Another way to think of a Scheme program is as a big machine made up of a bunch of smaller machines. For example, to make a machine that does 4 + 3 * 7, you would need one machine to multiply 3 by 7 and another to add 4 to that.


Here is a machine that can add. It can take any number of arguments at the top and returns one answer at the bottom.	Here is a machine that can multiply. It can take any number of arguments at the top and returns one answer at the bottom.

Here is how you put them together to get a machine that calculates 4 + 3 * 7:

Once you have the machine, you can write the Scheme code without too much trouble. Start at the bottom and work your way up.

At the very bottom is a + with a 4 coming in. From this, you know that the Scheme code looks something like (+ 4 ...).
The other thing coming into the + is the result from the * machine. This means the code looks more like (+ 4 (* ...)).
The * machine has 3 and 7 coming in. That's the end of the machine, so our Scheme code is (+ 4 (* 3 7)).

Now try sketching a machine that calculates square root(3² + 4²).