Page 3: Even Numbers and Keep

We want a block that takes a list of numbers as input, and reports a list of just the even numbers from the input.

You already know how to write this block using the keep higher-order function, but here’s what it looks like using recursion:

Here there are threepossible cases to consider, not just the usual base case and recursive case. There’s still a base case, namely an empty input list, in which case we report an empty list. But there are tworecursive cases, depending on whether or not the first item of the list is even. (There has to be a first item, if we’re not in the base case.) The green Operators blocks above take the remainder on dividing the first number by 2, and see if that remainder is 0, in which case the number is even.

If the first number is even, then we want to include that number in the result. So we report that number in front of the recursive call on the rest of the numbers. If the first number isn’t even, then we don’twant to include it in the result, so we simply report the value reported by the recursive call.