The archetypal undecidable predicate: answers Unknown everywhere. More...

Public Types
using	Domain = T
using	Codomain = typename Kleene::Ω
using	logic_species = Kleene

Public Member Functions
constexpr Codomain	operator() (const T &) const

Detailed Description

template<typename T>
struct dedekind::sets::UnknownPredicate< T >

The archetypal undecidable predicate: answers Unknown everywhere.

The Kleene-interior companion of UniversalPredicate (always \(\top\)) and EmptyPredicate (always \(\bot\)). Its characteristic map is constantly Ternary::Unknown, the interior of the chain \(K_3 = \{\bot < U < \top\}\), so membership is never decided: for any point x its answer sits outside the decided core \(\Sigma = \{\top,\bot\}\) that is_decided detects. It is intrinsically three-valued, hence Kleene-tagged, and a Set carrying it fails HasDecidableMembership.

It exists to exercise the lattice reducer against a genuinely undecidable operand. The Kleene annihilators are what recover a decided answer without ever consulting Unknown: a meet with the bottom Ø ( \(x \wedge \bot = \bot\), AND = min, and min(U,\bot) = \bot ) or a join with the top 𝔸 ( \(x \vee \top = \top\), OR = max, max(U,\top) = \top ) annihilates it, and the decided boundary is recovered structurally.

The documentation for this struct was generated from the following file:

src/main/modules/dedekind/sets/expressions.cppm

Public Types

Public Member Functions

Detailed Description