If Expressions

fun leap(year):
  if num-equal(num-modulo(year, 400), 0):
    true
  else if num-equal(num-modulo(year, 100), 0):
    false
  else if num-equal(num-modulo(year, 4), 0):
    true
  else:
    false
end

An if expression contains one or more branches with conditions that are checked sequentially and associated blocks of code. Once a condition produces true, the associated block is evaluated and its contents returned. No subsequent conditions will be tested. One of the conditions in the if expression must produce true or an error is thrown. Therefore, else is used to provide a branch that is evaluated when the other branches' conditions aren't satisified.

If a year is evenly divisible by 400, the first condition num-equal(num-modulo(year, 400), 0) produces true, and the associated block is evaluated, returning true.

If a year is divisible by 100, the second condition num-equal(num-modulo(year, 100), 0) produces true, and the associated block is evaluated, returning false. If this year had also been divisible by 400, the first condition would have been satisfied and the code would not have reached this point.

If a year is divisible by 4, the third condition num-equal(num-modulo(year, 4), 0) produces true, and the associated block is evaluated, returning true. Because of the previous conditions, this year isn't also divisible by 400 or 100.

Finally, if no other branches' conditions were true, the block associated with else is evaluated, representing when a year isn't divisible by 4, 100, or 400. Here, false is returned.