core API

The core package is the algebraic facade of the repository: it re-exports Dual together with the luna-generic structure traits that Dual[T] implements, and nothing from arithmetic. Import it when you write generic, ring-level code and want a dependency set without the arithmetic traits.

Source: src/core/alias.mbt.

Importing

import {
  "Luna-Flow/autodiff/core" @ad_core,
}

The alias @ad_core avoids confusion with other packages named core; the examples use it.

Re-exported type

`Dual`

The dual number type; see the dual API.

pub using @dual {type Dual}

Re-exported structure traits

Each trait is the original from luna-generic; Dual[T] implements it under the bound shown.

Trait	Required structure	`Dual[T]` instance when
`Zero`	`zero()`	`T : Zero`
`One`	`one()`	`T : One + Zero`
`AddMonoid`	`Add + Zero`	`T : AddMonoid`
`AddGroup`	`AddMonoid + Neg + Sub`	`T : AddGroup`
`MulMonoid`	`Mul + One`	`T : Semiring`
`Semiring`	`AddMonoid + MulMonoid`	`T : Semiring`
`Ring`	`Semiring + Neg + Sub`	`T : Ring`
`IntegralHomomorphism`	`from_integral` from integral types	`T : IntegralHomomorphism + Zero`

pub using @luna-generic {trait Zero}
pub using @luna-generic {trait One}
pub using @luna-generic {trait AddMonoid}
pub using @luna-generic {trait AddGroup}
pub using @luna-generic {trait MulMonoid}
pub using @luna-generic {trait Semiring}
pub using @luna-generic {trait Ring}
pub using @luna-generic {trait IntegralHomomorphism}

`Zero`

Additive identity.

`One`

Multiplicative identity.

`AddMonoid`

Addition with an identity.

`AddGroup`

Addition with negation and subtraction.

`MulMonoid`

Multiplication with an identity.

`Semiring`

Both monoids with distributivity.

`Ring`

A semiring with additive inverses.

`IntegralHomomorphism`

The canonical map from the integers, used for integer constants in generic code.

fn[T : @ad_core.Ring + @ad_core.IntegralHomomorphism] f(x : T) -> T {
  let five : T = @ad_core.IntegralHomomorphism::from_integral(5)
  x * x - five * x
}

test "ring-level generic code" {
  let y = f(@ad_core.Dual::variable(4.0))
  assert_eq(y.value(), -4.0)
  assert_eq(y.tangent(), 3.0) // 2x - 5
}