registration.cppm File Reference

Registration helpers for field-shaped carriers. More...

#include <concepts>
#include <cstddef>
#include <functional>
#include <type_traits>

Include dependency graph for registration.cppm:

Classes
struct	RigRegistration< T, Zero, One, Add, Mult >
	Base class for SpeciesTraits<T> of carriers forming a \emph{rig} (semiring) under (Add, Mult) with identities Zero (additive) and One (multiplicative). More...
struct	RingRegistration< T, Zero, One, Add, Mult >
	A rig whose additive monoid is an abelian group (i.e. has additive inverses). Mult is not required to commute here; see CommutativeRingRegistration for that. More...
struct	CommutativeRingRegistration< T, Zero, One, Add, Mult >
	A ring whose multiplication is also commutative. More...
struct	FieldRegistration< T, Zero, One, Add, Mult >
	A commutative ring in which every non-zero multiplicative element is also invertible. More...
struct	GaloisFieldRegistration< T, Zero, One, Order, Add, Mult >
	Extends FieldRegistration with the Galois-specific opt-ins: the carrier is declared a finite field of a given order. More...
struct	dedekind::category::is_associative< T, Op >
struct	dedekind::category::is_commutative< T, Op >
struct	dedekind::category::is_periodic< T, Op >
struct	dedekind::category::inverse_trait< T, Op >
struct	dedekind::category::unit_trait< T, Op, void >

Namespaces
namespace	dedekind::category

Concepts
concept	dedekind::category::RegisteredViaHelper
concept	dedekind::category::SpeciesTraitsHasIsAssociative
concept	dedekind::category::SpeciesTraitsHasIsCommutative
concept	dedekind::category::SpeciesTraitsHasIsPeriodic
concept	dedekind::category::SpeciesTraitsHasIsInvertible
concept	dedekind::category::SpeciesTraitsHasIsDistributive
concept	dedekind::category::SpeciesTraitsHasIdentity

Variables
template<typename T>
constexpr bool	dedekind::category::is_distributive_v< T, std::multiplies< T >, std::plus< T > >

Detailed Description

Registration helpers for field-shaped carriers.

@partition :registration

Copyright

2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

registration__Scope

Closes #382. When a concrete carrier T is registered as a field under some (Add, Mult), the per-carrier trait block has historically been ~40 lines of boilerplate (identity, associativity, commutativity, distributivity, periodicity, invertibility on each operation — all written out per (T, Op)).

This partition replaces that block with a single base-class inheritance into SpeciesTraits<T>:

template <>
struct SpeciesTraits<𝔽64>
    : dedekind::algebra::GaloisFieldRegistration<𝔽64, 𝔽64{}, 𝔽64{1}, 64> {
  using Domain = 𝔽64;
  using machine_type = std::uint8_t;
};

The mechanism has two pieces:

(1) FieldRegistration<T, Zero, One, Add, Mult> (and the derived GaloisFieldRegistration<..., Order>) — CRTP-ish base classes that expose member templates is_associative_v<Op>, is_commutative_v<Op>, is_invertible_v<Op>, is_periodic_v<Op>, unit_v<Op>, is_distributive_v<MultOp, AddOp>, with the obvious per-op conditions baked in.

(2) SpeciesTraits-based \emph{discovery} partial specialisations for each of the corresponding free-standing traits in dedekind.category (is_associative, is_commutative, \ldots, unit_trait, is_invertible_v, \ldots). Each one has the shape ``if SpeciesTraits<T> exposes member template is_foo_v, then is_foo<T, Op>::value is that''.

The discovery layer lives here (not in category:species), so :species stays a pure trait-definition layer. Carriers that do not inherit from a Registration helper are unaffected: the discovery only fires when the member template is actually present. The dedekind.algebra umbrella re-exports this partition, so any translation unit that uses a Registration- retargeted carrier already sees the discovery specs.

Note

"The machine does not give us the answer, nor does the answer give us the machine; what matters is that we see the form." — paraphrase of Christopher Strachey's remark on denotational method. */ module;

for std::same_as for std::size_t for std::plus, std::multiplies for std::bool_constant

export module dedekind.algebra:registration;

import dedekind.category;

namespace dedekind::algebra {

---

The Registration chain. Each level derives from the previous and adds the incremental axioms that define its algebraic species:

RigRegistration — additive commutative monoid + multiplicative monoid + distributive (no additive inverse) ↓ RingRegistration — + additive invertibility ↓ CommutativeRingRegistration — + multiplicative commutativity ↓ FieldRegistration — + multiplicative invertibility ↓ GaloisFieldRegistration — + finite-cardinality opt-in (Galois field)

A carrier picks the appropriate level for its species and the SpeciesTraits-based discovery below lifts the member templates

into the free-standing trait specialisations.

/**