// return (R[i])(R[i+1])....(R[len-1])
private RegEx <T> ConcatRegexes(int depth)
{
if (depth == Regexes.Length - 1)
{
return(Regexes [depth]);
}
return(RegExFactory.Concat(Regexes [depth], ConcatRegexes(depth + 1)));
}
// inter( X1, ... )^a = inter( X1^a, ... )
public override RegEx <T> Derivative(T c)
{
var derivatives = new List <RegEx <T> >();
foreach (var i in Regexes)
{
derivatives.Add(i.Derivative(c));
}
return(RegExFactory.Intersection(derivatives.ToArray()));
}
private static RegEx <char> ParseConcat()
{
var left = ParseStar();
if (left == null)
{
return(null);
}
var right = ParseConcat();
if (right != null)
{
return(RegExFactory.Concat(left, right));
}
return(left);
}
private RegEx <T> ComputeDerivative(int depth, T c)
{
// the last one
if (depth == Regexes.Length - 1)
{
return(Regexes[depth].Derivative(c));
}
// (R[i])^a(R[i+1])....
var this_level = RegExFactory.Concat(
Regexes [depth].Derivative(c),
ConcatRegexes(depth + 1)
);
// first can be skipped
if (Regexes [depth].HasEpsilon())
{
return(RegExFactory.Union(this_level, ComputeDerivative(depth + 1, c)));
}
// cannot be skipped
return(this_level);
}
private static RegEx <char> ParseBinaryOperators()
{
var left = ParseConcat();
bool union = false, intersection = false;
union |= HasPrefix("|");
intersection |= HasPrefix("&");
if (union || intersection)
{
Eat(1);
var right = ParseBinaryOperators();
if (right == null)
{
throw new ParseError("Missed one of the union/intersection argument.");
}
return(union ? RegExFactory.Union(left, right) : RegExFactory.Intersection(left, right));
}
return(left);
}
private static RegEx <char> ParseStar()
{
var left = ParseAtom();
if (HasPrefix("*") || HasPrefix("+"))
{
bool star = false;
while (HasPrefix("*") || HasPrefix("+"))
{
star |= HasPrefix("+");
Eat(1);
}
if (left == null)
{
throw new ParseError("Unassigned +/-.");
}
return(star ? RegExFactory.Concat(left, RegExFactory.Star(left)) : RegExFactory.Star(left));
}
return(left);
}
// epsi^a = empty ?
public override RegEx <T> Derivative(T c)
{
return(RegExFactory.Empty <T>());
}
// [a...) = sum( {a}, {a+1}, {a+2}, ... )
// [a...)^x = sum( {a}, ... )^x = sum( {a}^x, {a+1}^x, ... )
// = epsilon if x >= a else empty
public override RegEx <T> Derivative(T c)
{
return(Character.CompareTo(c) <= 0 ? RegExFactory.Epsilon <T>() : RegExFactory.Empty <T>());
}
// star(X)^a = concat(X^a, star(X))
public override RegEx <T> Derivative(T c)
{
return(RegExFactory.Concat(Regex.Derivative(c), RegExFactory.Star(Regex)));
}
// (~X)^a = ~(X^a)
public override RegEx <T> Derivative(T c)
{
return(RegExFactory.Complement(Regex.Derivative(c)));
}
private static RegEx <char> SingleChar(char c)
{
return(RegExFactory.Range(c, (char)(c + 1)));
}
private static RegEx <char> Sanitize(RegEx <char> result)
{
return(RegExFactory.Intersection(result, RegExFactory.Star(CharactersClasses.print)));
}
private static RegEx <char> ParseAtom()
{
if (HasPrefix("["))
{
Eat(1);
bool complement = false;
if (HasPrefix("^"))
{
Eat(1);
complement = true;
}
RegEx <char> atom = null;
if (HasPrefix(":digit:"))
{
atom = CharactersClasses.digit;
}
if (HasPrefix(":print:"))
{
atom = CharactersClasses.print;
}
if (HasPrefix(":space:"))
{
atom = CharactersClasses.space;
}
if (atom == null)
{
List <RegEx <char> > chars = new List <RegEx <char> > ();
char ch;
while ((ch = Peek()) != ']')
{
if (ch.Equals('\\'))
{
Accept("]");
chars.Add(SingleChar(']'));
}
else
{
chars.Add(SingleChar(ch));
}
}
atom = RegExFactory.Union(chars.ToArray());
}
else
{
Eat(7);
Accept("]");
}
if (complement)
{
return(RegExFactory.Intersection(RegExFactory.Range((char)0), RegExFactory.Complement(atom)));
}
else
{
return(atom);
}
}
if (HasPrefix("."))
{
Eat(1);
return(RegExFactory.Range((char)0));
}
if (HasPrefix("("))
{
Eat(1);
var node = ParseBinaryOperators();
if (node == null)
{
throw new ParseError("Parentheses around the null expression.");
}
Accept(")");
return(node);
}
if (HasPrefix("^"))
{
Eat(1);
var node = ParseAtom();
if (node == null)
{
throw new ParseError("Unassigned ^.");
}
return(RegExFactory.Complement(node));
}
if (HasPrefix("\\"))
{
Eat(1);
char a = Peek();
if (!specialCharacters.Contains("" + a))
{
throw new ParseError("Special character required.");
}
return(SingleChar(a));
}
if (HasNext())
{
var a = Peek();
if (specialCharacters.Contains("" + a))
{
--head;
return(null);
}
return(SingleChar(a));
}
return(null);
}