Lazy evaluations with generators

A function that returns a value does all of its computation and gives up control to its caller, which supplies that value. This is not the only possible behavior for a function. Instead, it can yield a value, which passes control (and the value) back to the caller but leaves the function’s state intact. Later, it can yield another value, or finally return to indicate that it is done. A function that yields is called a generator.

Generators are useful because they allow a program to defer or postpone calculating a result until it’s required. Finding the successive digits of π, for example, is hard work, and it gets harder as the number of digits increases. If you wrote a program to display the digits of π, you might calculate the first 1,000 digits. Much of that effort will be wasted if the user only asks to see the first 10 digits. Using a generator, you can put off the expensive work until your program requires the results...