dedekind::order::carrier_cardinality< T > Struct Template Reference

Cardinality class of a halfspace's carrier T (#848/#927). More...

Public Types
using	type

Detailed Description

template<typename T>
struct dedekind::order::carrier_cardinality< T >

Cardinality class of a halfspace's carrier T (#848/#927).

A carrier that declares its own cardinality_type is the authority (e.g. numbers::Rational → ℵ_0, ExtensionalCardinal → Finite): this partition (:order) is upstream of :numbers, so a countable non-integral carrier such as ℚ cannot be recognised structurally here (IsRingIntegral is false on Rational), and must self-declare so the point-free A|pred halfspace classifies identically to the scout comprehension (which inherits the ambient C directly). Otherwise fall back to the IsRingIntegral discriminator: the structural integers and the Cardinality / SignedCardinality (ℕ/ℤ) proxies are ℵ_0, and the real proxies (QuadraticReal, double) are the continuum ℶ_1. The bound only has to be tight enough for the countability verdict (IsCountable).

Member Typedef Documentation

type

template<typename T>

using dedekind::order::carrier_cardinality< T >::type

Initial value:

 
      std::conditional_t<std::is_enum_v<T> || IsRingIntegral<T>, ℵ_0, ℶ_1>

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

• src/main/modules/dedekind/order/runs.cppm