/// <summary>
/// Simplify context-free grammar by removing unreachable symbols and productions and productions of
/// the form V ::= V.
/// </summary>
/// <param name="grammar">target grammar</param>
/// <returns>simplified grammar</returns>
public static CFG Simplify(this CFG grammar)
{
OrderedHashSet <Production> productions = new OrderedHashSet <Production>();
OrderedHashSet <string> newSymbols = new OrderedHashSet <string>(), seenSymbols = new OrderedHashSet <string>();
newSymbols.Add(grammar.startVariable);
while (newSymbols.Count() > 0)
{
foreach (string symbol in newSymbols)
{
seenSymbols.Add(symbol);
}
OrderedHashSet <string> nextSymbols = new OrderedHashSet <string>();
foreach (Production production in grammar.productions)
{
if (newSymbols.Contains(production.lhs) && (production.rhs.Length != 1 || production.rhs[0] != production.lhs))
{
productions.Add(production);
foreach (string symbol in production.rhs)
{
if (!seenSymbols.Contains(symbol))
{
nextSymbols.Add(symbol);
}
}
}
}
newSymbols = nextSymbols;
}
return(verifyConsistency(grammar, new CFG(grammar.startVariable, productions)));
}
/// <summary>
/// Checks whether the grammar has a left-recursive production, i.e.,
/// of the form `v ::= v s1 s2...` (can also be indirect).
/// </summary>
/// <param name="grammar">context-free grammar</param>
/// <returns>whether grammar has left-recursion</returns>
public static bool HasLeftRecursion(this CFG grammar)
{
foreach (string variable in grammar.Variables())
{
OrderedHashSet <string> reachableVariables = new OrderedHashSet <string>();
reachableVariables.Add(variable);
int n = 0;
while (reachableVariables.Count() > n)
{
n = reachableVariables.Count();
OrderedHashSet <string> newReachableVariables = new OrderedHashSet <string>();
foreach (string reachableVariable in reachableVariables)
{
foreach (Production production in grammar.productions)
{
if (production.lhs == reachableVariable && production.rhs.Length > 0)
{
string first = production.rhs[0];
if (first == variable)
{
return(true);
}
else if (grammar.Variables().Contains(first))
{
newReachableVariables.Add(first);
}
}
}
}
foreach (string newVariable in newReachableVariables)
{
reachableVariables.Add(newVariable);
}
}
}
return(false);
}
