fix HTML

[web.git] / personal / _posts / 2018-04-05-a-formal-look-at-pinning.md

diff --git a/personal/_posts/2018-04-05-a-formal-look-at-pinning.md b/personal/_posts/2018-04-05-a-formal-look-at-pinning.md
index 4aed608945629e1ac8b10b4659ee213fc7aabfe8..5e51e7c747dbc01a0307a5f343b28e21cd27997c 100644 (file)
--- a/personal/_posts/2018-04-05-a-formal-look-at-pinning.md
+++ b/personal/_posts/2018-04-05-a-formal-look-at-pinning.md
@@ -4,10 +4,10 @@ categories: research rust
 forum: https://internals.rust-lang.org/t/a-formal-look-at-pinning/7236
 ---
 
 forum: https://internals.rust-lang.org/t/a-formal-look-at-pinning/7236
 ---
 

-Recently, a new API for "pinned references" has [landed as a new unstable feature](https://github.com/rust-lang/rust/pull/49058) in the standard library.
+Recently, a new [API for "pinned references"](https://github.com/rust-lang/rfcs/blob/master/text/2349-pin.md) has [landed as a new unstable feature](https://github.com/rust-lang/rust/pull/49058) in the standard library.

 The purpose of these references is to express that the data at the memory it points to will not, ever, be moved elsewhere.
 The purpose of these references is to express that the data at the memory it points to will not, ever, be moved elsewhere.

-Others have [written](https://boats.gitlab.io/blog/post/2018-03-20-async-vi/) about why this is important in the context of async IO.
-The purpose of this post is to take a closer, more formal look at that API: We are going to take a stab at extending the RustBelt model of types with support for pinning.
+@withoutboats has written about how this [solves](https://boats.gitlab.io/blog/post/2018-03-20-async-vi/) a [problem in the context of async IO](https://boats.gitlab.io/blog/post/2018-01-25-async-i-self-referential-structs/).
+In this post, we take a closer, more formal look at that API: We are going to take a stab at extending the RustBelt model of types with support for pinning.

 
 <!-- MORE -->
 
 
 <!-- MORE -->
 


@@ -15,7 +15,7 @@ But before we get started, I have to lay down some basics.
 
 ## Rust types: Recap
 
 
 ## Rust types: Recap
 

-I have discussed my model of Rust types [in a previous post]({{ site.baseurl }}{% post_url 2018-01-31-sharing-for-a-lifetime %}); this may me a good time to read that post as I will be using it as a starting point.
+I have discussed my model of Rust types [in a previous post]({% post_url 2018-01-31-sharing-for-a-lifetime %}); this may me a good time to read that post as I will be using it as a starting point.

 The short version is that I view Rust types with private invariants as not having just a single invariant, but different invariants that reflect the different "modes" the type can be in.
 @cramertj suggested to use "typestate" as terminology here, and I agree that this makes sense.
 
 The short version is that I view Rust types with private invariants as not having just a single invariant, but different invariants that reflect the different "modes" the type can be in.
 @cramertj suggested to use "typestate" as terminology here, and I agree that this makes sense.
 


@@ -34,7 +34,7 @@ The short version is that I view Rust types with private invariants as not havin
 You may be wondering why sharing is a separate typestate here; shouldn't that just be read-only access to a `T` that someone else owns?
 However, that clearly doesn't work for `&Cell`; to explain types with interior mutability we *need* sharing as a separate state.
 I explained this in more detail in the previous post, but as a quick example consider that, if you fully own a `RefCell`, the first field (storing the current count of readers/writers) has no special meaning whatsoever.
 You may be wondering why sharing is a separate typestate here; shouldn't that just be read-only access to a `T` that someone else owns?
 However, that clearly doesn't work for `&Cell`; to explain types with interior mutability we *need* sharing as a separate state.
 I explained this in more detail in the previous post, but as a quick example consider that, if you fully own a `RefCell`, the first field (storing the current count of readers/writers) has no special meaning whatsoever.

-This is witnessed by [`RefCell::get_mut`](https://doc.rust-lang.org/beta/std/cell/struct.RefCell.html#method.get_mut) ignoring that field.
+This is witnessed by [`RefCell::get_mut`](https://doc.rust-lang.org/stable/std/cell/struct.RefCell.html#method.get_mut) ignoring that field.

 In fact, it would be sound to add a `RefCell::reset(&mut self)` that just resets this field to `0`.
 
 ## Pinning
 In fact, it would be sound to add a `RefCell::reset(&mut self)` that just resets this field to `0`.
 
 ## Pinning


@@ -44,38 +44,40 @@ The core piece of the pinning API is a new reference type `Pin<'a, T>` that guar
 Crucially, **pinning does not provide immovable types**!
 Data is only pinned after a `Pin<T>` pointing to it has been created; it can be moved freely before that happens.
 
 Crucially, **pinning does not provide immovable types**!
 Data is only pinned after a `Pin<T>` pointing to it has been created; it can be moved freely before that happens.
 

-The [corresponding RFC](https://github.com/rust-lang/rfcs/blob/master/text/2349-pin.md) explains the entirey new API surface in quite some detail: [`Pin`](https://doc.rust-lang.org/nightly/std/mem/struct.Pin.html), [`PinBox`](https://doc.rust-lang.org/nightly/std/boxed/struct.PinBox.html) and the [`Unpin`](https://doc.rust-lang.org/nightly/std/marker/trait.Unpin.html) marker trait.
+The [corresponding RFC](https://github.com/rust-lang/rfcs/blob/master/text/2349-pin.md) explains the entirey new API surface in quite some detail: [`Pin`](https://doc.rust-lang.org/1.27.0/std/mem/struct.Pin.html), [`PinBox`](https://doc.rust-lang.org/1.27.0/std/boxed/struct.PinBox.html) and the [`Unpin`](https://doc.rust-lang.org/1.27.0/std/marker/trait.Unpin.html) marker trait.

 I will not repeat that here but only show one example of how to use `Pin` references and exploit their guarantees:
 {% highlight rust %}
 I will not repeat that here but only show one example of how to use `Pin` references and exploit their guarantees:
 {% highlight rust %}

-#![feature(pin, arbitrary_self_types)]
+#![feature(pin, arbitrary_self_types, optin_builtin_traits)]

 
 use std::ptr;
 use std::mem::Pin;
 use std::boxed::PinBox;
 
 use std::ptr;
 use std::mem::Pin;
 use std::boxed::PinBox;

+use std::marker::Unpin;

 
 struct SelfReferential {
     data: i32,
 
 struct SelfReferential {
     data: i32,

-    self_ref: Option<ptr::NonNull<i32>>,
+    self_ref: *const i32,

 }
 }

+impl !Unpin for SelfReferential {}

 
 impl SelfReferential {
 
 impl SelfReferential {

-    fn new() -> Self {
-        SelfReferential { data: 42, self_ref: None }
+    fn new() -> SelfReferential {
+        SelfReferential { data: 42, self_ref: ptr::null()  }

     }
 
     }
 

-    fn init(mut self: Pin<Self>) {
-        unsafe {
-            let this = Pin::get_mut(&mut self);
-            // Set up self_ref to point to this.data
-            this.self_ref = ptr::NonNull::new(&mut this.data as *mut _);
-        }
+    fn init(mut self: Pin<SelfReferential>) {
+        let this : &mut SelfReferential = unsafe { Pin::get_mut(&mut self) };
+        // Set up self_ref to point to this.data.
+        this.self_ref = &this.data as *const i32;

     }
     }

-    
-    fn read_ref(mut self: Pin<Self>) -> Option<i32> {
-        unsafe {
-            let this = Pin::get_mut(&mut self);
-            // Dereference self_ref if it is set
-            this.self_ref.map(|self_ref| *self_ref.as_ptr())
+
+    fn read_ref(self: Pin<SelfReferential>) -> Option<i32> {
+        let this : &SelfReferential = &*self;
+        // Dereference self_ref if it is non-NULL.
+        if this.self_ref == ptr::null() {
+            None
+        } else {
+            Some(unsafe { *this.self_ref })

         }
     }
 }
         }
     }
 }


@@ -86,10 +88,12 @@ fn main() {
     println!("{:?}", s.as_pin().read_ref()); // prints Some(42)
 }
 {% endhighlight %}
     println!("{:?}", s.as_pin().read_ref()); // prints Some(42)
 }
 {% endhighlight %}

-The most intersting piece of code here is `read_ref`, which dereferences a raw pointer.
-The reason this is legal is that we can rely on the entire `SelfReferential` not having been moved since `init()` was called (which is the only place that would set the pointer to `Some`).
+**Update:** Previously, the example code used `Option<ptr::NonNull<i32>>`. I think using raw pointers directly makes the code easier to follow. **/Update**
+
+The most intersting piece of code here is `read_ref`, which dereferences a raw pointer, `this.self_ref`.
+The reason this is legal is that we can rely on the entire `SelfReferential` not having been moved since `init()` was called (which is the only place that would set the pointer to something non-NULL).

 
 

-In particular, if we changed the signature of `init()` to take `&mut`, we could easily cause UB by writing the following code:
+In particular, if we changed the signature to `fn init(&mut self)`, we could easily cause UB by writing the following code:

 {% highlight rust %}
 fn main() {
     // Create an initialize a SelfReferential in a Box, move it out, and drop the Box
 {% highlight rust %}
 fn main() {
     // Create an initialize a SelfReferential in a Box, move it out, and drop the Box


@@ -107,7 +111,7 @@ In contrast, converting `Box<T>` to `PinBox<T>` is fine because this *consumes*
 `Pin` lets us give a type to `SelfReferantial` that makes it safe to use.
 This is in the best tradition of Rust: We are using an expressive type system to provide safe APIs for operations that only have unsafe APIs in other languages (e.g., iterators that avoid iterator invalidation which plague even memory safe languages like Java).
 In the following, I will explain how one can prove that our claim of safe encapsulation actually holds true.
 `Pin` lets us give a type to `SelfReferantial` that makes it safe to use.
 This is in the best tradition of Rust: We are using an expressive type system to provide safe APIs for operations that only have unsafe APIs in other languages (e.g., iterators that avoid iterator invalidation which plague even memory safe languages like Java).
 In the following, I will explain how one can prove that our claim of safe encapsulation actually holds true.

-This is building on the framework that we developed for the [RustBelt paper]({{ site.baseurl }}{% post_url 2017-07-08-rustbelt %}).
+This is building on the framework that we developed for the [RustBelt paper]({% post_url 2017-07-08-rustbelt %}).

 
 ## Formal Notation
 
 
 ## Formal Notation
 


@@ -121,29 +125,20 @@ forall |'a, ptr|
   borrowed('a, exists |bytes| ptr.points_to_owned(bytes) && T.own(bytes))
   -> T.shr('a, ptr)
 ```
   borrowed('a, exists |bytes| ptr.points_to_owned(bytes) && T.own(bytes))
   -> T.shr('a, ptr)
 ```

-I am using the usual mathematical quantifiers, with a Rust-y syntax (`forall |var| P` and `exists |var| P`), and `->` for implication.
+This is a formal statement that we have to prove whenever we define `T.own` and `T.shr` for our own type `T`.
+It says that for all lifetimes `'a` and pointers `ptr`, if `borrowed('a, ...)` holds, then `T.shr('a, ptr)` holds.
+I am using the usual mathematical quantifiers, with a Rust-y syntax (`forall |var| ...` and `exists |var| ...`), and `->` for implication.

 For disjunction (`||`) and conjunction (`&&`), I follow Rust.
 
 For disjunction (`||`) and conjunction (`&&`), I follow Rust.
 

-We also need some way to talk about ownership and contents of memory:
-I will write `ptr.points_to_owned_bytes(bytes)` (where `ptr: Pointer` and `bytes: List<Byte>`) to express that `ptr` points to `bytes.len()` many bytes of memory containing the given `bytes` of data, and that moreover, we *own* that memory.
-Ownership here means that we are free to read, write and deallocate that memory.
-
-Frequently, it is more convenient to not talk about raw lists of bytes but about some higher-level representation of the bytes, and not care about how exactly that data is laid out in memory.
-For example, we might want to say that `ptr` points to `42` of type `i32` by saying `ptr.points_to_owned(42i32)`.
-We can define a suitable `points_to_owned` as
-```
-ptr.points_to_owned(data: U) where List<Bytes>: TryInto<U> :=
-  exists |bytes| bytes.try_into() == Ok(data) && ptr.points_to_owned_bytes(bytes)
-```
-Here, we (ab)use the `TryInto` trait to convert a properly laid out list of bytes into something of type `U`.
-The conversion fails, in particular, if the list does not have exactly the right length.
-If `U == List<Bytes>`, this is just the same as `ptr.points_to_owned_bytes`.
+Because Rust types are a lot about pointers and what they point to, we also need some way to talk about memory:
+`ptr.points_to_owned(bytes)` (where `ptr: Pointer` and `bytes: List<Byte>`) means that `ptr` points to `bytes.len()` many bytes of memory containing the given `bytes` of data, and that moreover, we *own* that memory.
+*Ownership* here means that we are free to read, write and deallocate that memory, and that we are the only party that can do so.

 
 

-**Update:** In a previous version I called these predicates `mem_own_bytes` and `mem_own`. I decided that `points_to_owned` was actually easier to understand, and it also matches the standard terminology in the literature, so I switched to using that term instead. **/Update**
+**Update:** In a previous version I called this predicate `mem_own`. I decided that `points_to_owned` was actually easier to understand, and it also matches the standard terminology in the literature, so I switched to using that term instead. **/Update**

 
 Finally, `borrowed('a, P)` says that `P` is only temporarily owned, i.e., borrowed, for lifetime `'a`.
 
 Finally, `borrowed('a, P)` says that `P` is only temporarily owned, i.e., borrowed, for lifetime `'a`.

-`P` here is a *proposition* or *assertion*, i.e., a statement about what we expect to own. The axiom above is a proposition, as is `ptr.points_to_owned(42i32)`.
-You can think of propositions as a fancy version of `bool` where we can use things like quantifiers or borrowing, and talk about memory and ownership.
+`P` here is a *proposition* or *assertion*, i.e., a statement about what we expect to own. The axiom above is a proposition, as is `ptr.points_to_owned([0, 0])`.
+You can think of propositions as a fancy version of `bool` where we can use things like quantifiers and borrowing, and talk about memory and ownership.

 
 Let us see how we can define the owned typestate of `Box` and mutable reference using this notation:
 
 
 Let us see how we can define the owned typestate of `Box` and mutable reference using this notation:
 


@@ -154,18 +149,27 @@ Formally:
 ```
 Box<T>.own(bytes) := exists |ptr, inner_bytes| bytes.try_into() == Ok(ptr) &&
   ptr.points_to_owned(inner_bytes) && T.own(inner_bytes)
 ```
 Box<T>.own(bytes) := exists |ptr, inner_bytes| bytes.try_into() == Ok(ptr) &&
   ptr.points_to_owned(inner_bytes) && T.own(inner_bytes)

+```
+```

 (&'a mut T).own(bytes) := exists |ptr| bytes.try_into() == Ok(ptr) &&
   borrowed('a,
     exists |inner_bytes| ptr.points_to_owned(inner_bytes) && T.own(inner_bytes))
 ```
 
 (&'a mut T).own(bytes) := exists |ptr| bytes.try_into() == Ok(ptr) &&
   borrowed('a,
     exists |inner_bytes| ptr.points_to_owned(inner_bytes) && T.own(inner_bytes))
 ```
 

-It turns out that using `try_into` like we do above is actually a common pattern.
-We usually do not want to talk directly about the `List<Byte>` but convert them to some higher-level representation first.
+The `:=` means "is defined as"; this is a lot like a function definition in Rust where the part after the `:=` is the function body.
+Notice how we use `try_into` to try to convert a sequence of bytes into a higher-level representation, namely a pointer.
+This relies in `TryInto<U>` being implemented for `List<Byte>`.
+The conversion fails, in particular, if the list of bytes does not have exactly the right length.
+
+It turns out that using `try_into` like we do above is actually a common pattern:
+Often, when we define a predicate on bytes, we do not want to talk directly about the `List<Byte>` but convert them to some higher-level representation first.

 To facilitate this, we will typically define `T.own(data: U)` for some `U` such that `List<Byte>: TryInto<U>`, the idea being that the raw list of bytes is first converted to a `U` and the predicate can then directly access the higher-level data in `U`.
 This could look as follows:
 ```
 Box<T>.own(ptr: Pointer) :=
   exists |inner_bytes| ptr.points_to_owned(inner_bytes) && T.own(inner_bytes)
 To facilitate this, we will typically define `T.own(data: U)` for some `U` such that `List<Byte>: TryInto<U>`, the idea being that the raw list of bytes is first converted to a `U` and the predicate can then directly access the higher-level data in `U`.
 This could look as follows:
 ```
 Box<T>.own(ptr: Pointer) :=
   exists |inner_bytes| ptr.points_to_owned(inner_bytes) && T.own(inner_bytes)

+```
+```

 (&'a mut T).own(ptr: Pointer) :=
   borrowed('a, exists |inner_bytes| ptr.points_to_owned(inner_bytes) && T.own(inner_bytes))
 ```
 (&'a mut T).own(ptr: Pointer) :=
   borrowed('a, exists |inner_bytes| ptr.points_to_owned(inner_bytes) && T.own(inner_bytes))
 ```


@@ -177,9 +181,9 @@ exists |data: U| bytes.try_into() == Ok(data) && T.own(data)
 
 ## Extending Types to Verify `SelfReferential`
 
 
 ## Extending Types to Verify `SelfReferential`
 

-What would it take to *prove* that `SelfReferential` can be used by arbitrary safe code?
+Coming back to our example, what would it take to *prove* that `SelfReferential` can be used by arbitrary safe code?

 We have to start by writing down the private invariants (for all typestates) of the type.
 We have to start by writing down the private invariants (for all typestates) of the type.

-We want to say that if `self.read_ref` it set to `Some(data_ptr)`, then `data_ptr` is the address of `self.data`.
+We want to say that if `self.read_ref` is not NULL, then it is the address of `self.data`.

 However, if we go back to our notion of Rust types that I laid out at the beginning of this post, we notice that it is *impossible* to refer to the "address of `self.data`" in `T.own`!
 And that's not even surprising; this just reflects the fact that in Rust, if we own a type, we can always move it to a different location---and hence the invariant must not depend on the location.
 
 However, if we go back to our notion of Rust types that I laid out at the beginning of this post, we notice that it is *impossible* to refer to the "address of `self.data`" in `T.own`!
 And that's not even surprising; this just reflects the fact that in Rust, if we own a type, we can always move it to a different location---and hence the invariant must not depend on the location.
 


@@ -193,20 +197,30 @@ We will add a new, *third* typestate on top of the existing owned and shared typ
 
 Notice that this state talks about a *pointer* being valid, in contrast to `T.own` which talks about a *sequence of bytes*.
 This gives us the expressivity we need to talk about immovable data:
 
 Notice that this state talks about a *pointer* being valid, in contrast to `T.own` which talks about a *sequence of bytes*.
 This gives us the expressivity we need to talk about immovable data:

-`SelfReferential.pin(ptr)` says that `ptr` points to some memory we own, and that memory stores some pair `(data, self_ref)`.
-(In terms of memory layout, `SelfReferential` is the same as a pair of `i32` and `Option<ptr::NonNull<i32>>`.)
-Moreover, if `self_ref` is set to `Some(data_ptr)`, then `data_ptr` is the address of the first field of the pair:
+`SelfReferential.pin(ptr)` says that `ptr` points to some memory we own, and that memory stores some pair `(data, self_ref)`, and `self_ref` is either NULL or the address of the first field, `data`, at offset `0`:

 ```
 ```

-SelfReferential.pin(ptr) := exists |data: i32, self_ref: Option<ptr::NonNull<i32>>|
+SelfReferential.pin(ptr) := exists |data: i32, self_ref: *const i32|

   ptr.points_to_owned((data, self_ref)) &&
   ptr.points_to_owned((data, self_ref)) &&

-  match self_ref { Some(data_ptr) => data_ptr.as_ptr() == ptr.offset(0), None => True }
+  (self_ref == ptr::null() || self_ref == ptr.offset(0))

 ```
 ```

-The most important part of this is the last line, saying that if `data_ptr` is a `Some`, it actually points to the first field (at offset `0`).
-(I am of course glossing over plenty of details here, like handling of padding, but those details are not relevant right now.
+(In terms of memory layout, `SelfReferential` is the same as a pair of `i32` and `*const i32`.
+I am of course glossing over plenty of details here, but those details are not relevant right now.

 Moreover, `SelfReferential` also has an owned and a shared typestate, but nothing interesting happens there.)
 
 With this choice, it is easy to justify that `read_ref` is safe to execute: When the function begins, we can rely on `SelfReferential.pin(self)`.
 Moreover, `SelfReferential` also has an owned and a shared typestate, but nothing interesting happens there.)
 
 With this choice, it is easy to justify that `read_ref` is safe to execute: When the function begins, we can rely on `SelfReferential.pin(self)`.

-If the closure in `self_ref.map` runs, we are in the `Some` case of the `match` so the deref of the pointer obtained from `self_ref` is fine.
+If we enter the `else` branch, we know `self_ref` is not NULL, hence it must be `ptr.offset(0)`.
+As a consequence, the deref of `self_ref` is fine.
+
+Before we go on, I have to explain what I did with `points_to_owned` above.
+Before I said that this predicate operates on `List<Byte>`, but now I am using it on a pair of an `i32` and a raw pointer.
+Again this is an instance of using a higher-level view of memory than a raw list of bytes.
+For example, we might want to say that `ptr` points to `42` of type `i32` by saying `ptr.points_to_owned(42i32)`, without worrying about how to turn that value into a sequence of bytes.
+It turns out that we can define `points_to_owned` in terms of a lower-level `points_to_owned_bytes` that operates on `List<Byte>` as follows:
+```
+ptr.points_to_owned(data: U) where List<Bytes>: TryInto<U> :=
+  exists |bytes| bytes.try_into() == Ok(data) && ptr.points_to_owned_bytes(bytes)
+```
+Just like before, we (ab)use the `TryInto` trait to convert a properly laid out list of bytes into something of type `U`.

 
 ## Verifying the Pin API
 
 
 ## Verifying the Pin API
 


@@ -223,6 +237,8 @@ A list of bytes makes a valid `PinBox<T>` if those bytes form a pointer `ptr` su
 For `Pin<'a, T>`, `ptr` is valid if we have borrowed `T.pin(ptr)` for lifetime `'a`.
 ```
 PinBox<T>.own(ptr) := T.pin(ptr)
 For `Pin<'a, T>`, `ptr` is valid if we have borrowed `T.pin(ptr)` for lifetime `'a`.
 ```
 PinBox<T>.own(ptr) := T.pin(ptr)

+```
+```

 Pin<'a, T>.own(ptr) := borrowed('a, T.pin(ptr))
 ```
 
 Pin<'a, T>.own(ptr) := borrowed('a, T.pin(ptr))
 ```
 


@@ -302,7 +318,7 @@ forall |ptr| T.pin(ptr) -> (exists |bytes| ptr.points_to_owned(bytes) && T.own(b
 
 Note that this is exactly the inverse direction of axiom (b) added in definition 2b: For `Unpin` types, we can freely move between the owned and pinned typestate.
 
 
 Note that this is exactly the inverse direction of axiom (b) added in definition 2b: For `Unpin` types, we can freely move between the owned and pinned typestate.
 

-Clearly, `SelfReferential` is *not* `Unpin`.
+Clearly, `SelfReferential` is *not* `Unpin`, and the example code above makes that explicit with an `impl !Unpin`.

 On the other hand, for types like `i32`, their pinned typestate invariant `i32.pin(ptr)` will only care about the memory that `ptr` points to and not about the actual value of `ptr`, so they satisfy the `Unpin` axiom.
 
 With this definition at hand, it should be clear that if we assume `T: Unpin`, then `&'a mut T` and `Pin<'a, T>` are equivalent types, and so are `Box<T>` and `PinBox<T>`.
 On the other hand, for types like `i32`, their pinned typestate invariant `i32.pin(ptr)` will only care about the memory that `ptr` points to and not about the actual value of `ptr`, so they satisfy the `Unpin` axiom.
 
 With this definition at hand, it should be clear that if we assume `T: Unpin`, then `&'a mut T` and `Pin<'a, T>` are equivalent types, and so are `Box<T>` and `PinBox<T>`.


@@ -321,7 +337,7 @@ The latter is crucial, because it means we can automatically derive `Unpin` inst
 
 ## Conclusion
 
 
 ## Conclusion
 

-We have seen how the new `Pin` type can be used to give safe APIs to types like `SelfReferential`, and how we can (semi-)formally argue for the correctness of `SelfReferential` and the methods on `Pin` and `PinBox`.
+We have seen how the new `Pin` type can be used to give safe APIs to types like `SelfReferential` (which, previously, was not possible), and how we can (semi-)formally argue for the correctness of `SelfReferential` and the methods on `Pin` and `PinBox`.

 I hope I was able to shed some light both on how pinning is useful, and how we can reason about safety of a typed API in general.
 Next time, we are going to look at an extension to the pinning API proposed by @cramertj which guarantees that `drop` will be called under some circumstances, and how that is useful for intrusive collections.
 
 I hope I was able to shed some light both on how pinning is useful, and how we can reason about safety of a typed API in general.
 Next time, we are going to look at an extension to the pinning API proposed by @cramertj which guarantees that `drop` will be called under some circumstances, and how that is useful for intrusive collections.