public static LrItemNfa <TTokenKind> GetLr0AutomatonNfa <TTokenKind, TNonterminal>(Grammar <TTokenKind, TNonterminal> grammar)
where TTokenKind : struct, Enum
where TNonterminal : struct, Enum
{
// NOTE: These are all synonyms for what machine we are building here
// - 'characteristic strings' recognizer
// - 'viable prefix' recognizer (αβ is the viable prefix on top of the the stack)
// - 'handle' recognizer (β is the handle on top of the stack)
// - LR(0) automaton
if (!grammar.IsAugmented)
{
throw new InvalidOperationException("The grammar should be augmented with canonical S' → S production.");
}
if (!grammar.IsReduced)
{
throw new InvalidOperationException("The grammar contains useless symbols.");
}
var startItem = new ProductionItem <TTokenKind>(grammar.Productions[0], 0, 0);
var transitions = new List <Transition <Symbol, ProductionItem <TTokenKind> > >();
var acceptItems = new List <ProductionItem <TTokenKind> >();
// (a) For every terminal a ∈ T, if A → α•aβ is a marked production, then
// there is a transition on input a from state A → α•aβ to state A → αa•β
// obtained by "shifting the dot"
// (b) For every variable B ∈ V, if A → α•Bβ is a marked production, then
// there is a transition on input B from state A → α•Bβ to state A → αB•β
// obtained by "shifting the dot", and transitions on input ε (the empty string)
// to all states B → •γ(i), for all productions B → γ(i) ∈ P with left-hand side B.
int productionIndex = 0;
foreach (var production in grammar.Productions)
{
for (int dotPosition = 0; dotPosition <= production.Tail.Count; dotPosition += 1)
{
// (productionIndex, dotPosition) is identifier
var item = new ProductionItem <TTokenKind>(production, productionIndex, dotPosition);
// (a) A → α•aβ
if (item.IsShiftItem)
{
Symbol a = item.GetDotSymbol <Terminal <TTokenKind> >();
var shiftToItem = item.WithShiftedDot();
transitions.Add(Transition.Move(item, a, shiftToItem));
}
// (b) A → α•Bβ
if (item.IsGotoItem)
{
var B = item.GetDotSymbol <Nonterminal>();
var gotoItem = item.WithShiftedDot();
transitions.Add(Transition.Move(item, (Symbol)B, gotoItem));
// closure items
foreach (var(index, productionOfB) in grammar.ProductionsFor[B])
{
var closureItem = new ProductionItem <TTokenKind>(productionOfB, index, 0);
// Expecting to see a nonterminal 'B' (of Bβ) is the same as expecting to see
// RHS grammar symbols 'γ(i)', where B → γ(i) is a production ∈ P
transitions.Add(Transition.Move(item, Symbol.Epsilon, closureItem));
}
}
// (c) A → β• (Accepting states has dot shifted all the way to the end)
if (item.IsReduceItem)
{
acceptItems.Add(item);
}
}
productionIndex += 1;
}
return(new LrItemNfa <TTokenKind>(transitions, startItem, acceptItems));
}
