1093 Fundamental

Currying and Partial Application

FunctionsHigher-Order Programming

Tutorial Video

Text description (accessibility)

This video demonstrates the "Currying and Partial Application" functional Rust example. Difficulty level: Fundamental. Key concepts covered: Functions, Higher-Order Programming. Implement `let add x y = x + y` in Rust, showing how OCaml's automatic currying translates to Rust's explicit closures for partial application. Key difference from OCaml: 1. **Currying:** OCaml auto

Tutorial

The Problem

Implement let add x y = x + y in Rust, showing how OCaml's automatic currying translates to Rust's explicit closures for partial application.

🎯 Learning Outcomes

• How OCaml's auto-currying maps to Rust's impl Fn return types

• Using move closures to capture values for partial application

• Writing generic curried functions with trait bounds (Add + Copy)

• Building curry / uncurry combinators as higher-order functions

🦀 The Rust Way

Rust functions take all arguments at once. To get partial application, you return a closure: fn add_partial(x: i64) -> impl Fn(i64) -> i64. The move keyword transfers ownership of captured values into the closure.

Code Example

/// Plain two-argument function.
fn add(x: i64, y: i64) -> i64 {
    x + y
}

/// Partial application: return a closure capturing `x`.
fn add_partial(x: i64) -> impl Fn(i64) -> i64 {
    move |y| x + y
}

let add5 = add_partial(5);
assert_eq!(add5(3), 8);

(* All functions are automatically curried *)
let add x y = x + y

(* Partial application — just supply fewer arguments *)
let add5 = add 5

(* Equivalent desugared form *)
let add' = fun x -> fun y -> x + y

Key Differences

Currying: OCaml auto-curries all functions; Rust requires explicit closure returns

Type signatures: OCaml infers int -> int -> int; Rust needs impl Fn(i64) -> i64 return type

Capture semantics: OCaml closures capture by GC reference; Rust uses move for ownership transfer

Polymorphism: OCaml uses parametric polymorphism implicitly; Rust requires <T: Add + Copy> bounds

OCaml Approach

In OCaml, let add x y = x + y is sugar for let add = fun x -> fun y -> x + y. Every function is automatically curried — add 5 returns a function. No special syntax needed for partial application.

Full Source

#![allow(clippy::all)]
// # Currying and Partial Application
//
// OCaml: `let add x y = x + y` — all functions are automatically curried.
// Rust has no auto-currying, but closures make partial application natural.

// ---------------------------------------------------------------------------
// Solution 1: Idiomatic Rust — closures for partial application
// ---------------------------------------------------------------------------

/// A plain two-argument function — Rust's default style.
pub fn add(x: i64, y: i64) -> i64 {
    x + y
}

/// Returns a closure that adds `x` to its argument.
/// This is how Rust developers do partial application: return a closure.
pub fn add_partial(x: i64) -> impl Fn(i64) -> i64 {
    move |y| x + y
}

// ---------------------------------------------------------------------------
// Solution 2: Curried style — mirrors OCaml's `let add x y = x + y`
// ---------------------------------------------------------------------------

/// Fully curried: each argument returns a closure expecting the next.
/// Closest to OCaml's automatic currying, but explicit in Rust.
pub fn add_curried(x: i64) -> impl Fn(i64) -> i64 {
    move |y| x + y
}

/// A generic curried add for any type supporting `Add`.
/// Shows how Rust generics replace OCaml's polymorphism here.
pub fn add_curried_generic<T>(x: T) -> impl Fn(T) -> T
where
    T: std::ops::Add<Output = T> + Copy,
{
    move |y| x + y
}

// ---------------------------------------------------------------------------
// Solution 3: Higher-order — curry any two-argument function
// ---------------------------------------------------------------------------

/// Transforms a two-argument function into a curried chain.
/// `curry(f)` returns `|x| |y| f(x, y)`.
pub fn curry<A, B, C, F>(f: F) -> impl Fn(A) -> Box<dyn Fn(B) -> C>
where
    A: Copy + 'static,
    B: 'static,
    C: 'static,
    F: Fn(A, B) -> C + Copy + 'static,
{
    move |a: A| Box::new(move |b: B| f(a, b))
}

/// The inverse: uncurry a curried function back to a two-argument function.
pub fn uncurry<A, B, C, F, G>(f: F) -> impl Fn(A, B) -> C
where
    F: Fn(A) -> G,
    G: Fn(B) -> C,
{
    move |a, b| f(a)(b)
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_add_direct() {
        assert_eq!(add(3, 4), 7);
        assert_eq!(add(-1, 1), 0);
        assert_eq!(add(0, 0), 0);
    }

    #[test]
    fn test_partial_application() {
        let add5 = add_partial(5);
        assert_eq!(add5(3), 8);
        assert_eq!(add5(0), 5);
        assert_eq!(add5(-5), 0);
    }

    #[test]
    fn test_curried() {
        let add10 = add_curried(10);
        assert_eq!(add10(1), 11);
        assert_eq!(add10(-10), 0);

        // Call in one shot: add_curried(2)(3)
        assert_eq!(add_curried(2)(3), 5);
    }

    #[test]
    fn test_curried_generic() {
        let add_f64 = add_curried_generic(1.5_f64);
        assert!((add_f64(2.5) - 4.0).abs() < f64::EPSILON);

        let add_i32 = add_curried_generic(100_i32);
        assert_eq!(add_i32(23), 123);
    }

    #[test]
    fn test_curry_combinator() {
        let curried_add = curry(add);
        let add7 = curried_add(7);
        assert_eq!(add7(3), 10);
        assert_eq!(add7(0), 7);
    }

    #[test]
    fn test_uncurry_combinator() {
        let uncurried = uncurry(add_curried);
        assert_eq!(uncurried(3, 4), 7);
        assert_eq!(uncurried(0, 0), 0);
    }

    #[test]
    fn test_curry_with_multiply() {
        let mul = |a: i64, b: i64| a * b;
        let curried_mul = curry(mul);
        let double = curried_mul(2);
        assert_eq!(double(5), 10);
        assert_eq!(double(0), 0);
    }
}

(* Currying and Partial Application *)

(* In OCaml, ALL functions are automatically curried.
   `let add x y = x + y` is syntactic sugar for:
   `let add = fun x -> fun y -> x + y` *)

(* Idiomatic OCaml — currying is the default *)
let add x y = x + y

(* Partial application — just supply fewer arguments *)
let add5 = add 5
let add10 = add 10

(* Float version — OCaml needs a separate operator (+.) *)
let add_float x y = x +. y
let add_half = add_float 0.5

(* Generic curry/uncurry combinators *)
let curry f x y = f (x, y)
let uncurry f (x, y) = f x y

(* A tupled add to demonstrate curry combinator *)
let add_tupled (x, y) = x + y

let () =
  (* Direct call *)
  assert (add 3 4 = 7);

  (* Partial application *)
  assert (add5 3 = 8);
  assert (add5 0 = 5);
  assert (add10 1 = 11);

  (* Float partial application *)
  assert (add_half 1.5 = 2.0);

  (* curry combinator: turn tupled function into curried *)
  let curried = curry add_tupled in
  assert (curried 7 3 = 10);

  (* uncurry combinator: turn curried function into tupled *)
  let uncurried = uncurry add in
  assert (uncurried (3, 4) = 7);

  print_endline "ok"

✓ Tests Rust test suite

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_add_direct() {
        assert_eq!(add(3, 4), 7);
        assert_eq!(add(-1, 1), 0);
        assert_eq!(add(0, 0), 0);
    }

    #[test]
    fn test_partial_application() {
        let add5 = add_partial(5);
        assert_eq!(add5(3), 8);
        assert_eq!(add5(0), 5);
        assert_eq!(add5(-5), 0);
    }

    #[test]
    fn test_curried() {
        let add10 = add_curried(10);
        assert_eq!(add10(1), 11);
        assert_eq!(add10(-10), 0);

        // Call in one shot: add_curried(2)(3)
        assert_eq!(add_curried(2)(3), 5);
    }

    #[test]
    fn test_curried_generic() {
        let add_f64 = add_curried_generic(1.5_f64);
        assert!((add_f64(2.5) - 4.0).abs() < f64::EPSILON);

        let add_i32 = add_curried_generic(100_i32);
        assert_eq!(add_i32(23), 123);
    }

    #[test]
    fn test_curry_combinator() {
        let curried_add = curry(add);
        let add7 = curried_add(7);
        assert_eq!(add7(3), 10);
        assert_eq!(add7(0), 7);
    }

    #[test]
    fn test_uncurry_combinator() {
        let uncurried = uncurry(add_curried);
        assert_eq!(uncurried(3, 4), 7);
        assert_eq!(uncurried(0, 0), 0);
    }

    #[test]
    fn test_curry_with_multiply() {
        let mul = |a: i64, b: i64| a * b;
        let curried_mul = curry(mul);
        let double = curried_mul(2);
        assert_eq!(double(5), 10);
        assert_eq!(double(0), 0);
    }
}

Deep Comparison

OCaml vs Rust: Currying and Partial Application

Side-by-Side Code

OCaml

(* All functions are automatically curried *)
let add x y = x + y

(* Partial application — just supply fewer arguments *)
let add5 = add 5

(* Equivalent desugared form *)
let add' = fun x -> fun y -> x + y

Rust (idiomatic)

/// Plain two-argument function.
fn add(x: i64, y: i64) -> i64 {
    x + y
}

/// Partial application: return a closure capturing `x`.
fn add_partial(x: i64) -> impl Fn(i64) -> i64 {
    move |y| x + y
}

let add5 = add_partial(5);
assert_eq!(add5(3), 8);

Rust (functional/recursive)

/// Fully curried — mirrors OCaml's `fun x -> fun y -> x + y`.
fn add_curried(x: i64) -> impl Fn(i64) -> i64 {
    move |y| x + y
}

/// Generic version with trait bounds.
fn add_curried_generic<T: std::ops::Add<Output = T> + Copy>(x: T) -> impl Fn(T) -> T {
    move |y| x + y
}

// One-shot call reads like OCaml: add_curried(2)(3)
assert_eq!(add_curried(2)(3), 5);

Type Signatures

Concept	OCaml	Rust
Function signature	`val add : int -> int -> int`	`fn add(x: i64, y: i64) -> i64`
Curried signature	`int -> int -> int` (same!)	`fn(i64) -> impl Fn(i64) -> i64`
Partial application	`let add5 = add 5`	`let add5 = add_partial(5)`
Polymorphic	`val add : 'a -> 'a -> 'a` (with `(+)`)	`fn add<T: Add<Output=T> + Copy>(x: T) -> impl Fn(T) -> T`
Closure type	Implicit, GC-managed	`impl Fn(i64) -> i64` (stack or heap via `Box<dyn Fn>`)
Curry combinator	`val curry : ('a * 'b -> 'c) -> 'a -> 'b -> 'c`	`fn curry<A,B,C,F>(f: F) -> impl Fn(A) -> Box<dyn Fn(B) -> C>`

Key Insights

OCaml currying is invisible; Rust currying is explicit. In OCaml, let add x y = x + y is already fun x -> fun y -> x + y. In Rust, you must explicitly return a closure to achieve the same effect.

**move closures are Rust's capture mechanism.** Where OCaml's GC handles closure environments automatically, Rust's move |y| x + y transfers ownership of x into the closure — no garbage collection needed.

**impl Fn vs Box<dyn Fn> — static vs dynamic dispatch.** When the caller knows the concrete closure type, impl Fn gives zero-cost abstraction. When you need to store or return closures of varying types (e.g., from the curry combinator), Box<dyn Fn> provides dynamic dispatch.

Trait bounds replace OCaml's implicit polymorphism. OCaml's (+) works on any numeric type via ad-hoc polymorphism. Rust requires T: Add<Output = T> + Copy to express the same constraint — more verbose but explicit.

Rust's closures are zero-cost. Unlike OCaml's heap-allocated closure environments, Rust's move closures with impl Fn return types are monomorphized at compile time — no allocation, no indirection.

When to Use Each Style

Use idiomatic Rust when: You have a fixed-arity function and occasionally want partial application — add_partial(5) is clear and efficient.

Use curried Rust when: You're building combinator libraries or DSLs where function composition and point-free style improve readability, e.g., let transform = compose(scale(2.0), translate(1.0)).

Exercises

Write a curried add3 function i32 -> i32 -> i32 -> i32 and use partial application to create an increment and a add10 specialization.

Implement flip — a higher-order function that takes f: A -> B -> C and returns B -> A -> C — and use it to partially apply the second argument of a binary function.

Use currying and partial application to build a configurable string formatter: a curried format_field that accepts a padding width, an alignment, and finally a value, returning the formatted string.

Open Source Repos

functional-rust

View the source for this example on GitHub — OCaml and Rust side by side in the repo.

Rust