In some programming languages, any expression can be evaluated in a context that expects a Boolean data type.
[4] As opposed to Python, empty containers (Arrays, Maps, Sets) are considered truthy.
Logical biconditional becomes the equality binary relation, and negation becomes a bijection which permutes true and false.
Such truth values may express various aspects of validity, including locality, temporality, or computational content.
In realizability truth values are sets of programs, which can be understood as computational evidence of validity of a formula.
In particular, in a topos every formula of higher-order logic may be assigned a truth value in the subobject classifier.
Even though a Heyting algebra may have many elements, this should not be understood as there being truth values that are neither true nor false, because intuitionistic logic proves
For example, on the unit interval [0,1] such structure is a total order; this may be expressed as the existence of various degrees of truth.