public Production(Nonterminal lhs, GrammarSymbol[] rhsButLast, GrammarSymbol last)
{
this.Lhs = lhs;
this.Rhs = new GrammarSymbol[rhsButLast.Length + 1];
Array.Copy(rhsButLast, this.Rhs, rhsButLast.Length);
this.Rhs[rhsButLast.Length] = last;
}
IEnumerable <Production> EliminateNullables(Nonterminal v, HashSet <Nonterminal> nullables)
{
/*foreach (var p in this.productionMap[v])
* {
* if (p.Rhs.Length == 0)
* yield break;
*
* foreach (var symbols in EnumerateNullableFreeVariations(ConsList<GrammarSymbol>.Create(p.Rhs), nullables))
* if (symbols != null) //ignore the case when all nullables were replaced
* yield return new Production(v, symbols.ToArray());
* }*/
var res = new Dictionary <string, Production>();
foreach (var p in this.productionMap[v])
{
if (p.Rhs.Length == 0)
{
continue;
}
foreach (var symbols in EnumerateNullableFreeVariations(ConsList <GrammarSymbol> .Create(p.Rhs), nullables))
{
if (symbols != null)
{//ignore the case when all nullables were replaced
var newProd = new Production(v, symbols.ToArray());
res[newProd.Description] = newProd;
}
}
}
return(res.Values);
}
private GrammarParser(Lexer lex, Func <char, T> mkExprinal)
{
lexer = lex;
this.mkExprinal = mkExprinal;
startvar = null;
productions = new List <Production>();
}
static IEnumerable <ConsList <GrammarSymbol> > EnumerateNullableFreeVariations(ConsList <GrammarSymbol> symbols, HashSet <Nonterminal> nullables)
{
if (symbols == null)
{
yield return(null);
}
else
{
foreach (var rest in EnumerateNullableFreeVariations(symbols.Rest, nullables))
{
GrammarSymbol first = symbols.First;
Nonterminal variable = first as Nonterminal;
if (variable == null || !nullables.Contains(variable))
{
yield return(new ConsList <GrammarSymbol>(first, rest));
}
else
{
yield return(rest);
yield return(new ConsList <GrammarSymbol>(first, rest));
}
}
}
}
static Nonterminal Lookup(Dictionary <Nonterminal, Nonterminal> vars, Nonterminal key, ref int nonterminalID)
{
Nonterminal v;
if (vars.TryGetValue(key, out v))
{
return(v);
}
v = new Nonterminal(nonterminalID++);
vars[key] = v;
return(v);
}
public static HashSet <GrammarSymbol[]> findAllDerivations(IEnumerable <Production> productions, GrammarSymbol[] partialWord, int type = DERIVATION_ALL)
{
var result = new HashSet <GrammarSymbol[]>(comparator);
//find first and last NT
int first_NT = -1;
int last_NT = -1;
for (int i = 0; i < partialWord.Length; i++)
{
if (partialWord[i] is Nonterminal && first_NT == -1)
{
first_NT = i;
}
if (partialWord[i] is Nonterminal)
{
last_NT = i;
}
}
//find all next steps
for (int sym_i = 0; sym_i < partialWord.Length; sym_i++)
{
if (!(partialWord[sym_i] is Nonterminal))
{
continue; //not a NT
}
if (type == DERIVATION_LEFTMOST && sym_i != first_NT)
{
continue; //should be leftmost derivatation
}
if (type == DERIVATION_RIGHTMOST && sym_i != last_NT)
{
continue; //should be rightmost derivation
}
Nonterminal nt = (Nonterminal)partialWord[sym_i];
foreach (Production p in productions)
{
if (!p.Lhs.Equals(nt))
{
continue;
}
//build new partial word
var npw = applyPrduction(partialWord, sym_i, p);
result.Add(npw);
}
}
return(result);
}
/// <summary>
/// Genereates warnings for useless variables.
/// </summary>
/// <param name="g">the grammar</param>
/// <returns></returns>
public static List <string> getGrammarWarnings(ContextFreeGrammar g)
{
List <string> res = new List <string>();
HashSet <string> variables = new HashSet <string>();
foreach (var n in g.Variables)
{
variables.Add(n.ToString());
}
var productiv = g.GetUsefulNonterminals(true);
var unproductiv = variables.Except(productiv);
if (unproductiv.Count() > 0)
{
res.Add(string.Format("Warning: There are unproductive variables! ({0})", string.Join(", ", unproductiv)));
}
var reachable = new HashSet <string>();
//Lemma 4.2, p. 89, Hopcroft-Ullman
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(g.StartSymbol);
reachable.Add(g.StartSymbol.ToString());
while (stack.Count > 0)
{
Nonterminal v = stack.Pop();
foreach (Production p in g.GetProductions(v))
{
foreach (Nonterminal u in p.GetVariables())
{
if (!reachable.Contains(u.ToString()))
{
reachable.Add(u.ToString());
stack.Push(u);
}
}
}
}
var unreachable = variables.Except(reachable);
if (unproductiv.Count() > 0)
{
res.Add(string.Format("Warning: There are unreachable variables! ({0})", string.Join(", ", unreachable)));
}
return(res);
}
/// <summary>
/// Generates a CFG that accepts the prefix closure of a given grammar.
/// </summary>
/// <param name="g">the original grammar</param>
/// <returns>the prefix closure</returns>
public static ContextFreeGrammar getPrefixClosure(ContextFreeGrammar g)
{
Func <Nonterminal, Nonterminal> prefixFor = delegate(Nonterminal x)
{
return(new Nonterminal(x.Name + "PREFIX"));
};
if (g == null)
{
return(g);
}
if (!g.IsInCNF())
{
g = getEquivalentCNF(g);
}
if (g == null)
{
return(g);
}
Nonterminal prefixStart = prefixFor(g.StartSymbol);
var prefixProductions = new List <Production>();
foreach (Production p in g.GetProductions())
{
//add original
prefixProductions.Add(p);
Nonterminal prefixNT = prefixFor(p.Lhs);
if (p.Rhs.Length == 2) // case: X->AB ==> X' ->A' | AB'
{
prefixProductions.Add(new Production(prefixNT, new GrammarSymbol[] { p.Rhs[0], prefixFor((Nonterminal)p.Rhs[1]) }));
prefixProductions.Add(new Production(prefixNT, new GrammarSymbol[] { prefixFor((Nonterminal)p.Rhs[0]) }));
}
else // case: X->a ==> X'->a
{
prefixProductions.Add(new Production(prefixNT, new GrammarSymbol[] { p.Rhs[0] }));
}
}
var res = new ContextFreeGrammar(prefixStart, prefixProductions);
res.setAcceptanceForEmptyString(true);
return(res);
}
private string DescribeProductions(Nonterminal v)
{
StringBuilder sb = new StringBuilder();
sb.Append(v.Name);
List <Production> prods = productionMap[v];
if (prods.Count > 0)
{
sb.Append(" -> ");
sb.Append(prods[0].DescriptionOfRhs);
for (int i = 1; i < prods.Count; i++)
{
sb.Append(" | ");
sb.Append(prods[i].DescriptionOfRhs);
}
}
return(sb.ToString());
}
public ContextFreeGrammar(Nonterminal startSymbol, IEnumerable <Production> productions)
{
HashSet <Nonterminal> vars = new HashSet <Nonterminal>();
List <Nonterminal> varsList = new List <Nonterminal>();
bool startSymbolExisted = false;
foreach (Production p in productions)
{
if (p.Lhs.Equals(startSymbol))
{
startSymbolExisted = true;
}
if (vars.Add(p.Lhs))
{
varsList.Add(p.Lhs);
}
foreach (Nonterminal v in p.GetVariables())
{
if (vars.Add(v))
{
varsList.Add(v);
}
}
}
if (!startSymbolExisted)
{
throw new ArgumentException("Start symbol is not used as the LHS of any production.");
}
this.variables = varsList;
this.startSymbol = startSymbol;
var prodMap = new Dictionary <Nonterminal, List <Production> >();
foreach (Nonterminal v in varsList)
{
prodMap.Add(v, new List <Production>());
}
foreach (Production p in productions)
{
prodMap[p.Lhs].Add(p);
}
this.productionMap = prodMap;
}
HashSet <Nonterminal> GetUnitClosure(Nonterminal v)
{
HashSet <Nonterminal> res = new HashSet <Nonterminal>();
res.Add(v);
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(v);
while (stack.Count > 0)
{
foreach (Production p in productionMap[stack.Pop()])
{
if (p.IsUnit)
{
if (res.Add((Nonterminal)p.First)) //p.First is a new variable that is added to res
{
stack.Push((Nonterminal)p.First);
}
}
}
}
return(res);
}
private void Parse()
{
bool done = false;
Token cur = null;
Token last = null;
Nonterminal curlhs = new Nonterminal(ExpectNT().content);
startvar = curlhs;
ExpectArrow();
List <GrammarSymbol> currhs = new List <GrammarSymbol>();
last = cur;
cur = lexer.Next();
while (!done)
{
switch (cur.t)
{
case TokenType.NT:
currhs.Add(new Nonterminal(cur.content));
last = cur;
cur = lexer.Next();
break;
case TokenType.T:
currhs.Add(new Exprinal <T>(mkExprinal(cur.content[0]), cur.content));
last = cur;
cur = lexer.Next();
break;
case TokenType.OR:
productions.Add(new Production(curlhs, currhs.ToArray()));
currhs.Clear();
last = cur;
cur = lexer.Next();
break;
//case TokenType.ARR:
// if (currhs.Count < 1)
// {
// throw new ParseException(string.Format("A production cannot start with an arrow... ({0})", generateLocationString(cur)));
// }
// if (last.t != TokenType.NT)
// {
// throw new ParseException(string.Format("On the left hand side of every arrow has to be a Nonterminal... ({0})", generateLocationString(cur)));
// }
// Nonterminal newlhs = (Nonterminal)currhs[currhs.Count - 1];
// currhs.RemoveAt(currhs.Count - 1);
// productions.Add(new Production(curlhs, currhs.ToArray()));
// currhs.Clear();
// curlhs = newlhs;
// break;
case TokenType.NEL:
productions.Add(new Production(curlhs, currhs.ToArray()));
currhs.Clear();
last = cur;
cur = ExpectNT();
if (cur.t == TokenType.NT)
{
curlhs = new Nonterminal(cur.content);
ExpectArrow();
last = cur;
cur = lexer.Next();
}
break;
case TokenType.EOS:
productions.Add(new Production(curlhs, currhs.ToArray()));
currhs.Clear();
done = true;
break;
default:
throw new ParseException(string.Format("The grammar couldn't be parsed. Please check the syntax... ({0})", generateLocationString(cur)));
}
}
}
public static Tuple <int, IEnumerable <String> > gradeCYK(ContextFreeGrammar grammar, String word, HashSet <Nonterminal>[][] attempt, int maxGrade, int feedbackLevel)
{
List <String> feedback = new List <String>();
int n = word.Length;
int checked_length = 0;
var sol = GrammarUtilities.cyk(grammar, word);
bool all_correct_sofar = true;
for (int len = 1; len <= n; len++)
{
for (int start = 0; start + len <= n; start++)
{
HashSet <Nonterminal> must = sol[len - 1][start].Item1;
HashSet <Nonterminal> was = attempt[len - 1][start];
Nonterminal missingExample = null;
Production missingApplicableProduction = null;
int missing = 0;
Nonterminal tooMuchExample = null;
int tooMuch = 0;
//check if all must are present
foreach (Nonterminal nt in must)
{
if (!was.Contains(nt))
{
missing++;
all_correct_sofar = false;
//save as example and look for corresponding applicable production for hint
if (missingApplicableProduction != null)
{
continue; //not needed: already found example
}
missingExample = nt;
foreach (var applicable in sol[len - 1][start].Item2)
{
if (applicable.Item1.Lhs.Equals(nt))
{
missingApplicableProduction = applicable.Item1;
break;
}
}
}
}
//check if all given are correct
foreach (Nonterminal nt in was)
{
if (!must.Contains(nt))
{
tooMuchExample = nt;
tooMuch++;
all_correct_sofar = false;
}
}
//feedback
String fieldName = String.Format("({0},{1})", start + 1, start + len);
if (feedbackLevel >= 2)
{
if (missing != 0)
{
feedback.Add(String.Format("You are missing some nonterminals in field {0} e.g. {1}", fieldName, missingExample));
}
if (tooMuch != 0)
{
feedback.Add(String.Format("There are nonterminals in field {0} that don't belong there... e.g. {1}", fieldName, tooMuchExample));
}
}
else if (feedbackLevel >= 1)
{
if (missing != 0)
{
feedback.Add(String.Format("You are missing some nonterminals in field {0}... (hint: The production \"{1}\" is applicable.)", fieldName, missingApplicableProduction));
}
if (tooMuch != 0)
{
feedback.Add(String.Format("There are nonterminals in field {0} that don't belong there...", fieldName));
}
}
else
{
if (missing != 0)
{
feedback.Add(String.Format("You are missing some nonterminals in field {0}...", fieldName));
}
if (tooMuch != 0)
{
feedback.Add(String.Format("There are nonterminals in field {0} that don't belong there...", fieldName));
}
}
}
if (!all_correct_sofar)
{
break;
}
checked_length = len;
}
//grade
int grade = (int)Math.Floor(checked_length * maxGrade / (double)n);
//all correct?
if (feedback.Count == 0)
{
feedback.Add("Correct!");
}
return(Tuple.Create(grade, (IEnumerable <String>)feedback));
}
/// <summary>
/// Produces the EGNF (Extended Greibach Normal Form) for the grammar g.
/// Implements a variation of the Blum-Koch algorithm.
/// (Inf. and Comp. vol.150, pp.112-118, 1999)
/// </summary>
/// <param name="g">the grammar to be normalized</param>
/// <param name="removeEpsilonsAndUselessSymbols">if true, first removes epsilons and useless symbols, otherwise assumes that epsilons do not occur</param>
/// <returns>Extended Greibach Normal Form of g</returns>
public static ContextFreeGrammar MkEGNF(ContextFreeGrammar g, bool removeEpsilonsAndUselessSymbols)
{
if (removeEpsilonsAndUselessSymbols)
{
g = g.RemoveEpsilonsAndUselessSymbols();
}
if (g.IsInGNF())
{
return(g);
}
var leavesP = new List <Production>();
var revP = new Dictionary <Nonterminal, List <Pair <GrammarSymbol[], Nonterminal> > >();
int nonterminalID = 0;
#region compute leavesP and revP
foreach (Nonterminal v in g.variables)
{
revP[v] = new List <Pair <GrammarSymbol[], Nonterminal> >();
}
foreach (Production p in g.GetProductions())
{
if (!(p.First is Nonterminal))
{
leavesP.Add(p);
}
else
{
revP[(Nonterminal)p.First].Add(new Pair <GrammarSymbol[], Nonterminal>(p.Rest, p.Lhs));
}
}
#endregion
var W = new Dictionary <Nonterminal, HashSet <Nonterminal> >();
var startSymbol = new Dictionary <Nonterminal, Nonterminal>();
#region create new start symbols and compute unit closures
foreach (Nonterminal v in g.variables)
{
W[v] = g.GetUnitClosure(v);
startSymbol[v] = new Nonterminal(nonterminalID++);
}
#endregion
var P = new Dictionary <Nonterminal, List <Production> >();
#region construct intermediate productions in P for each variable B
foreach (Nonterminal B in g.variables)
{
var S_B = startSymbol[B];
var W_B = W[B]; //unit closure of B
var Bvar = new Dictionary <Nonterminal, Nonterminal>();
Stack <Nonterminal> stack = new Stack <Nonterminal>();
HashSet <Nonterminal> visited = new HashSet <Nonterminal>();
var S_B_list = new List <Production>();
P[S_B] = S_B_list;
foreach (Production p in leavesP)
{
S_B_list.Add(new Production(S_B, p.Rhs, Lookup(Bvar, p.Lhs, ref nonterminalID)));
if (visited.Add(p.Lhs))
{
stack.Push(p.Lhs);
}
if (W_B.Contains(p.Lhs))
{
S_B_list.Add(new Production(S_B, p.Rhs));
}
}
while (stack.Count > 0)
{
Nonterminal C = stack.Pop();
Nonterminal C_B = Lookup(Bvar, C, ref nonterminalID);
List <Production> C_B_list;
if (!P.TryGetValue(C_B, out C_B_list))
{
C_B_list = new List <Production>();
P[C_B] = C_B_list;
}
foreach (var t in revP[C])
{
Nonterminal D = t.Second;
Nonterminal D_B = Lookup(Bvar, D, ref nonterminalID);
C_B_list.Add(new Production(C_B, t.First, D_B));
if (t.First.Length > 0 && W_B.Contains(D))
{
C_B_list.Add(new Production(C_B, t.First));
}
if (visited.Add(D))
{
stack.Push(D);
}
}
}
}
#endregion
//produce the union of P and g.productionMap in H
//and replace each production 'A ::= B alpha' by 'A ::= S_B alpha"
var Hprods = new Dictionary <Nonterminal, List <Production> >();
#region compute Hprods
foreach (Nonterminal A in g.variables)
{
var A_prods = new List <Production>();
Hprods[A] = A_prods;
foreach (Production p in g.productionMap[A])
{
if (p.First is Nonterminal && !p.IsUnit)
{
GrammarSymbol[] rhs = new GrammarSymbol[p.Rhs.Length];
rhs[0] = startSymbol[(Nonterminal)p.First];
Array.Copy(p.Rhs, 1, rhs, 1, rhs.Length - 1);
Production q = new Production(p.Lhs, rhs);
A_prods.Add(q);
}
else
{
A_prods.Add(p);
}
}
}
foreach (Nonterminal A in P.Keys)
{
var A_prods = new List <Production>();
Hprods[A] = A_prods;
foreach (Production p in P[A])
{
if (p.First is Nonterminal && !p.IsUnit)
{
GrammarSymbol[] rhs = new GrammarSymbol[p.Rhs.Length];
rhs[0] = startSymbol[(Nonterminal)p.First];
Array.Copy(p.Rhs, 1, rhs, 1, rhs.Length - 1);
Production q = new Production(p.Lhs, rhs);
A_prods.Add(q);
}
else
{
A_prods.Add(p);
}
}
}
#endregion
ContextFreeGrammar H = new ContextFreeGrammar(new List <Nonterminal>(Hprods.Keys), g.startSymbol, Hprods);
//Console.WriteLine("--------- H:");
//H.Display(Console.Out);
//eliminate useless symbols from H
//this may dramatically decrease the number of productions
ContextFreeGrammar H1 = H.RemoveUselessSymbols();
//Console.WriteLine("---------- H1:");
//H1.Display(Console.Out);
List <Nonterminal> egnfVars = new List <Nonterminal>();
Dictionary <Nonterminal, List <Production> > egnfProds = new Dictionary <Nonterminal, List <Production> >();
Stack <Nonterminal> egnfStack = new Stack <Nonterminal>();
HashSet <Nonterminal> egnfVisited = new HashSet <Nonterminal>();
egnfStack.Push(H1.startSymbol);
egnfVisited.Add(H1.startSymbol);
egnfVars.Add(H1.startSymbol);
egnfProds[H1.startSymbol] = new List <Production>();
#region eliminate temp start symbols and produce the EGNF form
while (egnfStack.Count > 0)
{
var A = egnfStack.Pop();
List <Production> A_prods = egnfProds[A];
foreach (Production p in H1.productionMap[A])
{
if (!(p.First is Nonterminal) || p.IsUnit)
{
A_prods.Add(p);
foreach (Nonterminal x in p.GetVariables())
{
if (egnfVisited.Add(x))
{
egnfStack.Push(x);
egnfVars.Add(x);
egnfProds[x] = new List <Production>();
}
}
}
else
{
Nonterminal S_B = (Nonterminal)p.First; //here we know that S_B is a temp start symbol
foreach (Production t in H1.productionMap[S_B])
{
int k = t.Rhs.Length;
GrammarSymbol[] rhs = new GrammarSymbol[k + p.Rhs.Length - 1];
for (int i = 0; i < k; i++)
{
rhs[i] = t.Rhs[i];
}
for (int i = 1; i < p.Rhs.Length; i++)
{
rhs[k + i - 1] = p.Rhs[i];
}
Production q = new Production(A, rhs);
A_prods.Add(q);
foreach (Nonterminal x in q.GetVariables())
{
if (egnfVisited.Add(x))
{
egnfStack.Push(x);
egnfVars.Add(x);
egnfProds[x] = new List <Production>();
}
}
}
}
}
}
#endregion
ContextFreeGrammar egnf = new ContextFreeGrammar(egnfVars, H1.startSymbol, egnfProds);
return(egnf);
}
/// <summary>
/// Produces the GNF (Greibach Normal Form) for the grammar g.
/// If g is not already in GNF, first makes CNF.
/// Implements a variation of the Koch-Blum algorithm. (STACS 97, pp. 47-54)
/// </summary>
/// <param name="g"></param>
/// <param name="removeEpsilonsUselessSymbolsUnitsProductions"></param>
/// <returns></returns>
public static ContextFreeGrammar MkGNF(ContextFreeGrammar g, bool removeEpsilonsUselessSymbolsUnitsProductions)
{
if (removeEpsilonsUselessSymbolsUnitsProductions)
{
g = g.RemoveEpsilonsAndUselessSymbols().RemoveUnitProductions();
}
if (g.IsInGNF())
{
return(g);
}
ContextFreeGrammar cnf = MkCNF(g, false);
var Vars = cnf.variables;
int nonterminalID = 0;
var M = new Dictionary <Nonterminal, Automaton <GrammarSymbol> >();
#region construct the automata M[B] for all variables B
int id = 0;
var initStateMap = new Dictionary <Nonterminal, int>();
var finalStateMap = new Dictionary <Nonterminal, int>();
foreach (Nonterminal B in Vars)
{
initStateMap[B] = id++;
finalStateMap[B] = id++;
}
var movesOfM = new Dictionary <Nonterminal, List <Move <GrammarSymbol> > >();
foreach (Nonterminal B in Vars)
{
movesOfM[B] = new List <Move <GrammarSymbol> >();
}
#region construct the moves of the automata
foreach (Nonterminal B in Vars)
{
var variableToStateMap = new Dictionary <Nonterminal, int>();
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(B);
int initState = initStateMap[B];
variableToStateMap[B] = finalStateMap[B];
while (stack.Count > 0)
{
Nonterminal C = stack.Pop();
foreach (Production p in cnf.GetProductions(C))
{
if (p.IsSingleExprinal)
{
movesOfM[B].Add(Move <GrammarSymbol> .Create(initState, variableToStateMap[C], p.First));
}
else
{
Nonterminal D = (Nonterminal)p.First; //using the fact that the grammar is in CNF
if (!variableToStateMap.ContainsKey(D))
{
//visit all variables reachable that have not already been visited
variableToStateMap.Add(D, id++);
stack.Push(D);
}
GrammarSymbol E = p.Rhs[1];
movesOfM[B].Add(Move <GrammarSymbol> .Create(variableToStateMap[D], variableToStateMap[C], E));
}
}
}
}
#endregion
foreach (Nonterminal B in Vars)
{
M[B] = Automaton <GrammarSymbol> .Create(initStateMap[B], new int[] { finalStateMap[B] }, movesOfM[B]);
}
#endregion
var G_ = new Dictionary <Nonterminal, ContextFreeGrammar>();
#region construct corresponding intermediate grammars G_[B] corresponding to M[B]
foreach (Nonterminal B in Vars)
{
var MB = M[B];
bool MBfinalStateHasVariableMoves = FinalStateHasVariableMoves(MB);
var productions = new Dictionary <Nonterminal, List <Production> >();
Nonterminal startSymbol = new Nonterminal(nonterminalID++);
var vars = new List <Nonterminal>();
vars.Add(startSymbol);
productions[startSymbol] = new List <Production>();
foreach (var move in MB.GetMovesFrom(MB.InitialState))
{
if (move.TargetState == MB.FinalState)
{
productions[startSymbol].Add(new Production(startSymbol, move.Label));
}
if (move.TargetState != MB.FinalState || MBfinalStateHasVariableMoves)
{
var C = new Nonterminal("Q" + move.TargetState);
productions[startSymbol].Add(new Production(startSymbol, move.Label, C));
if (!productions.ContainsKey(C))
{
productions[C] = new List <Production>();
vars.Add(C);
}
}
}
foreach (int state in MB.States)
{
if (state != MB.InitialState)
{
foreach (Move <GrammarSymbol> move in MB.GetMovesFrom(state))
{
Nonterminal D = new Nonterminal("Q" + state);
Nonterminal C = new Nonterminal("Q" + move.TargetState);
if (!productions.ContainsKey(D))
{
productions[D] = new List <Production>();
vars.Add(D);
}
Nonterminal E = (Nonterminal)move.Label;
if (move.TargetState == MB.FinalState)
{
productions[D].Add(new Production(D, E));
}
if (move.TargetState != MB.FinalState || MBfinalStateHasVariableMoves)
{
productions[D].Add(new Production(D, E, C));
//we pretend here that E is a terminal
if (!productions.ContainsKey(C))
{
productions[C] = new List <Production>();
vars.Add(C);
}
}
}
}
}
G_[B] = new ContextFreeGrammar(vars, startSymbol, productions);
}
#endregion
var G = new Dictionary <Nonterminal, ContextFreeGrammar>();
#region construct the corresponding temporary G[B]'s
foreach (Nonterminal B in Vars)
{
var G_B = G_[B];
var productions = new Dictionary <Nonterminal, List <Production> >();
//var vars = new List<Variable>();
Nonterminal startSymbol = G_B.startSymbol;
productions[startSymbol] = G_B.productionMap[startSymbol];
foreach (Nonterminal D in G_B.variables)
{
if (!D.Equals(startSymbol))
{
var productions_D = new List <Production>();
productions[D] = productions_D;
foreach (Production p in G_B.productionMap[D])
{
Nonterminal E = (Nonterminal)p.First;
var G_E = G_[E];
if (p.IsUnit)
{
foreach (Production q in G_E.productionMap[G_E.startSymbol])
{
productions_D.Add(new Production(D, q.Rhs));
}
}
else
{
foreach (Production q in G_E.productionMap[G_E.startSymbol])
{
GrammarSymbol[] symbols = new GrammarSymbol[q.Rhs.Length + 1];
Array.Copy(q.Rhs, symbols, q.Rhs.Length);
symbols[q.Rhs.Length] = p.Rhs[1];
productions_D.Add(new Production(D, symbols));
}
}
}
}
}
//ignore the variable list, it is not used
G[B] = new ContextFreeGrammar(null, startSymbol, productions);
}
#endregion
#region construct the final GNF from the G[B]'s
var productionsGNF = new List <Production>();
foreach (Nonterminal A in cnf.variables)
{
foreach (Production p in cnf.productionMap[A])
{
if (p.IsSingleExprinal)
{
productionsGNF.Add(p);
}
else
{
Nonterminal B = (Nonterminal)p.Rhs[0];
Nonterminal C = (Nonterminal)p.Rhs[1];
var GB = G[B];
foreach (Production q in GB.productionMap[GB.startSymbol])
{
GrammarSymbol[] symbols = new GrammarSymbol[q.Rhs.Length + 1];
Array.Copy(q.Rhs, symbols, q.Rhs.Length);
symbols[q.Rhs.Length] = C;
productionsGNF.Add(new Production(A, symbols));
}
}
}
}
foreach (Nonterminal B in Vars)
{
var GB = G[B];
foreach (var kv in GB.productionMap)
{
if (!kv.Key.Equals(GB.startSymbol))
{
productionsGNF.AddRange(kv.Value);
}
}
}
#endregion
ContextFreeGrammar gnf = new ContextFreeGrammar(cnf.startSymbol, productionsGNF);
return(gnf);
}
/// <summary>
/// Return all useful nonterminal symbols. If checkBackwardsOnly is true, assume that all symbols are reachable from the start symbol.
/// </summary>
public HashSet <string> GetUsefulNonterminals(bool checkBackwardsOnly)
{
HashSet <Nonterminal> useful_backwards = new HashSet <Nonterminal>();
//Lemma 4.1, p. 88, Hopcroft-Ullman
#region backward reachability
var variableNodeMap = new Dictionary <Nonterminal, VariableNode>();
foreach (Nonterminal v in this.variables)
{
variableNodeMap[v] = new VariableNode();
}
List <ProductionNode> productionLeaves = new List <ProductionNode>();
foreach (Nonterminal v in this.variables)
{
VariableNode parent = variableNodeMap[v];
foreach (Production p in this.productionMap[v])
{
var children = Array.ConvertAll(new List <Nonterminal>(p.GetVariables()).ToArray(), w => variableNodeMap[w]);
ProductionNode pn = new ProductionNode(parent, children);
if (children.Length == 0)
{
productionLeaves.Add(pn);
}
else
{
foreach (VariableNode child in children)
{
child.parents.Add(pn);
}
}
}
}
foreach (ProductionNode leaf in productionLeaves)
{
leaf.PropagateMark();
}
foreach (Nonterminal v in this.variables)
{
if (variableNodeMap[v].isMarked)
{
useful_backwards.Add(v);
}
}
#endregion
//returns the empty set because the language is empty
if (!useful_backwards.Contains(this.startSymbol))
{
return(new HashSet <string>());
}
//don't bother to check forward
if (checkBackwardsOnly)
{
var res = new HashSet <string>();
foreach (var nt in useful_backwards)
{
res.Add(nt.Name);
}
return(res);
}
ContextFreeGrammar g1 = this.RestrictToVariables(useful_backwards);
HashSet <Nonterminal> useful_forwards = new HashSet <Nonterminal>();
//Lemma 4.2, p. 89, Hopcroft-Ullman
#region forward reachability
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(g1.StartSymbol);
useful_forwards.Add(g1.StartSymbol);
while (stack.Count > 0)
{
Nonterminal v = stack.Pop();
foreach (Production p in g1.GetProductions(v))
{
foreach (Nonterminal u in p.GetVariables())
{
if (!useful_forwards.Contains(u))
{
useful_forwards.Add(u);
stack.Push(u);
}
}
}
}
#endregion
HashSet <string> usefulSymbols = new HashSet <string>();
foreach (var nt in useful_forwards)
{
if (useful_backwards.Contains(nt))
{
usefulSymbols.Add(nt.Name);
}
}
return(usefulSymbols);
}
/// <summary>
/// Produces the CNF (Chomsky Normal Form) for the grammar g.
/// It first eliminates epsilons, useless symbols, and unit productions.
/// If Assumes that there are no epsilons, useless symbols or unit productions
/// </summary>
public static ContextFreeGrammar MkCNF(ContextFreeGrammar g, bool removeEpsilonsUselessSymbolsUnitsProductions)
{
if (removeEpsilonsUselessSymbolsUnitsProductions)
{
g = g.RemoveEpsilonsAndUselessSymbols();
g = g.RemoveUnitProductions();
}
var productions = new Dictionary <Nonterminal, List <Production> >();
List <Nonterminal> variables = new List <Nonterminal>(g.variables);
foreach (Nonterminal v in g.variables)
{
productions[v] = new List <Production>();
}
int nonterminalID = 0;
//Implements algo in Theorem 4.5, page 92-93, in Hopcroft-Ullman
#region make productions of the form V --> V0...Vn or V --> a
var freshVarMap = new Dictionary <GrammarSymbol, Nonterminal>();
foreach (Nonterminal v in g.variables)
{
foreach (Production p in g.productionMap[v])
{
if (p.ContainsNoExprinals || p.IsCNF)
{
productions[v].Add(p);
}
else
{
GrammarSymbol[] rhs = new GrammarSymbol[p.Rhs.Length];
for (int i = 0; i < rhs.Length; i++)
{
if (p.Rhs[i] is Nonterminal)
{
rhs[i] = p.Rhs[i];
}
else
{
Nonterminal u;
if (!freshVarMap.TryGetValue(p.Rhs[i], out u))
{
u = new Nonterminal(nonterminalID++);
freshVarMap[p.Rhs[i]] = u;
variables.Add(u);
var prods = new List <Production>();
prods.Add(new Production(u, p.Rhs[i]));
productions[u] = prods;
}
rhs[i] = u;
}
}
productions[v].Add(new Production(v, rhs));
}
}
}
#endregion
var productionsCNF = new Dictionary <Nonterminal, List <Production> >();
List <Nonterminal> variablesCNF = new List <Nonterminal>(variables);
foreach (Nonterminal v in variablesCNF)
{
productionsCNF[v] = new List <Production>();
}
#region replace V --> V0V1...Vn (n > 2), by V --> V0U0, U0 --> V1U1, ..., Un-2 --> Vn-1Vn
foreach (Nonterminal v in variables)
{
foreach (Production p in productions[v])
{
if (p.IsCNF)
{
productionsCNF[v].Add(p);
}
else
{
Nonterminal x = v;
Nonterminal y = new Nonterminal(nonterminalID++);
variablesCNF.Add(y);
productionsCNF[y] = new List <Production>();
for (int i = 0; i < p.Rhs.Length - 2; i++)
{
productionsCNF[x].Add(new Production(x, p.Rhs[i], y));
if (i < p.Rhs.Length - 3)
{
x = y;
y = new Nonterminal(nonterminalID++);
variablesCNF.Add(y);
productionsCNF[y] = new List <Production>();
}
}
productionsCNF[y].Add(new Production(y, p.Rhs[p.Rhs.Length - 2], p.Rhs[p.Rhs.Length - 1]));
}
}
}
#endregion
ContextFreeGrammar cnf = new ContextFreeGrammar(variablesCNF, g.startSymbol, productionsCNF);
return(cnf);
}
public IList <Production> GetProductions(Nonterminal v)
{
return(productionMap[v]);
}
internal ContextFreeGrammar(List <Nonterminal> variables, Nonterminal startSymbol, Dictionary <Nonterminal, List <Production> > productionMap)
{
this.variables = variables;
this.startSymbol = startSymbol;
this.productionMap = productionMap;
}
public bool IsValidVariable(Nonterminal v)
{
return(productionMap.ContainsKey(v));
}
private static HashSet <string> generateWordsWithLength(ContextFreeGrammar cnf, int length, Dictionary <Nonterminal, Dictionary <int, HashSet <string> > > dp)
{
HashSet <string> res = new HashSet <string>();
if (cnf == null)
{
return(res); //empty grammar -> can't generate any words
}
if (length == 0) //case: length = 0
{
if (cnf.acceptsEmptyString())
{
res.Add("");
}
}
else if (length == 1) //case: length = 1
{
foreach (Nonterminal nt in cnf.Variables)
{
//init dp[nt]
Dictionary <int, HashSet <string> > curDP = new Dictionary <int, HashSet <string> >();
dp.Add(nt, curDP);
//find words of length 1
HashSet <string> l = new HashSet <string>();
foreach (Production p in cnf.GetProductions(nt))
{
if (p.IsSingleExprinal)
{
l.Add(p.Rhs[0].ToString());
}
}
curDP.Add(1, l);
if (nt.Equals(cnf.StartSymbol))
{
res = l;
}
}
}
else //case: length > 1
{
foreach (KeyValuePair <Nonterminal, Dictionary <int, HashSet <string> > > entry in dp)
{
Nonterminal cur = entry.Key;
Dictionary <int, HashSet <string> > curDP = entry.Value;
HashSet <string> curSet = new HashSet <string>();
curDP.Add(length, curSet);
if (cur.Equals(cnf.StartSymbol))
{
res = curSet;
}
foreach (Production p in cnf.GetProductions(entry.Key))
{
if (p.Rhs.Length != 2)
{
continue; //ignore productions that don't have form X->AB
}
Nonterminal left = (Nonterminal)p.Rhs[0];
Dictionary <int, HashSet <string> > leftDP = null;
dp.TryGetValue(left, out leftDP);
Nonterminal right = (Nonterminal)p.Rhs[1];
Dictionary <int, HashSet <string> > rightDP = null;
dp.TryGetValue(right, out rightDP);
for (int leftPart = 1; leftPart < length; leftPart++)
{
int rightPart = length - leftPart;
HashSet <string> leftPossibilities = null;
leftDP.TryGetValue(leftPart, out leftPossibilities);
HashSet <string> rightPossibilities = null;
rightDP.TryGetValue(rightPart, out rightPossibilities);
foreach (string leftString in leftPossibilities)
{
foreach (string rightString in rightPossibilities)
{
curSet.Add(leftString + rightString);
}
}
}
}
}
}
return(res);
}
public Production(Nonterminal lhs, params GrammarSymbol[] rhs)
{
this.Lhs = lhs;
this.Rhs = rhs;
}
/// <summary>
/// Removes useless symbols from the grammar.
/// Assumes that the language is nonempty.
/// </summary>
public ContextFreeGrammar RemoveUselessSymbols()
{
HashSet <Nonterminal> useful_backwards = new HashSet <Nonterminal>();
//Lemma 4.1, p. 88, Hopcroft-Ullman
#region backward reachability
var variableNodeMap = new Dictionary <Nonterminal, VariableNode>();
foreach (Nonterminal v in this.variables)
{
variableNodeMap[v] = new VariableNode();
}
List <ProductionNode> productionLeaves = new List <ProductionNode>();
foreach (Nonterminal v in this.variables)
{
VariableNode parent = variableNodeMap[v];
foreach (Production p in this.productionMap[v])
{
var children = Array.ConvertAll(new List <Nonterminal>(p.GetVariables()).ToArray(), w => variableNodeMap[w]);
ProductionNode pn = new ProductionNode(parent, children);
if (children.Length == 0)
{
productionLeaves.Add(pn);
}
else
{
foreach (VariableNode child in children)
{
child.parents.Add(pn);
}
}
}
}
foreach (ProductionNode leaf in productionLeaves)
{
leaf.PropagateMark();
}
foreach (Nonterminal v in this.variables)
{
if (variableNodeMap[v].isMarked)
{
useful_backwards.Add(v);
}
}
#endregion
if (!useful_backwards.Contains(this.startSymbol))
{
throw new AutomataException(AutomataExceptionKind.LanguageOfGrammarIsEmpty);
}
ContextFreeGrammar g1 = this.RestrictToVariables(useful_backwards);
HashSet <Nonterminal> useful_forwards = new HashSet <Nonterminal>();
//Lemma 4.2, p. 89, Hopcroft-Ullman
#region forward reachability
Stack <Nonterminal> stack = new Stack <Nonterminal>();
stack.Push(g1.StartSymbol);
useful_forwards.Add(g1.StartSymbol);
while (stack.Count > 0)
{
Nonterminal v = stack.Pop();
foreach (Production p in g1.GetProductions(v))
{
foreach (Nonterminal u in p.GetVariables())
{
if (!useful_forwards.Contains(u))
{
useful_forwards.Add(u);
stack.Push(u);
}
}
}
}
#endregion
ContextFreeGrammar g2 = g1.RestrictToVariables(useful_forwards);
return(g2);
}