// The formula used here is
// x * y = 1 + (x - 1) + (y - 1) + ((x - 1) * (y - 1))
// It follows like this:
// x* y =
// (x - 1 + 1) * (y - 1 + 1) =
// ((x - 1) + 1) * ((y - 1) + 1) =
// ((x - 1) * (y - 1)) + ((x - 1) * 1) + ((y - 1) * 1) + 1 * 1 =
// ((x - 1) * (y - 1)) + (x - 1) + (y - 1) + 1
public static INaturalNumber Multiply(
this INaturalNumber x,
INaturalNumber y)
{
return(x.Accept(new MultiplyNaturalNumberVisitor(y)));
}
public static INaturalNumber Add(
this INaturalNumber x,
INaturalNumber y)
{
return(x.Accept(new AddNaturalNumberVisitor(y)));
}
public IChurchBoolean VisitSucc(INaturalNumber predecessor)
{
// Match previous
return(predecessor.Accept(
new IsEvenPredecessorNaturalNumberVisitor()));
}
// More memmbers go here...
public static int Count(this INaturalNumber n)
{
return(n.Accept(new CountNaturalNumberVisitor()));
}
public static IChurchBoolean IsEven(this INaturalNumber n)
{
return(n.Accept(new IsEvenNaturalNumberVisitor()));
}