Functions Reference

This section documents the keywords used to define functions and computations in L4. Functions represent individual rules.

Overview

L4 functions are defined using a combination of keywords that specify parameters, return types, and the function body. The typical structure is:

GIVEN parameter IS A Type      -- Parameters (optional)
GIVETH A ReturnType            -- Return type (optional)
DECIDE name MEANS expression   -- Definition

Keywords

Keyword	Purpose	Required
GIVEN	Declares function parameters with types	For functions with inputs
GIVETH / GIVES	Specifies the return type	Optional (can be inferred)
DECIDE	Defines a named value or function	Yes (or use bare MEANS)
MEANS	Connects the function name to its body	Yes
YIELD	Creates anonymous functions (lambdas)	For inline functions
WHERE	Adds local definitions after an expression	Optional
LET	Adds local definitions before an expression	Optional
AKA	Creates aliases for definitions	Optional

Quick Examples

Simple Function

GIVEN x IS A NUMBER
double x MEANS x TIMES 2

Fully Annotated Function

GIVEN n IS A NUMBER
GIVETH A NUMBER
DECIDE factorial n MEANS
  IF n EQUALS 0
  THEN 1
  ELSE n TIMES factorial (n MINUS 1)

With Local Definitions

circleArea radius MEANS
  pi TIMES radius TIMES radius
  WHERE
    pi MEANS 3.14159

With Aliases

`total cost` AKA `final price` MEANS
  basePrice PLUS tax

Anonymous Functions (Lambdas)

Use GIVEN ... YIELD for inline functions:

GIVEN numbers IS A LIST OF NUMBER
`all positive` MEANS all (GIVEN n YIELD n > 0) numbers

Function Definition Patterns

Named Constants

No parameters needed:

DECIDE pi IS 3.14159
DECIDE greeting IS "Hello, World!"

Single Parameter

GIVEN x IS A NUMBER
square x MEANS x TIMES x

Multiple Parameters

GIVEN a IS A NUMBER
      b IS A NUMBER
add a b MEANS a PLUS b

Boolean Decisions

Use DECIDE ... IF for boolean-returning functions:

GIVEN age IS A NUMBER
DECIDE `is adult` IF age >= 18

Mixfix Function Definitions

L4 functions do not have to put the function name first. In a mixfix definition, the parameters declared with GIVEN are interleaved with the identifier words of the function name, so calls read like natural language:

GIVEN mom IS A STRING
      dad IS A STRING
      kid IS A STRING
GIVES A STRING
mom and dad `have a baby named` kid MEANS
    CONCAT "mother: ", mom, ", father: ", dad, ", child: ", kid

The call site uses the same word order:

#EVAL "alice" and "bob" `have a baby named` "carol"

Key points:

Parameters may appear before, between, or after the function's identifier words — enabling infix (x plus y) and postfix (n squared) conventions as well.
Backtick-quoted identifiers may contain spaces, so the "name words" can be multi-word legal phrases (`is entitled to`).
The words of the pattern that are not parameters act as mixfix keywords. The typechecker records each mixfix definition — its written pattern and checked type signature — in a mixfix registry, which it uses to resolve call sites where arguments and keywords are interleaved.
Tooling reuses the registry: the document renderer derives prose headings for mixfix functions from the registered pattern, rendering each parameter slot in the author's original word order (so even functions that are never called elsewhere get proper headings).

For when to reach for mixfix and more worked examples, see Advanced Patterns: Mixfix Function Definitions.

Local Bindings

Two styles for introducing local definitions:

WHERE (definitions after)

result MEANS x PLUS y
  WHERE
    x MEANS 10
    y MEANS 20

LET (definitions before)

result MEANS
  LET x IS 10, y IS 20
  IN x PLUS y