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Optimizing Rust translation to Coq with THIR and bundled traits

· 6 min read

We continued our work on coq-of-rust, a tool to formally verify Rust programs using the proof system Coq 🐓. This tool translates Rust programs to an equivalent Coq program, which can then be verified using Coq's proof assistant. It opens the door to building mathematically proven bug-free Rust programs.

We present two main improvements we made to coq-of-rust:

  • Using the THIR intermediate language of Rust to have more information during the translation to Coq.
  • Bundling the type-classes representing the traits of Rust to have faster type-checking in Coq.

Rust and Coq

THIR intermediate language

To translate Rust programs to Coq, we plug into the compiler of Rust, which operates on a series of intermediate languages:

We were previously using the HIR language to start our translation to Coq, because it is not too low-level and close to what the user has originally in the .rs file. This helps relate the generated Coq code to the original Rust code.

However, at the level of HIR, there is still a lot of implicit information. For example, Rust has automatic dereferencing rules that are not yet explicit in HIR. In order not to make any mistakes during our translation to Coq, we prefer to use the next representation, THIR, that makes explicit such rules.

In addition, the THIR representation shows when a method call is from a trait (and which trait) or from a standalone impl block. Given that we still have trouble translating the traits with type-classes that are inferrable by Coq, this helps a lot.

A downside of the THIR representation is that it is much more verbose. For example, here is a formatting function generated from HIR:

Definition fmt
`{: State.Trait}
(self : ref Self)
(f : mut_ref core.fmt.Formatter)
: M core.fmt.Result :=
let* α0 := format_argument::["new_display"] (addr_of self.["radius"]) in
let* α1 :=
(addr_of [ "Circle of radius " ])
(addr_of [ α0 ]) in
f.["write_fmt"] α1.

This is the kind of functions generated by the #[derive(Debug)] macro of Rust, to implement a formatting function on a type. Here is the version translated from THIR, with explicit borrowing and dereferencing:

Definition fmt
`{: State.Trait}
(self : ref Self)
(f : mut_ref core.fmt.Formatter)
: M ltac:(core.fmt.Result) :=
let* α0 := deref f core.fmt.Formatter in
let* α1 := borrow_mut α0 core.fmt.Formatter in
let* α2 := borrow [ mk_str "Circle of radius " ] (list (ref str)) in
let* α3 := deref α2 (list (ref str)) in
let* α4 := borrow α3 (list (ref str)) in
let* α5 := pointer_coercion "Unsize" α4 in
let* α6 := deref self converting_to_string.Circle in
let* α7 := α6.["radius"] in
let* α8 := borrow α7 i32 in
let* α9 := deref α8 i32 in
let* α10 := borrow α9 i32 in
let* α11 := core.fmt.rt.Argument::["new_display"] α10 in
let* α12 := borrow [ α11 ] (list core.fmt.rt.Argument) in
let* α13 := deref α12 (list core.fmt.rt.Argument) in
let* α14 := borrow α13 (list core.fmt.rt.Argument) in
let* α15 := pointer_coercion "Unsize" α14 in
let* α16 := core.fmt.Arguments::["new_v1"] α5 α15 in
core.fmt.Formatter::["write_fmt"] α1 α16.

We went from a function having two intermediate variables to seventeen intermediate variables. This code is much more verbose, but it is also more explicit. In particular, it details when the:

  • borrowing (going from a value of type T to &T), and the
  • dereferencing (going from a value of type &T to T)

occur. It also shows that the method write_fmt is a method from the implementation of the type core.fmt.Formatter, generating:

core.fmt.Formatter::["write_fmt"] α1 α16

instead of:

f.["write_fmt"] α1

Bundled traits

Some Rust codebases can have a lot of traits. For example in paritytech/ink/crates/env/src/ the trait Environment references more than forty other traits:

pub trait Environment: Clone {
const MAX_EVENT_TOPICS: usize;

type AccountId: 'static
+ scale::Codec
+ CodecAsType
+ Clone
+ PartialEq
+ ...;

type Balance: 'static
+ scale::Codec
+ CodecAsType
+ ...;


We first used an unbundled approach to represent this trait by a type-class in Coq, as it felt more natural:

Module Environment.
Class Trait (Self : Set) `{Clone.Trait Self}
{AccountId : Set}
`{scale.Codec.Trait AccountId}
`{CodecAsType AccountId}
`{Clone AccountId}
`{PartialEq AccountId}

However, the backquote operator generated too many implicit arguments, and the type-checker of Coq was very slow. We then switched to a bundled approach, as advocated in this blog post: Exponential blowup when using unbundled typeclasses to model algebraic hierarchies. The Coq code for this trait now looks like this:

Module Environment.
Class Trait `{: State.Trait} (Self : Set) : Type := {
ℋ_0 :: Clone.Trait Self;
AccountId : Set;
ℒ_0 :: parity_scale_codec.codec.Codec.Trait AccountId;
ℒ_1 :: ink_env.types.CodecAsType.Trait AccountId;
ℒ_2 :: core.clone.Clone.Trait AccountId;
ℒ_3 ::
core.cmp.PartialEq.Trait AccountId
(Rhs := core.cmp.PartialEq.Default.Rhs AccountId);
Balance : Set;
ℒ_8 :: parity_scale_codec.codec.Codec.Trait Balance;
ℒ_9 :: ink_env.types.CodecAsType.Trait Balance;


We use the notation :: for fields that are trait instances. With this approach, traits have types as parameters but no other traits.

The type-checking is now much faster, and in particular, we avoid some cases with exponential blowup or non-terminating type-checking. But this is not a perfect solution as we still have cases where the instance inference does not terminate or fails with hard-to-understand error messages.


We have illustrated here some improvements we recently made to our coq-of-rust translator for two key areas:

  • the translation of traits;
  • the translation of the implicit borrowing and dereferencing, that can occur every time we call a function.

These improvements will allow us to formally verify some more complex Rust codebases. In particular, we are applying coq-of-rust to verify smart contracts written for the ink! platform, that is a subset of Rust.


If you have comments, similar experiences to share, or wish to formally verify your codebase to improve the security of your application, contact us at!