078 Intermediate

078 — Where Clauses

Functional Programming

Tutorial

The Problem

Express complex trait bounds on generic functions and types using Rust's where clause syntax. Implement print_if_equal, zip_with, sum_items, dot_product, and display_collection — each requiring multiple or compound constraints — and compare with OCaml's module functor approach to constraining polymorphic code.

🎯 Learning Outcomes

• Write where clauses to separate complex bounds from the function signature

• Combine multiple trait bounds on a single type parameter (T: Display + PartialEq)

• Apply bounds to associated types of iterator (I::Item: Add + Default)

• Use IntoIterator with I::Item: Display for generic collection printing

• Understand when where improves readability over inline bound syntax

• Map OCaml functor module signatures to Rust where constraints

Code Example

//! 078: Where Clauses — complex trait bounds in a readable form.
//!
//! Inline bounds (`fn f<T: A + B>()`) work for simple cases. `where`
//! clauses move bounds after the signature, which:
//! - keeps long bound lists from crowding the return type,
//! - spreads constraints across several type parameters cleanly,
//! - is the *only* place associated-type bounds like `I::Item: Display`
//!   can be written.
//!
//! OCaml expresses the same idea with module functors and signatures
//! (`module type SUMMABLE = sig … end`); Rust expresses it by constraining
//! generic parameters directly. The constraint surface is equivalent,
//! but Rust's monomorphization keeps it zero-cost at runtime.

use std::fmt::Display;
use std::ops::{Add, Mul};

/// Two bounds on a single parameter — readable either way, but `where`
/// scales when more show up.
pub fn print_if_equal<T>(a: &T, b: &T) -> String
where
    T: Display + PartialEq,
{
    if a == b {
        format!("{} == {}", a, b)
    } else {
        format!("{} != {}", a, b)
    }
}

/// Three unrelated type parameters plus a closure — the canonical case
/// where inline bounds turn illegible.
pub fn zip_with<A, B, C, F>(a: &[A], b: &[B], f: F) -> Vec<C>
where
    A: Clone,
    B: Clone,
    F: Fn(A, B) -> C,
{
    a.iter()
        .cloned()
        .zip(b.iter().cloned())
        .map(|(x, y)| f(x, y))
        .collect()
}

/// Associated-type bound — `I::Item: Add + Default` is only spellable in
/// a `where` clause. Mirrors OCaml's `MathOps(S : SUMMABLE).sum`.
pub fn sum_items<I>(iter: I) -> I::Item
where
    I: Iterator,
    I::Item: Add<Output = I::Item> + Default,
{
    iter.fold(I::Item::default(), |acc, x| acc + x)
}

/// Four bounds stacked — the `RING` signature from the OCaml example,
/// expressed as arithmetic + memory bounds on a single `T`.
pub fn dot_product<T>(a: &[T], b: &[T]) -> T
where
    T: Add<Output = T> + Mul<Output = T> + Default + Copy,
{
    a.iter()
        .zip(b.iter())
        .fold(T::default(), |acc, (&x, &y)| acc + x * y)
}

/// Generic pretty-printer: accepts any iterable whose items are `Display`.
pub fn display_collection<I>(iter: I) -> String
where
    I: IntoIterator,
    I::Item: Display,
{
    let items: Vec<String> = iter.into_iter().map(|x| format!("{}", x)).collect();
    format!("[{}]", items.join(", "))
}

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

    #[test]
    fn print_if_equal_formats_both_outcomes() {
        assert_eq!(print_if_equal(&5, &5), "5 == 5");
        assert_eq!(print_if_equal(&3, &4), "3 != 4");
        assert_eq!(print_if_equal(&"a", &"a"), "a == a");
    }

    #[test]
    fn zip_with_combines_two_slices() {
        assert_eq!(
            zip_with(&[1, 2, 3], &[4, 5, 6], |a, b| a + b),
            vec![5, 7, 9]
        );
        assert_eq!(zip_with(&[1, 2], &[3, 4], |a, b| a * b), vec![3, 8]);
    }

    #[test]
    fn sum_items_uses_associated_type_bound() {
        assert_eq!(sum_items(vec![1, 2, 3, 4, 5].into_iter()), 15);
        assert_eq!(sum_items::<std::vec::IntoIter<i32>>(vec![].into_iter()), 0);
    }

    #[test]
    fn dot_product_matches_ocaml_int_ring() {
        // OCaml: IntRing.dot_product [1; 2; 3] [4; 5; 6] = 32
        assert_eq!(dot_product(&[1, 2, 3], &[4, 5, 6]), 32);
        assert_eq!(dot_product::<f64>(&[1.0, 2.0], &[3.0, 4.0]), 11.0);
    }

    #[test]
    fn display_collection_works_on_any_iterable() {
        assert_eq!(display_collection(vec![1, 2, 3]), "[1, 2, 3]");
        assert_eq!(display_collection(["a", "b", "c"]), "[a, b, c]");
        assert_eq!(display_collection(Vec::<i32>::new()), "[]");
    }
}

(* 078: Where Clauses — OCaml functor constraints *)
(* OCaml uses module signatures as "where clause" equivalent *)

module type SUMMABLE = sig
  type t
  val zero : t
  val add : t -> t -> t
  val to_string : t -> string
end

module type MULTIPLIABLE = sig
  type t
  val one : t
  val mul : t -> t -> t
end

(* Functor with multiple constraints *)
module MathOps (S : SUMMABLE) = struct
  let sum lst = List.fold_left S.add S.zero lst
  let sum_to_string lst =
    S.to_string (sum lst)
end

module IntSum = MathOps(struct
  type t = int
  let zero = 0
  let add = ( + )
  let to_string = string_of_int
end)

module FloatSum = MathOps(struct
  type t = float
  let zero = 0.0
  let add = ( +. )
  let to_string = string_of_float
end)

(* Complex constraint: both summable and multipliable *)
module type RING = sig
  include SUMMABLE
  include MULTIPLIABLE with type t := t
end

module RingOps (R : RING) = struct
  let dot_product a b =
    List.fold_left2 (fun acc x y -> R.add acc (R.mul x y)) R.zero a b
end

module IntRing = RingOps(struct
  type t = int
  let zero = 0
  let one = 1
  let add = ( + )
  let mul = ( * )
  let to_string = string_of_int
end)

(* Tests *)
let () =
  assert (IntSum.sum [1; 2; 3; 4; 5] = 15);
  assert (IntSum.sum_to_string [1; 2; 3] = "6");
  assert (abs_float (FloatSum.sum [1.0; 2.0; 3.0] -. 6.0) < 0.001);
  assert (IntRing.dot_product [1; 2; 3] [4; 5; 6] = 32);
  Printf.printf "✓ All tests passed\n"

Key Differences

Aspect	Rust	OCaml
Syntax	`where T: Trait1 + Trait2`	`module type SIG = sig … end`
Scope	Per function/impl block	Module-level functor
Associated type bounds	`I::Item: Trait` in `where`	`with type item = t` refinement
Constraint composition	`+` on trait bounds	`include` in module types
Monomorphization	Yes, at compile time	Functors instantiated at application
Runtime cost	None	None

where syntax is purely cosmetic in most cases — it does not change semantics versus inline bounds. The exception is associated type constraints, which require where. OCaml functors produce named modules, making them first-class values; Rust generic functions are erased into monomorphized copies.

OCaml Approach

OCaml expresses constraints via module signatures. A functor MathOps(S : SUMMABLE) requires the input module to provide zero, add, and to_string. More complex constraints combine signatures: module type RING = sig include SUMMABLE include MULTIPLIABLE end. Concrete modules like IntSum and FloatSum are produced by applying the functor to struct-style anonymous modules. The type system ensures constraints are satisfied at functor application, not at call sites — equivalent to Rust's monomorphization.

Full Source

//! 078: Where Clauses — complex trait bounds in a readable form.
//!
//! Inline bounds (`fn f<T: A + B>()`) work for simple cases. `where`
//! clauses move bounds after the signature, which:
//! - keeps long bound lists from crowding the return type,
//! - spreads constraints across several type parameters cleanly,
//! - is the *only* place associated-type bounds like `I::Item: Display`
//!   can be written.
//!
//! OCaml expresses the same idea with module functors and signatures
//! (`module type SUMMABLE = sig … end`); Rust expresses it by constraining
//! generic parameters directly. The constraint surface is equivalent,
//! but Rust's monomorphization keeps it zero-cost at runtime.

use std::fmt::Display;
use std::ops::{Add, Mul};

/// Two bounds on a single parameter — readable either way, but `where`
/// scales when more show up.
pub fn print_if_equal<T>(a: &T, b: &T) -> String
where
    T: Display + PartialEq,
{
    if a == b {
        format!("{} == {}", a, b)
    } else {
        format!("{} != {}", a, b)
    }
}

/// Three unrelated type parameters plus a closure — the canonical case
/// where inline bounds turn illegible.
pub fn zip_with<A, B, C, F>(a: &[A], b: &[B], f: F) -> Vec<C>
where
    A: Clone,
    B: Clone,
    F: Fn(A, B) -> C,
{
    a.iter()
        .cloned()
        .zip(b.iter().cloned())
        .map(|(x, y)| f(x, y))
        .collect()
}

/// Associated-type bound — `I::Item: Add + Default` is only spellable in
/// a `where` clause. Mirrors OCaml's `MathOps(S : SUMMABLE).sum`.
pub fn sum_items<I>(iter: I) -> I::Item
where
    I: Iterator,
    I::Item: Add<Output = I::Item> + Default,
{
    iter.fold(I::Item::default(), |acc, x| acc + x)
}

/// Four bounds stacked — the `RING` signature from the OCaml example,
/// expressed as arithmetic + memory bounds on a single `T`.
pub fn dot_product<T>(a: &[T], b: &[T]) -> T
where
    T: Add<Output = T> + Mul<Output = T> + Default + Copy,
{
    a.iter()
        .zip(b.iter())
        .fold(T::default(), |acc, (&x, &y)| acc + x * y)
}

/// Generic pretty-printer: accepts any iterable whose items are `Display`.
pub fn display_collection<I>(iter: I) -> String
where
    I: IntoIterator,
    I::Item: Display,
{
    let items: Vec<String> = iter.into_iter().map(|x| format!("{}", x)).collect();
    format!("[{}]", items.join(", "))
}

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

    #[test]
    fn print_if_equal_formats_both_outcomes() {
        assert_eq!(print_if_equal(&5, &5), "5 == 5");
        assert_eq!(print_if_equal(&3, &4), "3 != 4");
        assert_eq!(print_if_equal(&"a", &"a"), "a == a");
    }

    #[test]
    fn zip_with_combines_two_slices() {
        assert_eq!(
            zip_with(&[1, 2, 3], &[4, 5, 6], |a, b| a + b),
            vec![5, 7, 9]
        );
        assert_eq!(zip_with(&[1, 2], &[3, 4], |a, b| a * b), vec![3, 8]);
    }

    #[test]
    fn sum_items_uses_associated_type_bound() {
        assert_eq!(sum_items(vec![1, 2, 3, 4, 5].into_iter()), 15);
        assert_eq!(sum_items::<std::vec::IntoIter<i32>>(vec![].into_iter()), 0);
    }

    #[test]
    fn dot_product_matches_ocaml_int_ring() {
        // OCaml: IntRing.dot_product [1; 2; 3] [4; 5; 6] = 32
        assert_eq!(dot_product(&[1, 2, 3], &[4, 5, 6]), 32);
        assert_eq!(dot_product::<f64>(&[1.0, 2.0], &[3.0, 4.0]), 11.0);
    }

    #[test]
    fn display_collection_works_on_any_iterable() {
        assert_eq!(display_collection(vec![1, 2, 3]), "[1, 2, 3]");
        assert_eq!(display_collection(["a", "b", "c"]), "[a, b, c]");
        assert_eq!(display_collection(Vec::<i32>::new()), "[]");
    }
}

(* 078: Where Clauses — OCaml functor constraints *)
(* OCaml uses module signatures as "where clause" equivalent *)

module type SUMMABLE = sig
  type t
  val zero : t
  val add : t -> t -> t
  val to_string : t -> string
end

module type MULTIPLIABLE = sig
  type t
  val one : t
  val mul : t -> t -> t
end

(* Functor with multiple constraints *)
module MathOps (S : SUMMABLE) = struct
  let sum lst = List.fold_left S.add S.zero lst
  let sum_to_string lst =
    S.to_string (sum lst)
end

module IntSum = MathOps(struct
  type t = int
  let zero = 0
  let add = ( + )
  let to_string = string_of_int
end)

module FloatSum = MathOps(struct
  type t = float
  let zero = 0.0
  let add = ( +. )
  let to_string = string_of_float
end)

(* Complex constraint: both summable and multipliable *)
module type RING = sig
  include SUMMABLE
  include MULTIPLIABLE with type t := t
end

module RingOps (R : RING) = struct
  let dot_product a b =
    List.fold_left2 (fun acc x y -> R.add acc (R.mul x y)) R.zero a b
end

module IntRing = RingOps(struct
  type t = int
  let zero = 0
  let one = 1
  let add = ( + )
  let mul = ( * )
  let to_string = string_of_int
end)

(* Tests *)
let () =
  assert (IntSum.sum [1; 2; 3; 4; 5] = 15);
  assert (IntSum.sum_to_string [1; 2; 3] = "6");
  assert (abs_float (FloatSum.sum [1.0; 2.0; 3.0] -. 6.0) < 0.001);
  assert (IntRing.dot_product [1; 2; 3] [4; 5; 6] = 32);
  Printf.printf "✓ All tests passed\n"

✓ Tests Rust test suite

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

    #[test]
    fn print_if_equal_formats_both_outcomes() {
        assert_eq!(print_if_equal(&5, &5), "5 == 5");
        assert_eq!(print_if_equal(&3, &4), "3 != 4");
        assert_eq!(print_if_equal(&"a", &"a"), "a == a");
    }

    #[test]
    fn zip_with_combines_two_slices() {
        assert_eq!(
            zip_with(&[1, 2, 3], &[4, 5, 6], |a, b| a + b),
            vec![5, 7, 9]
        );
        assert_eq!(zip_with(&[1, 2], &[3, 4], |a, b| a * b), vec![3, 8]);
    }

    #[test]
    fn sum_items_uses_associated_type_bound() {
        assert_eq!(sum_items(vec![1, 2, 3, 4, 5].into_iter()), 15);
        assert_eq!(sum_items::<std::vec::IntoIter<i32>>(vec![].into_iter()), 0);
    }

    #[test]
    fn dot_product_matches_ocaml_int_ring() {
        // OCaml: IntRing.dot_product [1; 2; 3] [4; 5; 6] = 32
        assert_eq!(dot_product(&[1, 2, 3], &[4, 5, 6]), 32);
        assert_eq!(dot_product::<f64>(&[1.0, 2.0], &[3.0, 4.0]), 11.0);
    }

    #[test]
    fn display_collection_works_on_any_iterable() {
        assert_eq!(display_collection(vec![1, 2, 3]), "[1, 2, 3]");
        assert_eq!(display_collection(["a", "b", "c"]), "[a, b, c]");
        assert_eq!(display_collection(Vec::<i32>::new()), "[]");
    }
}

Deep Comparison

Core Insight

Where clauses move trait bounds after the function signature for clarity. Essential when bounds involve associated types, multiple type parameters, or complex relationships.

OCaml Approach

• No direct equivalent — module functors handle complex constraints

• Type constraints in module signatures

Rust Approach

• where T: Trait, U: Trait after signature

• Required for associated type bounds: where I::Item: Display

• Cleaner than inline bounds for complex cases

Comparison Table

Feature	OCaml	Rust
Simple bound	N/A	`<T: Display>`
Complex bound	Functor signature	`where T: A + B, U: C`
Associated type	Module type	`where I::Item: Display`

Exercises

Add a min_max function with signature fn min_max<T>(slice: &[T]) -> Option<(&T, &T)> using a where clause requiring T: PartialOrd.

Write map_collect<I, F, B>(iter: I, f: F) -> Vec<B> using where to express the iterator and closure bounds separately.

Implement a Printable trait with a print method, then use where T: Printable + Clone in a function that clones and prints each element of a slice.

Create a functor in OCaml called Sorted(C : COMPARABLE) and implement a sorted insertion function. Compare the constraint surface area with the Rust where equivalent.

Explore the difference between fn f<T: A + B>() and fn f<T>() where T: A + B. Verify both compile identically with cargo expand or by checking the generated MIR.

Open Source Repos

functional-rust

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

Rust