Using Infix, Postfix, and Mixfix Functions

This tutorial shows how to define and call functions that read like natural language. L4's mixfix operators let you write code that mirrors the structure of legal prose.

Overview

Traditional programming languages use prefix notation where the function name comes first:

add(3, 5)
isEligible(person, program)

L4 supports multiple calling patterns that read more naturally:

Pattern	Example	Natural Reading
Prefix	`add` 3 5	"add 3 and 5"
Infix	3 `plus` 5	"3 plus 5"
Postfix	50 `percent`	"50 percent"
Mixfix	alice `is eligible for` medicare	"alice is eligible for medicare"

Prerequisites

• Basic understanding of L4 functions (see Your First L4 File)
• Familiarity with GIVEN and MEANS keywords (see MEANS)

Infix Functions

An infix function takes two arguments with the function name between them.

GIVEN a IS A NUMBER, b IS A NUMBER
GIVETH A NUMBER
a `plus` b MEANS a + b

Notice the pattern: param keyword param. The parameters a and b come from the GIVEN clause. The backticked `plus` becomes the function name.

Calling Infix Functions

You can call infix functions in two ways:

-- Infix style (natural reading)
#EVAL 3 `plus` 5

-- Prefix style (also works)
#EVAL `plus` 3 5

Both return 8.

Multi-Word Keywords

Backticks allow spaces in function names, enabling very natural syntax:

GIVEN person IS A STRING, program IS A STRING
GIVETH A BOOLEAN
person `is eligible for` program MEANS TRUE

-- Call site reads like English
#EVAL "Alice" `is eligible for` "Medicare"

Postfix Functions

A postfix function takes one argument that appears before the function name.

Definition

GIVEN amount IS A NUMBER
GIVETH A NUMBER
amount `percent` MEANS amount / 100

Calling Postfix Functions

-- Postfix style
#EVAL 50 `percent`

-- Prefix style alternative
#EVAL `percent` 50

Both return 0.5.

Single-Word Operators

For single-word function names, backticks are optional at the call site:

GIVEN n IS A NUMBER
n squared MEANS n * n

-- Both work:
#EVAL 5 squared
#EVAL 5 `squared`

Mixfix Functions (Ternary and Beyond)

Mixfix functions have keywords interspersed with multiple arguments. They can have any number of parameters.

Ternary Mixfix (Three Arguments)

GIVEN cond IS A BOOLEAN, thenVal IS A NUMBER, elseVal IS A NUMBER
GIVETH A NUMBER
`myif` cond `mythen` thenVal `myelse` elseVal MEANS
  IF cond THEN thenVal ELSE elseVal

-- Call with full mixfix syntax
#EVAL `myif` TRUE `mythen` 42 `myelse` 0

This function starts with a keyword (`myif`), so the first token isn't an argument.

Quaternary Mixfix (Four Arguments)

GIVEN mummy IS A STRING, daddy IS A STRING, baby IS A STRING, nickname IS A STRING
GIVETH A STRING
mummy `and` daddy `had` baby `called` nickname MEANS baby

-- Call site
#EVAL "Alice" `and` "Bob" `had` "Charlie" `called` "Chuck"

Higher Arity

You can define functions with any number of parameters:

GIVEN a IS A NUMBER, b IS A NUMBER, c IS A NUMBER, d IS A NUMBER, e IS A NUMBER
GIVETH A NUMBER
a `op1` b `op2` c `op3` d `op4` e MEANS a + b + c + d + e

#EVAL 1 `op1` 2 `op2` 3 `op3` 4 `op4` 5
-- Returns: 15

Multi-Line Layout

Mixfix operators can span multiple lines when keywords align with the operand's indentation:

GIVEN base IS A NUMBER, exponent IS A NUMBER
base `raised to` exponent MEANS base * exponent

DECIDE demo_multiline base exponent IS
  base
  `raised to`
  exponent

This is useful for complex expressions with long keywords.

Practical Examples

Legal Eligibility Rules

DECLARE Person HAS
  name IS A STRING
  age IS A NUMBER
  income IS A NUMBER

GIVEN person IS A Person, threshold IS A NUMBER
GIVETH A BOOLEAN
person `has income above` threshold MEANS
  person's income > threshold

GIVEN person IS A Person
GIVETH A BOOLEAN
person `is an adult` MEANS
  person's age >= 18

Financial Calculations

GIVEN principal IS A NUMBER, rate IS A NUMBER, years IS A NUMBER
GIVETH A NUMBER
principal `at` rate `percent for` years `years` MEANS
  principal * (1 + rate / 100) * years

Range Checks

GIVEN lower IS A NUMBER, value IS A NUMBER, upper IS A NUMBER
GIVETH A BOOLEAN
lower `<=` value `<=` upper MEANS
  lower <= value AND value <= upper

#EVAL 0 `<=` 5 `<=` 10
-- Returns: TRUE

Best Practices

Use Natural Language Names

L4's target audience is legal professionals. Write functions that read like legal prose:

-- ✅ Good: reads like legal text
person `is eligible for benefits` MEANS ...
amount `exceeds the threshold` MEANS ...

-- ❌ Poor: reads like code
isEligible person MEANS ...
exceedsThreshold amount MEANS ...

Use Backticks for Multi-Word Names

-- ✅ Good: clear, readable
`the applicant` `has submitted a valid claim` MEANS ...

-- ❌ Avoid: hard to read
theApplicant hasSubmittedAValidClaim MEANS ...

Define Mixfix Operators in WHERE Clauses

When defining helper mixfix operators inside a function, use WHERE (not LET):

-- ✅ Correct: mixfix in WHERE
GIVEN radius IS A NUMBER
GIVETH A NUMBER
`circle area` radius MEANS
  radius `squared` TIMES pi
  WHERE
    pi MEANS 3.14159
    GIVEN r IS A NUMBER
    r `squared` MEANS r * r

-- ❌ Incorrect: mixfix operators in LET won't work
-- LET blocks don't register mixfix operators

Use Parentheses for Complex Expressions

When nesting mixfix calls, use parentheses for clarity:

#EVAL (1 + 2) `plus` (3 + 4)
#EVAL `myif` (x > 0) `mythen` (x * 2) `myelse` 0

Complete Example File

See the full working example:

§ `Natural Language Functions Tutorial`

-- This file demonstrates infix, postfix, and mixfix function patterns
-- that allow L4 code to read like natural language.

-- ============================================================================
-- INFIX FUNCTIONS
-- Pattern: param `keyword` param
-- ============================================================================

-- Simple numeric infix operator
GIVEN a IS A NUMBER, b IS A NUMBER
GIVETH A NUMBER
a `plus` b MEANS a + b

-- Multi-word infix operator
GIVEN person IS A STRING, program IS A STRING
GIVETH A BOOLEAN
person `is eligible for` program MEANS TRUE

-- Test infix calls
#EVAL 3 `plus` 5
#EVAL "Alice" `is eligible for` "Medicare"

-- Infix can also be called with prefix notation
#EVAL `plus` 10 20

-- ============================================================================
-- POSTFIX FUNCTIONS
-- Pattern: param `keyword`
-- ============================================================================

-- Simple postfix operator
GIVEN amount IS A NUMBER
GIVETH A NUMBER
amount `percent` MEANS amount / 100

-- Another postfix example
GIVEN n IS A NUMBER
GIVETH A NUMBER
n squared MEANS n * n

-- Test postfix calls
#EVAL 50 `percent`
#EVAL 75 percent
#EVAL 5 squared
#EVAL 7 `squared`

-- Postfix with expressions
#EVAL (10 + 5) `percent`

-- ============================================================================
-- TERNARY MIXFIX FUNCTIONS
-- Pattern: `keyword` param `keyword` param `keyword` param
-- ============================================================================

-- Custom conditional operator
GIVEN cond IS A BOOLEAN, thenVal IS A NUMBER, elseVal IS A NUMBER
GIVETH A NUMBER
`myif` cond `mythen` thenVal `myelse` elseVal MEANS
  IF cond THEN thenVal ELSE elseVal

-- Test ternary mixfix
#EVAL `myif` TRUE `mythen` 42 `myelse` 0
#EVAL `myif` FALSE `mythen` 42 `myelse` 0
#EVAL `myif` (1 = 1) `mythen` (10 + 5) `myelse` (20 - 5)

-- ============================================================================
-- QUATERNARY MIXFIX FUNCTIONS
-- Pattern: param `keyword` param `keyword` param `keyword` param
-- ============================================================================

GIVEN mummy IS A STRING, daddy IS A STRING, baby IS A STRING, nickname IS A STRING
GIVETH A STRING
mummy `and` daddy `had` baby `called` nickname MEANS baby

-- Test quaternary mixfix
#EVAL "Alice" `and` "Bob" `had` "Charlie" `called` "Chuck"

-- Prefix notation also works
#EVAL `and` "Mom" "Dad" "Kid" "Kiddo"

-- ============================================================================
-- ARITY-5 MIXFIX FUNCTIONS
-- ============================================================================

GIVEN a IS A NUMBER, b IS A NUMBER, c IS A NUMBER, d IS A NUMBER, e IS A NUMBER
GIVETH A NUMBER
a `op1` b `op2` c `op3` d `op4` e MEANS a + b + c + d + e

#EVAL 1 `op1` 2 `op2` 3 `op3` 4 `op4` 5
#EVAL (10 - 9) `op1` (1 + 1) `op2` 3 `op3` (2 * 2) `op4` 5

-- ============================================================================
-- RANGE CHECK MIXFIX
-- A practical example for legal conditions
-- ============================================================================

GIVEN lower IS A NUMBER, value IS A NUMBER, upper IS A NUMBER
GIVETH A BOOLEAN
lower `is at most` value `which is at most` upper MEANS
  lower <= value AND value <= upper

#EVAL 0 `is at most` 5 `which is at most` 10
#EVAL 0 `is at most` 15 `which is at most` 10

-- ============================================================================
-- PRACTICAL LEGAL EXAMPLE
-- Functions that read like legal prose
-- ============================================================================

DECLARE Person HAS
  name IS A STRING
  age IS A NUMBER

GIVEN person IS A Person
GIVETH A BOOLEAN
person `is an adult` MEANS person's age >= 18

GIVEN person IS A Person
GIVETH A BOOLEAN
person `is a minor` MEANS person's age < 18

-- Create test data
`test adult` MEANS Person WITH name IS "Alice", age IS 30
`test minor` MEANS Person WITH name IS "Bob", age IS 15

-- Test legal predicates
#EVAL `test adult` `is an adult`
#EVAL `test minor` `is a minor`

-- ============================================================================
-- MIXFIX WITH WHERE CLAUSE
-- Defining helper operators locally
-- ============================================================================

GIVEN radius IS A NUMBER
GIVETH A NUMBER
`circle area for radius` radius MEANS
  radius `squared locally` TIMES pi
  WHERE
    pi MEANS 3.14159
    GIVEN r IS A NUMBER
    r `squared locally` MEANS r * r

#EVAL `circle area for radius` 10

Summary

Pattern	Definition	Call Site
Infix	a `keyword` b MEANS ...	x `keyword` y
Postfix	a `keyword` MEANS ...	x `keyword`
Prefix	`keyword` a b MEANS ...	`keyword` x y
Mixfix	a `kw1` b `kw2` c MEANS ...	x `kw1` y `kw2` z

Related Documentation

• DECIDE - Function declaration keyword
• MEANS - Function body keyword
• GIVEN - Parameter declaration