Tristate Logic

Library for working with tri-state (true/false/null) logic in javascript

Rationale

Tri-state logic is occasionally more useful than strict boolean logic, as it handles the real world case where the truth of some propositions is unknown. Most SQL databases in fact implement a form of tri-state logic. For example, the WHERE clause a = b OR c = d will return results if a is null so long as c = d, because 'UKNOWN or TRUE' is deemed TRUE.

Truth tables for classic tri-state logic are below:

Truth Table for AND(a,b)

a	b	AND
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	FALSE
FALSE	FALSE	FALSE
UNKNOWN	FALSE	FALSE
UNKNOWN	TRUE	UNKNOWN
FALSE	UNKNOWN	FALSE
TRUE	UNKNOWN	UNKNOWN
UNKNOWN	UNKNOWN	UNKNOWN

Truth Table for OR(a,b)

a	b	OR
TRUE	TRUE	TRUE
TRUE	FALSE	TRUE
FALSE	TRUE	TRUE
FALSE	FALSE	FALSE
UNKNOWN	FALSE	UNKNOWN
UNKNOWN	TRUE	TRUE
FALSE	UNKNOWN	UNKNOWN
TRUE	UNKNOWN	TRUE
UNKNOWN	UNKNOWN	UNKNOWN

If we map 'UKNOWN' to 'null' in javascript, the behaviour of the standard operators is frustratingly close to the above:

Comparison of Tristate AND(a,b) with a && b

a	b	a && b	AND
false	false	false	false
false	true	false	false
true	false	false	false
true	true	true	true
null	true	null	null
null	false	null	false
true	null	null	null
false	null	false	false
null	null	null	null

Comparison of Tristate OR(a,b) with a || b

a	b	js or	OR
false	false	false	false
false	true	true	true
true	false	true	true
true	true	true	true
null	true	true	true
null	false	false	null
true	null	true	true
false	null	null	null
null	null	null	null

The exceptions (in italics) unfortunately break some important cases; for if we want to iterate over a collection until some condition is definitely false, being unable to reliably destinguish between 'unknown' and 'false' is a problem.

Example

let result1 = and(null, false)
let result2 = or(null, false)

and result1 should equal false while result2 equals null. In other cases and(a,b) === a && b.

These simple binary and and or functions have to do some extra checks and comparisons in order to work. Some additional API is defined, which can be (very, very, slightly) more efficient and more explicit.

let a = FALSE;
let b = TRUE;
let c = UNKNOWN;
 
if (a.and(c) === FALSE) console.log('hello'); 

will log 'hello'.

For the latest API documentation see The Software Plumbers Site

Project Status

Beta. It seems functional, and the unit tests pass.