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Operators

Operators combine values into expressions: arithmetic, comparisons and logic. Most have a word form, which reads well in legal text, and a symbol form; the two mean the same and can be mixed. Words suit rules that lawyers read; symbols are shorter.

Pages

Word and symbol forms

Word Symbol Word Symbol
PLUS + EQUALS =
MINUS - GREATER THAN, ABOVE >
TIMES * LESS THAN, BELOW <
DIVIDED BY / AT LEAST >=
MODULO AT MOST <=
AND && OR ||
IMPLIES => NOT, UNLESS

Example file:

-- Example: Textual vs symbolic operators
-- All forms are equivalent and can be mixed

age MEANS 25
citizen MEANS TRUE

-- All equivalent forms
eligible1 MEANS (age > 18) AND (citizen EQUALS TRUE)
eligible2 MEANS (age GREATER THAN 18) AND (citizen = TRUE)
eligible3 MEANS (age > 18) && (citizen EQUALS TRUE)

#EVAL eligible1
#EVAL eligible2
#EVAL eligible3

Precedence

From the tightest-binding to the loosest:

Level Operators Grouping
1 function application, 's
2 TIMES, DIVIDED BY, MODULO left to right
3 PLUS, MINUS left to right
4 FOLLOWED BY to the right
5 EQUALS, GREATER THAN, LESS THAN, AT LEAST, AT MOST and their symbols
6 AND, ..., RAND to the right
7 OR, .., ROR to the right
8 IMPLIES, UNLESS to the right
  • 2 + 3 * 4 is 14, and 10 - 4 - 3 is 3.
  • A call of a user-defined infix function binds tighter than the operators in levels 2 to 8 of the table, so it needs no parentheses next to one. a AND n `exceeds by at least` x means a AND (n `exceeds by at least` x). For a function written x SCALEDBY y, 10 PLUS 2 SCALEDBY 3 means 10 PLUS (2 SCALEDBY 3). See Mixfix functions.
  • NOT is not in the table: it applies to everything after it on its line. See NOT.
  • Parentheses override precedence: (2 + 3) * 4 is 20.
  • When an expression spans several lines, an operator written further left than the lines above it applies to all of them together. See Several lines.

Example files:

-- Example: Operator precedence
-- Demonstrates how operators are evaluated in order

x MEANS 3
y MEANS 4
z MEANS 5

-- Multiplication before addition
#EVAL x PLUS y TIMES z
-- Evaluates as: 3 + (4 * 5) = 23

-- Use parentheses for clarity
#EVAL (x PLUS y) TIMES z
-- Evaluates as: 7 * 5 = 35

,

-- Example: Operator associativity
-- Demonstrates left and right associative operators

-- Left-associative: subtraction
a MEANS 10
b MEANS 3
c MEANS 2

#EVAL a MINUS b MINUS c
-- Evaluates as: (10 - 3) - 2 = 5

-- Right-associative: list cons
#EVAL 1 FOLLOWED BY 2 FOLLOWED BY 3 FOLLOWED BY EMPTY
-- Evaluates as: 1 FOLLOWED BY (2 FOLLOWED BY (3 FOLLOWED BY EMPTY))

Asyndetic AND and OR

Legal text often lists conditions with punctuation instead of "and" or "or". L4 has two such forms:

  • ... (three dots) means AND: `is a citizen` ... `is over 18` ... `has ID`
  • .. (two dots) means OR: approved .. pending .. `under review`

They have the same precedence as AND and OR.

Example file:

-- Example: Asyndetic operators (... and ..)
-- Implicit AND and OR using punctuation

citizen MEANS TRUE
over18 MEANS TRUE
`has ID` MEANS TRUE

approved MEANS TRUE
pending MEANS FALSE
review MEANS FALSE

-- Ellipsis (...) = implicit AND
eligible1 MEANS citizen ... over18 ... `has ID`
-- Equivalent to: (citizen AND over18 AND has ID)

-- Double dot (..) = implicit OR
`in progress` MEANS approved .. pending .. review
-- Equivalent to: (approved OR pending OR review)

#EVAL eligible1
#EVAL `in progress`

Other operators