Implementing Nat in Rust (a la Haskell)

The power of Algebraic Data Types comes to the fore when dealing with complex problem domains. Most modern languages tend towards supporting some form of ADTs, but the complexity of expressing such paradigms is not completely lost when compared to languages that were designed with such support in mind.

Case in point – defining the prototypical example of an algebraic data type, defining the Natural Number type (Nat). Let’s compare the naive implementation in two languages that do have varying support for ADTs – Haskell, and Rust.

First, the Haskell version. Haskell, just like ML and other members of this family, is eminently suited for describing such types almost effortlessly:

module NatDemo where

import Test.HUnit

data Nat = Zero | Succ Nat deriving (Show, Eq)

nat2int :: Nat -> Int
nat2int Zero = 0
nat2int (Succ n) = 1 + nat2int n

int2nat :: Int -> Nat
int2nat 0 = Zero
int2nat n = Succ (int2nat (n-1))

add :: Nat -> Nat -> Nat
add Zero n = n
add (Succ m) n = Succ (add m n)

-- test cases
test1 = TestCase (assertEqual "nat to int" (nat2int (Succ (Succ Zero))) 2)
test2 = TestCase (assertEqual "int to nat" (int2nat 5) (Succ (Succ (Succ (Succ (Succ Zero))))))
test3 = TestCase (assertEqual "add two nats" (add (int2nat 5) (int2nat 6)) (int2nat 11))

tests = TestList [test1, test2, test3]

run = runTestTT tests

Running it to confirm:

Macushla:Nat-in-Rust z0ltan$ ghci
GHCi, version 8.0.2:  😕 for help
Loaded GHCi configuration from /Users/z0ltan/.ghci

Prelude> :l Nat.hs
[1 of 1] Compiling NatDemo          ( Nat.hs, interpreted )
Ok, modules loaded: NatDemo.

*NatDemo> run
Cases: 3  Tried: 3  Errors: 0  Failures: 0
Counts {cases = 3, tried = 3, errors = 0, failures = 0}

As can be seen, it’s almost trivial to define the Nat type in Haskell, as well as write functions that operate on this type. It reads almost exactly like the mathematical version of the concept. Simply beautiful.

Now let’s show the Rust version first, and then perhaps a comment or two on the implementation.

#[derive(Debug, PartialEq)]
enum Nat {

/// open it up for code readability
use Nat::{Zero, Succ};

fn nat_to_int(n: Nat) -> i32 {
    match n {
        Zero => 0,
        Succ(n) => 1 + nat_to_int(*n),

fn int_to_nat(n: i32) -> Nat {
    match n {
        0 => Zero,
        n => Succ(Box::new(int_to_nat(n-1))),

fn add(m: Nat, n: Nat) -> Nat {
    match (m, n) {
        (Zero, n) => n,
        (Succ(m), n) => Succ(Box::new(add(*m, n))),

fn main() {
    assert_eq!(nat_to_int(Succ(Box::new(Succ(Box::new(Succ(Box::new(Zero))))))), 3);
    assert_eq!(int_to_nat(5), Succ(Box::new(Succ(Box::new(Succ(Box::new(Succ(Box::new(Succ(Box::new(Zero)))))))))));
    assert_eq!(add(int_to_nat(5), int_to_nat(11)), int_to_nat(16));

Let’s make sure that it’s all in working condition:

Macushla:Nat-in-Rust z0ltan$ rustc && ./nat
Macushla:Nat-in-Rust z0ltan$

Excellent! It all just works. However, a couple of points to notice – first of all, because Rust doesn’t really have a runtime, we need to wrap the recursive part in a Box (amongst other choices) so that the compiler knows what size the data is (a box, being a pointer, is of a fixed size determinable at compile time). Of course, the test code is positively ghastly because we have to wrap all calls with Box::new, not to mention to remember to dereference the boxed value inside the functions.

Secondly, the code is surprisingly clean for the most part. However, writing the code in not nearly as intuitive as writing the same in Haskell (or ML for that matter). I can only imagine how much more daunting the task would be in a language without pattern matching (amongst other higher-level features) such as Java. Of course we would make it work, but the distance between the intent of the code and the code itself would be much much higher. Syntax does matter, folks!

Well, that was a nice little experiment of an evening.


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