks" 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