public static NFA RepeatZeroOrMore(NFA input)
{
NFA nfa = new NFA();
// Add everything from the input
nfa.AddAll(input);
// Create a new starting state, link it to the old accept state with Epsilon
nfa.StartState = new NFA.State();
nfa.States.Add(nfa.StartState);
NFA.State oldAcceptState = input.States.First(f => f.AcceptState);
nfa.Transitions.Add(new Transition <NFA.State>(nfa.StartState, oldAcceptState));
// Add epsilon link from old accept state of input to start, to allow for repetition
nfa.Transitions.Add(new Transition <NFA.State>(oldAcceptState, input.StartState));
// Create new accept state, link old accept state to new accept state with epsilon
NFA.State acceptState = new NFA.State {
AcceptState = true
};
nfa.States.Add(acceptState);
oldAcceptState.AcceptState = false;
nfa.Transitions.Add(new Transition <NFA.State>(oldAcceptState, acceptState));
return(nfa);
}
protected internal NFA Copy()
{
NFA newNFA = new NFA();
Dictionary <State, State> stateMap = new Dictionary <State, State>();
foreach (State state in States)
{
State newState = new State {
AcceptState = state.AcceptState, StateNumber = state.StateNumber
};
stateMap.Add(state, newState);
newNFA.States.Add(newState);
}
foreach (Transition <State> transition in Transitions)
{
// Hard copy the valid input
Transition <State> newTransition = new Transition <State>(stateMap[transition.From], stateMap[transition.To],
transition.ValidInput);
newNFA.Transitions.Add(newTransition);
}
newNFA.StartState = stateMap[StartState];
return(newNFA);
}
private static NFA RepeatZeroOrOnce(NFA nfa)
{
// Easy enough, add an epsilon transition from the start state to the end state. Done
nfa.Transitions.Add(new Transition <NFA.State>(nfa.StartState, nfa.States.First(f => f.AcceptState)));
return(nfa);
}
public static NFA Or(NFA a, NFA b)
{
NFA nfa = new NFA();
// Composite NFA contains all the and all edges in both NFAs
nfa.AddAll(a);
nfa.AddAll(b);
// Add a start state, link to both NFAs old start state with
// epsilon links
nfa.StartState = new NFA.State();
nfa.States.Add(nfa.StartState);
nfa.Transitions.Add(new Transition <NFA.State>(nfa.StartState, a.StartState));
nfa.Transitions.Add(new Transition <NFA.State>(nfa.StartState, b.StartState));
// Add a new accept state, link all old accept states to the new accept
// state with an epsilon link and remove the accept flag
NFA.State newAcceptState = new NFA.State {
AcceptState = true
};
foreach (NFA.State oldAcceptState in nfa.States.Where(f => f.AcceptState))
{
oldAcceptState.AcceptState = false;
nfa.Transitions.Add(new Transition <NFA.State>(oldAcceptState, newAcceptState));
}
nfa.States.Add(newAcceptState);
return(nfa);
}
protected internal void AddAll(NFA nfa)
{
foreach (State state in nfa.States)
{
States.Add(state);
}
foreach (Transition <State> edge in nfa.Transitions)
{
Transitions.Add(edge);
}
}
private static NFA NumberedRepeat(NFA nfa, int minRepetitions, int maxRepetitions)
{
// To create a suitable expression, the special case of infinite max repetitions
// must be separately handled.
bool infiniteMax = false;
if (maxRepetitions == int.MaxValue)
{
infiniteMax = true;
maxRepetitions = minRepetitions;
}
else if (maxRepetitions < minRepetitions)
{
maxRepetitions = minRepetitions;
}
// Copy the NFA max repetitions times, link them together.
NFA output = nfa.Copy();
Stack <NFA.State> epsilonLinkStates = new Stack <NFA.State>();
for (int i = 1; i < maxRepetitions; ++i)
{
NFA newNfa = nfa.Copy();
if (i >= minRepetitions || (infiniteMax && i == maxRepetitions - 1))
{
epsilonLinkStates.Push(newNfa.StartState);
}
output = And(output, newNfa);
}
if (infiniteMax)
{
// Use Single to force an exception if this has gone astray
NFA.State finalState = epsilonLinkStates.Single();
// Make a little epsilon loop from the final accept state to the start state of the final state
output.Transitions.Add(new Transition <NFA.State>(output.States.Single(f => f.AcceptState), finalState));
}
else
{
// Add epsilon transitions from accept to beginning states of NFAs in the chain
NFA.State acceptState = output.States.Single(f => f.AcceptState);
while (epsilonLinkStates.Count > 0)
{
output.Transitions.Add(new Transition <NFA.State>(epsilonLinkStates.Pop(), acceptState));
}
}
return(output);
}
private static NFA RepeatOnceOrMore(NFA nfa)
{
// Add an epsilon transition from the accept state back to the start state
NFA.State oldAcceptState = nfa.States.First(f => f.AcceptState);
nfa.Transitions.Add(new Transition <NFA.State>(oldAcceptState, nfa.StartState));
// Add a new accept state, since we cannot have edges exiting the accept state
NFA.State newAcceptState = new NFA.State {
AcceptState = true
};
nfa.Transitions.Add(new Transition <NFA.State>(oldAcceptState, newAcceptState));
nfa.States.Add(newAcceptState);
// Clear the accept flag of the old accept state
oldAcceptState.AcceptState = false;
return(nfa);
}
private static NFA Accept(CharSet acceptCharacters)
{
// Generate a NFA with a simple path with one state transitioning into an accept state.
NFA nfa = new NFA();
NFA.State state = new NFA.State();
nfa.States.Add(state);
NFA.State acceptState = new NFA.State {
AcceptState = true
};
nfa.States.Add(acceptState);
nfa.Transitions.Add(new Transition <NFA.State>(state, acceptState, acceptCharacters));
nfa.StartState = state;
return(nfa);
}
public static NFA Merge(IList <NFA> nfas)
{
// Create a new NFA, add everything to it.
NFA merged = new NFA();
foreach (NFA nfa in nfas)
{
merged.AddAll(nfa);
}
// Add a new start state
State state = new State();
merged.States.Add(state);
merged.StartState = state;
// Add epsilon transiontions from the start state to all the previous start states
foreach (NFA nfa in nfas)
{
merged.Transitions.Add(new Transition <State>(state, nfa.StartState));
}
return(merged);
}
public static NFA And(NFA first, NFA second)
{
// Create a new NFA and use the first NFAs start state as the starting point
NFA nfa = new NFA {
StartState = first.StartState
};
// Change all links in to first acceptstate to go to seconds
// start state
foreach (Transition <NFA.State> edge in first.Transitions.Where(f => f.To.AcceptState))
{
edge.To = second.StartState;
}
// Remove acceptstate from first
first.States.Remove(first.States.First(f => f.AcceptState));
// Add all states and edges in both NFAs
// Second NFA already has an accept state, there is no need to create another one
nfa.AddAll(first);
nfa.AddAll(second);
return(nfa);
}
public static NFA Create(ShuntingYard yard, bool ignorecase)
{
Stack <NFA> stack = new Stack <NFA>();
foreach (RegExToken token in yard.ShuntedTokens(ignorecase))
{
try
{
switch (token.Type)
{
case RegExToken.TokenType.OperatorMul:
stack.Push(RepeatZeroOrMore(stack.Pop()));
break;
case RegExToken.TokenType.OperatorQuestion:
stack.Push(RepeatZeroOrOnce(stack.Pop()));
break;
case RegExToken.TokenType.OperatorOr:
stack.Push(Or(stack.Pop(), stack.Pop()));
break;
case RegExToken.TokenType.OperatorPlus:
stack.Push(RepeatOnceOrMore(stack.Pop()));
break;
case RegExToken.TokenType.Accept:
stack.Push(Accept(token.Characters));
break;
case RegExToken.TokenType.OperatorConcat:
// & is not commutative, and the stack is reversed.
NFA second = stack.Pop();
NFA first = stack.Pop();
stack.Push(And(first, second));
break;
case RegExToken.TokenType.NumberedRepeat:
stack.Push(NumberedRepeat(stack.Pop(), token.MinRepetitions, token.MaxRepetitions));
break;
default:
throw new LexerConstructionException("Unknown operator!");
}
}
catch (InvalidOperationException) when(stack.Count == 0) // stack popping failed
{
FieldInfo field = typeof(StringReader).GetField("_s", BindingFlags.Instance | BindingFlags.NonPublic);
TextReader reader = yard.lexer.input;
throw new LexerConstructionException($"Malformed regexp expression: '{field.GetValue(reader)}'");
}
}
// We should end up with only ONE NFA on the stack or the expression is malformed.
if (stack.Count != 1)
{
throw new LexerConstructionException("Malformed regexp expression!");
}
// Pop it from the stack, and assign each state a number, primarily for debugging purposes,
// they dont _really_ need it. The state numbers actually used are the one used in the DFA.
NFA nfa = stack.Pop();
nfa.AssignStateNumbers();
return(nfa);
}
public static DFA Create(NFA nfa)
{
var closures = nfa.GetAllClosures();
// The valid input ranges that the NFA contains will need to be split up so that
// the smallest possible units which NEVER overlaps will be contained in each of the
// states
nfa.DistinguishValidInputs();
// Get the closure set of S0
var dfa = new DFA();
dfa.States.Add(new State(closures[nfa.StartState]));
while (true)
{
// Get an unmarked state in dfaStates
var t = dfa.States.FirstOrDefault(f => !f.Mark);
if (null == t)
{
// We're done!
break;
}
t.Mark = true;
// Get the move states by stimulating this DFA state with
// all possible characters.
var fromTransitions = nfa.Transitions.Where(f => t.NfaStates.Contains(f.From)).ToArray();
var moveDestinations = new Dictionary <CharRange, List <NFA.State> >();
foreach (var fromTransition in fromTransitions)
{
foreach (var range in fromTransition.ValidInput.Ranges)
{
List <NFA.State> destList;
if (!moveDestinations.TryGetValue(range, out destList))
{
destList = new List <NFA.State>();
moveDestinations.Add(range, destList);
}
destList.Add(fromTransition.To);
}
}
foreach (CharRange c in t.LegalMoves(fromTransitions))
{
var moveSet = moveDestinations[c];
if (moveSet.Any())
{
// Get the closure of the move set. This is the NFA states that will form the new set
ISet <NFA.State> moveClosure = new HashSet <NFA.State>();
foreach (var moveState in moveSet)
{
moveClosure.UnionWith(closures[moveState]);
}
var newState = new State(moveClosure);
// See if the new state already exists. If so change the reference to point to
// the already created object, since we will need to add a transition back to the same object
var oldState = dfa.States.FirstOrDefault(f => f.NfaStates.SetEquals(newState.NfaStates));/* f.NfaStates.Count == newState.NfaStates.Count &&
* !f.NfaStates.Except(newState.NfaStates).Any() &&
* !newState.NfaStates.Except(f.NfaStates).Any());*/
if (oldState == null)
{
dfa.States.Add(newState);
}
else
{
// New state wasn't that new. We already have one exacly like it in the DFA. Set
// netstate to oldstate so that the created transition will be correct (still need to
// create a transition)
newState = oldState;
}
// See if there already is a transition. In that case, add our character to the list
// of valid values
var transition = dfa.Transitions.SingleOrDefault(f => f.From == t && f.To == newState);
if (transition == null)
{
// No transition has been found. Create a new one.
transition = new Transition <State>(t, newState);
dfa.Transitions.Add(transition);
}
transition.ValidInput.AddRange(c.From, c.To, false);
}
}
}
dfa.StartState = dfa.States[0];
dfa.AssignStateNumbers();
return(dfa);
}
