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@@ -1,4 +1,149 @@
 // Rust-101, Part 09: Iterators
 // ============================
 
-// [index](main.html) | [previous](part08.html) | [next](main.html)
+use part05::BigInt;
+
+//@ In the following, we will look into the iterator mechanism of Rust and make our `BigInt` compatible
+//@ with the `for` loops. Of course, this is all about implementing certain traits again. In particular,
+//@ an iterator is something that implements the `Iterator` trait. As you can see in [the documentation](https://doc.rust-lang.org/stable/std/iter/trait.Iterator.html),
+//@ this trait mandates a single function `next` returning an `Option<Self::Item>`, where `Item` is an
+//@ associated type chosen by the implementation. (There are many more methods provided for `Iterator`,
+//@ but they all have default implementations, so we don't have to worry about them right now.)
+//@ 
+//@ For the case of `BigInt`, we want our iterator to iterate over the digits in normal, notational order: The most-significant
+//@ digit comes first. So, we have to write down some type, and implement `Iterator` for it such that `next` returns the digits
+//@ one-by-one. Clearly, the iterator must somehow be able to access the number it iterates over, and it must store its current
+//@ location. However, it cannot *own* the `BigInt`, because then the number would be gone after iteration! That'd certainly be bad.
+//@ The only alternative is for the iterator to *borrow* the number, so it takes a reference.
+
+//@ In writing this down, we again have to be explicit about the lifetime of the reference: We can't just have an
+//@ `Iter`, we must have an `Iter<'a>` that borrows the number for lifetime `'a`. This is our first example of
+//@ a data-type that's polymorphic in a lifetime, as opposed to a type. <br/>
+//@ `usize` here is the type of unsigned, pointer-sized numbers. It is typically the type of "lengths of things",
+//@ in particular, it is the type of the length of a `Vec` and hence the right type to store an offset into the vector of digits.
+pub struct Iter<'a> {
+    num: &'a BigInt,
+    idx: usize, // the index of the last number that was returned
+}
+
+// Now we are equipped to implement `Iterator` for `Iter`.
+impl<'a> Iterator for Iter<'a> {
+    // We choose the type of things that we iterate over to be the type of digits, i.e., `u64`.
+    type Item = u64;
+
+    fn next(&mut self) -> Option<u64> {
+        // First, check whether there's any more digits to return.
+        if self.idx == 0 {
+            // We already returned all the digits, nothing to do.
+            None                                                    /*@*/
+        } else {
+            // Otherwise: Decrement, and return next digit.
+            self.idx = self.idx - 1;                                /*@*/
+            Some(self.num.data[self.idx])                           /*@*/
+        }
+    }
+}
+
+// All we need now is a function that creates such an iterator for a given `BigInt`.
+impl BigInt {
+    //@ Notice that when we write the type of `iter`, we don't actually have to give the lifetime parameter of `Iter`. Just as it is
+    //@ the case with functions returning references, you can elide the lifetime. The rules for adding the lifetimes are exactly the
+    //@ same. (See the last section of [part 06](part06.html).)
+    fn iter(&self) -> Iter {
+        Iter { num: self, idx: self.data.len() }                    /*@*/
+    }
+}
+
+// We are finally ready to iterate! Remember to edit `main.rs` to run this function.
+pub fn main() {
+    let b = BigInt::new(1 << 63) + BigInt::new(1 << 16) + BigInt::new(1 << 63);
+    for digit in b.iter() {
+        println!("{}", digit);
+    }
+}
+
+// Of course, we don't have to use `for` to apply the iterator. We can also explicitly call `next`.
+fn print_digits_v1(b: &BigInt) {
+    let mut iter = b.iter();
+    //@ `loop` is the keyword for a loop without a condition: It runs endlessly, or until you break out of
+    //@ it with `break` or `return`.
+    loop {
+        // Each time we go through the loop, we analyze the next element presented by the iterator - until it stops.
+        match iter.next() {                                         /*@*/
+            None => break,                                          /*@*/
+            Some(digit) => println!("{}", digit)                    /*@*/
+        }                                                           /*@*/
+    }
+}
+
+//@ Now, it turns out that this combination of doing a loop and a pattern matching is fairly common, and Rust
+//@ provides some convenient syntactic sugar for it.
+fn print_digits_v2(b: &BigInt) {
+    let mut iter = b.iter();
+    //@ `while let` performs the given pattern matching on every round of the loop, and cancels the loop if the pattern
+    //@ doesn't match. There's also `if let`, which works similar, but of course without the loopy part.
+    while let Some(digit) = iter.next() {
+        println!("{}", digit)
+    }
+}
+
+// **Exercise 09.1**: Write a testcase for the iterator, making sure it yields the corrects numbers.
+// 
+// **Exercise 09.2**: Write a function `iter_ldf` that iterators over the digits with the least-significant
+// digits coming first. Write a testcase for it.
+
+// ## Iterator invalidation and lifetimes
+//@ You may have been surprised that we had to explicitly annotate a lifetime when we wrote `Iter`. Of
+//@ course, with lifetimes being present at every reference in Rust, this is only consistent. But do we at
+//@ least gain something from this extra annotation burden? (Thankfully, this burden only occurs when we
+//@ define *types*, and not when we define functions - which is typically much more common.)
+
+//@ It turns out that the answer to this question is yes! This particular aspect of the concept of
+//@ lifetimes helps Rust to eliminate the issue of *iterator invalidation*. Consider the following
+//@ piece of code.
+fn iter_invalidation_demo() {
+    let mut b = BigInt::new(1 << 63) + BigInt::new(1 << 16) + BigInt::new(1 << 63);
+    for digit in b.iter() {
+        println!("{}", digit);
+        /*b = b + BigInt::new(1);*/                                 /* BAD! */
+    }
+}
+//@ If you enable the bad line, Rust will reject the code. Why? The problem is that we are modifying the
+//@ number while iterating over it. In other languages, this can have all sorts of effects from inconsistent
+//@ data or throwing an exception (Java) to bad pointers being dereferenced (C++). Rust, however, is able to
+//@ detect this situation. When you call `iter`, you have to borrow `b` for some lifetime `'a`, and you obtain
+//@ `Iter<'a>`. This is an iterator that's only valid for lifetime `'a`. Gladly, we have this annotation available
+//@ to make such a statement. Rust enforces that `'a` spans every call to `next`, which means it has to span the loop.
+//@ Thus `b` is borrowed for the duration of the loop, and we cannot mutate it. This is yet another example for
+//@ how the combination of mutation and aliasing leads to undesired effects (not necessarily crashes, think of Java),
+//@ which Rust successfully prevents.
+
+// ## Iterator conversion trait
+//@ If you closely compare the `for` loop in `main` above, with the one in `part06::vec_min`, you will notice that we were able to write
+//@ `for e in v` earlier, but now we have to call `iter`. Why is that? Well, the `for` sugar is not actually tied to `Iterator`.
+//@ Instead, it demands an implementation of [`IntoIterator`](https://doc.rust-lang.org/stable/std/iter/trait.IntoIterator.html).
+//@ That's a trait of types that provide a *conversion* function into some kind of iterator. These conversion traits are a frequent
+//@ pattern in Rust: Rather than demanding that something is an iterator, or a string, or whatever; one demands that something
+//@ can be converted to an iterator/string/whatever. This provides convenience similar to overloading of functions: The function
+//@ can be called with lots of different types. By implementing such traits for your types, you can even make your own types
+//@ work smoothly with existing library functions. As usually for Rust, this abstraction comes at zero cost: If your data is already
+//@ of the right type, the conversion function will not do anything and trivially be optimized away.
+
+//@ If you have a look at the documentation of `IntoIterator`, you will notice that the function `into_iter` it provides actually
+//@ consumes its argument. So we implement the trait for *references to* numbers, such that the number is not lost after the iteration.
+impl<'a> IntoIterator for &'a BigInt {
+    type Item = u64;
+    type IntoIter = Iter<'a>;
+    fn into_iter(self) -> Iter<'a> {
+        self.iter()
+    }
+}
+// With this in place, you can now replace `b.iter()` in `main` by `&b`. Go ahead and try it! <br/>
+//@ Wait, `&b`? Why that? Well, we implemented `IntoIterator` for `&BigInt`. If we are in a place where `b` is already borrowed, we can
+//@ just do `for digit in b`. If however, we own `b`, we have to create a reference to it. Alternatively, we could implement `IntoIterator`
+//@ for `BigInt` - which, as already mentioned, would mean that `b` is actually consumed by the iteration, and gone. This can easily happen,
+//@ for example, with a `Vec`: Both `Vec` and `&Vec` (and `&mut Vec`) implement `IntoIterator`, so if you do `for e in v`, and `v` has type `Vec`,
+//@ then you will obtain ownership of the elements during the iteration - and destroy the vector in the process. We actually did that in
+//@ `part01::vec_min`, but we did not care. You can write `for e in &v` or `for e in v.iter()` to avoid this.
+
+//@ [index](main.html) | [previous](part08.html) | [raw source](workspace/src/part09.rs) | [next](part10.html)