# Module 4: Functions In this module, you'll learn how to define reusable functions in L4. ## Learning Objectives By the end of this module, you will be able to: - Define functions with GIVEN and GIVETH - Use DECIDE and MEANS appropriately - Create local definitions with WHERE - Write recursive functions - Understand function application --- ## Function Basics This is the complete working examples to work along. ```l4-file -- Module 4: Decision Logic - Complete Examples -- All examples are validated and use natural language identifiers IMPORT prelude -- ======================================= -- SECTION 1: Basic Eligibility Decisions -- ======================================= -- Simple age-based eligibility GIVEN `the person's age` IS A NUMBER GIVETH A BOOLEAN DECIDE `the person is an adult` IF `the person's age` >= 18 -- Voting eligibility GIVEN `the person's age` IS A NUMBER `is citizen` IS A BOOLEAN GIVETH A BOOLEAN DECIDE `the person is eligible to vote` IF `the person's age` >= 18 AND `is citizen` -- Senior discount qualification GIVEN `the customer's age` IS A NUMBER GIVETH A BOOLEAN DECIDE `qualifies for senior discount` IF `the customer's age` >= 65 -- Student status determination GIVEN `the person's age` IS A NUMBER `is enrolled` IS A BOOLEAN GIVETH A BOOLEAN DECIDE `the person is a student` IF `the person's age` >= 16 AND `the person's age` <= 25 AND `is enrolled` -- ======================================= -- SECTION 2: Using DECIDE IF vs DECIDE IS vs MEANS -- ======================================= -- DECIDE IF: Best for yes/no questions with conditions GIVEN `the income` IS A NUMBER GIVETH A BOOLEAN DECIDE `qualifies for exemption` IF `the income` < 10000 -- DECIDE IS: Best for classification or value assignment GIVEN `the income` IS A NUMBER GIVETH A STRING DECIDE `the tax bracket` IS BRANCH IF `the income` < 10000 THEN "exempt" IF `the income` < 50000 THEN "standard" OTHERWISE "higher rate" -- MEANS: Best for computations and definitions GIVEN `the income` IS A NUMBER GIVETH A STRING `the income category` MEANS BRANCH IF `the income` < 20000 THEN "low" IF `the income` < 80000 THEN "medium" OTHERWISE "high" -- ======================================= -- SECTION 3: Tax and Financial Calculations with WHERE -- ======================================= -- Simple tax calculation GIVEN `the gross income` IS A NUMBER `the tax rate` IS A NUMBER GIVETH A NUMBER `the tax owed` MEANS `the taxable income` * `the tax rate` WHERE `the standard deduction` MEANS 12000 `the taxable income` MEANS IF `the gross income` > `the standard deduction` THEN `the gross income` - `the standard deduction` ELSE 0 -- Progressive tax with multiple brackets GIVEN `the income` IS A NUMBER GIVETH A NUMBER `the income tax owed` MEANS `tax on first bracket` + `tax on second bracket` + `tax on third bracket` WHERE `tax on first bracket` MEANS `amount in first bracket` * 0.10 `tax on second bracket` MEANS `amount in second bracket` * 0.20 `tax on third bracket` MEANS `amount in third bracket` * 0.30 `amount in first bracket` MEANS BRANCH IF `the income` <= 10000 THEN `the income` OTHERWISE 10000 `amount in second bracket` MEANS BRANCH IF `the income` <= 10000 THEN 0 IF `the income` <= 50000 THEN `the income` - 10000 OTHERWISE 40000 `amount in third bracket` MEANS BRANCH IF `the income` <= 50000 THEN 0 OTHERWISE `the income` - 50000 -- Net income calculation GIVEN `the gross income` IS A NUMBER `the expenses` IS A NUMBER GIVETH A NUMBER `the net income` MEANS `the gross income` - `the total deductions` WHERE `the standard deduction` MEANS IF `calculated deduction` >= 1000 THEN `calculated deduction` ELSE 1000 `calculated deduction` MEANS `the gross income` * 0.10 `the total deductions` MEANS `the standard deduction` + `the expenses` -- ======================================= -- SECTION 4: Structured Entity Examples -- ======================================= DECLARE Person HAS name IS A STRING age IS A NUMBER citizenship IS A STRING `annual income` IS A NUMBER `criminal record` IS A BOOLEAN -- Comprehensive benefit eligibility GIVEN `the applicant` IS A Person GIVETH A BOOLEAN DECIDE `the applicant is eligible for benefit` IF `the applicant is a qualifying resident` AND `the applicant is of age` AND `the applicant meets income threshold` AND NOT `the applicant is disqualified` WHERE `the applicant is a qualifying resident` MEANS `the applicant`'s citizenship = "citizen" `the applicant is of age` MEANS `the applicant`'s age >= 21 AND `the applicant`'s age < 65 `the applicant meets income threshold` MEANS `the applicant`'s `annual income` < 30000 `the applicant is disqualified` MEANS `the applicant`'s `criminal record` -- Tax bracket determination with record GIVEN `the taxpayer` IS A Person GIVETH A STRING DECIDE `the taxpayer's bracket` IS BRANCH IF `the taxpayer`'s `annual income` < 10000 THEN "exempt" IF `the taxpayer`'s `annual income` < 50000 THEN "standard" IF `the taxpayer`'s `annual income` < 100000 THEN "higher" OTHERWISE "top rate" -- ======================================= -- SECTION 5: Multi-Factor Decisions -- ======================================= -- Loan approval decision GIVEN `the income` IS A NUMBER `the credit score` IS A NUMBER `the loan amount` IS A NUMBER GIVETH A BOOLEAN DECIDE `the loan is approved` IF `income requirement is met` AND `credit score is sufficient` AND `debt to income ratio is acceptable` WHERE `income requirement is met` MEANS `the income` >= `the loan amount` * 0.3 `credit score is sufficient` MEANS `the credit score` >= 650 `debt to income ratio is acceptable` MEANS `the loan amount` <= `the income` * 4 -- Insurance premium calculation GIVEN `the insured age` IS A NUMBER `the coverage amount` IS A NUMBER `is smoker` IS A BOOLEAN GIVETH A NUMBER `the annual premium` MEANS `the base premium` * `the age factor` * `the smoking factor` WHERE `the base premium` MEANS `the coverage amount` * 0.001 `the age factor` MEANS BRANCH IF `the insured age` < 30 THEN 1.0 IF `the insured age` < 50 THEN 1.5 OTHERWISE 2.0 `the smoking factor` MEANS IF `is smoker` THEN 1.5 ELSE 1.0 -- ======================================= -- SECTION 6: Real-World Contract Scenarios -- ======================================= -- Late payment penalty calculation GIVEN `the principal amount` IS A NUMBER `days overdue` IS A NUMBER GIVETH A NUMBER `the late payment penalty` MEANS BRANCH IF `days overdue` <= 0 THEN 0 IF `days overdue` <= 30 THEN `the principal amount` * 0.02 OTHERWISE `the principal amount` * 0.05 -- Lease renewal qualification GIVEN `years as tenant` IS A NUMBER `late payments` IS A NUMBER `current rent` IS A NUMBER `market rent` IS A NUMBER GIVETH A BOOLEAN DECIDE `qualifies for lease renewal` IF `tenant is in good standing` AND `rent is at market rate` WHERE `tenant is in good standing` MEANS `years as tenant` >= 1 AND `late payments` = 0 `rent is at market rate` MEANS `current rent` >= `market rent` * 0.9 -- ======================================= -- SECTION 7: Test Data -- ======================================= `test person eligible` MEANS Person "Alice" 25 "citizen" 25000 FALSE `test person ineligible age` MEANS Person "Bob" 17 "citizen" 20000 FALSE `test person ineligible citizenship` MEANS Person "Carol" 30 "permanent resident" 20000 FALSE `test person ineligible income` MEANS Person "David" 30 "citizen" 50000 FALSE `test person disqualified` MEANS Person "Eve" 30 "citizen" 20000 TRUE -- ======================================= -- SECTION 8: Tests -- ======================================= -- Basic eligibility tests #EVAL `the person is an adult` 21 #EVAL `the person is an adult` 16 #EVAL `the person is eligible to vote` 25 TRUE #EVAL `the person is eligible to vote` 16 TRUE #EVAL `qualifies for senior discount` 70 #EVAL `qualifies for senior discount` 50 -- Tax calculation tests #EVAL `the tax owed` 50000 0.20 #EVAL `the income tax owed` 75000 #EVAL `the net income` 100000 15000 -- Structured entity tests #EVAL `the applicant is eligible for benefit` `test person eligible` #EVAL `the applicant is eligible for benefit` `test person ineligible age` #EVAL `the applicant is eligible for benefit` `test person ineligible citizenship` #EVAL `the applicant is eligible for benefit` `test person ineligible income` #EVAL `the applicant is eligible for benefit` `test person disqualified` #EVAL `the taxpayer's bracket` `test person eligible` -- Multi-factor decision tests #EVAL `the loan is approved` 60000 700 200000 #EVAL `the loan is approved` 40000 700 200000 #EVAL `the annual premium` 35 100000 FALSE #EVAL `the annual premium` 35 100000 TRUE -- Contract scenario tests #EVAL `the late payment penalty` 1000 15 #EVAL `the late payment penalty` 1000 45 #EVAL `qualifies for lease renewal` 2 0 1800 2000 #EVAL `qualifies for lease renewal` 2 3 1800 2000 ``` ### The Structure of a Function Every L4 function has these parts: ```l4 GIVEN x IS A NUMBER -- Parameters (inputs) y IS A NUMBER GIVETH A NUMBER -- Return type (output) `the sum of x and y` MEANS -- Name and definition x + y ``` ### DECIDE vs MEANS Both define the same thing—use whichever reads better: ```l4 -- These are equivalent DECIDE `the person is an adult` IF age >= 18 `the person is an adult` MEANS age >= 18 DECIDE `the person is an adult` IS age >= 18 ``` | Syntax | Best for | | --------------------- | ---------------------------- | | `DECIDE name IS expr` | Rules, decisions, conditions | | `DECIDE name IF expr` | Boolean predicates | | `name MEANS expr` | Definitions, computations | ### Type Signatures The `GIVETH` clause declares what type the function returns: - `GIVETH A NUMBER` — Returns a number - `GIVETH A STRING` — Returns a string - `GIVETH A BOOLEAN` — Returns true/false - `GIVETH A Person` — Returns a Person record - `GIVETH A LIST OF NUMBER` — Returns a list of numbers - `GIVETH A MAYBE NUMBER` — Returns a number or nothing --- ## Function Parameters ### Multiple Parameters List parameters with `GIVEN`, separated by newlines or commas: ```l4 GIVEN firstName IS A STRING lastName IS A STRING age IS A NUMBER GIVETH A Person `create person` MEANS Person firstName lastName age ``` ### Polymorphic Functions Use `TYPE` for functions that work with any type: ```l4 GIVEN a IS A TYPE x IS AN a y IS AN a GIVETH AN a `the first of` MEANS x ``` --- ## Calling Functions ### Simple Function Calls ```l4 -- Define a function GIVEN n IS A NUMBER GIVETH A NUMBER `the square of` MEANS n * n -- Call it #EVAL `the square of` 5 -- Result: 25 #EVAL `the square of` (3 + 2) -- Result: 25 ``` ### Multi-Argument Calls ```l4 -- Arguments separated by spaces #EVAL `add` 3 5 -- Result: 8 ``` --- ## Local Definitions with WHERE Use `WHERE` to define helper values and functions: ```l4 GIVEN principal IS A NUMBER rate IS A NUMBER years IS A NUMBER GIVETH A NUMBER `the compound interest` MEANS principal * (factor ^ years) WHERE factor MEANS 1 + rate ``` ### Multiple Local Definitions ```l4 `the monthly payment` MEANS loan * (monthlyRate * compoundFactor) / (compoundFactor - 1) WHERE monthlyRate MEANS annualRate / 12 compoundFactor MEANS (1 + monthlyRate) ^ months ``` --- ## Recursive Functions L4 supports recursion—functions that call themselves: ### Simple Recursion ```l4 GIVEN n IS A NUMBER GIVETH A NUMBER `the factorial of` MEANS IF n <= 1 THEN 1 ELSE n * `the factorial of` (n - 1) #EVAL `the factorial of` 5 -- Result: 120 ``` ### List Recursion ```l4 GIVEN xs IS A LIST OF NUMBER GIVETH A NUMBER `the sum of` MEANS CONSIDER xs WHEN EMPTY THEN 0 WHEN x FOLLOWED BY rest THEN x + `the sum of` rest ``` --- ## Higher-Order Functions Functions that take or return other functions. **Note:** You must `IMPORT prelude` to use `map`, `filter`, `all`, `any`, etc. ### Anonymous Functions (Lambdas) Use `GIVEN ... YIELD`: ```l4 -- Double each number map (GIVEN n YIELD n * 2) (LIST 1, 2, 3) -- Result: LIST 2, 4, 6 -- Filter positive numbers filter (GIVEN n YIELD n > 0) (LIST -1, 2, -3, 4) -- Result: LIST 2, 4 ``` --- ## Exercises ### Exercise 1: Simple Function Write a function that calculates the area of a rectangle. ### Exercise 2: Function with WHERE Write a function that calculates the area of a circle using π ≈ 3.14159. ### Exercise 3: Recursive Function Write a recursive function to calculate the sum of a list of numbers. ### Exercise 4: Higher-Order Function Use `filter` to get all numbers greater than 10 from a list. (Remember to `IMPORT prelude`.) --- ## Common Mistakes ### 1. Missing Return Type ```l4 -- ❌ Wrong: No GIVETH GIVEN n IS A NUMBER `the square of` MEANS n * n -- ✅ Right: Include GIVETH GIVEN n IS A NUMBER GIVETH A NUMBER `the square of` MEANS n * n ``` ### 2. Wrong Argument Order in Calls ```l4 -- Definition GIVEN x IS A NUMBER y IS A NUMBER GIVETH A NUMBER `subtract` MEANS x - y -- ❌ Wrong: Gets 3 - 10 = -7, not 10 - 3 #EVAL `subtract` 3 10 -- ✅ Right: Match the order in GIVEN #EVAL `subtract` 10 3 -- Gets 10 - 3 = 7 ``` ### 3. Missing Parentheses in Function Calls ```l4 -- ❌ Wrong: f applied to g, not to result of g x f g x -- ✅ Right: Apply g to x, then f to result f (g x) ``` --- ## Summary | Concept | Syntax | | -------------------- | ------------------------------------------ | | Function definition | `GIVEN params GIVETH Type name MEANS expr` | | Decision function | `DECIDE name IF condition` | | Local definitions | `expr WHERE localDef MEANS value` | | Recursion | Function calls itself in definition | | Lambda | `GIVEN x YIELD expression` | | Function application | `functionName arg1 arg2` | --- ## What's Next? In [Module 5: Regulative Rules](/l4/courses/foundation/module-5-regulative.md), you'll learn how to model legal obligations, permissions, and prohibitions using L4's deontic constructs.