private static Dictionary <Nonterminal, Set <Terminal <TTokenKind> > > ComputeFollow(
Grammar <TTokenKind, TNonterminal> grammar,
IFirstSymbolsAnalyzer <TTokenKind> analyzer)
{
var(initFollowSets, graph) = DigraphAlgorithm.GetFollowGraph(grammar, analyzer);
var followSets = DigraphAlgorithm.Traverse(graph, initFollowSets);
var followMap = grammar.Nonterminals.ToDictionary(v => v, v => followSets[v.Index]);
return(followMap);
}
// TODO: Insert into symbols overload
// FIRST can be thought of as the extension of START, but often FIRST is defined for both single symbols
// and sentential forms. That is FIRST is extended to all grammar symbols (i.e. sentential forms)
// The FIRST function is a simple extension of START (single symbol) to the domain of sentential forms.
// FIRST(α) = { x ∈ T | α ∗⇒ xβ }
// An alternative definition which shows how to derive FIRST from START recursively is
// FIRST(X1X2...Xk) = START(X1) ∪ FIRST(X2...Xk), if X1 is nullable
// FIRST(X1X2...Xk) = START(X1) otherwise
// FIRST(ε) = Ø = { }
/// <summary>
/// The First function yields the set of starter symbols for a sequence of grammar symbols. It is formally
/// defined as
/// FIRST(α) = { a ∈ T | α ∗⇒ aβ }
/// for any sentential form α ∈ (T ∪ N)*. We have therefore extended the set-valued function to all sentential forms.
/// </summary>
/// <param name="analyzer"></param>
/// <param name="symbols">The sequence of symbols (possibly empty, aka epsilon)</param>
public static IReadOnlySet <Terminal <TTokenKind> > First <TTokenKind>(
this IFirstSymbolsAnalyzer <TTokenKind> analyzer,
IEnumerable <Symbol> symbols) where TTokenKind : struct, Enum
{
// If α is any string of grammar symbols, let First(α) be the set of terminals that begin the
// strings derived from α. In some texts (dragon book) if α *=> ε, then ε is also in First(α).
// We prefer to keep nullable in a separate Erasable function.
var first = new Set <Terminal <TTokenKind> >();
foreach (var symbol in symbols)
{
first.AddRange(analyzer.First(symbol));
if (!analyzer.Erasable(symbol))
{
break;
}
}
return(first);
}
