Module atsamd_hal::typelevel

Module supporting type-level programming

Introduction

Embedded software is often difficult to debug, so there is a strong motivation to catch as many bugs as possible at compile-time. However, the performance requirements of embedded software also make it difficult to justify changes that impose additional overhead in terms of size or speed. Ideally, we would like to add as many compile-time checks as possible, while also producing the fewest possible assembly instructions.

The Rust type system can help accomplish this goal. By expressing software constraints within the type system, developers can enforce invariants at compile-time.

Sometimes this is done using Rust macros. However, that approach can produce code that is difficult to read and understand. Moreover, macro-generated code can only be extended by more macros, which further spreads the problem. In atsamd-hal specifically, issue #214 discussed the extent to which macros were once used in the repository.

Alternatively, many of the same goals can be accomplished with the Rust type & trait system directly, which is quite powerful. In fact, it is turing complete. By expressing our invariants entirely within the type system, we can encode the desired compile-time checks in a form that is easier to read, understand and document.

This module documents some of the type-level programming techniques used throughout this HAL, and it contains a few items used to implement them.

Contents

• Basics of type-level programming
  • Type-level enums
  • Type classes
  • Type-level containers
  • Type-level functions
• OptionalKind trait pattern
• AnyKind trait pattern
  • Defining an AnyKind trait
  • Using an AnyKind trait

Basics of type-level programming

Type-level programming aims to execute a form of compile-time computation. But to perform such computation, we need to map our traditional notions of programming to the Rust type system.

In normal Rust, individual values are grouped or categorized into types. For example, 0, 1, 2, etc. are all members of the usize type. Similarly, Enum::A and Enum::B are members of the Enum type, defined as

enum Enum { A, B }

We use composite types and containers to create more complex data structures, and we use functions to map between values.

All of these concepts can also be expressed within the Rust type system. However, in this case, types are grouped and categorized into traits. For instance, the typenum crate provides the types U0, U1, U2, etc., which are all members of the Unsigned trait. Similarly, the following sections will illustrate how to define type-level enums, containers and functions.

Type-level enums

Type-level enums are one of the foundational concepts of type-level programming used in this HAL.

At the value-level, a typical Rust enum represents some set of variants that can be assigned to a particular variable. Similarly, a type-level enum represents some set of types that can be assigned to a particular type parameter.

To lift an enum from the value level to the type level, you typically map the enum variants to types and the enum itself to a trait. For instance, the value-level enum

enum Enum {
    A,
    B,
}

would be mapped to the type level like so.

trait Enum {}

enum A {}
enum B {}

impl Enum for A {}
impl Enum for B {}

At the value level, the variants A and B are grouped by the Enum type, while at the type level, the types A and B are grouped by the Enum trait.

Type classes

At the value-level, a type restricts the possible values that can be taken by some free variable. While at the type-level, a trait bound restricts the possible types that can be taken by some free type parameter. In effect, trait bounds can be used to create a kind of meta-type, or type class. The type-level enums in the previous section represent the most primitive application of the concept, but type classes can take other forms. The OptionalKind and AnyKind trait patterns discussed below are more advanced applications of the same concept.

Type-level containers

To represent more complex relationships, we need a way to form composite data structures at the type level.

At the value level, a container holds an instance of a particular type. The exact value of that instance is usually not known to the author, it is only known at run-time.

At the type level, we don’t have the same notion of “run-time”, but we do have two different notions of “compile-time” that form a similar relationship. There is compile time for the HAL authors, and there is a separate compile-time for the HAL users. We want to create a type-level container where the exact type is not known at author-time, but it is known at user-time.

For example, take the following, value-level container struct. It contains two fields, a and b, of different types, EnumOne and EnumTwo.

struct Container {
    a: EnumOne,
    b: EnumTwo,
}

We can create an instance of this container with specific values.

let x = Container { a: EnumOne::VariantX, b: EnumTwo::VariantY };

Next, suppose we had already translated EnumOne and EnumTwo to the type level using the technique in the previous section. If we wanted to create a similar, composite data structure at the type level, we could use type parameters in place of struct fields to represent the unknown types.

struct Container<A, B>
where
    A: EnumOne,
    B: EnumTwo,
{
    a: PhantomData<A>,
    b: PhantomData<B>,
}

And we could create an instance of this container with specific types.

type X = Container<VariantX, VariantY>;

You might notice the use of PhantomData in the definition of the type-level container. Because it is geared more toward value-level programming, Rust requires all type parameters actually be used by the corresponding type. However, we don’t need to “store” a type in the same way we store values. The compiler is responsible for tracking the concrete type for each type parameter. But the language still requires us to act as if we used each type parameter. PhantomData is the solution here, because it lets us make use of the type parameters without actually storing any values.

Separately, PhantomData also allows us to create “instances” of types that normally can’t be instantiated, like empty enums. For example, instances of Enum below can never exist directly.

enum Enum {}

But instances of PhantomData<Enum> are perfectly valid. In this way, library authors can create types that only exist at the type level, which can sometimes simplify a design.

Type-level functions

To perform type-level computations, we need some way to map or transform types into other types.

At the value level, functions and methods map values of the input types to values of the output types. The same can be accomplished at the type level using traits and associated types. Type-level functions are implemented as traits, where the implementing type and any type parameters are the inputs, and associated types are the outputs.

For example, consider the value level not method below.

enum Bool {
    False,
    True,
}

impl Bool {
    fn not(self) -> Self {
        use Bool::*;
        match self {
            True => False,
            False => True,
        }
    }
}

We can translate this example to the type level like so.

trait Bool {}

enum True {}
enum False {}

impl Bool for True {}
impl Bool for False {}

trait Not: Bool {
    type Result: Bool;
}

impl Not for True {
    type Result = False;
}

impl Not for False {
    type Result = True;
}

We can use the Not trait bound to transform one type to another. For instance, we can create a container that accepts one type parameter but stores a different one.

struct Container<B: Not> {
    not: PhantomData<B::Result>;
}

Alternatively, we could redefine the trait and declar a corresponding type alias as

trait NotFunction: Bool {
    type Result: Bool;
}

type Not<B> = <B as NotFunction>::Result;

Doing so would allow us to us reframe the last example as

struct Container<B: NotFunction> {
    not: PhantomData<Not<B>>;
}

Type-level functions can be more complicated than this example, but they ultimately represent a mapping from a set of input types (the implementing type and any type parameters) to a set of output types (the associated types).

OptionalKind trait pattern

As mentioned above, traits can be used to define a kind of meta-type or type class, essentially forming a set of valid types for a given type parameter. They also represent the concept of types lifted from the value level to the type level.

What if we want to define a type class representing either a set of useful types or some useless, null type? Essentially, how do we take the notion of an Option type and raise it to the type level?

Suppose we have some existing type class, defined by the Class trait, that we want to make optional. We can define a new type class that includes all instances of Class as well as some null type. For the latter we use NoneT, defined in this module.

trait OptionalClass {}

impl OptionalClass for NoneT {}
impl<C: Class> OptionalClass for C {}

We can use this new type class to store an optional instance of a Class type in a struct.

struct Container<C: OptionalClass> {
    class: PhantomData<C>,
}

And we can restrict some of its methods to only operate on instances with a valid Class.

impl<C: Class> Container<C> {
    fn method(self) { ... }
}

Although it is not strictly necessary, we can also introduce a new type class to differentiate the bare usage of Class from instances of some Class where an OptionalClass is accepted.

trait SomeClass: OptionalClass + Class {}

impl<C: Class> SomeClass for C {}

This new trait doesn’t add any new information, but it can still help readers understand that a particular type parameter is restricted to an instances of Class when an OptionalClass could be accepted.

Note that when Class and OptionalClass contain associated types, name clashes may occur when using SomeClass as a trait bound. This can be avoided by removing the OptionalClass super trait from SomeClass. Ultimately, it is redundant anyway, because any implementer of Class also implements OptionalClass.

AnyKind trait pattern

The AnyKind trait pattern allows you to encapsulate types with multiple type parameters and represent them with only a single type parameter. It lets you introduce a layer of abstraction, which can simplify interfaces and make them more readable. But most of all, it does so without sacrificing any of our normal, type-level abilities.

Defining an AnyKind trait

Suppose you had a composite, type-level data structure. For example, the GPIO Pin struct contains instances of two type-level enums, a PinId and a PinMode. It looks something like this.

struct Pin<I: PinId, M: PinMode> {
    // ...
}

Rust does not provide any way to speak about a Pin generally. Any mention of the Pin type must also include its type parameters, i.e. Pin<I, M>. This is not a deal-breaker, but it is less than ideal for type-level programming. It would be nice if there were a way to succinctly refer to any Pin, regardless of its type parameters.

We’ve seen above that we can use traits to form a type class. What if we were to introduce a new trait to label all instances of Pin? It would look something like this.

trait AnyPin {}

impl<I: PinId, M: PinMode> AnyPin for Pin<I, M> {}

Now, instead of refering to Pin<I, M>, we can refer to instances of the AnyPin type class.

fn example<P: AnyPin>(pin: P) { ... }

Unfortunately, while this is more ergonomic, it is not very useful. As authors of the code, we know that AnyPin is only implemented for Pin types. But the compiler doesn’t know that. Traits in Rust are open, so the compiler must consider that AnyPin could be implemented for other types.

As a consequence, the compiler knows very little about the type P in the function above. In fact, because the AnyPin trait is completely empty, the compiler knows absolutely nothing about the type P.

Is there a way to make the AnyPin trait more useful? We can see from the current implementation that we are throwing away information.

impl<I: PinId, M: PinMode> AnyPin for Pin<I, M> {}

The implementation of AnyPin is identical for every Pin, regardless of the type parameters I and M, which erases that information. Instead, we could choose to save that information in the form of associated types.

Let’s redesign the AnyPin trait to record the PinId and PinMode.

trait AnyPin {
    type Id: PinId;
    type Mode: PinMode;
}

impl<I: PinId, M: PinMode> AnyPin for Pin<I, M> {
    type Id = I;
    type Mode = M;
}

This is better. When P implements AnyPin, we can at least recover the corresponding PinId and PinMode types. However, AnyPin still doesn’t include any trait methods nor any super traits, so the compiler won’t allow us to do anything useful with an instances of P.

We need some way to tell the compiler that when P implements AnyPin, it is equivalent to saying P is exactly Pin<P::Id, P::Mode>. Essentially, we want to take a generic type parameter P and treat it as if it were an instance of a specific Pin type.

We can start by defining a trait alias to recover the specific Pin type.

type SpecificPin<P> = Pin<<P as AnyPin>::Id, <P as AnyPin>::Mode>;

With this new definition, we can rephrase our statement above. We need some way to tell the compiler that when P implements AnyPin, P == SpecificPin<P>. There’s no way to do that exactly, but we can come close with some useful trait bounds: From, Into, AsRef and AsMut.

trait AnyPin
where
    Self: From<SpecificPin<Self>>,
    Self: Into<SpecificPin<Self>>,
    Self: AsRef<SpecificPin<Self>>,
    Self: AsMut<SpecificPin<Self>>,
{
    type Id: PinId;
    type Mode: PinMode;
}

Now we’ve given the compiler some useful information. When a type implements AnyPin, it can be converted from and into instances of Pin. And references to types that implement AnyPin can be converted into references to Pins.

fn example<P: AnyPin>(mut any_pin: P) {
    // None of the type annotations here are necessary
    // Everything can be inferred
    // Remember that SpecificPin<P> is Pin<P::Id, P::Mode>
    let pin_mut: &mut SpecificPin<P> = any_pin.as_mut();
    let pin_ref: &SpecificPin<P> = any_pin.as_ref();
    let pin: SpecificPin<P> = any_pin.into();
}

Finally, to simplify this pattern, we can gather all of the super trait bounds into a single, reusable trait.

trait Is
where
    Self: From<IsType<Self>>,
    Self: Into<IsType<Self>>,
    Self: AsRef<IsType<Self>>,
    Self: AsMut<IsType<Self>>,
{
    type Type;
}

type IsType<T> = <T as Is>::Type;

impl<T: AsRef<T> + AsMut<T>> Is for T {
    type Type = T;
}

And we can rewrite our AnyPin trait as

trait AnyPin: Is<Type = SpecificPin<Self>> {
    type Id: PinId;
    type Mode: PinMode;
}

Using an AnyKind trait

If a type takes multiple type parameters, storing it within a container requires repeating all of the corresponding type parameters. For instance, imagine a container that stores two completely generic Pin types.

struct TwoPins<I1, I2, M1, M2>
where
    I1: PinId,
    I2: PinId,
    M1: PinMode,
    M2: PinMode,
{
    pin1: Pin<I1, M1>,
    pin2: Pin<I2, M2>,
}

This struct has already ballooned to four type parameters, without even doing much useful work. Given its heavy use of type parameters, this limitation can make type-level programming tedious, cumbersome and error-prone.

Instead, we can use the AnyKind trait pattern to encapsulate each Pin with a single type parameter.

struct TwoPins<P1, P2>
where
    P1: AnyPin,
    P2: AnyPin,
{
    pin1: P1,
    pin2: P2,
}

The result is far more readable and generally more comprehensible. Moreover, although we no longer have direct access to the PinId and PinMode type parameters, we haven’t actually lost any expressive power.

In the first version of TwoPins, suppose we wanted to implement a method for pins in FloatingInput mode while simultaneously restricting the possible PinIds based on some type class. The result might look like this.

impl<I1, I2> for TwoPins<I1, I2, FloatingInput, FloatingInput>
where
    I1: PinId + Class,
    I2: PinId + Class,
{
    fn method(&self) {
        // ...
    }
}

The same method could be expressed with the AnyPin approach like so

impl<P1, P2> for TwoPins<P1, P2>
where
    P1: AnyPin<Mode = FloatingInput>,
    P2: AnyPin<Mode = FloatingInput>,
    P1::Id: Class,
    P2::Id: Class,
{
    fn method(&self) {
        // ...
    }
}

This example demonstrates the simultaneous readability and expressive power of the AnyKind pattern.

However, remember that when working with a type P that implements AnyPin, the compiler can only use what it knows about the AnyPin trait. But all of the functionality for GPIO pins is defined on the Pin type. To make use of a generic type P implementing AnyPin, you must first convert it to its corresponding SpecificPin using Into, AsRef or AsMut. And, in some instances, you may also need to convert back to the type P.

Suppose you wanted to store a completely generic Pin within a struct.

pub struct Example<P: AnyPin> {
    pin: P,
}

Next, suppose you want to create a method that would take the Pin out of the struct, perform some operations in different PinModes, and put it back into the struct before returning. The elided method below shows such an example. However, it can be a bit tricky to follow all of the type conversions here. For clarity, the expanded method shows the same behavior with each transformation given its proper type annotation.

impl<P: AnyPin> Example<P> {
    pub fn elided(mut self) -> Self {
        let pin = self.pin.into();
        let mut pin = pin.into_push_pull_output();
        pin.set_high().ok();
        let pin = pin.into_floating_input();
        let _bit = pin.is_low().unwrap();
        let pin = pin.into_mode();
        self.pin = pin.into();
        self
    }
    pub fn expanded(mut self) -> Self {
        let pin: SpecificPin<P> = self.pin.into();
        let mut pin: Pin<P::Id, PushPullOutput> = pin.into_push_pull_output();
        pin.set_high().ok();
        let pin: Pin<P::Id, FloatingInput> = pin.into_floating_input();
        let _bit = pin.is_low().unwrap();
        let pin: SpecificPin<P> = pin.into_mode::<P::Mode>();
        self.pin = pin.into();
        self
    }
}

Notice that it is not enough to simply put back the correct SpecificPin. Even though the SpecificPin implements AnyPin<Id = P::Id, Mode = P::Mode> the compiler doesn’t understand that SpecificPin<P> == P for all P. As far as the compiler is concerned, there could be several different types that implement AnyPin<Id = P::Id, Mode = P::Mode>. Instead, the compiler requires that you put back an instance of P exactly. The final use of Into is key here. It transforms the SpecificPin back into P itself.

Structs

• NoneT
  Type-level version of the None variant

Traits

• Decrement
  Trait mapping each countable type to its predecessor
• Increment
  Trait mapping each countable type to its successor
• Is
  Marker trait for type identity

Type Aliases

• IsType
  Type alias for Is::Type