/// <summary>
/// Remove epsilon productions.
/// If the grammar derives epsilon, then only the start variable may derive epsilon, but then it
/// would not be found on the right-hand side of any production.
/// </summary>
/// <param name="grammar">target grammar</param>
/// <returns>grammar without epsilon productions</returns>
public static CFG RemoveEpsilonProductions(this CFG grammar)
{
bool hasNullableStartSymbolInRHS = grammar.HasNullableStartSymbolInRHS();
if (!grammar.HasEpsilonProductionsExceptStartVariable() && !hasNullableStartSymbolInRHS)
{
return(grammar);
}
if (hasNullableStartSymbolInRHS)
{
OrderedHashSet <Production> newProductions = new OrderedHashSet <Production>();
foreach (Production production in grammar.productions)
{
newProductions.Add(production);
}
string newStartVariable = GenerateAuxiliaryVariable(grammar.Symbols(), grammar.startVariable);
newProductions.Add(new Production(newStartVariable, grammar.startVariable));
newProductions.Add(new Production(newStartVariable));
return(RemoveEpsilonProductions(new CFG(newStartVariable, newProductions)));
}
OrderedHashSet <Production> productions = grammar.productions;
while (true)
{
OrderedHashSet <string> nullableVariables = new OrderedHashSet <string>(), nullVariables = new OrderedHashSet <string>();
foreach (Production production in productions)
{
if (production.IsEpsilonProduction())
{
nullableVariables.Add(production.lhs);
nullVariables.Add(production.lhs);
}
}
foreach (Production production in productions)
{
if (!production.IsEpsilonProduction())
{
nullVariables.Remove(production.lhs);
}
}
if (nullableVariables.Count == 0 || nullableVariables.Count == 1 && nullableVariables.Contains(grammar.startVariable))
{
return(verifyConsistency(grammar, new CFG(grammar.startVariable, productions).Simplify()));
}
OrderedHashSet <Production> newProductions = new OrderedHashSet <Production>();
foreach (Production production in productions)
{
OrderedHashSet <List <string> > rhss = new OrderedHashSet <List <string> >();
rhss.Add(new List <string>());
foreach (string symbol in production.rhs)
{
OrderedHashSet <List <string> > newRHSs = new OrderedHashSet <List <string> >();
foreach (var rhs in rhss)
{
if (nullVariables.Contains(symbol))
{
newRHSs.AddUnique(rhs);
}
else if (!nullableVariables.Contains(symbol))
{
List <string> newRHS = new List <string>();
newRHS.AddRange(rhs);
newRHS.Add(symbol);
newRHSs.Add(newRHS);
}
else
{
newRHSs.AddUnique(rhs);
List <string> newRHS = new List <string>();
newRHS.AddRange(rhs);
newRHS.Add(symbol);
newRHSs.Add(newRHS);
}
}
rhss = newRHSs;
}
foreach (var newRHS in rhss)
{
newProductions.Add(new Production(production.lhs, newRHS.ToArray()));
}
}
foreach (string nullableVariable in nullableVariables)
{
if (nullableVariable != grammar.startVariable)
{
newProductions.Remove(new Production(nullableVariable));
}
}
productions = newProductions;
}
}
/// <summary>
/// Removes left-recursive productions from the grammar.
/// Implementation of Paull's algorithm.
/// </summary>
/// <param name="grammar">target grammar</param>
/// <returns>grammar without left recursion</returns>
public static CFG RemoveLeftRecursion(this CFG grammar)
{
if (!grammar.HasLeftRecursion())
{
return(grammar);
}
grammar = grammar.Simplify().RemoveEpsilonProductions();
if (!grammar.HasLeftRecursion())
{
return(grammar);
}
bool epsilonIsDerived = grammar.productions.Contains(new Production(grammar.startVariable));
OrderedHashSet <Production> productions = new OrderedHashSet <Production>();
foreach (Production production in grammar.productions)
{
productions.Add(production);
}
if (epsilonIsDerived)
{
productions.Remove(new Production(grammar.startVariable));
}
List <string> variables = new List <string>(grammar.Variables());
OrderedHashSet <string> usedSymbols = new OrderedHashSet <string>();
foreach (string symbol in grammar.Symbols())
{
usedSymbols.Add(symbol);
}
for (int i = 0; i < variables.Count; ++i)
{
string vi = variables[i];
for (int j = 0; j < i; ++j)
{
string vj = variables[j];
OrderedHashSet <Production> toRemove = new OrderedHashSet <Production>();
OrderedHashSet <Production> toAdd = new OrderedHashSet <Production>();
foreach (Production production in productions)
{
if (production.lhs == vi && production.rhs.Length > 0 && production.rhs[0] == vj)
{
toRemove.Add(production);
foreach (Production otherProduction in productions)
{
if (otherProduction.lhs == vj)
{
List <string> newRHS = new List <string>();
newRHS.AddRange(otherProduction.rhs);
newRHS.AddRange(production.rhs.Skip(1));
toAdd.Add(new Production(vi, newRHS.ToArray()));
}
}
break;
}
}
foreach (Production addedProduction in toAdd)
{
productions.Add(addedProduction);
}
foreach (Production removedProduction in toRemove)
{
productions.Remove(removedProduction);
}
}
OrderedHashSet <Production> productionsWithoutViDirectLeftRecursion = new OrderedHashSet <Production>();
OrderedHashSet <Production> newViProductions = new OrderedHashSet <Production>();
foreach (Production production in productions)
{
if (production.lhs != vi)
{
productionsWithoutViDirectLeftRecursion.Add(production);
}
else
{
newViProductions.Add(production);
}
}
foreach (Production newViProduction in RemoveDirectLeftRecursion(usedSymbols, newViProductions))
{
productionsWithoutViDirectLeftRecursion.Add(newViProduction);
}
productions = productionsWithoutViDirectLeftRecursion;
}
if (epsilonIsDerived)
{
productions.Add(new Production(grammar.startVariable));
}
return(verifyConsistency(grammar, new CFG(grammar.startVariable, productions)));
}