gravity language

gravity.md

The gravity language operates on a stack and has three basic operations:

• Z_i sets the i th element of the stack to zero
• I_i increments the i th element by one
• J_i,j compares the i th and j th elements and jumps if not equal

The stack looks like this:

+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
  0   1   2   3   4   5   6   7

Assume you want to write an algorithm that compares two numbers and returns 1 if the former is greater than the latter. Let's pick 2 and 3. You can load the number 2 on the stack like this:

1. Z₀
2. I₀
3. I₀

+---+---+---+---+---+---+---+---+
| 2 |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
0   1   2   3   4   5   6   7

This will load the number 3 on the stack:

1. Z₁
2. I₁
3. I₁
4. I₁

+---+---+---+---+---+---+---+---+
| 2 | 3 |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
0   1   2   3   4   5   6   7

We can compare the numbers in position 0 and 1 and if they're different we jump and execute a different instruction:

1. Z₄
2. J_0,1 JUMP TO 4
3. END
4. I₄
5. END

+---+---+---+---+---+---+---+---+
| 2 | 3 |   |   | 1 |   |   |   |
+---+---+---+---+---+---+---+---+
  0   1   2   3   4   5   6   7

Great, we just compared 2 numbers!

You're now familiar with the gravity language. Can you write an algorithm that sums two numbers?