/// <summary>
/// Compute the LR(1) closure including lookaheads in the item sets (page 261 of Compilers 2nd Ed.)
/// </summary>
private LrItemSet Lr1Closure(SymbolMetaDictionary symbolMeta, LrItemSet items)
{
// Initialize the return set to the item set
var newset = new LrItemSet(items)
{
IsClosed = true
};
var toAdd = new List <LrItem>();
var newLookaheads = new HashSet <SymbolId>();
do
{
toAdd.Clear();
// For each item in the set with a marker before a nonterminal
foreach (var item in newset.Where(i => (i.Marker < i.Length) && (this.symbols[i.Rule.RuleSymbolIds[i.Marker]] == SymbolKind.Nonterminal)))
{
var nonterminal = item.Rule.RuleSymbolIds[item.Marker];
// Get all the possible lookaheads past this symbol
newLookaheads.Clear();
foreach (var lookahead in item.LookaheadIds)
{
var followingSymbols = item.Rule.RuleSymbolIds.Skip(item.Marker + 1).Append(lookahead);
newLookaheads.UnionWith(symbolMeta.FirstOfAll(followingSymbols));
}
if (newLookaheads.Any())
{
// For each rule of the production past the marker for this item
toAdd.AddRange(this.ProductionRulesBySymbol[nonterminal].Select(rule => new LrItem(rule, 0, false, newLookaheads)));
}
}
} while ((toAdd.Count > 0) && newset.MergeWith(toAdd));
return(newset);
}
/// <summary>
/// Time- and space-optimized goto which returns gotos for all relevant symbols, storing kernels only.
/// For this function, the input state must have its closure production heads computed (with LR0ComputeClosureNonterminals).
/// The output states do not have closure productions.
/// </summary>
private Dictionary <SymbolId, LrItemSet> Lr0GotoKernels(LrItemSet itemSet)
{
if (itemSet.ClosureProductions == null)
{
throw new InvalidOperationException();
}
// Create new items by advancing the marker for the input kernels
var kernelItems = itemSet
.Kernels
.Where(k => k.Marker < k.Length)
.Select(k => new KeyValuePair <SymbolId, LrItem>(k.Rule.RuleSymbolIds[k.Marker], new LrItem(k.Rule, k.Marker + 1, true)));
// Create new items from the nonkernels (using closure production heads)
// Since goto is to be computed for ALL symbols, advance the marker for all nonkernels
// The first item in the rule is the goto symbol, and the marker is advanced past the first item
var nonKernelItems = itemSet
.ClosureProductions
.SelectMany(n => this.ProductionRulesBySymbol[n])
.Where(r => r.RuleSymbolIds.Count > 0)
.Select(r => new KeyValuePair <SymbolId, LrItem>(r.RuleSymbolIds[0], new LrItem(r, 1, true)));
// The dictionary will contain item sets for all possible goto symbols X, Y, and Z for the given input state
return(kernelItems
.Concat(nonKernelItems)
.GroupBy(t => t.Key, t => t.Value)
.ToDictionary(g => g.Key, g => new LrItemSet(g)));
}
private void Lr0ComputeClosureNonterminals(LrItemSet itemSet)
{
if (itemSet.ClosureProductions != null)
{
return;
}
// Initialize the set with the next symbol at each marker
var nonterminalSet = new HashSet <SymbolId>(MarkedSymbols(itemSet).Where(this.IsNonterminal));
var queue = new Queue <SymbolId>(nonterminalSet);
while (queue.Count > 0)
{
var current = queue.Dequeue();
// Get the first nonterminal from rules starting with these
foreach (var nonterminal in FirstSymbols(this.ProductionRulesBySymbol[current]).Where(this.IsNonterminal).Distinct())
{
if (nonterminalSet.Add(nonterminal))
{
// New production, add it to the closure
queue.Enqueue(nonterminal);
}
}
}
itemSet.ClosureProductions = nonterminalSet;
}
private void ComputeLr0ItemSetKernelsAndGotoLookup(out LrItemSetCollection itemSets, out Dictionary <int, Dictionary <SymbolId, int> > gotos, out int acceptIndex)
{
itemSets = new LrItemSetCollection();
gotos = new Dictionary <int, Dictionary <SymbolId, int> >();
var itemSetByKernels = new Dictionary <IEnumerable <LrItem>, LrItemSet>(SetEqualityComparer <LrItem> .Default);
var queue = new Queue <LrItemSet>();
var startItem = new LrItemSet(new LrItem(this.ProductionRulesBySymbol[this.Init].Single(), 0, true));
this.Lr0ComputeClosureNonterminals(startItem);
itemSets.StartState = startItem;
acceptIndex = this.ProductionRulesBySymbol[this.Init].Single().Index;
startItem.Index = itemSets.Count;
itemSets.Add(startItem);
itemSetByKernels.Add(startItem.Kernels.ToArray(), startItem);
queue.Enqueue(startItem);
while (queue.Count > 0)
{
var itemSet = queue.Dequeue();
var gotoLookup = this.Lr0GotoKernels(itemSet);
var gotosForState = new Dictionary <SymbolId, int>();
gotos.Add(itemSet.Index, gotosForState);
foreach (var symbol in gotoLookup.Keys)
{
if (!itemSetByKernels.TryGetValue(gotoLookup[symbol].Kernels, out var gotoState))
{
gotoState = gotoLookup[symbol];
this.Lr0ComputeClosureNonterminals(gotoState);
gotoState.Index = itemSets.Count;
itemSets.Add(gotoState);
itemSetByKernels.Add(gotoState.Kernels.ToArray(), gotoState);
queue.Enqueue(gotoState);
}
gotosForState.Add(symbol, gotoState.Index);
}
}
}
private LrItemSetCollection ComputeItemSets(SymbolMetaDictionary symbolMeta, out int acceptIndex)
{
this.ComputeLr0ItemSetKernelsAndGotoLookup(out var itemSets, out var gotoSymbol, out acceptIndex);
var dummyLookahead = new[] { this.Unknown };
itemSets.StartState.Single().LookaheadIds.Add(this.Eof);
var rulePropagations = new Dictionary <StateKey <LrItem>, HashSet <StateKey <LrItem> > >();
foreach (var itemSet in itemSets)
{
var gotosForState = gotoSymbol[itemSet.Index];
foreach (var kernelItem in itemSet)
{
var itemKey = new StateKey <LrItem>(itemSet.Index, kernelItem);
// Create an item set with a dummy lookahead, based on the current item set
var dummyItem = new LrItem(kernelItem.Rule, kernelItem.Marker, kernelItem.Marker > 0, dummyLookahead);
var dummyItemSet = new LrItemSet(dummyItem.Yield());
var j = this.Lr1Closure(symbolMeta, dummyItemSet);
foreach (var gotoForState in gotosForState)
{
var gotoItemSet = itemSets[gotoForState.Value];
var gotoItemLookup = gotoItemSet.ToDictionary(g => g, g => g);
// Find the items in the dummy set with the marker before this symbol
foreach (var b in j.Where(bb => (bb.Marker < bb.Length) && bb.Rule.RuleSymbolIds[bb.Marker].Equals(gotoForState.Key)))
{
// Get the item corresponding to the goto state with the marker past the current symbol
var gotoItem = gotoItemLookup[new LrItem(b.Rule, b.Marker + 1, true)];
if (b.LookaheadIds.Any(l => l == this.Unknown))
{
if (!rulePropagations.ContainsKey(itemKey))
{
rulePropagations[itemKey] = new HashSet <StateKey <LrItem> >();
}
rulePropagations[itemKey].Add(new StateKey <LrItem>(gotoItemSet.Index, gotoItem));
}
gotoItem.LookaheadIds.UnionWith(b.LookaheadIds.Where(l => l != this.Unknown));
}
}
}
}
bool changed;
do
{
changed = false;
foreach (var itemSet in itemSets)
{
foreach (var item in itemSet)
{
var itemKey = new StateKey <LrItem>(itemSet.Index, item);
if (!rulePropagations.TryGetValue(itemKey, out var propagated))
{
continue;
}
foreach (var key in propagated)
{
if (key.Value.LookaheadIds.AddRange(item.LookaheadIds))
{
changed = true;
}
}
}
}
} while (changed);
// Close all kernels
for (var i = 0; i < itemSets.Count; i++)
{
itemSets[i] = this.Lr1Closure(symbolMeta, itemSets[i]);
itemSets[i].Index = i;
}
return(itemSets);
}
