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Commit0bf63ffd7e8643198223e3820260082cfbb3b654 (patch)
Author
 Dimitar Trendafilov <dimitar@coherent-labs.com>		2018-10-25 18:22:39 +0300
Committer
 Dimitar Trendafilov <dimitar@coherent-labs.com>		2018-10-25 18:22:39 +0300
Files7b7562803acce80037e96622601d856996db2d4a /website
IPL-0bf63ffd7e8643198223e3820260082cfbb3b654.tar
IPL-0bf63ffd7e8643198223e3820260082cfbb3b654.tar.gz
IPL-0bf63ffd7e8643198223e3820260082cfbb3b654.zip
Parentdea978cda53392281afae2ba57f9e310d8b395e7 (diff)
Parent33481e105a24471e91beb1099f31e6a44f645680 (diff)
Merge branch 'parser_generators'
3 files changed, 447 insertions, 0 deletions
-rw-r--r--website/content/post/contents.md3
-rw-r--r--website/content/slides/04_parser_generators/_index.md110
-rw-r--r--website/content/slides/04_parser_generators/parser.html334
diff --git a/website/content/post/contents.md b/website/content/post/contents.md
index bfe75ef..ec568e8 100644
--- a/website/content/post/contents.md
+++ b/website/content/post/contents.md
@@ -19,3 +19,6 @@ Table of contents for the course.
0. Parsing - [slides]({{< ref "/slides/03_parsing" >}}),
[doc](https://github.com/SofiaCPP/IPL/blob/master/website/content/slides/03_parsing/_index.md)
+
+0. Parser generators - [slides]({{< ref "/slides/04_parser_generators" >}}),
+ [doc](https://github.com/SofiaCPP/IPL/blob/master/website/content/slides/04_parser_generators/_index.md)
diff --git a/website/content/slides/04_parser_generators/_index.md b/website/content/slides/04_parser_generators/_index.md
new file mode 100644
index 0000000..b1e4075
--- /dev/null
+++ b/website/content/slides/04_parser_generators/_index.md
@@ -0,0 +1,110 @@
+---
+title: "Parser Generators"
+date: 2018-10-02T17:45:53+03:00
+draft: false
+outputs: ["Reveal"]
+---
+
+# Parser Generators
+
+Contents:
+
+- LR Parsers
+- Bison
+
+---
+# LR Parsers
+
+- L - the parsers reads the text only once, without backing up
+- R - rightmost derivation
+- bottom-up parser
+- LR(1) - 1 - the number of look-ahead symbols necessary to parse the grammar
+
+---
+### Rightmost derivation
+
+- The tree created for an expression would replace the rightmost non-terminal at
+ each step
+
+---
+### Bottom-up
+
+The tree is constructed from the bottom - from the leaves to the root.
+
+---
+## Algorithm
+
+The parser:
+
+- keeps a stack of the parsed sub-trees so far
+- runs in a loop over the input and on each iteration it does either
+a *shift* or a *reduce* action.
+
+ - shift - push the token on the stack
+ - reduce - pop N subtrees from the stack, make a new tree that has them as
+ children and push it to the stack
+
+---
+#### Ring any bells?
+
+---
+#### Ring any bells?
+
+Same as the shunting yard algorithm, but:
+- without the operator precedence
+ - it replaced by the grammar structure
+- There all the rules had just two children
+
+---
+### To shift or to reduce?
+
+- Depends on the grammar rules.
+- The algorithm uses a Finite State Automaton (FSA)
+
+---
+### To shift or to reduce?
+
+The FSA has for each (state, next token) -> (action, next state)
+
+- action - whether to shift or reduce
+
+---
+# Bison
+
+- Bison generates LR(1) and GLR parsers
+ - GLR parsers can have arbitrary lookahead and be ambigous
+- You don't always have to convert the grammar in an LR form
+ - operator precedence and assiociativity are handled for your
+
+---
+### Input
+
+ %{
+ /* verbatim copy */
+ %}
+
+ /* definitions */
+
+ %%
+ /* rules */
+ %%
+ /* verbatim copy */
+
+---
+### Parsing expressions
+
+https://github.com/SofiaCPP/IPL/blob/master/demo/bison/calc/parser.y
+
+---
+### Understanding the parser
+
+https://www.gnu.org/software/bison/manual/html_node/Debugging.html#Debugging
+
+---
+###
+
+[bison output for the expression grammar](parser)
+
+---
+# ?
+
diff --git a/website/content/slides/04_parser_generators/parser.html b/website/content/slides/04_parser_generators/parser.html
new file mode 100644
index 0000000..724b703
--- /dev/null
+++ b/website/content/slides/04_parser_generators/parser.html
@@ -0,0 +1,334 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" xmlns:bison="http://www.gnu.org/software/bison/">
+ <head>
+ <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
+ <title>parser.y - GNU Bison XML Automaton Report</title>
+ <style type="text/css">
+ body {
+ font-family: "Nimbus Sans L", Arial, sans-serif;
+ font-size: 9pt;
+ }
+ a:link {
+ color: #1f00ff;
+ text-decoration: none;
+ }
+ a:visited {
+ color: #1f00ff;
+ text-decoration: none;
+ }
+ a:hover {
+ color: red;
+ }
+ #menu a {
+ text-decoration: underline;
+ }
+ .i {
+ font-style: italic;
+ }
+ .pre {
+ font-family: monospace;
+ white-space: pre;
+ }
+ ol.decimal {
+ list-style-type: decimal;
+ }
+ ol.lower-alpha {
+ list-style-type: lower-alpha;
+ }
+ .point {
+ color: #cc0000;
+ }
+ #footer {
+ margin-top: 3.5em;
+ font-size: 7pt;
+ }
+ </style>
+ </head>
+ <body><h1>GNU Bison XML Automaton Report</h1><p>
+ input grammar: <span class="i">parser.y</span></p>
+
+<h3>Table of Contents</h3><ul id="menu"><li><a href="#reductions">Reductions</a><ul class="lower-alpha"><li><a href="#nonterminals_useless_in_grammar">Nonterminals useless in grammar</a></li><li><a href="#terminals_unused_in_grammar">Terminals unused in grammar</a></li><li><a href="#rules_useless_in_grammar">Rules useless in grammar</a></li></ul></li><li><a href="#conflicts">Conflicts</a></li><li><a href="#grammar">Grammar</a><ul class="lower-alpha"><li><a href="#grammar">Itemset</a></li><li><a href="#terminals">Terminal symbols</a></li><li><a href="#nonterminals">Nonterminal symbols</a></li></ul></li><li><a href="#automaton">Automaton</a></li></ul><h2><a name="reductions" id="reductions"></a> Reductions</h2><h3><a name="nonterminals_useless_in_grammar" id="nonterminals_useless_in_grammar"></a> Nonterminals useless in grammar</h3>
+
+<h3><a name="terminals_unused_in_grammar" id="terminals_unused_in_grammar"></a> Terminals unused in grammar</h3>
+
+<h3><a name="rules_useless_in_grammar" id="rules_useless_in_grammar"></a> Rules useless in grammar</h3>
+<h2><a name="conflicts" id="conflicts"></a> Conflicts</h2>
+
+<h2><a name="grammar" id="grammar"></a> Grammar</h2>
+<p class="pre">
+<a name="rule_0" id="rule_0"></a> 0 <span class="i">$accept</span> → <span class="i">input</span> <b>$end</b>
+
+<a name="rule_1" id="rule_1"></a> 1 <span class="i">input</span> → %empty
+<a name="rule_2" id="rule_2"></a> 2 | <span class="i">expr</span>
+
+<a name="rule_3" id="rule_3"></a> 3 <span class="i">expr</span> → <b>NUMBER</b>
+<a name="rule_4" id="rule_4"></a> 4 | <b>'('</b> <span class="i">expr</span> <b>')'</b>
+<a name="rule_5" id="rule_5"></a> 5 | <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span>
+<a name="rule_6" id="rule_6"></a> 6 | <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span>
+<a name="rule_7" id="rule_7"></a> 7 | <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span>
+<a name="rule_8" id="rule_8"></a> 8 | <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span>
+</p>
+
+<h3><a name="terminals" id="terminals"></a> Terminals, with rules where they appear</h3>
+
+<p class="pre"><b>$end</b> (0) <a href="#rule_0">0</a>
+<b>'('</b> (40) <a href="#rule_4">4</a>
+<b>')'</b> (41) <a href="#rule_4">4</a>
+<b>error</b> (256)
+<b>NUMBER</b> (258) <a href="#rule_3">3</a>
+<b>PLUS</b> (259) <a href="#rule_5">5</a>
+<b>MINUS</b> (260) <a href="#rule_6">6</a>
+<b>MULT</b> (261) <a href="#rule_7">7</a>
+<b>DIV</b> (262) <a href="#rule_8">8</a>
+</p>
+
+<h3><a name="nonterminals" id="nonterminals"></a> Nonterminals, with rules where they appear</h3>
+
+<p class="pre"><b>$accept</b> (10)
+ on left: <a href="#rule_0">0</a>
+<b>input</b> (11)
+ on left: <a href="#rule_1">1</a> <a href="#rule_2">2</a>
+ on right: <a href="#rule_0">0</a>
+<b>expr</b> (12)
+ on left: <a href="#rule_3">3</a> <a href="#rule_4">4</a> <a href="#rule_5">5</a> <a href="#rule_6">6</a> <a href="#rule_7">7</a> <a href="#rule_8">8</a>
+ on right: <a href="#rule_2">2</a> <a href="#rule_4">4</a> <a href="#rule_5">5</a> <a href="#rule_6">6</a> <a href="#rule_7">7</a> <a href="#rule_8">8</a>
+</p><h2><a name="automaton" id="automaton"></a> Automaton</h2>
+
+<h3><a name="state_0" id="state_0"></a>state 0</h3>
+
+<p class="pre"> <a href="#rule_0"> 0</a> <span class="i">$accept</span> → <span class="point">.</span> <span class="i">input</span> <b>$end</b>
+ <a href="#rule_1"> 1</a> <span class="i">input</span> → <span class="point">.</span> %empty [$end]
+ <a href="#rule_2"> 2</a> | <span class="point">.</span> <span class="i">expr</span>
+ <a href="#rule_3"> 3</a> <span class="i">expr</span> → <span class="point">.</span> <b>NUMBER</b>
+ <a href="#rule_4"> 4</a> | <span class="point">.</span> <b>'('</b> <span class="i">expr</span> <b>')'</b>
+ <a href="#rule_5"> 5</a> | <span class="point">.</span> <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="point">.</span> <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="point">.</span> <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="point">.</span> <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span>
+
+ NUMBER <a href="#state_1">shift, and go to state 1</a>
+ '(' <a href="#state_2">shift, and go to state 2</a>
+
+ $default <a href="#rule_1">reduce using rule 1</a> (input)
+
+ input <a href="#state_3">go to state 3</a>
+ expr <a href="#state_4">go to state 4</a>
+</p>
+
+<h3><a name="state_1" id="state_1"></a>state 1</h3>
+
+<p class="pre"> <a href="#rule_3"> 3</a> <span class="i">expr</span> → <b>NUMBER</b> <span class="point">.</span>
+
+ $default <a href="#rule_3">reduce using rule 3</a> (expr)
+</p>
+
+<h3><a name="state_2" id="state_2"></a>state 2</h3>
+
+<p class="pre"> <a href="#rule_3"> 3</a> <span class="i">expr</span> → <span class="point">.</span> <b>NUMBER</b>
+ <a href="#rule_4"> 4</a> | <span class="point">.</span> <b>'('</b> <span class="i">expr</span> <b>')'</b>
+ <a href="#rule_4"> 4</a> | <b>'('</b> <span class="point">.</span> <span class="i">expr</span> <b>')'</b>
+ <a href="#rule_5"> 5</a> | <span class="point">.</span> <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="point">.</span> <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="point">.</span> <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="point">.</span> <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span>
+
+ NUMBER <a href="#state_1">shift, and go to state 1</a>
+ '(' <a href="#state_2">shift, and go to state 2</a>
+
+ expr <a href="#state_5">go to state 5</a>
+</p>
+
+<h3><a name="state_3" id="state_3"></a>state 3</h3>
+
+<p class="pre"> <a href="#rule_0"> 0</a> <span class="i">$accept</span> → <span class="i">input</span> <span class="point">.</span> <b>$end</b>
+
+ $end <a href="#state_6">shift, and go to state 6</a>
+</p>
+
+<h3><a name="state_4" id="state_4"></a>state 4</h3>
+
+<p class="pre"> <a href="#rule_2"> 2</a> <span class="i">input</span> → <span class="i">expr</span> <span class="point">.</span> [$end]
+ <a href="#rule_5"> 5</a> <span class="i">expr</span> → <span class="i">expr</span> <span class="point">.</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <span class="point">.</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <span class="point">.</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <span class="point">.</span> <b>DIV</b> <span class="i">expr</span>
+
+ PLUS <a href="#state_7">shift, and go to state 7</a>
+ MINUS <a href="#state_8">shift, and go to state 8</a>
+ MULT <a href="#state_9">shift, and go to state 9</a>
+ DIV <a href="#state_10">shift, and go to state 10</a>
+
+ $default <a href="#rule_2">reduce using rule 2</a> (input)
+</p>
+
+<h3><a name="state_5" id="state_5"></a>state 5</h3>
+
+<p class="pre"> <a href="#rule_4"> 4</a> <span class="i">expr</span> → <b>'('</b> <span class="i">expr</span> <span class="point">.</span> <b>')'</b>
+ <a href="#rule_5"> 5</a> | <span class="i">expr</span> <span class="point">.</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <span class="point">.</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <span class="point">.</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <span class="point">.</span> <b>DIV</b> <span class="i">expr</span>
+
+ PLUS <a href="#state_7">shift, and go to state 7</a>
+ MINUS <a href="#state_8">shift, and go to state 8</a>
+ MULT <a href="#state_9">shift, and go to state 9</a>
+ DIV <a href="#state_10">shift, and go to state 10</a>
+ ')' <a href="#state_11">shift, and go to state 11</a>
+</p>
+
+<h3><a name="state_6" id="state_6"></a>state 6</h3>
+
+<p class="pre"> <a href="#rule_0"> 0</a> <span class="i">$accept</span> → <span class="i">input</span> <b>$end</b> <span class="point">.</span>
+
+ $default accept
+</p>
+
+<h3><a name="state_7" id="state_7"></a>state 7</h3>
+
+<p class="pre"> <a href="#rule_3"> 3</a> <span class="i">expr</span> → <span class="point">.</span> <b>NUMBER</b>
+ <a href="#rule_4"> 4</a> | <span class="point">.</span> <b>'('</b> <span class="i">expr</span> <b>')'</b>
+ <a href="#rule_5"> 5</a> | <span class="point">.</span> <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_5"> 5</a> | <span class="i">expr</span> <b>PLUS</b> <span class="point">.</span> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="point">.</span> <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="point">.</span> <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="point">.</span> <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span>
+
+ NUMBER <a href="#state_1">shift, and go to state 1</a>
+ '(' <a href="#state_2">shift, and go to state 2</a>
+
+ expr <a href="#state_12">go to state 12</a>
+</p>
+
+<h3><a name="state_8" id="state_8"></a>state 8</h3>
+
+<p class="pre"> <a href="#rule_3"> 3</a> <span class="i">expr</span> → <span class="point">.</span> <b>NUMBER</b>
+ <a href="#rule_4"> 4</a> | <span class="point">.</span> <b>'('</b> <span class="i">expr</span> <b>')'</b>
+ <a href="#rule_5"> 5</a> | <span class="point">.</span> <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="point">.</span> <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <b>MINUS</b> <span class="point">.</span> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="point">.</span> <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="point">.</span> <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span>
+
+ NUMBER <a href="#state_1">shift, and go to state 1</a>
+ '(' <a href="#state_2">shift, and go to state 2</a>
+
+ expr <a href="#state_13">go to state 13</a>
+</p>
+
+<h3><a name="state_9" id="state_9"></a>state 9</h3>
+
+<p class="pre"> <a href="#rule_3"> 3</a> <span class="i">expr</span> → <span class="point">.</span> <b>NUMBER</b>
+ <a href="#rule_4"> 4</a> | <span class="point">.</span> <b>'('</b> <span class="i">expr</span> <b>')'</b>
+ <a href="#rule_5"> 5</a> | <span class="point">.</span> <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="point">.</span> <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="point">.</span> <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <b>MULT</b> <span class="point">.</span> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="point">.</span> <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span>
+
+ NUMBER <a href="#state_1">shift, and go to state 1</a>
+ '(' <a href="#state_2">shift, and go to state 2</a>
+
+ expr <a href="#state_14">go to state 14</a>
+</p>
+
+<h3><a name="state_10" id="state_10"></a>state 10</h3>
+
+<p class="pre"> <a href="#rule_3"> 3</a> <span class="i">expr</span> → <span class="point">.</span> <b>NUMBER</b>
+ <a href="#rule_4"> 4</a> | <span class="point">.</span> <b>'('</b> <span class="i">expr</span> <b>')'</b>
+ <a href="#rule_5"> 5</a> | <span class="point">.</span> <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="point">.</span> <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="point">.</span> <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="point">.</span> <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <b>DIV</b> <span class="point">.</span> <span class="i">expr</span>
+
+ NUMBER <a href="#state_1">shift, and go to state 1</a>
+ '(' <a href="#state_2">shift, and go to state 2</a>
+
+ expr <a href="#state_15">go to state 15</a>
+</p>
+
+<h3><a name="state_11" id="state_11"></a>state 11</h3>
+
+<p class="pre"> <a href="#rule_4"> 4</a> <span class="i">expr</span> → <b>'('</b> <span class="i">expr</span> <b>')'</b> <span class="point">.</span>
+
+ $default <a href="#rule_4">reduce using rule 4</a> (expr)
+</p>
+
+<h3><a name="state_12" id="state_12"></a>state 12</h3>
+
+<p class="pre"> <a href="#rule_5"> 5</a> <span class="i">expr</span> → <span class="i">expr</span> <span class="point">.</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_5"> 5</a> | <span class="i">expr</span> <b>PLUS</b> <span class="i">expr</span> <span class="point">.</span> [$end, PLUS, MINUS, ')']
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <span class="point">.</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <span class="point">.</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <span class="point">.</span> <b>DIV</b> <span class="i">expr</span>
+
+ MULT <a href="#state_9">shift, and go to state 9</a>
+ DIV <a href="#state_10">shift, and go to state 10</a>
+
+ $default <a href="#rule_5">reduce using rule 5</a> (expr)
+
+ Conflict between <a href="#rule_5">rule 5</a> and token PLUS resolved as reduce (%left PLUS).
+ Conflict between <a href="#rule_5">rule 5</a> and token MINUS resolved as reduce (%left MINUS).
+ Conflict between <a href="#rule_5">rule 5</a> and token MULT resolved as shift (PLUS &lt; MULT).
+ Conflict between <a href="#rule_5">rule 5</a> and token DIV resolved as shift (PLUS &lt; DIV).
+</p>
+
+<h3><a name="state_13" id="state_13"></a>state 13</h3>
+
+<p class="pre"> <a href="#rule_5"> 5</a> <span class="i">expr</span> → <span class="i">expr</span> <span class="point">.</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <span class="point">.</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <b>MINUS</b> <span class="i">expr</span> <span class="point">.</span> [$end, PLUS, MINUS, ')']
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <span class="point">.</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <span class="point">.</span> <b>DIV</b> <span class="i">expr</span>
+
+ MULT <a href="#state_9">shift, and go to state 9</a>
+ DIV <a href="#state_10">shift, and go to state 10</a>
+
+ $default <a href="#rule_6">reduce using rule 6</a> (expr)
+
+ Conflict between <a href="#rule_6">rule 6</a> and token PLUS resolved as reduce (%left PLUS).
+ Conflict between <a href="#rule_6">rule 6</a> and token MINUS resolved as reduce (%left MINUS).
+ Conflict between <a href="#rule_6">rule 6</a> and token MULT resolved as shift (MINUS &lt; MULT).
+ Conflict between <a href="#rule_6">rule 6</a> and token DIV resolved as shift (MINUS &lt; DIV).
+</p>
+
+<h3><a name="state_14" id="state_14"></a>state 14</h3>
+
+<p class="pre"> <a href="#rule_5"> 5</a> <span class="i">expr</span> → <span class="i">expr</span> <span class="point">.</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <span class="point">.</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <span class="point">.</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <b>MULT</b> <span class="i">expr</span> <span class="point">.</span> [$end, PLUS, MINUS, MULT, DIV, ')']
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <span class="point">.</span> <b>DIV</b> <span class="i">expr</span>
+
+ $default <a href="#rule_7">reduce using rule 7</a> (expr)
+
+ Conflict between <a href="#rule_7">rule 7</a> and token PLUS resolved as reduce (PLUS &lt; MULT).
+ Conflict between <a href="#rule_7">rule 7</a> and token MINUS resolved as reduce (MINUS &lt; MULT).
+ Conflict between <a href="#rule_7">rule 7</a> and token MULT resolved as reduce (%left MULT).
+ Conflict between <a href="#rule_7">rule 7</a> and token DIV resolved as reduce (%left DIV).
+</p>
+
+<h3><a name="state_15" id="state_15"></a>state 15</h3>
+
+<p class="pre"> <a href="#rule_5"> 5</a> <span class="i">expr</span> → <span class="i">expr</span> <span class="point">.</span> <b>PLUS</b> <span class="i">expr</span>
+ <a href="#rule_6"> 6</a> | <span class="i">expr</span> <span class="point">.</span> <b>MINUS</b> <span class="i">expr</span>
+ <a href="#rule_7"> 7</a> | <span class="i">expr</span> <span class="point">.</span> <b>MULT</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <span class="point">.</span> <b>DIV</b> <span class="i">expr</span>
+ <a href="#rule_8"> 8</a> | <span class="i">expr</span> <b>DIV</b> <span class="i">expr</span> <span class="point">.</span> [$end, PLUS, MINUS, MULT, DIV, ')']
+
+ $default <a href="#rule_8">reduce using rule 8</a> (expr)
+
+ Conflict between <a href="#rule_8">rule 8</a> and token PLUS resolved as reduce (PLUS &lt; DIV).
+ Conflict between <a href="#rule_8">rule 8</a> and token MINUS resolved as reduce (MINUS &lt; DIV).
+ Conflict between <a href="#rule_8">rule 8</a> and token MULT resolved as reduce (%left MULT).
+ Conflict between <a href="#rule_8">rule 8</a> and token DIV resolved as reduce (%left DIV).
+</p>
+
+<div id="footer"><hr />This document was generated using
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+ GNU Bison 3.0.4</a>
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