# Property-Based Testing

Property-based testing is a powerful testing technique where you define properties that should hold for all inputs, and the testing framework generates random inputs to verify those properties. This guide shows how to use property-based testing in Lux.

## Overview

Instead of writing tests with specific inputs:

```lux
fn test_reverse(): Unit with {Test} = {
    Test.assertEqual([3, 2, 1], List.reverse([1, 2, 3]))
    Test.assertEqual([], List.reverse([]))
}
```

Property-based testing verifies general properties:

```lux
// Property: Reversing a list twice gives back the original list
fn testReverseInvolutive(n: Int): Bool with {Console, Random} = {
    if n <= 0 then true
    else {
        let xs = genIntList(0, 100, 20)
        if List.reverse(List.reverse(xs)) == xs then
            testReverseInvolutive(n - 1)
        else
            false
    }
}
```

## Generators

Generators create random test data. The `Random` effect provides the building blocks.

### Basic Generators

```lux
// Generate random integer in range
fn genInt(min: Int, max: Int): Int with {Random} =
    Random.int(min, max)

// Generate random boolean
fn genBool(): Bool with {Random} =
    Random.bool()

// Generate random float
fn genFloat(): Float with {Random} =
    Random.float()
```

### String Generators

```lux
let CHARS = "abcdefghijklmnopqrstuvwxyz"

// Generate random character
fn genChar(): String with {Random} = {
    let idx = Random.int(0, 25)
    String.substring(CHARS, idx, idx + 1)
}

// Generate random string up to maxLen characters
fn genString(maxLen: Int): String with {Random} = {
    let len = Random.int(0, maxLen)
    genStringHelper(len)
}

fn genStringHelper(len: Int): String with {Random} = {
    if len <= 0 then ""
    else genChar() + genStringHelper(len - 1)
}
```

### List Generators

```lux
// Generate random list of integers
fn genIntList(min: Int, max: Int, maxLen: Int): List<Int> with {Random} = {
    let len = Random.int(0, maxLen)
    genIntListHelper(min, max, len)
}

fn genIntListHelper(min: Int, max: Int, len: Int): List<Int> with {Random} = {
    if len <= 0 then []
    else List.concat([Random.int(min, max)], genIntListHelper(min, max, len - 1))
}
```

## Writing Property Tests

### Pattern: Recursive Test Function

The most common pattern is a recursive function that runs N iterations:

```lux
fn testProperty(n: Int, count: Int): Bool with {Console, Random} = {
    if n <= 0 then {
        Console.print("  PASS property_name (" + toString(count) + " tests)")
        true
    } else {
        // Generate random inputs
        let x = genInt(0, 100)
        let y = genInt(0, 100)

        // Check property
        if x + y == y + x then
            testProperty(n - 1, count)
        else {
            Console.print("  FAIL property_name")
            Console.print("  Counterexample: x=" + toString(x) + ", y=" + toString(y))
            false
        }
    }
}
```

### Common Properties

Here are properties commonly verified in property-based testing:

**Involution** - Applying a function twice returns the original value:
```lux
// f(f(x)) == x
List.reverse(List.reverse(xs)) == xs
```

**Idempotence** - Applying a function multiple times has the same effect as once:
```lux
// f(f(x)) == f(x)
List.sort(List.sort(xs)) == List.sort(xs)
```

**Commutativity** - Order of arguments doesn't matter:
```lux
// f(a, b) == f(b, a)
a + b == b + a
a * b == b * a
```

**Associativity** - Grouping doesn't matter:
```lux
// f(f(a, b), c) == f(a, f(b, c))
(a + b) + c == a + (b + c)
(a * b) * c == a * (b * c)
```

**Identity** - An element that doesn't change the result:
```lux
x + 0 == x
x * 1 == x
List.concat(xs, []) == xs
```

**Length Preservation**:
```lux
List.length(List.reverse(xs)) == List.length(xs)
List.length(List.map(xs, f)) == List.length(xs)
```

**Length Addition**:
```lux
List.length(List.concat(xs, ys)) == List.length(xs) + List.length(ys)
String.length(s1 + s2) == String.length(s1) + String.length(s2)
```

## Complete Example

```lux
// Property-Based Testing Example
// Run with: lux examples/property_testing.lux

let CHARS = "abcdefghijklmnopqrstuvwxyz"

// Generators
fn genInt(min: Int, max: Int): Int with {Random} =
    Random.int(min, max)

fn genIntList(min: Int, max: Int, maxLen: Int): List<Int> with {Random} = {
    let len = Random.int(0, maxLen)
    genIntListHelper(min, max, len)
}

fn genIntListHelper(min: Int, max: Int, len: Int): List<Int> with {Random} = {
    if len <= 0 then []
    else List.concat([Random.int(min, max)], genIntListHelper(min, max, len - 1))
}

// Test helper
fn printResult(name: String, passed: Bool, count: Int): Unit with {Console} = {
    if passed then
        Console.print("  PASS " + name + " (" + toString(count) + " tests)")
    else
        Console.print("  FAIL " + name)
}

// Property: reverse(reverse(xs)) == xs
fn testReverseInvolutive(n: Int, count: Int): Bool with {Console, Random} = {
    if n <= 0 then {
        printResult("reverse(reverse(xs)) == xs", true, count)
        true
    } else {
        let xs = genIntList(0, 100, 20)
        if List.reverse(List.reverse(xs)) == xs then
            testReverseInvolutive(n - 1, count)
        else {
            printResult("reverse(reverse(xs)) == xs", false, count - n + 1)
            false
        }
    }
}

// Property: addition is commutative
fn testAddCommutative(n: Int, count: Int): Bool with {Console, Random} = {
    if n <= 0 then {
        printResult("a + b == b + a", true, count)
        true
    } else {
        let a = genInt(-1000, 1000)
        let b = genInt(-1000, 1000)
        if a + b == b + a then
            testAddCommutative(n - 1, count)
        else {
            printResult("a + b == b + a", false, count - n + 1)
            false
        }
    }
}

fn main(): Unit with {Console, Random} = {
    Console.print("Property-Based Testing Demo")
    Console.print("")
    Console.print("Running 100 iterations per property...")
    Console.print("")

    testReverseInvolutive(100, 100)
    testAddCommutative(100, 100)

    Console.print("")
    Console.print("All tests completed!")
}

let result = run main() with {}
```

## Stdlib Testing Module

The `stdlib/testing.lux` module provides pre-built generators:

```lux
import stdlib.testing

// Available generators:
genInt(min, max)          // Random integer in range
genIntUpTo(max)           // Random integer 0 to max
genPositiveInt(max)       // Random integer 1 to max
genBool()                 // Random boolean
genChar()                 // Random lowercase letter
genAlphaNum()             // Random alphanumeric character
genString(maxLen)         // Random string
genStringOfLength(len)    // Random string of exact length
genIntList(min, max, maxLen)    // Random list of integers
genBoolList(maxLen)       // Random list of booleans
genStringList(maxStrLen, maxLen) // Random list of strings

// Helper functions:
shrinkInt(n)              // Shrink integer toward zero
shrinkList(xs)            // Shrink list by removing elements
shrinkString(s)           // Shrink string by removing characters
isSorted(xs)              // Check if list is sorted
sameElements(xs, ys)      // Check if lists have same elements
```

## Best Practices

1. **Start with many iterations**: Use 100+ iterations per property to catch edge cases.

2. **Test edge cases explicitly**: Property tests are great for general cases, but also write unit tests for known edge cases.

3. **Keep properties simple**: Each property should test one thing. Complex properties are harder to debug.

4. **Use good generators**: Match the distribution of your generators to realistic inputs.

5. **Print counterexamples**: When a test fails, print the failing inputs to help debugging.

6. **Combine with shrinking**: Shrinking finds minimal failing inputs, making debugging easier.

## Limitations

Current limitations of property-based testing in Lux:

- No automatic shrinking (must be done manually)
- No seed control for reproducible tests
- No integration with `lux test` command (uses `Random` effect)

## See Also

- [Testing Guide](../testing.md) - Unit testing with the Test effect
- [Effects Guide](./05-effects.md) - Understanding the Random effect
- [Example](../../examples/property_testing.lux) - Complete working example