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https://github.com/flux-rs/flux-demo

Small examples that demonstrate how flux works
https://github.com/flux-rs/flux-demo

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Small examples that demonstrate how flux works

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# `Flux`: Liquid types for Rust



**Nico Lehmann**, Adam Geller, Gilles Barthe, Niki Vazou, Ranjit Jhala



---



## Motivation



_Types vs. Floyd-Hoare logic_



## Demonstration



Flux - Liquid Types for Rust



## Evaluation



Flux v. Prusti for Memory safety



---



# Types vs. Floyd-Hoare logic



---



## Liquid/Refinements 101



```haskell

type Nat = {v: Int | 0 <= v}

```



- `Int` is the _base type_ of the value

- `v` names the _value_ being described

- `0 <=v` is a _predicate_ constraint



---



## Liquid/Refinements 101



Generate the sequence of values between `lo` and `hi`



```haskell

range :: lo:Int -> {hi:Int | lo <= hi} -> List {v:Int|lo <= v && v < hi}

```



---



## Liquid/Refinements 101



Generate the sequence of values between `lo` and `hi`



```haskell

range :: lo:Int -> {hi:Int | lo <= hi} -> List {v:Int|lo <= v && v < hi}

```



#### Input Type is a Precondition



`lo <= hi`



---



## Liquid/Refinements 101



Generate the sequence of values between `lo` and `hi`



```haskell

range :: lo:Int -> {hi:Int | lo <= hi} -> List {v:Int|lo <= v && v < hi}

```



#### Output Type is a Postcondition



_Every element_ in sequence is between `lo` and `hi`



---



# Types vs. Floyd-Hoare logic



> Types _decompose_ (quantified) assertions to _quantifier-free_ refinements



---



## Lists in Dafny vs LiquidHaskell







![width:1100px](img/why_types_1_1.png)



---



## Accessing the `i`-th List Element



![width:1100px](img/why_types_1_2.png)



**Floyd-Hoare** requires `elements` and _quantified_ axioms



**Liquid** Parametric _polymorphism_ yields spec for free



---



## Building and Using Lists



![width:1100px](img/why_types_1_3.png)



**Floyd-Hoare** _Quantified_ postcondition (hard to infer)



---



## Building and Using Lists



![width:1100px](img/why_types_1_3.png)



**Liquid** _Quantifier-free_ type (easy to infer)



```haskell

Int -> k:Int -> List {v:Int| k <= v}

```



---



# Types vs. Floyd-Hoare logic



Types decompose assertions to quantif-free refinements ...



... but what about **imperative programs**



---



## Motivation



Types vs. Floyd-Hoare logic



## Demonstration



_`Flux` Liquid Types for Rust_



## Evaluation



`Flux` v. `Prusti` for Memory Safety



---



## `Flux` Liquid Types for Rust



`flux` (/flʌks/)



n. 1 a flowing or flow. 2 a substance used to refine metals. v. 3 to melt; make fluid.



---



## `Flux` Liquid Types for Rust



1. [`basics`](src/basics.rs)



2. [`borrows`](src/borrows.rs)



3. [`rvec-api`](src/rvec.rs)



4. [`vectors`](src/vectors.rs)



---



## Motivation



Types vs. Floyd-Hoare logic



## Demonstration



_`Flux` Liquid Types for Rust_



## Evaluation



`Flux` v. `Prusti` for Memory Safety



---



## Evaluation



`Flux` v. `Prusti` for Memory Safety



---



## `Flux` v. `Prusti` by the numbers



![width:800px center](img/flux-v-prusti.png)



---



## `Flux` v. `Prusti` : Types Simplify Specifications



```rust

// Rust

fn store(&mut self, idx: usize, value: T)



// Flux

fn store(self: &mut RVec[@n], idx: usize{idx < n}, value: T)



// Prusti

requires(index < self.len())

ensures(self.len() == old(self.len()))

ensures(forall(|i:usize| (i < self.len() && i != index) ==>

                    self.lookup(i) == old(self.lookup(i))))

ensures(self.lookup(index) == value)

```



**Quantifiers make SMT _slow_!**



---



## `Flux` v. `Prusti` : Types Enable Code Reuse







### **Example:** `kmeans.rs` in `flux`







```rust

fn kmeans(n:usize, cs: k@RVec[n]>, ps: &RVec[n]>, iters: i32) -> RVec[n]>[k] where 0 < k

```



- **Point** is an `n` dimensional float-vec `RVec[n]`



- **Centers** are a vector of `k` points `RVec[n]>[k]`



---



## `Flux` v. `Prusti` : Types Enable Code Reuse







### **Example:** `kmeans.rs` in `prusti`







```rust

ensures(forall(|i:usize| (i < self.len() && i != index) ==>

                    self.lookup(i) == old(self.lookup(i))))

```



### Value equality _prevents vector nesting!_



Have to duplicate code in new (untrusted) [wrapper library](compare/matwrapper.rs)



---



## `Flux` v. `Prusti` : Types Simplify Invariants & Inference



### Dimension preservation obfuscated by `Prusti` spec



```rust

#[requires(i < self.rows() && j < self.cols())]

#[ensures(self.cols() == old(self.cols()) && self.rows() == old(self.rows()))]

pub fn set(&mut self, i: usize, j: usize, value: T) {

  self.inner[i][j] = value;

}

```



### Hassle programmer for dimension preservation invariants



- `kmeans::normalize_centers` in [prusti](prusti-kmeans.rs) vs. [flux](flux-kmeans.rs)



- `fft::loop_a` in [prusti](prusti-fft.rs) vs. [flux](flux-fft.rs)



---



### Burden programmer with dimension preservation invariants



- `fft::loop_a` in [prusti](prusti-fft.rs) vs. [flux](flux-fft.rs)



![width:850px center](img/flux-v-prusti-fft.png)



---



## `Flux` v. `Prusti` : Types Simplify Invariants & Inference



![width:850px](img/flux-v-prusti-vectors.png)



### Types _decompose_ quantified assertions to _quantifier-free_ refinements



`flux` infers quantifier-free refinements via Horn-clauses/Liquid Typing



---



## `Flux` v. `Prusti` : Types Simplify Invariants & Inference



`kmp_search` in [prusti](prusti-kmp.rs) vs. [flux](flux-kmp.rs)



```rust

// Prusti

body_invariant!(forall(|x: usize| x < t.len() ==> t.lookup(x) < pat_len));



// Flux

t: RVec<{v:v < pat_len}>

```







### Types _decompose_ quantified assertions to _quantifier-free_ refinements



`flux` infers quantifier-free refinements via Horn-clauses/Liquid Typing



---



### Types _decompose_ quantified assertions to _quantifier-free_ refinements



`kmp_search` in [prusti](prusti-kmp.rs) vs. [flux](flux-kmp.rs)



![width:1000px](img/flux-v-prusti-kmp.png)



---



## Motivation



Types vs. Floyd-Hoare logic



## Demonstration



`Flux` Liquid Types for Rust



## Evaluation



_`Flux` v. `Prusti` for Memory Safety_



---



## Conclusions



**Refinements + Rust's Ownership = Ergonomic Imperative Verification...**



- Specify complex invariants by _composing_ type constructors & QF refinements



- Verify complex invariants by _decomposing_ validity checks via syntactic subtyping



---



## Conclusions



**Refinements + Rust's Ownership = Ergonomic Imperative Verification...**



- Specify complex invariants by _composing_ type constructors & QF refinements



- Verify complex invariants by _decomposing_ validity checks via syntactic subtyping



**... But this is just the beginning**



- `Flux` restricts specifications, `Prusti` allows _way_ more ...



- ... how to stretch types to "full functional correctness"?



**What are interesting application domains to focus on?**



---



# `flux` https://github.com/liquid-rust/flux/