private static IEnumerable <Match> matchRepeatRepeat(SymbolicString s1, SymbolicString s2)
{
Debug.Assert(s1.root.isWord());
Debug.Assert(s2.root.isWord());
// Assume s1 is fully consumed
foreach (var m in allLeftMatches(s1, s2))
{
yield return(m);
}
// Assume s2 is fully consumed
foreach (var m in allLeftMatches(s2, s1))
{
yield return(m.reverse());
}
// Assume both are fully consumed
if (omegaEqual(s1.root, s2.root))
{
yield return(Match.FullMatch(ComparisonExpression.Equal(
LinearIntegerExpression.Times(s1.root.wordLength(), s1.repeat),
LinearIntegerExpression.Times(s2.root.wordLength(), s2.repeat)
)));
}
else
{
yield return(Match.FullMatch(LogicalExpression.And(
ComparisonExpression.Equal(s2.length(), 0),
ComparisonExpression.Equal(s1.length(), 0)
)));
}
}
private static IEnumerable <Match> longLeftMatches(SymbolicString s1, SymbolicString s2)
{
var l1 = s1.root.wordLength();
var l2 = s2.root.wordLength();
var g = gcd(l1, l2);
var v_beg = LinearIntegerExpression.FreshVariable();
var v_end = LinearIntegerExpression.FreshVariable();
// Split exactly at s2 root border
yield return(Match.PartialSecond(
LogicalExpression.And(
// the beginning matches the s1
ComparisonExpression.Equal(
LinearIntegerExpression.Times(l2, v_beg),
LinearIntegerExpression.Times(l1, s1.repeat)
),
// left over right bit is nonempty
ComparisonExpression.GreaterThan(
LinearIntegerExpression.Times(l2, v_end),
0
),
// beginning and end match s2
ComparisonExpression.Equal(v_beg + v_end, s2.repeat),
ComparisonExpression.GreaterThanOrEqual(v_beg, 0),
ComparisonExpression.GreaterThanOrEqual(v_end, 0)
),
SymbolicString.Repeat(s2.root, v_end)
));
// Split in the middle of s2 root
if (l2 != 1)
{
for (int i = g; i < l2; i += g)
{
var suffix = SymbolicString.Concat(s2.root.sub_strings.Skip(i));
yield return(Match.PartialSecond(
LogicalExpression.And(
ComparisonExpression.Equal(
LinearIntegerExpression.Times(l2, v_beg) + g,
LinearIntegerExpression.Times(l1, s1.repeat)
),
ComparisonExpression.GreaterThan(
LinearIntegerExpression.Times(l2, v_beg) + suffix.length(),
0
),
ComparisonExpression.Equal(v_beg + v_end + 1, s2.repeat),
ComparisonExpression.GreaterThanOrEqual(v_beg, 0),
ComparisonExpression.GreaterThanOrEqual(v_end, 0)
),
SymbolicString.Concat(suffix, SymbolicString.Repeat(s2.root, v_end))
));
}
}
}
public LinearIntegerExpression length()
{
switch (this.expression_type)
{
case SymbolicStringType.Symbol:
return(LinearIntegerExpression.Constant(1));
case SymbolicStringType.Concat:
return(LinearIntegerExpression.Plus(this.sub_strings.Select(x => x.length())));
case SymbolicStringType.Repeat:
var sub = this.root.length();
Contract.Assert(sub.isConstant());
return(LinearIntegerExpression.Times(sub.constant, this.repeat));
default:
throw new ArgumentOutOfRangeException();
}
}
public static LinearIntegerExpression operator -(LinearIntegerExpression a, LinearIntegerExpression b)
{
return(Plus(a, LinearIntegerExpression.Times(-1, b)));
}