dedekind::category::Boole Struct Reference

The internal logic of the Classical Topos ({True, False}). More...

Public Types
using	Ω = bool
using	JoinOp = std::logical_or<bool>
	The op-types OR / AND / RFL are, for the :species / :total law registry. 𝔹's join / meet are || / && (std::logical_or / std::logical_and on bool), under which the distributive-, bounded- and Boolean-algebra laws (incl. the complement) are registered; ¬ is logic_complement<Boole>.
using	MeetOp = std::logical_and<bool>
using	RflOp = logic_complement<Boole>

Static Public Member Functions
static constexpr bool	AND (bool a, bool b)
static constexpr bool	OR (bool a, bool b)
static constexpr bool	RFL (bool a)

Static Public Attributes
static constexpr bool	True = true
static constexpr bool	False = false

Detailed Description

The internal logic of the Classical Topos ({True, False}).

logic__Species

Boole defines the standard Boolean algebra where the Law of Excluded Middle holds. It maps the structuralist AND/OR/RFL morphisms directly to C++ hardware-level logical primitives.

Note

This species is the "Zero-Cost" foundation for standard set operations. Because it uses bool, the compiler can often resolve these operations into single bitwise assembly instructions during DAG pruning.

Textbook term: the two-element Boolean algebra.

Member Typedef Documentation

JoinOp

using dedekind::category::Boole::JoinOp = std::logical_or<bool>

The op-types OR / AND / RFL are, for the :species / :total law registry. 𝔹's join / meet are || / && (std::logical_or / std::logical_and on bool), under which the distributive-, bounded- and Boolean-algebra laws (incl. the complement) are registered; ¬ is logic_complement<Boole>.

(#923)

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

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