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//! Loop

use super::{
    identity::Identity,
    operator::{Addition, Multiplication, Operator},
    quasigroup::Quasigroup,
};

/// A quasigroup with an unique identity element.
///
/// $`\exists e \in \mathbb{Q}, \forall a \in \mathbb{Q}, \exists r, l \in
/// \mathbb{Q}`$ such that $`l ∘ a = a ∘ r = e `$ The left inverse $`r`$ and
/// right inverse $`l`$ are not required to be equal. The following property is
/// added to the quasigroup structure:
///
/// This property follows from
///
/// $`\forall a \in \mathbb{Q}, \exists e \in \mathbb{Q}`$, such that $`e ∘ a =
/// a ∘ e = a`$.
pub trait Loop<O: Operator>: Quasigroup<O> + Identity<O>
{
}

macro_rules! impl_loop(
    ($T:ty, $($S:ty),*) =>
    {
        $(
        impl Loop<$T> for $S
        {
        }
        )*
    }
);

impl_loop!(Addition, i8, i16, i32, i64, i128, f32, f64);
impl_loop!(Multiplication, f32, f64);