1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
/*
* SPDX-License-Identifier: MIT
* Copyright (c) 2023 - 2026. The DeepCausality Authors and Contributors. All Rights Reserved.
*/
use crateFloat106;
/// Marker trait: Promises that `a * (b + c) == (a * b) + (a * c)`.
///
/// The compiler cannot check this, so implementing it is a promise by the developer.
///
/// # Which types promise it
///
/// Past the primitives below, seven types carry `Distributive`, each in the crate that defines it:
/// `Complex<T>`, `Quaternion<T>` and `Octonion<T>` in `deep_causality_num_complex`, `Dual<T>` in
/// `deep_causality_num_dual`, `Rational<T>` in `deep_causality_num_rational`, and
/// `CausalTensor<T>` and `CausalTensorTrain<T>` in `deep_causality_tensor`.
///
/// This is the widest of the three multiplicative laws, and the list shows why. ℍ and 𝕆 appear
/// here even though they are missing from [`Commutative`](crate::Commutative) and 𝕆 is missing
/// from [`Associative`](crate::Associative): distributivity is what makes a division algebra an
/// algebra at all, so it survives where the other two fail.
///
/// One absence is structural. `CsrMatrix<T>` in `deep_causality_sparse` stops at
/// [`AbelianGroup`](crate::AbelianGroup) and carries none of the multiplicative markers.
///
/// For `f32`, `f64` and `Float106` the promise covers the finite values. See the scope note on
/// [`Annihilating`](crate::Annihilating).
///
/// # Why these are written out one by one
///
/// This trait was once blanket-implemented over `Num`, which is unsealed: any downstream type
/// implementing `Num` silently acquired this law without anyone promising it, and could then enter
/// `CommutativeRing` and `Field` on a claim nobody made. A marker whose whole purpose is to record
/// an unverifiable promise cannot be handed out by inference.
///
/// Listing the types is the point, not an accident of style. Each line is one deliberate
/// assertion about one type, and the repetition is the cost of making the promise explicit.
/// `AGENTS.md` also steers library code away from macros, so the list stays literal.
// The real scalars.
// The integers. ℤ is a commutative ring, so all three laws hold.
// The naturals. ℕ is a commutative semiring: it has no additive inverses, but the three
// multiplicative laws are unaffected by that.