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use std::ops::{Add, Sub};
use typenum::uint::{Unsigned, UInt};
use typenum::bit::Bit;
use typenum::consts::{U0, U1};
use typenum::{Cmp, Same, Greater};
pub type Add1<T> = <T as Add<U1>>::Output;
pub type Sub1<T> = <T as Sub<U1>>::Output;
#[derive(Clone, Copy, PartialEq, Debug)]
pub enum IndexType {
Covariant,
Contravariant,
}
pub trait Variance {
type Rank: Unsigned + Add<U1>;
fn rank() -> usize {
Self::Rank::to_usize()
}
fn variance() -> Vec<IndexType>;
}
impl Variance for () {
type Rank = U0;
fn variance() -> Vec<IndexType> {
vec![]
}
}
pub trait TensorIndex: Variance {
fn index_type() -> IndexType;
}
pub struct ContravariantIndex;
impl TensorIndex for ContravariantIndex {
fn index_type() -> IndexType {
IndexType::Contravariant
}
}
pub struct CovariantIndex;
impl TensorIndex for CovariantIndex {
fn index_type() -> IndexType {
IndexType::Covariant
}
}
impl Variance for ContravariantIndex {
type Rank = U1;
fn variance() -> Vec<IndexType> {
vec![IndexType::Contravariant]
}
}
impl Variance for CovariantIndex {
type Rank = U1;
fn variance() -> Vec<IndexType> {
vec![IndexType::Covariant]
}
}
pub trait OtherIndex: TensorIndex {
type Output: TensorIndex;
}
impl OtherIndex for CovariantIndex {
type Output = ContravariantIndex;
}
impl OtherIndex for ContravariantIndex {
type Output = CovariantIndex;
}
impl<T, U> Variance for (T, U)
where U: Variance,
Add1<U::Rank>: Unsigned + Add<U1>,
T: TensorIndex
{
type Rank = Add1<U::Rank>;
fn variance() -> Vec<IndexType> {
let mut result = vec![T::index_type()];
result.append(&mut U::variance());
result
}
}
pub trait Concat<T: Variance>: Variance {
type Output: Variance;
}
pub type Joined<T, U> = <T as Concat<U>>::Output;
impl<T, U> Concat<U> for T
where T: TensorIndex,
U: TensorIndex,
Add1<<U as Variance>::Rank>: Unsigned + Add<U1>
{
type Output = (T, U);
}
impl<T, U, V> Concat<V> for (T, U)
where T: TensorIndex,
V: TensorIndex,
U: Variance + Concat<V>,
<U as Concat<V>>::Output: Variance,
Add1<<U as Variance>::Rank>: Unsigned + Add<U1>,
Add1<<Joined<U, V> as Variance>::Rank>: Unsigned + Add<U1>
{
type Output = (T, <U as Concat<V>>::Output);
}
impl<T, U, V> Concat<(U, V)> for T
where T: TensorIndex,
U: TensorIndex,
V: Variance,
Add1<<V as Variance>::Rank>: Unsigned + Add<U1>,
Add1<Add1<<V as Variance>::Rank>>: Unsigned + Add<U1>
{
type Output = (T, (U, V));
}
impl<T, U, V, W> Concat<(V, W)> for (T, U)
where T: TensorIndex,
U: Variance + Concat<(V, W)>,
V: TensorIndex,
W: Variance,
Add1<<U as Variance>::Rank>: Unsigned + Add<U1>,
Add1<<W as Variance>::Rank>: Unsigned + Add<U1>,
Add1<<Joined<U, (V, W)> as Variance>::Rank>: Unsigned + Add<U1>
{
type Output = (T, Joined<U, (V, W)>);
}
pub trait Index<T: Unsigned>: Variance {
type Output: TensorIndex;
}
pub type At<T, U> = <T as Index<U>>::Output;
impl Index<U0> for CovariantIndex {
type Output = CovariantIndex;
}
impl Index<U0> for ContravariantIndex {
type Output = ContravariantIndex;
}
impl<T, V, U, B> Index<UInt<U, B>> for (V, T)
where V: TensorIndex,
U: Unsigned,
B: Bit,
UInt<U, B>: Sub<U1>,
Sub1<UInt<U, B>>: Unsigned,
T: Variance + Index<Sub1<UInt<U, B>>>,
Add1<<T as Variance>::Rank>: Unsigned + Add<U1>
{
type Output = At<T, Sub1<UInt<U, B>>>;
}
impl<T, V> Index<U0> for (V, T)
where V: TensorIndex,
T: Variance,
Add1<<T as Variance>::Rank>: Unsigned + Add<U1>
{
type Output = V;
}
pub trait RemoveIndex<T: Unsigned>: Variance {
type Output: Variance;
}
pub type Removed<T, U> = <T as RemoveIndex<U>>::Output;
impl RemoveIndex<U0> for CovariantIndex {
type Output = ();
}
impl RemoveIndex<U0> for ContravariantIndex {
type Output = ();
}
impl<U, V> RemoveIndex<U0> for (U, V)
where U: TensorIndex,
V: Variance,
Add1<<V as Variance>::Rank>: Unsigned + Add<U1>
{
type Output = V;
}
impl<T, B, U, V> RemoveIndex<UInt<T, B>> for (U, V)
where T: Unsigned,
B: Bit,
U: TensorIndex,
UInt<T, B>: Sub<U1>,
Sub1<UInt<T, B>>: Unsigned,
V: Variance + RemoveIndex<Sub1<UInt<T, B>>>,
(U, V): Variance,
(U, Removed<V, Sub1<UInt<T, B>>>): Variance
{
type Output = (U, Removed<V, Sub1<UInt<T, B>>>);
}
pub trait Contract<Ul: Unsigned, Uh: Unsigned>: Variance {
type Output: Variance;
}
pub type Contracted<V, Ul, Uh> = <V as Contract<Ul, Uh>>::Output;
impl<Ul, Uh, V> Contract<Ul, Uh> for V
where Ul: Unsigned,
Uh: Unsigned + Sub<U1> + Cmp<Ul>,
Sub1<Uh>: Unsigned,
<Uh as Cmp<Ul>>::Output: Same<Greater>,
V: Index<Ul> + Index<Uh> + RemoveIndex<Ul>,
At<V, Ul>: OtherIndex,
At<V, Uh>: Same<<At<V, Ul> as OtherIndex>::Output>,
Removed<V, Ul>: RemoveIndex<Sub1<Uh>>,
Removed<Removed<V, Ul>, Sub1<Uh>>: Variance
{
type Output = Removed<Removed<V, Ul>, Sub1<Uh>>;
}
#[cfg(test)]
mod test {
use super::*;
use typenum::consts::{U0, U1, U2};
#[test]
fn test_variance() {
assert_eq!(<(CovariantIndex, ContravariantIndex) as Variance>::variance(), vec![IndexType::Covariant, IndexType::Contravariant]);
}
#[test]
fn test_variance_concat() {
assert_eq!(<Joined<CovariantIndex, ContravariantIndex> as Variance>::variance(),
vec![IndexType::Covariant, IndexType::Contravariant]);
assert_eq!(<Joined<(CovariantIndex, CovariantIndex), ContravariantIndex> as Variance>::variance(),
vec![IndexType::Covariant, IndexType::Covariant, IndexType::Contravariant]);
assert_eq!(<Joined<CovariantIndex, (CovariantIndex, ContravariantIndex)> as Variance>::variance(),
vec![IndexType::Covariant, IndexType::Covariant, IndexType::Contravariant]);
assert_eq!(<Joined<(ContravariantIndex, CovariantIndex), (CovariantIndex, ContravariantIndex)> as Variance>::variance(),
vec![IndexType::Contravariant, IndexType::Covariant, IndexType::Covariant, IndexType::Contravariant]);
}
#[test]
fn test_index() {
assert_eq!(<At<CovariantIndex, U0> as TensorIndex>::index_type(),
IndexType::Covariant);
assert_eq!(<At<(CovariantIndex, ContravariantIndex), U0> as TensorIndex>::index_type(),
IndexType::Covariant);
assert_eq!(<At<(CovariantIndex, ContravariantIndex), U1> as TensorIndex>::index_type(),
IndexType::Contravariant);
assert_eq!(<At<(ContravariantIndex, (CovariantIndex, CovariantIndex)), U0> as TensorIndex>::index_type(),
IndexType::Contravariant);
assert_eq!(<At<(ContravariantIndex, (CovariantIndex, CovariantIndex)), U2> as TensorIndex>::index_type(),
IndexType::Covariant);
}
#[test]
fn test_remove() {
assert_eq!(<Removed<CovariantIndex, U0> as Variance>::variance(),
vec![]);
assert_eq!(<Removed<(CovariantIndex, ContravariantIndex), U0> as Variance>::variance(),
vec![IndexType::Contravariant]);
assert_eq!(<Removed<(CovariantIndex, ContravariantIndex), U1> as Variance>::variance(),
vec![IndexType::Covariant]);
assert_eq!(<Removed<(ContravariantIndex, (CovariantIndex, CovariantIndex)), U1> as Variance>::variance(),
vec![IndexType::Contravariant, IndexType::Covariant]);
}
#[test]
fn test_contract() {
assert_eq!(<Contracted<(CovariantIndex, ContravariantIndex), U0, U1> as Variance>::variance(),
vec![]);
assert_eq!(<Contracted<(ContravariantIndex, CovariantIndex), U0, U1> as Variance>::variance(),
vec![]);
assert_eq!(<Contracted<(ContravariantIndex, (CovariantIndex, CovariantIndex)), U0, U1> as Variance>::variance(),
vec![IndexType::Covariant]);
assert_eq!(<Contracted<(ContravariantIndex, (CovariantIndex, CovariantIndex)), U0, U2> as Variance>::variance(),
vec![IndexType::Covariant]);
}
}