Semiring Applications - All pairs shortest path (Tropical semiring) + Ridge Linear Regression (Semiring)

lattices/src/lib.rs

@@ -16,6 +16,7 @@ pub mod map_union_with_tombstones;
 mod ord;
 mod pair;
 mod point;
+pub mod semiring_application;
 pub mod set_union;
 pub mod set_union_with_tombstones;
 pub mod test;
@@ -40,6 +41,51 @@ pub trait Lattice: Sized + Merge<Self> + LatticeOrd + NaiveLatticeOrd + IsBot +
 #[sealed]
 impl<T> Lattice for T where T: Sized + Merge<Self> + LatticeOrd + NaiveLatticeOrd + IsBot + IsTop {}
 
+/// Alias trait for semirings.
+#[sealed]
+pub trait Semiring<T>: Addition<T> + Multiplication<T> + Zero<T> + One<T> {}
+
+/// Trait for Semiring Addition.
+pub trait Addition<Other> {
+    /// Add-assign `other` into self.
+    fn add(&mut self, other: Self);
+
+    /// Add `this` and `delta` together, returning the new value.
+    fn add_owned(mut self, other: Self) -> Self
+    where
+        Self: Sized,
+    {
+        self.add(other);
+        self
+    }
+}
+
+/// Trait for Semiring Multiplication.
+pub trait Multiplication<Other> {
+    /// Multiply-assign `other` into self.
+    fn mul(&mut self, other: Self);
+
+    /// Multiply `this` and `delta` together, returning the new value.
+    fn mul_owned(mut self, other: Self) -> Self
+    where
+        Self: Sized,
+    {
+        self.mul(other);
+        self
+    }
+}
+
+/// Trait to check if semiring contains a zero.
+pub trait Zero<T> {
+    /// Returns the zero element of the semiring. Identify for the Addition operation.
+    fn zero(&self) -> Self;
+}
+
+/// Trait to define a one in a semiring.
+pub trait One<T> {
+    /// Returns the one element of the semiring. Identity for the multiplication operation.
+    fn one(&self) -> Self;
+}
 /// Trait for lattice merge (AKA "join" or "least upper bound").
 pub trait Merge<Other> {
     /// Merge `other` into the `self` lattice.