623 Fundamental

Optics: functional rust grand tour

Functional Programming

Tutorial Video

Text description (accessibility)

This video demonstrates the "Optics: functional rust grand tour" functional Rust example. Difficulty level: Fundamental. Key concepts covered: Functional Programming. Optics are composable data accessors originating from Haskell's lens library (Edward Kmett, 2012). Key difference from OCaml: 1. **HKT requirement**: Haskell's van Laarhoven encoding uses Functor/Applicative for optic unification requiring HKT; Rust uses explicit struct types per optic kind.

Tutorial

The Problem

Optics are composable data accessors originating from Haskell's lens library (Edward Kmett, 2012). They solve the deeply-nested update problem in immutable data: updating a field three levels deep requires rebuilding all intermediate values. Optics compose — a lens into a struct field composed with a prism for an enum variant gives a combined accessor that can get, set, and modify deeply nested optional values. The optic hierarchy includes Lens (exactly one focus), Prism (zero or one focus on enum variants), Traversal (zero or more foci), and Iso (lossless bidirectional conversion).

🎯 Learning Outcomes

• The specific optic demonstrated in this example and what it focuses on

• How to implement the optic manually using closures or structs in Rust

• How this optic composes with others in the hierarchy

• The laws the optic must satisfy for correct behavior

• Where optics are used: state management, config manipulation, nested data transformation

Code Example

#![allow(clippy::all)]
//! # Functional Rust Grand Tour
//! Summary of functional programming patterns in Rust.

// Re-exports and summaries of patterns covered

/// Option: Maybe monad
pub fn option_demo() -> Option<i32> {
    Some(42).map(|x| x * 2)
}

/// Result: Error monad
pub fn result_demo() -> Result<i32, &'static str> {
    Ok(10).map(|x| x + 1)
}

/// Iterator: List operations
pub fn iter_demo() -> i32 {
    (1..=10).filter(|x| x % 2 == 0).sum()
}

/// Pattern matching
pub fn match_demo(x: Option<i32>) -> &'static str {
    match x {
        Some(n) if n > 0 => "positive",
        Some(_) => "other",
        None => "none",
    }
}

/// Higher-order functions
pub fn hof_demo<F: Fn(i32) -> i32>(f: F) -> i32 {
    f(10)
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_all() {
        assert_eq!(option_demo(), Some(84));
        assert_eq!(result_demo(), Ok(11));
        assert_eq!(iter_demo(), 30);
        assert_eq!(match_demo(Some(5)), "positive");
        assert_eq!(hof_demo(|x| x * 2), 20);
    }
}

(* Grand tour of FP in OCaml *)
(* A mini order-processing system *)

type currency = USD | EUR | GBP
type price = { amount: float; currency: currency }
type product = { id: string; name: string; price: price; stock: int }
type order_item = { product: product; qty: int }
type order = { id: string; items: order_item list; discount: float }

(* Pure functions *)
let item_subtotal item = item.product.price.amount *. float_of_int item.qty
let order_total order =
  let subtotal = List.fold_left (fun acc i -> acc +. item_subtotal i) 0.0 order.items in
  subtotal *. (1.0 -. order.discount)

let validate_order order =
  let check_stock item =
    if item.qty <= item.product.stock then Ok item
    else Error (Printf.sprintf "%s: only %d in stock" item.product.name item.product.stock)
  in
  let rec validate = function
    | []      -> Ok []
    | x :: xs ->
      match (check_stock x, validate xs) with
      | (Ok i, Ok rest) -> Ok (i :: rest)
      | (Error e, _) | (_, Error e) -> Error e
  in
  match validate order.items with
  | Error e -> Error e
  | Ok _    -> if order.discount < 0.0 || order.discount > 1.0
               then Error "invalid discount" else Ok order

let () =
  let p1 = { id="A"; name="Widget"; price={amount=9.99;currency=USD}; stock=10 } in
  let p2 = { id="B"; name="Gadget"; price={amount=24.99;currency=USD}; stock=2 } in
  let order = { id="ORD-001"; discount=0.1;
    items=[{product=p1;qty=2};{product=p2;qty=1}] } in
  (match validate_order order with
  | Ok o   -> Printf.printf "Order total: $%.2f\n" (order_total o)
  | Error e -> Printf.printf "Error: %s\n" e)

Key Differences

HKT requirement: Haskell's van Laarhoven encoding uses Functor/Applicative for optic unification requiring HKT; Rust uses explicit struct types per optic kind.

Operator syntax: Haskell uses ^., .~, %~ for terse optic use; Rust uses method calls, more verbose but explicit.

Derive macros: lens-rs and similar crates provide derive macros for automatic lens generation; OCaml uses ppx_lens for the same.

Performance: Boxed closure implementations have runtime overhead; monomorphized generic versions compile to zero-cost abstractions.

OCaml Approach

OCaml optics use the same record-with-function approach:

type ('s, 'a) lens = { get: 's -> 'a; set: 's -> 'a -> 's }
let name_lens = { get = (fun u -> u.name); set = (fun u n -> { u with name = n }) }
let compose l1 l2 = { get = (fun s -> l2.get (l1.get s)); set = (fun s a -> l1.set s (l2.set (l1.get s) a)) }

Full Source

#![allow(clippy::all)]
//! # Functional Rust Grand Tour
//! Summary of functional programming patterns in Rust.

// Re-exports and summaries of patterns covered

/// Option: Maybe monad
pub fn option_demo() -> Option<i32> {
    Some(42).map(|x| x * 2)
}

/// Result: Error monad
pub fn result_demo() -> Result<i32, &'static str> {
    Ok(10).map(|x| x + 1)
}

/// Iterator: List operations
pub fn iter_demo() -> i32 {
    (1..=10).filter(|x| x % 2 == 0).sum()
}

/// Pattern matching
pub fn match_demo(x: Option<i32>) -> &'static str {
    match x {
        Some(n) if n > 0 => "positive",
        Some(_) => "other",
        None => "none",
    }
}

/// Higher-order functions
pub fn hof_demo<F: Fn(i32) -> i32>(f: F) -> i32 {
    f(10)
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_all() {
        assert_eq!(option_demo(), Some(84));
        assert_eq!(result_demo(), Ok(11));
        assert_eq!(iter_demo(), 30);
        assert_eq!(match_demo(Some(5)), "positive");
        assert_eq!(hof_demo(|x| x * 2), 20);
    }
}

(* Grand tour of FP in OCaml *)
(* A mini order-processing system *)

type currency = USD | EUR | GBP
type price = { amount: float; currency: currency }
type product = { id: string; name: string; price: price; stock: int }
type order_item = { product: product; qty: int }
type order = { id: string; items: order_item list; discount: float }

(* Pure functions *)
let item_subtotal item = item.product.price.amount *. float_of_int item.qty
let order_total order =
  let subtotal = List.fold_left (fun acc i -> acc +. item_subtotal i) 0.0 order.items in
  subtotal *. (1.0 -. order.discount)

let validate_order order =
  let check_stock item =
    if item.qty <= item.product.stock then Ok item
    else Error (Printf.sprintf "%s: only %d in stock" item.product.name item.product.stock)
  in
  let rec validate = function
    | []      -> Ok []
    | x :: xs ->
      match (check_stock x, validate xs) with
      | (Ok i, Ok rest) -> Ok (i :: rest)
      | (Error e, _) | (_, Error e) -> Error e
  in
  match validate order.items with
  | Error e -> Error e
  | Ok _    -> if order.discount < 0.0 || order.discount > 1.0
               then Error "invalid discount" else Ok order

let () =
  let p1 = { id="A"; name="Widget"; price={amount=9.99;currency=USD}; stock=10 } in
  let p2 = { id="B"; name="Gadget"; price={amount=24.99;currency=USD}; stock=2 } in
  let order = { id="ORD-001"; discount=0.1;
    items=[{product=p1;qty=2};{product=p2;qty=1}] } in
  (match validate_order order with
  | Ok o   -> Printf.printf "Order total: $%.2f\n" (order_total o)
  | Error e -> Printf.printf "Error: %s\n" e)

✓ Tests Rust test suite

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_all() {
        assert_eq!(option_demo(), Some(84));
        assert_eq!(result_demo(), Ok(11));
        assert_eq!(iter_demo(), 30);
        assert_eq!(match_demo(Some(5)), "positive");
        assert_eq!(hof_demo(|x| x * 2), 20);
    }
}

Deep Comparison

Functional Rust Grand Tour

Summary of all FP patterns covered in this series

Exercises

Lens laws: Write tests for all three lens laws: get-set (get after set returns set value), set-get (set to current value is identity), set-set (second set wins).

Prism laws: Write tests for prism laws: preview after review returns Some, set via review then preview round-trips.

Compose two levels: Create a lens for a struct field and a prism for an enum variant in that field — compose them and modify the inner value when the variant is present.

Open Source Repos

functional-rust

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

Rust