Boolean Operations

true and false;

is false. You receive similarly sensible results for or, not and xor, and comparison operators return boolean values:

10 < 12 and 12 < 14; // true

Evaluation of boolean operators is short circuited appropriately so true or something will not evaluate something.

One surprise, booleans can have a third value: unknown. Truth tables for the boolean operators involving unknown are as follows:

and

lhs	rhs	result
true	true	true
true	unknown	unknown
true	false	false
unknown	true	unknown
unknown	unknown	unknown
unknown	false	false
false	true	false
false	unknown	false
false	false	false

or

lhs	rhs	result
true	unknown	true
true	true	true
true	false	true
unknown	unknown	unknown
unknown	true	true
unknown	false	unknown
false	unknown	unknown
false	true	true
false	false	false

xor

lhs	rhs	result
true	true	false
true	unknown	unknown
true	false	true
unknown	true	unknown
unknown	unknown	unknown
unknown	false	unknown
false	true	true
false	unknown	unknown
false	false	false

not

rhs	result
true	false
unknown	unknown
false	true

Of special interest is that certain operations involving unknown do not result in unknown. Specifically false and unknown is false, as false and anything will always be false; likewise true or unknown is true.

unknown cannot result from any boolean operation on known truth values and (so far) no comparison operators result in unknown, so unless you explicitly introduce the value you do not need to know about it.

Equality of booleans in a three-valued logic system could be tricky, specifically if unknown means "either true or false" then any_boolean == unknown should be unknown, but given we need a way to test for unknown, I've chosen the simpler option where true == true, false == false and unknown == unknown.

This makes possible things like result == unknown and back (see later for then and back) which might be useful in decidability algorithms. If you actually want that more "correct" behaviour when comparing booleans with unknown, you can replace a == b with not (a xor b).

Comparison Operators

The standard comparison operators are available. They require that the types of their arguments agree, and all types can be compared (sometimes somewhat arbitrarily, for example false < unknown and unknown < true.) The operators are:

op	name
==	equal to
!=	not equal to
<	less than
>	greater than
<=	less than or equal to
>=	greater than or equal to

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