Writing an Iterator

Start with the idea

Iterator requires only next(); everything else — map, filter, take, zip, sum — arrives as default methods. That is why a custom sequence composes with the standard library exactly like a Vec does, without any of it knowing your type exists.

Implementing Iterator means defining the type of each item and one method, next. Each call either returns Some(item) and advances internal state or returns None when the sequence is finished. The default adapters then work automatically because they are expressed in terms of repeated next calls. That is the core composability advantage: your Fibonacci can be filtered, zipped, limited, and summed like an iterator from the standard library.

Walk through the sample with initial a and b values. Record the returned value before updating the state, then compute the pair for the next call. Test the first six outputs by hand.