/// <summary>
/// 计算指定 LR(1) 项集的闭包。
/// </summary>
/// <param name="items">要计算闭包的项集。</param>
/// <param name="first">非终结符号的 FIRST 集合。</param>
private static void LR1Closure(LRItemCollection <T> items,
Dictionary <Symbol <T>, HashSet <Terminal <T> > > first)
{
bool changed = true;
while (changed)
{
changed = false;
for (int i = 0; i < items.Count; i++)
{
LRItem <T> item = items[i];
// 项的定点右边是非终结符。
NonTerminal <T> nextSym = item.SymbolAtIndex as NonTerminal <T>;
if (nextSym == null)
{
continue;
}
int index = item.Index + 1;
Production <T> production = item.Production;
HashSet <Terminal <T> > forwards = null;
if (index < production.Body.Count)
{
forwards = new HashSet <Terminal <T> >();
Symbol <T> nNextSym = production.Body[index];
Terminal <T> tSym = nNextSym as Terminal <T>;
if (tSym != null)
{
forwards.Add(tSym);
}
else
{
forwards.UnionWith(first[nNextSym]);
if (forwards.Contains(Empty))
{
// FIRST 中包含 ε，需要被替换为 item 的向前看符号。
forwards.Remove(Empty);
forwards.UnionWith(item.Forwards);
}
}
}
else
{
forwards = item.Forwards;
}
int pCnt = nextSym.Productions.Count;
for (int j = 0; j < pCnt; j++)
{
LRItem <T> newItem = items.AddOrGet(nextSym.Productions[j], 0);
if (newItem.AddForwards(forwards) && !changed)
{
changed = true;
}
}
}
}
}
/// <summary>
/// 对向前看符号进行传播，生成 LALR(1) 项集族。
/// </summary>
/// <param name="grammar">语法规则。</param>
/// <param name="itemsets">LR(0) 项集族。</param>
/// <param name="first">非终结符号的 FIRST 集。</param>
private static void SpreadForward(Grammar <T> grammar, List <LRItemset <T> > itemsets,
Dictionary <Symbol <T>, HashSet <Terminal <T> > > first)
{
// LALR 向前看符号的传播规则。
List <Tuple <LRItem <T>, LRItem <T> > > forwardSpread = new List <Tuple <LRItem <T>, LRItem <T> > >();
int cnt = itemsets.Count;
for (int i = 0; i < cnt; i++)
{
LRItemset <T> itemset = itemsets[i];
// 计算向前看符号的传播和自发生。
foreach (LRItem <T> item in itemset.Items)
{
// 为 item 临时添加传递标志。
item.Forwards.Add(SpreadFlag);
// 当前项的集合。
LRItemCollection <T> closure = new LRItemCollection <T>()
{
item
};
LR1Closure(closure, first);
foreach (LRItem <T> closureItem in closure)
{
// 仅对定点右边有符号的项进行处理。
Symbol <T> sym = closureItem.SymbolAtIndex;
if (sym == null)
{
continue;
}
LRItemCollection <T> gotoTarget = itemsets[itemset.Goto[sym]].Items;
LRItem <T> gotoItem = gotoTarget.AddOrGet(closureItem.Production, closureItem.Index + 1);
// 自发生成的向前看符号。
gotoItem.AddForwards(closureItem.Forwards);
// 传播的向前看符号。
if (gotoItem.Forwards.Contains(SpreadFlag))
{
forwardSpread.Add(new Tuple <LRItem <T>, LRItem <T> >(item, gotoItem));
gotoItem.Forwards.Remove(SpreadFlag);
}
}
// 移除 item 的传递标志。
item.Forwards.Remove(SpreadFlag);
}
}
// 为起始符号添加向前看符号 EOF
itemsets[0].Items[0].Forwards.Add(EndOfFile);
// 需要继续传播向前看符号。
bool continueSpread = true;
while (continueSpread)
{
continueSpread = false;
foreach (Tuple <LRItem <T>, LRItem <T> > tuple in forwardSpread)
{
int oldCnt = tuple.Item2.Forwards.Count;
tuple.Item2.Forwards.UnionWith(tuple.Item1.Forwards);
if (oldCnt < tuple.Item2.Forwards.Count)
{
continueSpread = true;
}
}
}
// 根据核心项构造完整项集。
for (int i = 0; i < cnt; i++)
{
LR1Closure(itemsets[i].Items, first);
}
}