# Module 3: Control Flow In this module, you'll learn how to handle conditional logic, work with lists, and use boolean operators in L4. ## Learning Objectives By the end of this module, you will be able to: - Write conditional expressions with IF/THEN/ELSE - Use pattern matching with CONSIDER - Work with lists using prelude functions - Combine boolean conditions with AND, OR, NOT - Understand operator precedence --- ## Conditional Expressions This is the complete working example to work along. ```l4-file -- Module 3: Control Flow - Complete Examples -- All examples are validated and use natural language identifiers IMPORT prelude -- ============================================================================= -- SECTION 1: Conditional Expressions -- ============================================================================= -- Categorize a person's age GIVEN age IS A NUMBER GIVETH A STRING `the age category` MEANS IF age < 18 THEN "minor" ELSE "adult" -- Grade a score with nested conditionals GIVEN score IS A NUMBER GIVETH A STRING `the letter grade` MEANS IF score >= 90 THEN "A" ELSE IF score >= 80 THEN "B" ELSE IF score >= 70 THEN "C" ELSE IF score >= 60 THEN "D" ELSE "F" -- Categorize an amount GIVEN amount IS A NUMBER GIVETH A STRING `the amount category` MEANS IF amount < 100 THEN "small" ELSE IF amount < 1000 THEN "medium" ELSE "large" -- ============================================================================= -- SECTION 2: Boolean Logic -- ============================================================================= -- Can a person vote? GIVEN age IS A NUMBER `is registered` IS A BOOLEAN GIVETH A BOOLEAN DECIDE `the person can vote` IF age >= 18 AND `is registered` -- Does a transaction need review? GIVEN amount IS A NUMBER `is high risk` IS A BOOLEAN GIVETH A BOOLEAN DECIDE `the transaction needs review` IF amount > 10000 OR `is high risk` -- Is the person a minor? GIVEN age IS A NUMBER GIVETH A BOOLEAN DECIDE `the person is a minor` IF NOT age >= 18 -- ============================================================================= -- SECTION 3: Working with Lists -- ============================================================================= -- Check if all numbers are positive GIVEN numbers IS A LIST OF NUMBER GIVETH A BOOLEAN DECIDE `all numbers are positive` IF all (GIVEN n YIELD n > 0) numbers -- Check if any number is negative GIVEN numbers IS A LIST OF NUMBER GIVETH A BOOLEAN DECIDE `some number is negative` IF any (GIVEN n YIELD n < 0) numbers -- Get numbers greater than a threshold GIVEN numbers IS A LIST OF NUMBER threshold IS A NUMBER GIVETH A LIST OF NUMBER `numbers above threshold` MEANS filter (GIVEN n YIELD n > threshold) numbers -- ============================================================================= -- SECTION 4: Pattern Matching on Lists -- ============================================================================= -- Describe a list GIVEN items IS A LIST OF STRING GIVETH A STRING `describe the list` MEANS CONSIDER items WHEN EMPTY THEN "no items" WHEN first FOLLOWED BY EMPTY THEN "one item" WHEN first FOLLOWED BY rest THEN "multiple items" -- ============================================================================= -- SECTION 5: Complex Eligibility Example -- ============================================================================= -- A conviction record DECLARE Conviction HAS `the description` IS A STRING `the conviction is spent` IS A BOOLEAN -- A person with potential convictions DECLARE Person HAS `the person's name` IS A STRING `the person's age` IS A NUMBER `the person is bankrupt` IS A BOOLEAN `the person's convictions` IS A LIST OF Conviction -- Check if a person has an unspent conviction GIVEN person IS A Person GIVETH A BOOLEAN DECIDE `the person has an unspent conviction` IF any (GIVEN c YIELD c's `the conviction is spent` EQUALS FALSE) (person's `the person's convictions`) -- Check if a person is eligible for a position GIVEN person IS A Person GIVETH A BOOLEAN DECIDE `the person is eligible for the position` IF person's `the person's age` >= 21 AND NOT person's `the person is bankrupt` AND NOT `the person has an unspent conviction` person -- ============================================================================= -- SECTION 6: Test Data -- ============================================================================= -- Test lists `positive numbers` MEANS LIST 1, 2, 3, 4, 5 `mixed numbers` MEANS LIST -1, 2, -3, 4 `empty list` MEANS LIST `single item` MEANS LIST "apple" `multiple items` MEANS LIST "apple", "banana", "cherry" -- Test people `spent conviction` MEANS Conviction "Minor offense 2010" TRUE `unspent conviction` MEANS Conviction "Fraud 2023" FALSE `eligible person` MEANS Person "Alice" 30 FALSE (LIST) `bankrupt person` MEANS Person "Bob" 35 TRUE (LIST) `person with unspent conviction` MEANS Person "Charlie" 40 FALSE (LIST `unspent conviction`) `young person` MEANS Person "Diana" 19 FALSE (LIST) -- ============================================================================= -- SECTION 7: Tests -- ============================================================================= -- Conditional tests #EVAL `the age category` 16 #EVAL `the age category` 25 #EVAL `the letter grade` 85 #EVAL `the amount category` 50 #EVAL `the amount category` 500 #EVAL `the amount category` 5000 -- Boolean tests #EVAL `the person can vote` 21 TRUE #EVAL `the person can vote` 16 TRUE #EVAL `the person is a minor` 16 -- List tests #EVAL `all numbers are positive` `positive numbers` #EVAL `all numbers are positive` `mixed numbers` #EVAL `some number is negative` `mixed numbers` #EVAL `numbers above threshold` `positive numbers` 3 -- Pattern matching tests #EVAL `describe the list` `empty list` #EVAL `describe the list` `single item` #EVAL `describe the list` `multiple items` -- Eligibility tests #EVAL `the person is eligible for the position` `eligible person` #EVAL `the person is eligible for the position` `bankrupt person` #EVAL `the person is eligible for the position` `person with unspent conviction` #EVAL `the person is eligible for the position` `young person` ``` ### Basic IF/THEN/ELSE ```l4 GIVEN age IS A NUMBER GIVETH A STRING `the age category` MEANS IF age < 18 THEN "minor" ELSE "adult" ``` Every `IF` must have both `THEN` and `ELSE` branches—L4 requires you to handle all cases. ### Multi-Way Decisions with BRANCH When you need to choose between multiple alternatives based on conditions, use `BRANCH` instead of nesting `IF/THEN/ELSE` statements. **Why BRANCH?** Nested IF/THEN/ELSE can lead to indentation problems and is harder to read: ```l4 -- ❌ Avoid: Nested IF/THEN/ELSE (fragile indentation) `grade` MEANS IF score >= 90 THEN "A" ELSE IF score >= 80 THEN "B" ELSE IF score >= 70 THEN "C" ELSE IF score >= 60 THEN "D" ELSE "F" ``` BRANCH provides a cleaner, more readable alternative: ```l4 -- ✅ Better: BRANCH (clear, flat structure) GIVEN score IS A NUMBER GIVETH A STRING `grade` MEANS BRANCH IF score >= 90 THEN "A" IF score >= 80 THEN "B" IF score >= 70 THEN "C" IF score >= 60 THEN "D" OTHERWISE "F" ``` **When to use BRANCH:** - Multiple conditions checked in sequence - Classification into categories - Any time you'd write nested IF/THEN/ELSE **Key points:** - Conditions are checked top-to-bottom - First matching condition wins - `OTHERWISE` provides the default case - All branches must have same return type ### Conditional in Context Conditionals are expressions—they can be used anywhere a value is expected: ```l4 message MEANS IF isActive THEN "Active" ELSE "Inactive" ``` --- ## Pattern Matching with CONSIDER For more complex branching, especially with enumeration types, use `CONSIDER`: ```l4 GIVEN status IS A Status GIVETH A STRING `the status message` MEANS CONSIDER status WHEN Active THEN "The account is active" WHEN Suspended reason THEN "Suspended: " + reason WHEN Closed THEN "The account has been closed" ``` ### Pattern Matching on Lists ```l4 GIVEN items IS A LIST OF STRING GIVETH A STRING `describe the list` MEANS CONSIDER items WHEN EMPTY THEN "no items" WHEN first FOLLOWED BY EMPTY THEN "one item" WHEN first FOLLOWED BY rest THEN "multiple items" ``` The pattern `first FOLLOWED BY rest` destructures a list into its head and tail. --- ## Boolean Logic ### Basic Operators | Operator | Meaning | Example | | ----------------- | ----------------- | ------------- | | `AND` or `&&` | Both must be true | `a AND b` | | `OR` or `\|\|` | At least one true | `a OR b` | | `NOT` | Negation | `NOT a` | | `IMPLIES` or `=>` | If-then | `a IMPLIES b` | ### Examples ```l4 -- AND: Both conditions must be true DECIDE `the person can vote` IF age >= 18 AND isRegistered -- OR: At least one condition must be true DECIDE `the case needs review` IF amount > 10000 OR isHighRisk -- NOT: Negation DECIDE `the person is a minor` IF NOT age >= 18 -- IMPLIES: If first is true, second must be true DECIDE `the rule holds` IF hasPermit IMPLIES paidFee ``` ### Operator Precedence From highest to lowest precedence: 1. `NOT` (tightest) 2. `AND` 3. `OR` 4. `IMPLIES` (loosest) This means: ```l4 a OR b AND c -- means: a OR (b AND c) NOT a AND b -- means: (NOT a) AND b ``` Use parentheses to make precedence explicit: ```l4 (a OR b) AND c -- clear: OR first, then AND ``` --- ## Comparison Operators | Operator | Alternative | Meaning | | -------- | -------------- | --------------------- | | `=` | `EQUALS` | Equal to | | `>` | `GREATER THAN` | Greater than | | `<` | `LESS THAN` | Less than | | `>=` | `AT LEAST` | Greater than or equal | | `<=` | `AT MOST` | Less than or equal | ### Examples ```l4 -- Numeric comparisons age >= 18 amount LESS THAN 1000 score AT LEAST 70 -- String comparison status EQUALS "Active" name = "Alice" -- Boolean comparison (often unnecessary) isActive EQUALS TRUE -- same as just: isActive isActive EQUALS FALSE -- same as: NOT isActive ``` --- ## Working with Lists L4 provides prelude functions for working with lists. **Note:** You must `IMPORT prelude` to use these functions. ### Creating Lists ```l4 numbers MEANS LIST 1, 2, 3, 4, 5 empty MEANS EMPTY ``` ### Common List Functions | Function | Purpose | Example | | -------- | ---------------- | ----------------- | | `null` | Is empty? | `null myList` | | `map` | Transform each | `map f myList` | | `filter` | Keep matching | `filter f myList` | | `all` | All satisfy? | `all f myList` | | `any` | Any satisfy? | `any f myList` | | `elem` | Check membership | `elem 3 myList` | ### Using Quantifiers ```l4 -- All elements positive? all (GIVEN n YIELD n > 0) numbers -- Any element negative? any (GIVEN n YIELD n < 0) numbers ``` The `GIVEN ... YIELD` creates an anonymous function (lambda). ### Important: Parentheses with Field Access When passing field access to functions, use parentheses: ```l4 -- ❌ Wrong: Parser confusion all (GIVEN g YIELD g's age >= 18) charity's governors -- ✅ Right: Parentheses around the list argument all (GIVEN g YIELD g's age >= 18) (charity's governors) ``` This is one of the most common mistakes in L4! --- ## Combining Conditions in Legal Rules ```l4 GIVEN person IS A Person charity IS A `Registered Charity` DECIDE `the person can be a governor` IF person's age >= 18 AND NOT person's `is bankrupt` AND NOT any (GIVEN c YIELD NOT c's `is spent`) (person's convictions) ``` --- ## Real-World Example: Eligibility Check ```l4 -- Helper: Check for unspent convictions GIVEN person IS A Person GIVETH A BOOLEAN `the person has an unspent conviction` MEANS any (GIVEN c YIELD c's `is spent` EQUALS FALSE) (person's convictions) -- Main eligibility rule GIVEN person IS A Person GIVETH A BOOLEAN DECIDE `the person is eligible for the position` IF person's age >= 21 AND NOT person's `is bankrupt` AND NOT `the person has an unspent conviction` person ``` --- ## Exercises ### Exercise 1: BRANCH for Classification Write a function that categorizes an amount as "small" (< 100), "medium" (100-999), or "large" (>= 1000). Use `BRANCH` for the multi-way decision. **Hint:** ```l4 GIVEN amount IS A NUMBER GIVETH A STRING `the amount category` MEANS BRANCH IF ... THEN "small" -- Complete this ``` ### Exercise 2: List Validation Write a function that checks if all items in a list of numbers are positive. (Remember to `IMPORT prelude`.) ### Exercise 3: Complex Condition Write a rule: "A person can purchase alcohol if they are at least 21, have valid ID, and are not on the banned list." --- ## Common Mistakes ### 1. Missing ELSE ```l4 -- ❌ Wrong: No ELSE branch result MEANS IF condition THEN "yes" -- ✅ Right: Both branches required result MEANS IF condition THEN "yes" ELSE "no" ``` ### 2. Precedence Confusion ```l4 -- ❌ Confusing: What does this mean? a OR b AND c IMPLIES d -- ✅ Clear: Use parentheses (a OR (b AND c)) IMPLIES d ``` ### 3. Forgetting Parentheses with Functions ```l4 -- ❌ Wrong: Parser error length person's items > 0 -- ✅ Right: Parentheses around field access length (person's items) > 0 ``` ### 4. Forgetting to IMPORT prelude Functions like `all`, `any`, `filter`, `map` require `IMPORT prelude`. --- ## Summary | Concept | Syntax | | ---------------- | ---------------------------------------------- | | Conditional | `IF condition THEN result1 ELSE result2` | | Multi-way | `BRANCH IF cond1 THEN res1 ... OTHERWISE resN` | | Pattern match | `CONSIDER expr WHEN pattern THEN result` | | List destructure | `WHEN first FOLLOWED BY rest THEN ...` | | Boolean AND | `condition1 AND condition2` | | Boolean OR | `condition1 OR condition2` | | Boolean NOT | `NOT condition` | | Check all | `all (GIVEN x YIELD condition) list` | | Check any | `any (GIVEN x YIELD condition) list` | | List membership | `elem item list` | --- ## What's Next? In [Module 4: Decision Logic](/l4/courses/foundation/module-4-decision-logic.md), you'll learn how to express constitutive rules for legal decision-making using DECIDE and MEANS, break down complex calculations with WHERE, and build legal determinations that read like natural language.