dedekind::category::Truth< L > Class Template Reference

The Monic Wrapper for a Logical Species (Ω). More...

Public Types
using	logic_species = L
using	machine_type = typename L::Ω

Public Member Functions
constexpr	Truth (machine_type v) noexcept
	Wrap a raw carrier value as a Truth (the monic promotion).
constexpr	operator machine_type () const noexcept
constexpr bool	operator== (const Truth &) const =default

Public Attributes
machine_type	value

Friends
constexpr Truth	operator! (Truth a) noexcept
constexpr Truth	operator&& (Truth a, Truth b) noexcept(noexcept(L::AND(a.value, b.value)))
	Meet ∧ = L::AND and join ∨ = L::OR on two wrappers, spelled && / || to complete the && / || / ! register (matching the raw carriers bool / Ternary).
constexpr Truth	operator|| (Truth a, Truth b) noexcept(noexcept(L::OR(a.value, b.value)))
	Join ∨ of two wrappers.This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
constexpr Truth	operator<= (Truth a, Truth b) noexcept
	The truth order: a <= b iff the join a ∨ b is b. Meet / join / reflection themselves are the species morphisms L::AND / L::OR / L::RFL, spelled && / || / ! on the wrapper. The rig + / * surface was retired (#901): a truth value is a De Morgan-lattice element, not a semiring element, so it carries the involution and the lattice order, not + / * / one().

Detailed Description

template<typename L = Boole>
class dedekind::category::Truth< L >

The Monic Wrapper for a Logical Species (Ω).

Wraps a raw truth type (bool, Ternary) as a De Morgan-lattice element, carrying meet && , join || , the involution ! and the lattice order <= , while preventing machine-level integral promotion. The former rig (+ / *) surface was retired: a truth value is a lattice element, not a semiring element (#901).

Constructor & Destructor Documentation

Truth()

template<typename L = Boole>

dedekind::category::Truth< L >::Truth ( machine_type v )

inlineexplicitconstexprnoexcept

Wrap a raw carrier value as a Truth (the monic promotion).

logic__Monic_Construction

explicit by design: a raw carrier does not implicitly become a Truth. This keeps Truth<Boole> && bool decaying to the built-in bool && (short-circuit preserved, which matters if the raw operand has side effects), rather than binding a strict eager wrapper overload. Opt into the lattice register by wrapping explicitly: Truth<L>{v}.

Note

This is a deliberate source-breaking change from the previous implicit constructor: a Truth<L>-returning function can no longer return a bare carrier (write return Truth<L>{v}). No in-tree caller relied on the implicit form, and per the project's experimental-API-break posture no compatibility shim is kept.

Member Function Documentation

operator machine_type()

template<typename L = Boole>

dedekind::category::Truth< L >::operator machine_type ( ) const

inlineexplicitconstexprnoexcept

logic__Conversion

Friends And Related Symbol Documentation

operator&&

template<typename L = Boole>

Truth operator&& ( Truth< L > a, Truth< L > b )

friend

Meet ∧ = L::AND and join ∨ = L::OR on two wrappers, spelled && / || to complete the && / || / ! register (matching the raw carriers bool / Ternary).

logic__Lattice_Register

Note

Same-species only (Truth<L> op Truth<L>). A mixed Truth op carrier expression is deliberately not captured: because the carrier ctor is explicit the raw operand does not promote to Truth, so Truth<Boole> && bool falls to the built-in bool && bool, preserving short-circuit. Wrap explicitly to stay in the lattice. The register is strict (no short-circuit): on two wrappers both operands are already-computed, side-effect-free values, so eager meet/join is extensionally the built-in behaviour.

operator<=

template<typename L = Boole>

Truth operator<= ( Truth< L > a, Truth< L > b )

friend

The truth order: a <= b iff the join a ∨ b is b. Meet / join / reflection themselves are the species morphisms L::AND / L::OR / L::RFL, spelled && / || / ! on the wrapper. The rig + / * surface was retired (#901): a truth value is a De Morgan-lattice element, not a semiring element, so it carries the involution and the lattice order, not + / * / one().

logic__Lattice_Order

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

• src/main/modules/dedekind/category/logic.cppm