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<html>
<head>
<title>Top Down Parser</title>
<link rel="stylesheet" type="text/css" href="css/styles.css">
<style>
H1, H2, H3, H4, H5, H6 {
margin:0 0 0 0;
padding:0;
}
H4 {
font: bold 1.2em Verdana;
text-align: center;
color: green;
}
H5 {
font: italic 0.8em Verdana;
text-align: center;
}
TABLE {
border: 1px solid #CCC;
font: normal 1em Verdana;
padding: 1px;
}
TD, TH {
padding: 1px 1em;
}
.grammar {
border: 1px solid #000;
background: #FFF;
box-shadow: 0 0 10px #666;
opacity: 0.5;
padding: 0 1em;
}
#eGrammar { float:left; }
.others,
#eProduction {
float: left;
margin: 1em 0 1em 3em;
}
#eParsing {
float: left;
margin: 1em 0 1em 3em;
}
.algo {
border: 1px solid #CCC;
float:left;
font: normal 0.8em Verdana;
margin: 1em 0 1em 2em;
padding: 1em;
}
#eFirstFollow { float:left; }
#eLL1 { float:left; }
#eParsing TABLE { margin: 0 0 1em; }
</style>
</head>
<body>
<h1>Top Down Parser : LL(1) Parser</h1>
<div class="grammar">
<h1>Grammaire G=(T,N,s,δ)</h1>
<pre id="eGrammar"></pre>
<pre class="others"><h2>T =</h2><h3 id="eT"></h3><h2>N =</h2><h3 id="eN"></h3><h2>s =</h2><h3 id="eStartSymbol"></h3></pre>
<pre id="eProduction"></pre>
<div style="clear:both;"></div>
</div>
<div class="firstfollow">
<pre id="eFirstFollow"></pre>
<pre class="algo"><h2>Algorithme</h2>
<b>Pour chaque</b> a ∈ N ∪ T ∪ { ε }
NULLABLE[a] ← false
<b>Si</b> a ∈ N
FIRST[a] ← {}
FOLLOW[a] ← {} // Ensemble vide
<b>Si</b> a ∈ T ∪ { ε }
FIRST[a] ← { a }
NULLABLE[ε] ← true
FOLLOW[s] ← { $ }
<b>Faire</b>
<b>Pour chaque</b> production X → Y<sub>0</sub>Y<sub>1</sub> … Y<sub>k</sub> // avec Y<sub>i</sub> = symbole
<b>Si</b> Y<sub>0</sub> … Y<sub>k</sub> sont annulables
NULLABLE[X] ← true
<b>Pour chaque</b> i de 0 à k
<b>Si</b> i = 0 <b>ou</b> Y<sub>0</sub> … Y<sub>i-1</sub> sont annulables
FIRST[X] ← FIRST[X] ∪ FIRST[Y<sub>i</sub>]
<b>Si</b> Y<sub>i</sub> ∈ T
<b>Si</b> i = k <b>ou</b> Y<sub>i+1</sub> … Y<sub>k</sub> sont annulables
FOLLOW[Y<sub>i</sub>] ← FOLLOW[Y<sub>i</sub>] ∪ FOLLOW[X]
<b>Pour chaque</b> j de i + 1 à k
<b>Si</b> j = i + 1 <b>ou</b> Y<sub>i+1</sub> … Y<sub>j-1</sub> sont annulables
FOLLOW[Y<sub>i</sub>] ← FOLLOW[Y<sub>i</sub>] ∪ FIRST[Y<sub>j</sub>]
<b>Tant que</b> au moins une des variables FIRST, FOLLOW ou NULLABLE est modifiée
// Note:
// FOLLOW[symbole terminal] sera toujours égale à un ensemble vide
// NULLABLE[symbole terminal] sera toujours égale à false
</pre>
<div style="clear:both;"></div>
</div>
<pre id="eResult"></pre>
<div class="LL1">
<pre id="eLL1"></pre>
<pre class="algo"><h2>Algorithme</h2>
<b>Pour chaque</b> production X → Y<sub>0</sub> … Y<sub>k</sub>
<b>Pour chaque</b> a ∈ <b>FIRST</b>(Y<sub>0</sub>)
M[X][a] ← Y<sub>0</sub> … Y<sub>k</sub>
<b>Si</b> a = ε
<b>Pour chaque</b> b ∈ <b>FOLLOW</b>(X)
M[X][b] ← Y<sub>0</sub> … Y<sub>k</sub>
// Note : Avant affectation
<b>Si</b> ∃ M[X][c] <b>et</b> M[X][c] ≠ Y<sub>0</sub> … Y<sub>k</sub>
<i>Erreur plusieurs sorties existent ! il ne sagit pas dune grammaire LL(1)</i>
</pre>
<div style="clear:both;"></div>
</div>
<div class="LL1">
<h1>LL(1) Parsing</h1>
<pre id="eParsing"></pre>
<pre class="algo"><h2>Algorithme</h2>
Phrase ← Phrase + $
Pile ← [ $ s ]
i ← index du premier T de la Phrase
bContinue ← true
<b>Faire</b>
X ← dépilé un élément de la Pile
<b>Si</b> X ≠ ε
a ← T de la phrase à la position i
<b>Si</b> X = a
<b>Si</b> X = $
Succès : La phrase est reconnue !
<b>Sinon</b>
positionnement de i sur le T suivant
<b>Sinon</b>
<b>Si</b> X ∈ T
Erreur: Il manque X dans la Phrase à lindex i
bContinue ← false
<b>Si</b> X ∈ N
<b>Si</b> M[X][a] existe
On empile M[X][a] en ordre inverse
<b>Sinon</b>
Erreur: Lentrée M[X][a] nexiste pas !
bContinue ← false
<b>Tant que</b> i pointe dans la phrase <b>et</b> Pile ≠ vide <b>et</b> bContinue
</pre>
</div>
<!-- FRAMEWORK... -->
<script src="js/framework.js"></script>
<script>
var aGRAMMAR=[
[ 'E', 'T X' ],
[ 'X', '+ E | ε' ],
[ 'T', 'int Y | ( E )' ],
[ 'Y', '* T | ε' ]
/*
[ Z, S ],
[ S, A a A b | B b B a ],
[ V, id ],
[ A, ε ],
[ B, ε ]
*/
/*
[ S, if C then S X ],
[ X, else S | ε ],
[ C, b ]
*/
]
_( 'eGrammar,eProduction,eStartSymbol,eT,eN,eFirstFollow,eLL1,eResult,eParsing' )
var sStartSymbol = aGRAMMAR[0][0]
, aPRODUCTIONS = []
, aSymbols = []
, aNonTerminalSymbols = []
, aTerminalSymbols = []
, oFIRST = { 'ε':['ε'] }
, oFOLLOW = {}
, oNULLABLE = { 'ε':true }
// Initialise les variables
;(function(){
aGRAMMAR.every( function( aRule ){
var X = aRule[0]
aNonTerminalSymbols.push( X )
var a = aRule[1].split('|')
a.every( function( s ){
if( s ) aSymbols = aSymbols.concat( s.trim().split(' '))
return aPRODUCTIONS.push([ X, s.trim()])
})
return 1
})
aSymbols = Array.unique( aSymbols )
aSymbols.remove( 'ε' )
aSymbols.sort()
aSymbols.every( function( s ){
if( ! aNonTerminalSymbols.have( s )) aTerminalSymbols.push( s )
return 1
})
aSymbols = aTerminalSymbols.concat( aNonTerminalSymbols )
// Initialize FIRST and FOLLOW to all empty sets, and NULLABLE to all false.
aSymbols.every( function( s ){
oFIRST[s] = [] // for each terminal symbol FIRST[Z] <- {Z}
oFOLLOW[s] = []
oNULLABLE[s] = false
return 1
})
aTerminalSymbols.every( function( s ){
oFIRST[s] = [s] // for each terminal symbol FIRST[Z] <- {Z}
return 1
})
oFOLLOW[sStartSymbol]= ['$']
})()
// Affiche la grammaire
if( 1 )(function(){
Bufferize.init(' ')
aGRAMMAR.every(function( a ){
return Bufferize( '<h3>'+a[0]+' → '+a[1]+'</h3>' )
})
eGrammar.innerHTML = Bufferize.init()
Bufferize( '<h2>δ =\n</h2>' )
aPRODUCTIONS.every(function( a ){
return Bufferize( '<h3>'+a[0]+' → '+a[1]+'</h3>' )
})
eProduction.innerHTML = Bufferize.init()
eStartSymbol.innerHTML = sStartSymbol
eT.innerHTML = aTerminalSymbols.join(' ')
eN.innerHTML = aNonTerminalSymbols.join(' ')
})()
function FIRST ( sSymbol ){ return oFIRST[sSymbol] }
function FOLLOW ( sSymbol ){ return oFOLLOW[sSymbol] }
function areAllNullable( aY, n1, n2 ){
var b = true
for(var i=n1; i<=n2; i++ ){
b = b && oNULLABLE[ aY[i]]
if( ! b ) return false
}
return b
}
Bufferize( '<h4>FOLLOW['+sStartSymbol+'] change to [$]</h4>' )
// do until FIRST, FOLLOW, and NULLABLE did not change in this iteration.
for( var nCounter=1, bChange=true; bChange ; nCounter++ ){
bChange = false
Bufferize( "<h1>LOOP "+nCounter+"</h1>" )
aPRODUCTIONS.every( function( a, nIndex ){
var X = a[0], aY = a[1].split(' '), k = aY.length-1
if( ! oNULLABLE[X] && areAllNullable( aY, 0, aY.length-1 )){
oNULLABLE[X] = true
Bufferize( "<h5>" + a[0] +" → "+ a[1] + " </h5>" )
Bufferize( '<h5>if Y1 … Yk are all nullable (or if k = 0)</h5>' )
Bufferize( '<h4>NULLABLE['+X+'] change to ['+oNULLABLE[X]+']</h4>' )
bChange = true
}
Bufferize( "<h2>" + (nIndex+1) +'. '+ a[0] +" → "+ a[1] +" <small>(k=="+ (k+1) +")</small></h2>" )
Bufferize( "<small> foreach i from 1 to "+ (k+1) + "</small>\n" )
Bufferize( "<small>\t foreach j from i+1 to "+ (k+1) + "</small>\n" )
for( var i=0; i<=k; i++ ){
var Yi = aY[i]
Bufferize( "\t[<b><small>i:" + (i+1) +"</small></b>]\n" )
Bufferize( "\t Y<sub>i</sub>=Y<sub>"+(i+1)+"</sub>="+Yi+" is a "+(aNonTerminalSymbols.have( Yi )?'non ':'')+"terminal symbol \n" )
if( aY[i+1]) Bufferize( "\t Y<sub>(i+1)</sub>=Y<sub>"+(i+2)+"</sub>="+aY[i+1]+" is a "+(aNonTerminalSymbols.have( aY[i+1] )?'non ':'')+"terminal symbol \n" )
Bufferize( "<h5> if Y<sub>1</sub> … Y<sub>(i-1)</sub> are all nullable (or if i = 1) then FIRST[X] = FIRST[X] + FIRST[Y<sub>i</sub>] </h5>" )
var b = ( i==0 || areAllNullable( aY, 0, i-1 ))
Bufferize( '<center>'
+(b?'':'<strike>')
+(i==0?i==1:""+aY.slice( 0, i )+" are all nullable ")
+(b?'<h3>':'\n')+"FIRST["+X+"] = FIRST["+X+"] + FIRST["+Yi+"]"+(b?'</h3>':'\n')
+(b?'':'</strike>')
+'</center>' )
if( i==0 || areAllNullable( aY, 0, i-1 )){
var aFirst = Array.unique( oFIRST[X].concat( oFIRST[Yi]))
if( oFIRST[X].toString() != aFirst.toString()){
oFIRST[X] = aFirst
Bufferize( '<h4>FIRST['+X+'] change to ['+aFirst+']</h4>' )
bChange = true
}
}
if( ! aNonTerminalSymbols.have( Yi )){
Bufferize( '\t[<small>BREAK Yi is a terminal symbol</small>]\n' )
continue ;
}
Bufferize( "<h5> if Y<sub>(i+1)</sub> … Y<sub>k</sub> are all nullable (or if i = k) then FOLLOW[Y<sub>i</sub>] = FOLLOW[Y<sub>i</sub>] + FOLLOW[X] </h5>" )
var b = ( i==k || areAllNullable( aY, i+1, k ))
Bufferize( '<center>'
+(b?'':'<strike>')
+(i==k?i==k:""+aY.slice( i+1, k+1 )+" are all nullable ")
+(b?'<h3>':'\n')+"FOLLOW["+Yi+"] = FOLLOW["+Yi+"] + FOLLOW["+X+"]"+(b?'</h3>':'\n')
+(b?'':'</strike>')
+'/center>' )
if( i==k || areAllNullable( aY, i+1, k )){
var aFollow = Array.unique( oFOLLOW[Yi].concat( oFOLLOW[X]))
aFollow.remove('ε')
if( oFOLLOW[Yi].toString() != aFollow.toString()){
oFOLLOW[Yi] = aFollow
Bufferize( '<h4>FOLLOW['+Yi+'] change to ['+aFollow+']</h4>' )
bChange = true
}
}
for( var j=i+1; j<=k; j++ ){
var Yj = aY[j]
Bufferize( "\t[<b><small>j:"+ (j+1) + "</small></b>]\n" )
Bufferize( "\t X="+X+"\n" )
if( Yj ) Bufferize( "\t Y<sub>j</sub>=Y<sub>"+(j+1)+"</sub>="+Yj+" is a "+(aNonTerminalSymbols.have( Yj )?'non ':'')+"terminal symbol \n" )
Bufferize( "\t Y<sub>(j-1)</sub>=Y<sub>"+(j)+"</sub>="+aY[j-1]+" is a "+(aNonTerminalSymbols.have( aY[j-1] )?'non ':'')+"terminal symbol \n" )
Bufferize( "<h5> if Y<sub>(i+1)</sub> … Y<sub>(j-1)</sub> are all nullable (or if i + 1 = j ) then FOLLOW[Y<sub>i</sub>] = FOLLOW[Y<sub>i</sub>] + FIRST[Y<sub>j</sub>] </h5>" )
var b = ( j==i+1 || areAllNullable( aY, i+1, j-1 ))
Bufferize( '<center>'
+(b?'':'<strike>')
+(j==i+1?j==i+1:""+aY.slice( i+1, j )+" are all nullable ")
+(b?'<h3>':'\n')+"FOLLOW["+Yi+"] = FOLLOW["+Yi+"] + FIRST["+Yj+"]"+(b?'</h3>':'\n')
+(b?'':'</strike>')
+'</center>' )
if( j==i+1 || areAllNullable( aY, i+1, j-1 )){
var aFollowYi = Array.unique( oFOLLOW[Yi].concat( oFIRST[Yj]))
aFollowYi.remove('ε')
if( oFOLLOW[Yi].toString() != aFollowYi.toString()){
oFOLLOW[Yi] = aFollowYi
Bufferize(' <h4>FOLLOW['+Yi+'] change to ['+aFollowYi+']</h4>' )
bChange = true
}
}
}
}
return 1
})
if( ! bChange ) break;
}
// Check if grammar is LL(1)
;( function isLL1 (){
aGRAMMAR.every( function( aRule ){
var a = aRule[1].split('|')
/*
G is LL(1) if for a rule A -> alpha | beta
a) First(alpha) intersection First(beta) = ensemble vide
b) alpha ou beta dérive epsilon
c) If beta dérive epsilon, Follow(alpha) intersection Follow(beta) = ensemble vide
*/
a.every( function(){
return 1
})
return 1
})
})()
// Affiche le calcul
if( 1 ){
eResult.innerHTML += Bufferize.init()
eResult.innerHTML += '<h2>'+ nCounter +' loops <h2>'
}
// Affiche la table FIRST / FOLLOW
var showFirstFollowTable =function( aSymbols, oNULLABLE, oFIRST, oFOLLOW ){
Bufferize.init( '<h1>Table First/Follow </h1>' )
Bufferize( '<table border="1" cellspacing="0"><tr><th>Symbol</th><th>Nullable</th><th>First</th><th>Follow</th></tr>' )
Bufferize( '<tr><th>ε</th><td>'+ oNULLABLE['ε'] +'</td><td>'+ oFIRST['ε'] +'</td><td></td></tr>' )
aSymbols.every( function( s ){
Bufferize( '<tr><th>'+ s +'</th><td>'+ oNULLABLE[s] +'</td><td>'+ oFIRST[s] +'</td><td>'+ ( oFOLLOW[s]) +'</td></tr>' )
return 1
})
return Bufferize('</table>')
}
if( 1 ) eFirstFollow.innerHTML = showFirstFollowTable( aSymbols, oNULLABLE, oFIRST, oFOLLOW )
// Construit la table LL(1)
var setLL1Table =function( aPRODUCTIONS, aNonTerminalSymbols, FIRST, FOLLOW ){
var M = {}
aNonTerminalSymbols.every( function( s ){ return M[s] = {} })
var setEntry =function( X, RHS, s ){
if( M[X][s] && M[X][s] != RHS ){
var sError = "Grammar isnt LL(1) : there is a multi-rule entry in table."
+'\nM[ '+ X +' ][ '+ s +' ]'
+'\n\t '+ X +' -> '+ M[X][s]
// +\n\t + aRule.join( -> )
alert( sError )
throw new Error ( sError )
}
return M[X][s] = RHS
}
aPRODUCTIONS.every( function( aRule ){
var X=aRule[0], RHS=aRule[1], Y0=RHS.split(' ')[0]
FIRST(Y0).every( function( sSymbolA ){
if( sSymbolA == 'ε' )
FOLLOW(X).every( function( sSymbolB ){
return setEntry( X, RHS, sSymbolB )
})
return setEntry( X, RHS, sSymbolA )
})
return 1
})
return M
}
var M = setLL1Table( aPRODUCTIONS, aNonTerminalSymbols, FIRST, FOLLOW )
// Affiche la table LL(1)
var showLL1Table =function( M, aTerminalSymbols, aNonTerminalSymbols ){
Bufferize.init( '<h1>Table LL(1)</h1>' )
var a = aTerminalSymbols.concat(['$'])
Bufferize( '<table border="1" cellspacing="0"><tr><td></td>' )
a.every( function( S ){
return Bufferize( "<th>"+ S +"</th>" )
})
Bufferize( "</tr>" )
aNonTerminalSymbols.every( function( NT ){
Bufferize( "<tr><th>"+ NT +"</th>" )
a.every( function( S ){
return Bufferize( "<td>"+ ( M[NT][S] || ' ' ) +"</td>" )
})
return Bufferize( "</tr>" )
})
return Bufferize( "</table>" )
}
if( 1 ) eLL1.innerHTML = showLL1Table( M, aTerminalSymbols, aNonTerminalSymbols )
// NEEDED : aPhrase, M, sStartSymbol, aTerminalSymbols, aNonTerminalSymbols
function LL1ParsingAlgo ( aPhrase ){
Bufferize.init( )
Bufferize( '<table border="1" cellspacing="0"><tr><th class="right">Stack</th><th class="right">Input</th><th class="left">Action</th></tr>' )
var aStack = [ '$', sStartSymbol ]
var i=0
, sAction
, bContinue=true
do{
var GRR = aStack.join(',').split(',').reverse().join(' ')
var X=aStack.pop()
if( X=='ε' ) continue;
var a=aPhrase[i]
Bufferize( '<tr><td class="right">'+GRR+'</td><td class="right">'+aPhrase.slice( i ).join(' ')+'</td>' )
if( X==a ){
if( X=='$' ){
sAction = '<b style="color:green;">Success</b>'
}
if( X!='$' ){
i++
sAction = "<b>terminal</b>"
}
}
if( X!=a ){
if( aTerminalSymbols.have( X )){
var sAction = '<b style="color:red;">Failed: '+X+' not found in input!</b>'
bContinue = false
}
if( aNonTerminalSymbols.have( X )){
if( M[X][a]){
sAction = X+" → "+M[X][a]
aStack = aStack.concat( M[X][a].split(' ').reverse())
}
else{
var sAction = '<b style="color:red;">Failed: rule M['+X+']['+a+'] not found !</b>'
bContinue = false
}
}
}
Bufferize( '<td class="left">'+sAction+'</td></tr>' )
}while( i<aPhrase.length && aStack.length && bContinue )
eParsing.innerHTML += Bufferize( "</table>" )
}
LL1ParsingAlgo( 'int * int $'.split(' '))
LL1ParsingAlgo( '( E $'.split(' '))
LL1ParsingAlgo( 'red error $'.split(' '))
LL1ParsingAlgo( 'int * $'.split(' '))
</script>
</body>
</html>