static void _Concat(FA <TInput, TAccept> lhs, FA <TInput, TAccept> rhs)
{
var f = lhs.FirstAcceptingState;
lhs.FirstAcceptingState.EpsilonTransitions.Add(rhs);
f.Accept = default(TAccept);
f.IsAccepting = false;
}
/// <summary>
/// Creates a new FA that matches the specified FA expression or empty
/// </summary>
/// <param name="expr">The expression to make optional</param>
/// <param name="accept">The symbol to accept</param>
/// <returns>A new FA that will match the specified expression or empty</returns>
public static FA <TInput, TAccept> Optional(FA <TInput, TAccept> expr, TAccept accept = default(TAccept))
{
var result = expr.Clone();
var f = result.FirstAcceptingState;
f.Accept = accept;
f.IsAccepting = true;
result.EpsilonTransitions.Add(f);
return(result);
}
/// <summary>
/// Creates a finite state machine that represents the LL(k) parsing rules
/// </summary>
/// <returns></returns>
public FA <string, CfgRule> ToLLkFsm()
{
var predict = FillPredict();
var follows = FillFollows();
var nts = FillNonTerminals();
var result = new FA <string, CfgRule>();
for (int ic = nts.Count, i = 0; i < ic; i++)
{
var nt = nts[i];
var fa = new FA <string, CfgRule>();
result.Transitions.Add(nt, fa);
foreach (var p in predict[nt])
{
if (null != p.Symbol)
{
var ffa = new FA <string, CfgRule>();
ffa.IsAccepting = true;
ffa.Accept = p.Rule;
FA <string, CfgRule> fad;
if (fa.Transitions.TryGetValue(p.Symbol, out fad))
{
System.Diagnostics.Debugger.Break();
fa.Transitions.Remove(p.Symbol);
//
// FIRST FIRST conflict
}
else
{
fa.Transitions.Add(p.Symbol, ffa);
}
}
else
{
foreach (var f in follows[nt])
{
var ffa = new FA <string, CfgRule>();
ffa.IsAccepting = true;
ffa.Accept = p.Rule;
FA <string, CfgRule> fad;
if (fa.Transitions.TryGetValue(f, out fad))
{
System.Diagnostics.Debugger.Break();
// FIRST FOLLOW conflict
}
fa.Transitions.Add(f, ffa);
}
}
}
}
return(result);
}
/// <summary>
/// Creates an FA that will match any one of a set of a characters
/// </summary>
/// <param name="set">The set of characters that will be matched</param>
/// <param name="accept">The symbol to accept</param>
/// <returns>An FA that will match the specified set</returns>
public static FA <TInput, TAccept> Set(IEnumerable <TInput> set, TAccept accept = default(TAccept))
{
var result = new FA <TInput, TAccept>();
var final = new FA <TInput, TAccept>();
final.Accept = accept;
final.IsAccepting = true;
foreach (TInput ch in set)
{
result.Transitions.Add(ch, final);
}
return(result);
}
/// <summary>
/// Creates an FA that matches a literal string
/// </summary>
/// <param name="string">The string to match</param>
/// <param name="accept">The symbol to accept</param>
/// <returns>A new FA machine that will match this literal</returns>
public static FA <TInput, TAccept> Literal(IEnumerable <TInput> @string, TAccept accept = default(TAccept))
{
var result = new FA <TInput, TAccept>();
var current = result;
foreach (TInput ch in @string)
{
current.Accept = default(TAccept);
current.IsAccepting = false;
var fa = new FA <TInput, TAccept>();
fa.Accept = accept;
fa.IsAccepting = true;
current.Transitions.Add(ch, fa);
current = fa;
}
return(result);
}
/// <summary>
/// Creates a new FA that matche any one of the FA expressions passed
/// </summary>
/// <param name="exprs">The expressions to match</param>
/// <param name="accept">The symbol to accept</param>
/// <returns>A new FA that will match the union of the FA expressions passed</returns>
public static FA <TInput, TAccept> Or(IEnumerable <FA <TInput, TAccept> > exprs, TAccept accept = default(TAccept))
{
var result = new FA <TInput, TAccept>();
var final = new FA <TInput, TAccept>();
final.Accept = accept;
final.IsAccepting = true;
foreach (var fa in exprs)
{
fa.EpsilonTransitions.Add(fa);
var nfa = fa.Clone();
var nffa = fa.FirstAcceptingState;
nfa.FirstAcceptingState.EpsilonTransitions.Add(final);
nffa.Accept = default(TAccept);
nffa.IsAccepting = false;
}
return(result);
}
public FA <TInput, TAccept> ToDfa()
{
// The DFA states are keyed by the set of NFA states they represent.
var dfaMap = new Dictionary <List <FA <TInput, TAccept> >, FA <TInput, TAccept> >(_SetComparer.Default);
var unmarked = new HashSet <FA <TInput, TAccept> >();
// compute the epsilon closure of the initial state in the NFA
var states = new List <FA <TInput, TAccept> >();
FillEpsilonClosure(states);
// create a new state to represent the current set of states. If one
// of those states is accepting, set this whole state to be accepting.
FA <TInput, TAccept> dfa = new FA <TInput, TAccept>();
var al = new List <TAccept>();
foreach (var fa in states)
{
if (fa.IsAccepting)
{
if (!al.Contains(fa.Accept))
{
al.Add(fa.Accept);
}
}
}
int ac = al.Count;
if (1 == ac)
{
dfa.Accept = al[0];
dfa.IsAccepting = true;
}
else if (1 < ac)
{
// TODO: Give a detailed error message of the conflict
throw new InvalidOperationException("Ambiguity in the FA.");
}
FA <TInput, TAccept> result = dfa; // store the initial state for later, so we can return it.
// add it to the dfa map
dfaMap.Add(states, dfa);
// add it to the unmarked states, signalling that we still have work to do.
unmarked.Add(dfa);
bool done = false;
while (!done)
{
done = true;
HashSet <List <FA <TInput, TAccept> > > mapKeys = new HashSet <List <FA <TInput, TAccept> > >(dfaMap.Keys, _SetComparer.Default);
foreach (List <FA <TInput, TAccept> > mapKey in mapKeys)
{
dfa = dfaMap[mapKey];
if (unmarked.Contains(dfa))
{
// when we get here, mapKey represents the epsilon closure of our
// current dfa state, which is indicated by kvp.Value
// build the transition list for the new state by combining the transitions
// from each of the old states
// retrieve every possible input for these states
HashSet <TInput> inputs = new HashSet <TInput>();
foreach (FA <TInput, TAccept> state in mapKey)
{
foreach (var inp in state.Transitions.Keys)
{
inputs.Add(inp);
}
}
foreach (var input in inputs)
{
var acc = new List <TAccept>();
List <FA <TInput, TAccept> > ns = new List <FA <TInput, TAccept> >();
foreach (var state in mapKey)
{
FA <TInput, TAccept> dst = null;
if (state.Transitions.TryGetValue(input, out dst))
{
foreach (var d in dst.FillEpsilonClosure())
{
if (d.IsAccepting)
{
if (!acc.Contains(d.Accept))
{
acc.Add(d.Accept);
}
}
if (!ns.Contains(d))
{
ns.Add(d);
}
}
}
}
FA <TInput, TAccept> ndfa;
if (!dfaMap.TryGetValue(ns, out ndfa))
{
ndfa = new FA <TInput, TAccept>();
ac = acc.Count;
if (1 == ac)
{
ndfa.Accept = acc[0];
ndfa.IsAccepting = true;
}
else if (1 < ac)
{
// TODO: Give a detailed error message of the conflict
throw new InvalidOperationException("Ambiguity in the FA.");
}
else
{
ndfa.Accept = default(TAccept);
}
dfaMap.Add(ns, ndfa);
unmarked.Add(ndfa);
done = false;
}
dfa.Transitions.Add(input, ndfa);
}
unmarked.Remove(dfa);
}
}
}
return(result);
}