# Module 4: Decision Logic
**Prerequisites:** Modules 1–3
In this module, you'll learn how to encode **constitutive rules** - legal rules that determine facts, classifications, and eligibility.
## Learning Objectives
By the end of this module, you will be able to:
- Distinguish between constitutive rules (decision logic) and regulative rules (obligations)
- Express eligibility determinations using DECIDE
- Define computations and definitions using MEANS
- Break down complex calculations with WHERE
- Write decision logic that reads like legal text
---
## What is Decision Logic?
### Constitutive vs Regulative Rules
Legal systems contain two types of rules:
**Regulative rules** (Modules 1 and 6) specify what parties **must**, **may**, or **must not** do:
- "The applicant **must** submit documentation **within** 30 days"
- "The landlord **may** terminate the lease if rent is unpaid"
- "The seller **shall not** disclose confidential information"
**Constitutive rules** (this module) determine **facts**, **classifications**, and **eligibility**:
- "An applicant **is eligible** if they are a citizen and over 18"
- "The tax owed **is** 20% of gross income minus deductions"
- "A person **is a resident** if they have lived here for 183 days or more"
In L4, we express constitutive rules as **decision logic** using functions.
---
## Why Functional Purity Matters for Legal Rules
L4 follows the **functional programming** principle that **every input needed to make a decision must be explicitly declared**. This is a feature, not a bug.
### Explicit Dependencies
When you write decision logic in L4, the `GIVEN` clause declares **exactly what information is needed**:
```l4
GIVEN `the applicant` IS A Person
`today` IS A DATE
GIVETH A BOOLEAN
DECIDE `the application is timely` IF ...
```
This signature tells you immediately: "To determine if an application is timely, I need to know **who the applicant is** and **what today's date is**."
### No Hidden Dependencies
In natural language, legal rules often have implicit dependencies:
> "The applicant is eligible if they are a resident."
**Questions immediately arise:**
- What makes someone a resident?
- How long must they have resided?
- Where must they reside?
In L4, you **must** make these dependencies explicit:
```l4
GIVEN `the applicant` IS A Person
`the jurisdiction` IS A STRING
GIVETH A BOOLEAN
DECIDE `the applicant is eligible` IF
`the applicant is a resident of the jurisdiction`
WHERE
`the applicant is a resident of the jurisdiction` MEANS
`the applicant`'s `country of residence` EQUALS `the jurisdiction`
AND `the applicant`'s `years of residence` >= 5
```
Notice how the helper decision `is a resident of` **also** declares its dependencies. You can't hide information - if a decision needs something, you must pass it explicitly.
### "It Depends" - On What, Exactly?
This explicit dependency tracking has a **huge benefit for legal reasoning**:
**When someone says "it depends"** - L4 forces you to specify **what "it" depends ON**.
```l4
-- ❌ Unclear: What does eligibility depend on?
"The person is eligible"
-- ✅ Clear: Eligibility depends on these specific factors
GIVEN `the person` IS A Person
`the application date` IS A DATE
`the jurisdiction rules` IS A `Rule Set`
GIVETH A BOOLEAN
DECIDE `the person is eligible` IF ...
```
The function signature **documents the complete set of factors** that affect the decision. This makes legal rules:
- **Auditable**: You can trace exactly what information influenced a decision
- **Testable**: You know exactly what inputs to vary in your test scenarios
- **Maintainable**: When requirements change, you know what dependencies need updating
- **Explainable**: You can show stakeholders exactly what factors matter
### Parameter Threading
If a sub-decision needs information, you must "thread" it through the caller:
```l4
GIVEN `the applicant` IS A Person
`today` IS A DATE -- We need this
GIVETH A BOOLEAN
DECIDE `qualifies for benefit` IF
`is eligible` `the applicant` `today` -- Pass it through!
AND ...
WHERE
GIVEN person IS A Person
`the current date` IS A DATE -- Sub-decision needs it too!
GIVETH A BOOLEAN
`is eligible` MEANS ...
```
This might seem verbose, but it's **transparency, not bureaucracy**. Every piece of information that influences the legal outcome is **visible and traceable**.
---
## Working Examples
All examples in this module are in:
```l4-file
-- Module 4: Decision Logic - Complete Examples
-- All examples are validated and use natural language identifiers
IMPORT prelude
IMPORT daydate
-- =======================================
-- 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: Optional Values and Dates
-- =======================================
-- A contract with an optional termination date
DECLARE Contract HAS
`the effective date` IS A DATE
`the termination date` IS A MAYBE DATE
`the notice period in days` IS A NUMBER
-- A party who may or may not have given notice
DECLARE `Contract Party` HAS
`the party's name` IS A STRING
`notice was given on` IS A MAYBE DATE
-- Days between two dates, using serial day numbers
GIVEN `the first date` IS A DATE
`the second date` IS A DATE
GIVETH A NUMBER
`the days between` MEANS
DATE_SERIAL `the second date` - DATE_SERIAL `the first date`
-- Contract clause interpretation with MAYBE and dates
GIVEN `the contract` IS A Contract
`the party` IS A `Contract Party`
`today` IS A DATE
GIVETH A BOOLEAN
DECIDE `the party may terminate` IF
`the contract is active`
AND `the party has given sufficient notice`
WHERE
`the contract is active` MEANS
`today` >= `the contract`'s `the effective date`
AND CONSIDER `the contract`'s `the termination date`
WHEN NOTHING THEN TRUE
WHEN JUST `the end date` THEN `today` < `the end date`
`the party has given sufficient notice` MEANS
CONSIDER `the party`'s `notice was given on`
WHEN NOTHING THEN FALSE
WHEN JUST `the notice date` THEN
`the days between` `the notice date` `today` >= `the contract`'s `the notice period in days`
-- =======================================
-- SECTION 8: 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
`the open-ended contract` MEANS Contract (Date 1 1 2024) NOTHING 30
`the party with notice` MEANS `Contract Party` "Acme Ltd" (JUST (Date 1 3 2024))
`the party without notice` MEANS `Contract Party` "Beta Ltd" NOTHING
-- =======================================
-- SECTION 9: 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
-- Optional values and dates tests
#EVAL `the days between` (Date 1 3 2024) (Date 15 4 2024)
#EVAL `the party may terminate` `the open-ended contract` `the party with notice` (Date 15 4 2024)
#EVAL `the party may terminate` `the open-ended contract` `the party without notice` (Date 15 4 2024)
```
---
## Basic Decisions with DECIDE
### Eligibility Determinations
The most common legal decision: "Does X qualify?"
```l4
GIVEN `the applicant` IS A Person
GIVETH A BOOLEAN
DECIDE `the applicant is eligible for benefits` IF
`the applicant is a citizen`
AND `the applicant's age` >= 18
AND NOT `the applicant is disqualified`
```
**Key points:**
- Use **DECIDE IF** for yes/no questions
- Use backticks for natural language identifiers
- Conditions follow IF, connected by AND/OR/NOT
### Classification Rules
"What category does X fall into?"
Use `BRANCH` for multi-way classification decisions:
```l4
GIVEN `the income` IS A NUMBER
GIVETH A STRING
DECIDE `the tax bracket` IS
BRANCH
IF `the income` < 10000 THEN "low"
IF `the income` < 50000 THEN "medium"
OTHERWISE "high"
```
**Note:** `BRANCH` is clearer than nested `IF/THEN/ELSE` for classification decisions. It avoids indentation problems and reads more like a legal test with multiple conditions. See [Module 3: Control Flow](/l4/courses/foundation/module-3-control-flow.md#multi-way-decisions-with-branch) for details.
### DECIDE IS vs DECIDE IF
Use whichever reads more naturally:
```l4
-- These are equivalent:
DECIDE `the person is an adult` IF age >= 18
DECIDE `the person is an adult` IS age >= 18
-- Use IF when it reads like a legal condition:
DECIDE `qualifies for exemption` IF
`is a first-time buyer`
AND `purchase price` < 500000
-- Use IS with BRANCH for multi-way classification:
DECIDE `the applicable rate` IS
BRANCH
IF `customer type` = "premium" THEN 0.05
IF `customer type` = "standard" THEN 0.10
OTHERWISE 0.15
```
---
## Computations with MEANS
### Defining Calculations
Use **MEANS** to define computed values and formulas:
```l4
GIVEN `the gross income` IS A NUMBER
`the deductions` IS A NUMBER
GIVETH A NUMBER
`the taxable income` MEANS
`the gross income` - `the deductions`
```
### Simple Tax Calculation
```l4
GIVEN `the taxable income` IS A NUMBER
GIVETH A NUMBER
`the tax owed` MEANS
`the taxable income` * `the tax rate`
```
### DECIDE vs MEANS
Both define things - use whichever reads better:
| Use DECIDE when... | Use MEANS when... |
| --------------------------------- | --------------------------------- |
| Asking a yes/no question | Defining a value or computation |
| Determining classification/status | Stating what something equals |
| Condition reads naturally with IF | Definition reads naturally with = |
**Examples:**
```l4
-- ✅ Good: DECIDE for questions
DECIDE `the person is eligible` IF age >= 18
-- ✅ Good: MEANS for definitions
`the person's status` MEANS
IF age >= 18 THEN "adult" ELSE "minor"
-- Both work, but one reads better:
DECIDE `the person is an adult` IF age >= 18 -- More natural
`the person is an adult` MEANS age >= 18 -- Also valid
`the net income` MEANS `gross income` - `expenses` -- More natural
DECIDE `the net income` IS `gross income` - `expenses` -- Also valid
```
---
## Breaking Down Complex Logic with WHERE
### Local Helper Calculations
Legal formulas often involve intermediate calculations. Use **WHERE** to break them down:
```l4
GIVEN `the principal` IS A NUMBER
`the annual rate` IS A NUMBER
`the years` IS A NUMBER
GIVETH A NUMBER
`the compound interest` MEANS
`the principal` * EXPONENT `the growth factor` `the years`
WHERE
`the growth factor` MEANS 1 + `the annual rate`
```
(`EXPONENT base power` is L4's built-in exponentiation function.)
**Benefits:**
- Makes complex formulas readable
- Gives meaningful names to intermediate values
- Matches how legal documents explain calculations
### Multiple WHERE Definitions
```l4
GIVEN `the loan amount` IS A NUMBER
`the annual rate` IS A NUMBER
`the term in months` IS A NUMBER
GIVETH A NUMBER
`the monthly payment` MEANS
`the loan amount` *
(`the monthly rate` * `the compound factor`) /
(`the compound factor` - 1)
WHERE
`the monthly rate` MEANS `the annual rate` / 12
`the compound factor` MEANS EXPONENT (1 + `the monthly rate`) `the term in months`
```
---
## Realistic Legal Scenarios
### Example 1: Benefit Eligibility
From
```l4-file
-- Module 4: Decision Logic - Complete Examples
-- All examples are validated and use natural language identifiers
IMPORT prelude
IMPORT daydate
-- =======================================
-- 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: Optional Values and Dates
-- =======================================
-- A contract with an optional termination date
DECLARE Contract HAS
`the effective date` IS A DATE
`the termination date` IS A MAYBE DATE
`the notice period in days` IS A NUMBER
-- A party who may or may not have given notice
DECLARE `Contract Party` HAS
`the party's name` IS A STRING
`notice was given on` IS A MAYBE DATE
-- Days between two dates, using serial day numbers
GIVEN `the first date` IS A DATE
`the second date` IS A DATE
GIVETH A NUMBER
`the days between` MEANS
DATE_SERIAL `the second date` - DATE_SERIAL `the first date`
-- Contract clause interpretation with MAYBE and dates
GIVEN `the contract` IS A Contract
`the party` IS A `Contract Party`
`today` IS A DATE
GIVETH A BOOLEAN
DECIDE `the party may terminate` IF
`the contract is active`
AND `the party has given sufficient notice`
WHERE
`the contract is active` MEANS
`today` >= `the contract`'s `the effective date`
AND CONSIDER `the contract`'s `the termination date`
WHEN NOTHING THEN TRUE
WHEN JUST `the end date` THEN `today` < `the end date`
`the party has given sufficient notice` MEANS
CONSIDER `the party`'s `notice was given on`
WHEN NOTHING THEN FALSE
WHEN JUST `the notice date` THEN
`the days between` `the notice date` `today` >= `the contract`'s `the notice period in days`
-- =======================================
-- SECTION 8: 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
`the open-ended contract` MEANS Contract (Date 1 1 2024) NOTHING 30
`the party with notice` MEANS `Contract Party` "Acme Ltd" (JUST (Date 1 3 2024))
`the party without notice` MEANS `Contract Party` "Beta Ltd" NOTHING
-- =======================================
-- SECTION 9: 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
-- Optional values and dates tests
#EVAL `the days between` (Date 1 3 2024) (Date 15 4 2024)
#EVAL `the party may terminate` `the open-ended contract` `the party with notice` (Date 15 4 2024)
#EVAL `the party may terminate` `the open-ended contract` `the party without notice` (Date 15 4 2024)
```
:
```l4
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
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`
```
**Notice:**
- Natural language identifiers with backticks
- WHERE breaks down the eligibility logic
- Each condition has a clear name
- Logic mirrors how legislation is written
### Example 2: Progressive Tax Calculation
```l4
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
```
### Optional Values with MAYBE
Legal data is often incomplete: a contract may or may not have a termination date; notice may or may not have been given. L4 models "a value that might be absent" with the **MAYBE** type:
- `MAYBE DATE` means "a date, or nothing"
- `NOTHING` is the value when it's absent
- `JUST value` wraps a value when it's present
You inspect a MAYBE with `CONSIDER`, handling both cases:
```l4
CONSIDER `the contract`'s `the termination date`
WHEN NOTHING THEN TRUE -- no termination date: contract is open-ended
WHEN JUST `the end date` THEN ... -- there is one: use `the end date`
```
The type system forces you to say what happens in **both** cases—no "null pointer" surprises, and no silently ignored edge case.
### Working with Dates
L4 has a built-in `DATE` type. With `IMPORT daydate`, you can construct dates as `Date day month year` (for example, `Date 15 4 2024`) and compare them directly with `<`, `>=`, and so on.
To count the days between two dates, convert them to serial day numbers with `DATE_SERIAL`:
```l4
GIVEN `the first date` IS A DATE
`the second date` IS A DATE
GIVETH A NUMBER
`the days between` MEANS
DATE_SERIAL `the second date` - DATE_SERIAL `the first date`
```
### Example 3: Contract Clause Interpretation
Putting MAYBE and dates together (from
```l4-file
-- Module 4: Decision Logic - Complete Examples
-- All examples are validated and use natural language identifiers
IMPORT prelude
IMPORT daydate
-- =======================================
-- 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: Optional Values and Dates
-- =======================================
-- A contract with an optional termination date
DECLARE Contract HAS
`the effective date` IS A DATE
`the termination date` IS A MAYBE DATE
`the notice period in days` IS A NUMBER
-- A party who may or may not have given notice
DECLARE `Contract Party` HAS
`the party's name` IS A STRING
`notice was given on` IS A MAYBE DATE
-- Days between two dates, using serial day numbers
GIVEN `the first date` IS A DATE
`the second date` IS A DATE
GIVETH A NUMBER
`the days between` MEANS
DATE_SERIAL `the second date` - DATE_SERIAL `the first date`
-- Contract clause interpretation with MAYBE and dates
GIVEN `the contract` IS A Contract
`the party` IS A `Contract Party`
`today` IS A DATE
GIVETH A BOOLEAN
DECIDE `the party may terminate` IF
`the contract is active`
AND `the party has given sufficient notice`
WHERE
`the contract is active` MEANS
`today` >= `the contract`'s `the effective date`
AND CONSIDER `the contract`'s `the termination date`
WHEN NOTHING THEN TRUE
WHEN JUST `the end date` THEN `today` < `the end date`
`the party has given sufficient notice` MEANS
CONSIDER `the party`'s `notice was given on`
WHEN NOTHING THEN FALSE
WHEN JUST `the notice date` THEN
`the days between` `the notice date` `today` >= `the contract`'s `the notice period in days`
-- =======================================
-- SECTION 8: 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
`the open-ended contract` MEANS Contract (Date 1 1 2024) NOTHING 30
`the party with notice` MEANS `Contract Party` "Acme Ltd" (JUST (Date 1 3 2024))
`the party without notice` MEANS `Contract Party` "Beta Ltd" NOTHING
-- =======================================
-- SECTION 9: 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
-- Optional values and dates tests
#EVAL `the days between` (Date 1 3 2024) (Date 15 4 2024)
#EVAL `the party may terminate` `the open-ended contract` `the party with notice` (Date 15 4 2024)
#EVAL `the party may terminate` `the open-ended contract` `the party without notice` (Date 15 4 2024)
```
):
```l4
DECLARE Contract HAS
`the effective date` IS A DATE
`the termination date` IS A MAYBE DATE
`the notice period in days` IS A NUMBER
DECLARE `Contract Party` HAS
`the party's name` IS A STRING
`notice was given on` IS A MAYBE DATE
GIVEN `the contract` IS A Contract
`the party` IS A `Contract Party`
`today` IS A DATE
GIVETH A BOOLEAN
DECIDE `the party may terminate` IF
`the contract is active`
AND `the party has given sufficient notice`
WHERE
`the contract is active` MEANS
`today` >= `the contract`'s `the effective date`
AND CONSIDER `the contract`'s `the termination date`
WHEN NOTHING THEN TRUE
WHEN JUST `the end date` THEN `today` < `the end date`
`the party has given sufficient notice` MEANS
CONSIDER `the party`'s `notice was given on`
WHEN NOTHING THEN FALSE
WHEN JUST `the notice date` THEN
`the days between` `the notice date` `today` >= `the contract`'s `the notice period in days`
```
Try it with the test data from the examples file:
```l4
`the open-ended contract` MEANS Contract (Date 1 1 2024) NOTHING 30
`the party with notice` MEANS `Contract Party` "Acme Ltd" (JUST (Date 1 3 2024))
#EVAL `the party may terminate` `the open-ended contract` `the party with notice` (Date 15 4 2024)
-- Result: TRUE
```
---
## Function Signatures
Every decision or computation needs a **type signature** that declares:
1. **Inputs** (GIVEN): What information is needed
2. **Output** (GIVETH): What type of result is produced
### Common Patterns
**Boolean decisions** (yes/no questions):
```l4
GIVEN `the person` IS A Person
GIVETH A BOOLEAN
DECIDE `the person is eligible` IF ...
```
**Classification** (categorizing into types):
```l4
GIVEN `the entity` IS AN Entity
GIVETH A STRING
DECIDE `the entity type` IS ...
```
**Computation** (calculating a value):
```l4
GIVEN `the income` IS A NUMBER
GIVETH A NUMBER
`the tax owed` MEANS ...
```
**Multiple inputs**:
```l4
GIVEN `the applicant` IS A Person
`the application date` IS A DATE
`today` IS A DATE
GIVETH A BOOLEAN
DECIDE `the application is timely` IF ...
```
---
## Exercises
### Exercise 1: Simple Eligibility
Write a decision that determines if a person qualifies for a senior discount (age 65 or older):
```l4
GIVEN `the person's age` IS A NUMBER
GIVETH A BOOLEAN
DECIDE `qualifies for senior discount` IF
-- Your code here
```
Solution
```l4
GIVEN `the person's age` IS A NUMBER
GIVETH A BOOLEAN
DECIDE `qualifies for senior discount` IF
`the person's age` >= 65
#EVAL `qualifies for senior discount` 70
#EVAL `qualifies for senior discount` 50
```
### Exercise 2: Multi-Condition Eligibility
A person qualifies for a student loan if they:
- Are between 18 and 35 years old
- Are enrolled in an accredited institution
- Have no prior loan defaults
Write the decision logic.
Solution
```l4
GIVEN `the applicant's age` IS A NUMBER
`the applicant is enrolled in an accredited institution` IS A BOOLEAN
`the applicant has prior loan defaults` IS A BOOLEAN
GIVETH A BOOLEAN
DECIDE `the applicant qualifies for a student loan` IF
`the applicant is of eligible age`
AND `the applicant is enrolled in an accredited institution`
AND NOT `the applicant has prior loan defaults`
WHERE
`the applicant is of eligible age` MEANS
`the applicant's age` >= 18
AND `the applicant's age` <= 35
#EVAL `the applicant qualifies for a student loan` 25 TRUE FALSE
#EVAL `the applicant qualifies for a student loan` 40 TRUE FALSE
#EVAL `the applicant qualifies for a student loan` 25 TRUE TRUE
```
### Exercise 3: Tax Bracket Classification
Write a decision that classifies income into tax brackets:
- Income < $10,000: "exempt"
- Income $10,000-$50,000: "standard"
- Income > $50,000: "higher rate"
Solution
```l4
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"
#EVAL `the tax bracket` 5000
#EVAL `the tax bracket` 30000
#EVAL `the tax bracket` 80000
```
### Exercise 4: Calculation with WHERE
Write a computation for net income that:
- Starts with gross income
- Subtracts standard deduction (calculated as 10% of gross, minimum $1000)
- Subtracts itemized deductions
Use WHERE to break down the calculation clearly.
Solution
```l4
GIVEN `the gross income` IS A NUMBER
`the itemized deductions` IS A NUMBER
GIVETH A NUMBER
`the net income` MEANS
`the gross income` - `the standard deduction` - `the itemized deductions`
WHERE
`the standard deduction` MEANS
IF `the calculated deduction` >= 1000
THEN `the calculated deduction`
ELSE 1000
`the calculated deduction` MEANS
`the gross income` * 0.10
#EVAL `the net income` 100000 5000
#EVAL `the net income` 8000 500
```
---
## Common Mistakes
### 1. Missing Type Signature
```l4
-- ❌ Wrong: No GIVETH
GIVEN `the person's age` IS A NUMBER
DECIDE `is adult` IF `the person's age` >= 18
-- ✅ Right: Include GIVETH
GIVEN `the person's age` IS A NUMBER
GIVETH A BOOLEAN
DECIDE `is adult` IF `the person's age` >= 18
```
### 2. Using Programmer Names
```l4
-- ❌ Wrong: Programmer style
GIVEN p IS A Person
GIVETH A BOOLEAN
isEligible p MEANS p.age >= 18 && !p.disqualified
-- ✅ Right: Natural language
GIVEN `the person` IS A Person
GIVETH A BOOLEAN
DECIDE `the person is eligible` IF
`the person`'s age >= 18
AND NOT `the person`'s disqualified
```
### 3. Complex Logic Without WHERE
```l4
-- ❌ Wrong: Everything inline, hard to read
`the result` MEANS
(x * 0.1 + y * 0.2) / EXPONENT (1 + r) n
-- ✅ Right: Break down with WHERE
`the result` MEANS
`the combined amount` / `the discount factor`
WHERE
`the combined amount` MEANS x * 0.1 + y * 0.2
`the discount factor` MEANS EXPONENT (1 + r) n
```
### 4. Wrong DECIDE vs MEANS Choice
```l4
-- ❌ Awkward: MEANS for a yes/no question
`is eligible` MEANS age >= 18 AND income < 50000
-- ✅ Better: DECIDE IF for questions
DECIDE `is eligible` IF
age >= 18
AND income < 50000
-- ❌ Awkward: DECIDE for a simple definition
DECIDE `the net amount` IS gross - deductions
-- ✅ Better: MEANS for definitions
`the net amount` MEANS gross - deductions
```
### 5. Nested IF/THEN/ELSE Instead of BRANCH
```l4
-- ❌ Fragile: Nested IF/THEN/ELSE (indentation-sensitive)
`the category` MEANS
IF score >= 90 THEN "excellent"
ELSE IF score >= 70 THEN "good"
ELSE IF score >= 50 THEN "pass"
ELSE "fail"
-- ✅ Better: BRANCH (clear, flat structure)
`the category` MEANS
BRANCH
IF score >= 90 THEN "excellent"
IF score >= 70 THEN "good"
IF score >= 50 THEN "pass"
OTHERWISE "fail"
```
---
## Summary
| Concept | Use for | Syntax |
| -------------------- | --------------------------------- | ----------------------------------------- |
| DECIDE IF | Yes/no questions, eligibility | `DECIDE name IF condition` |
| DECIDE IS | Classification, value assignment | `DECIDE name IS expression` |
| MEANS | Definitions, computations | `name MEANS expression` |
| BRANCH | Multi-way classification | `BRANCH IF cond1 THEN val1 ... OTHERWISE` |
| WHERE | Breaking down complex logic | `expression WHERE helpers` |
| GIVEN ... GIVETH ... | Type signature (always required!) | `GIVEN inputs GIVETH OutputType name...` |
**Key principles:**
- Write code that reads like legal text
- Use backticks liberally for natural language
- Use WHERE to make complex logic transparent
- Choose DECIDE vs MEANS based on readability
---
## What's Next?
In [Module 5: Functions](/l4/courses/foundation/module-5-functions.md), you'll go deeper into the machinery behind decision logic: reusable functions, recursion, and higher-order functions like `map` and `filter` that let you apply decisions across whole lists of cases.
After that, [Module 6: Regulative Rules](/l4/courses/foundation/module-6-regulative.md) shows how to combine constitutive rules (decision logic) with regulative rules (obligations, permissions, prohibitions) to model complete legal workflows.