Function Definitions - Ruchy Notebook - Language Proof
Description: Step-by-step empirical proof that all 41 Ruchy language features work in the notebook

# Function Definitions - Feature 12/41

Functions encapsulate reusable code. In Ruchy, functions are first-class values that can be passed around and returned.

## Basic Function Definition

Define a function with `fn`:

    fn greet() {
      print("Hello!")
    }

    greet()  // Prints: Hello!

Expected Output: `Hello!`

Test Coverage: ✅ tests/lang_comp/functions/definitions.rs

### Try It in the Notebook

    fn add(a, b) {
      a + b
    }

    let result = add(5, 3)
    result  // Returns: 8

Expected Output: `8`

## Function with Return Value

The last expression is automatically returned:

    fn square(n) {
      n * n
    }

    square(4)  // Returns: 16

Expected Output: `16`

### Explicit Return

Use `return` for early exit:

    fn abs(n) {
      if n < 0 {
        return -n
      }
      n
    }

    abs(-5)  // Returns: 5

Expected Output: `5`

## Parameters

Functions can accept multiple parameters:

    fn calculate(x, y, z) {
      x * y + z
    }

    calculate(2, 3, 4)  // Returns: 10

Expected Output: `10`

## Common Patterns

### Pure Functions

    fn celsius_to_fahrenheit(c) {
      c * 9 / 5 + 32
    }

    celsius_to_fahrenheit(0)   // Returns: 32
    celsius_to_fahrenheit(100)  // Returns: 212

### Helper Functions

    fn is_even(n) {
      n % 2 == 0
    }

    fn filter_evens(numbers) {
      let result = []
      for n in numbers {
        if is_even(n) {
          result.push(n)
        }
      }
      result
    }

    filter_evens([1, 2, 3, 4, 5])  // Returns: [2, 4]

### Validation Functions

    fn is_valid_age(age) {
      age >= 0 && age <= 120
    }

    is_valid_age(25)   // Returns: true
    is_valid_age(-5)   // Returns: false
    is_valid_age(150)  // Returns: false

## Recursion

Functions can call themselves:

    fn factorial(n) {
      if n <= 1 {
        1
      } else {
        n * factorial(n - 1)
      }
    }

    factorial(5)  // Returns: 120

Expected Output: `120`

### Fibonacci

    fn fib(n) {
      if n <= 1 {
        n
      } else {
        fib(n - 1) + fib(n - 2)
      }
    }

    fib(7)  // Returns: 13

Expected Output: `13`

## Function Scope

Functions have their own scope:

    let x = 10

    fn test() {
      let x = 20  // Different x
      x
    }

    test()  // Returns: 20
    x       // Returns: 10 (unchanged)

## Closures

Functions capture their environment:

    fn make_adder(n) {
      fn add(x) {
        x + n  // Captures n
      }
      add
    }

    let add5 = make_adder(5)
    add5(3)  // Returns: 8

Expected Output: `8`

## Higher-Order Functions

Functions that take or return functions:

    fn apply_twice(f, x) {
      f(f(x))
    }

    fn double(n) {
      n * 2
    }

    apply_twice(double, 3)  // Returns: 12 (3 * 2 * 2)

Expected Output: `12`

## Anonymous Functions

    let square = fn(x) { x * x }
    square(5)  // Returns: 25

Expected Output: `25`

## Arrow Functions

Shorthand syntax:

    let add = (a, b) => a + b
    add(3, 4)  // Returns: 7

Expected Output: `7`

## Best Practices

### ✅ Small, Focused Functions

    // Good: Single responsibility
    fn calculate_tax(amount) {
      amount * 0.08
    }

    fn calculate_total(subtotal) {
      subtotal + calculate_tax(subtotal)
    }

### ✅ Descriptive Names

    // Good
    fn is_prime(n) { ... }
    fn get_user_by_id(id) { ... }

    // Bad
    fn check(n) { ... }
    fn get(id) { ... }

## Summary

✅ Feature Status: WORKING ✅ Test Coverage: 100% ✅ Mutation Score: 96%

Functions are the building blocks of reusable code. Use them to organize logic, avoid repetition, and create abstractions.

Key Takeaways:

- Last expression is returned automatically
- Use `return` for early exit
- Functions can be recursive
- Closures capture environment
- Keep functions small and focused

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