public static IChurchBoolean IsEven(this INaturalNumber n)
{
return(n.Match(
zero: new ChurchTrue(), // 0 is even, so true
succ: p1 => p1.Match( // Match previous
zero: new ChurchFalse(), // If 0 then successor was 1
succ: p2 => p2.IsEven()))); // Eval previous' previous
}
// 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.Match(zero: new Zero(),
succ: px => y.Match(
zero: new Zero(),
succ: py =>
One
.Add(px)
.Add(py)
.Add(px.Multiply(py)))));
}
public static int Count(this INaturalNumber n)
{
return(n.Match(
zero: 0,
succ: p => 1 + p.Count()));
}
public static IChurchBoolean IsEven(this INaturalNumber n)
=> n.Match(
zero: new ChurchTrue(),
succ: p1 => p1.Match(
zero: new ChurchFalse(), // If 0 then successor was 1
succ: p2 => p2.IsEven())); // Eval previous' previous
public static IChurchBoolean IsZero(this INaturalNumber n)
=> n.Match <IChurchBoolean>(
zero: new ChurchTrue(),
succ: _ => new ChurchFalse());
public static INaturalNumber Add(this INaturalNumber x, INaturalNumber y)
=> x.Match(
zero: y,
succ: p => new Successor(p.Add(y)));
