diff --git a/src/main.rs b/src/main.rs
index d5cdc82..e7101c7 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,20 +1,120 @@
 use std::iter::Sum;
-use std::ops::Mul;
+use std::ops::{Mul, Sub};
 
 type Point<A, const N: usize> = [A; N];
 
 type Parameters<A, const N: usize, const M: usize> = [Point<A, N>; M];
 
+#[macro_export]
+macro_rules! tensor {
+    ($x:ty , $i: expr) => {[$x; $i]};
+    ($x:ty , $i: expr, $($is:expr),+) => {[tensor!($x, $($is),+); $i]};
+}
+
+pub trait Extensible1<A> {
+    fn apply<F>(&self, other: &A, op: &F) -> Self
+    where
+        F: Fn(&A, &A) -> A;
+}
+
+pub trait Extensible2<A> {
+    fn apply<F>(&self, other: &Self, op: &F) -> Self
+    where
+        F: Fn(&A, &A) -> A;
+}
+
+impl<A, T, const N: usize> Extensible1<A> for [T; N]
+where
+    T: Extensible1<A> + Copy + Default,
+{
+    fn apply<F>(&self, other: &A, op: &F) -> Self
+    where
+        F: Fn(&A, &A) -> A,
+    {
+        let mut result = [Default::default(); N];
+        for (i, coord) in self.iter().enumerate() {
+            result[i] = T::apply(coord, other, op);
+        }
+        result
+    }
+}
+
+impl<A, T, const N: usize> Extensible2<A> for [T; N]
+where
+    T: Extensible2<A> + Copy + Default,
+{
+    fn apply<F>(&self, other: &Self, op: &F) -> Self
+    where
+        F: Fn(&A, &A) -> A,
+    {
+        let mut result = [Default::default(); N];
+        for (i, coord) in self.iter().enumerate() {
+            result[i] = T::apply(coord, &other[i], op);
+        }
+        result
+    }
+}
+
+#[macro_export]
+macro_rules! extensible1 {
+    ($x: ty) => {
+        impl Extensible1<$x> for $x {
+            fn apply<F>(&self, other: &$x, op: &F) -> Self
+            where
+                F: Fn(&Self, &Self) -> Self,
+            {
+                op(self, other)
+            }
+        }
+    };
+}
+
+#[macro_export]
+macro_rules! extensible2 {
+    ($x: ty) => {
+        impl Extensible2<$x> for $x {
+            fn apply<F>(&self, other: &Self, op: &F) -> Self
+            where
+                F: Fn(&Self, &Self) -> Self,
+            {
+                op(self, other)
+            }
+        }
+    };
+}
+
+extensible1!(u8);
+extensible1!(f64);
+
+extensible2!(u8);
+extensible2!(f64);
+
+pub fn extension1<T, A, F>(t1: &T, t2: &A, op: F) -> T
+where
+    T: Extensible1<A>,
+    F: Fn(&A, &A) -> A,
+{
+    t1.apply::<F>(t2, &op)
+}
+
+pub fn extension2<T, A, F>(t1: &T, t2: &T, op: F) -> T
+where
+    T: Extensible2<A>,
+    F: Fn(&A, &A) -> A,
+{
+    t1.apply::<F>(t2, &op)
+}
+
 fn dot_points<A: Mul, const N: usize>(x: &Point<A, N>, y: &Point<A, N>) -> A
 where
-    A: Sum<<A as Mul>::Output> + Copy,
+    A: Sum<<A as Mul>::Output> + Copy + Default + Mul<Output = A> + Extensible2<A>,
 {
-    x.iter().zip(y).map(|(&x, &y)| x * y).sum()
+    extension2(x, y, |&x, &y| x * y).into_iter().sum()
 }
 
 fn dot<A, const N: usize, const M: usize>(x: &Point<A, N>, y: &Parameters<A, N, M>) -> Point<A, M>
 where
-    A: Mul<A> + Sum<<A as Mul>::Output> + Copy + Default,
+    A: Mul<Output = A> + Sum<<A as Mul>::Output> + Copy + Default + Extensible2<A>,
 {
     let mut result = [Default::default(); M];
     for (i, coord) in y.iter().map(|y| dot_points(x, y)).enumerate() {
@@ -23,30 +123,69 @@ where
     result
 }
 
-fn line<A, const N: usize>(x: &Point<A, N>, theta: &Parameters<A, N, 1>) -> Point<A, 1>
+fn sum<A, const N: usize>(x: &tensor!(A, N)) -> A
 where
-    A: Mul<A> + Sum<<A as Mul>::Output> + Copy + Default,
+    A: Sum<A> + Copy,
 {
-    dot(x, theta)
+    A::sum(x.iter().cloned())
 }
 
-//fn data_set() -> ([f64; 4], [f64; 4]) {
-//    ([2.0, 1.0, 4.0, 3.0], [1.8, 1.2, 4.2, 3.3])
-//}
-
-fn linear_params_2d<A>(m: A, c: A) -> Parameters<A, 2, 1> {
-    [[c, m]]
+fn squared<A, const N: usize>(x: &tensor!(A, N)) -> tensor!(A, N)
+where
+    A: Mul<Output = A> + Extensible2<A> + Copy + Default,
+{
+    extension2(x, x, |&a, &b| (a * b))
 }
 
-#[macro_export]
-macro_rules! tensor {
-    ($x:ty , $i: expr) => {[$x; $i]};
-    ($x:ty , $i: expr, $($is:expr),+) => {[tensor!($x, $($is),+); $i]};
+fn l2_norm<A, const N: usize>(prediction: &tensor!(A, N), data: &tensor!(A, N)) -> A
+where
+    A: Sum<A> + Mul<Output = A> + Extensible2<A> + Copy + Default + Sub<Output = A>,
+{
+    let diff = extension2(prediction, data, |&x, &y| x - y);
+    sum(&squared(&diff))
+}
+
+pub fn l2_loss<A, F, Params, const N: usize>(
+    target: F,
+    data_xs: &tensor!(A, N),
+    data_ys: &tensor!(A, N),
+    params: &Params,
+) -> A
+where
+    F: Fn(&tensor!(A, N), &Params) -> tensor!(A, N),
+    A: Sum<A> + Mul<Output = A> + Extensible2<A> + Copy + Default + Sub<Output = A>,
+{
+    let pred_ys = target(data_xs, params);
+    l2_norm(&pred_ys, data_ys)
+}
+
+trait One {
+    const ONE: Self;
+}
+
+impl One for f64 {
+    const ONE: f64 = 1.0;
+}
+
+fn predict_line<A, const N: usize>(xs: &tensor!(A, N), theta: &tensor!(A, 2)) -> tensor!(A, N)
+where
+    A: Mul<Output = A> + Sum<<A as Mul>::Output> + Copy + Default + Extensible2<A> + One,
+{
+    let mut result: tensor!(A, N) = [Default::default(); N];
+    for (i, &x) in xs.iter().enumerate() {
+        result[i] = dot(&[x, One::ONE], &[*theta])[0];
+    }
+    result
 }
 
 fn main() {
-    let y = line(&[1.0, 7.3], &linear_params_2d(3.0, 1.0));
-    println!("{:?}", y);
+    let loss = l2_loss(
+        predict_line,
+        &[2.0, 1.0, 4.0, 3.0],
+        &[1.8, 1.2, 4.2, 3.3],
+        &[0.0099, 0.0],
+    );
+    println!("{:?}", loss);
 }
 
 #[cfg(test)]
@@ -54,7 +193,52 @@ mod tests {
     use super::*;
 
     #[test]
-    fn test_tensor() {
+    fn test_tensor_type() {
         let _: tensor!(f64, 1, 2, 3) = [[[1.0, 3.0, 6.0], [-1.3, -30.0, -0.0]]];
     }
+
+    #[test]
+    fn test_extension() {
+        let x: tensor!(u8, 1) = [2];
+        assert_eq!(extension1(&x, &7, |x, y| x + y), [9]);
+        let y: tensor!(u8, 1) = [7];
+        assert_eq!(extension2(&x, &y, |x, y| x + y), [9]);
+
+        let x: tensor!(u8, 3) = [5, 6, 7];
+        assert_eq!(extension1(&x, &2, |x, y| x + y), [7, 8, 9]);
+        let y: tensor!(u8, 3) = [2, 0, 1];
+        assert_eq!(extension2(&x, &y, |x, y| x + y), [7, 6, 8]);
+
+        let x: tensor!(u8, 2, 3) = [[4, 6, 7], [2, 0, 1]];
+        assert_eq!(extension1(&x, &2, |x, y| x + y), [[6, 8, 9], [4, 2, 3]]);
+        let y: tensor!(u8, 2, 3) = [[1, 2, 2], [6, 3, 1]];
+        assert_eq!(extension2(&x, &y, |x, y| x + y), [[5, 8, 9], [8, 3, 2]]);
+    }
+
+    #[test]
+    fn test_l2_norm() {
+        assert_eq!(
+            l2_norm(&[4.0, -3.0, 0.0, -4.0, 3.0], &[0.0, 0.0, 0.0, 0.0, 0.0]),
+            50.0
+        )
+    }
+
+    #[test]
+    fn test_l2_loss() {
+        let loss = l2_loss(
+            predict_line,
+            &[2.0, 1.0, 4.0, 3.0],
+            &[1.8, 1.2, 4.2, 3.3],
+            &[0.0, 0.0],
+        );
+        assert_eq!(loss, 33.21);
+
+        let loss = l2_loss(
+            predict_line,
+            &[2.0, 1.0, 4.0, 3.0],
+            &[1.8, 1.2, 4.2, 3.3],
+            &[0.0099, 0.0],
+        );
+        assert_eq!((100.0 * loss).round() / 100.0, 32.59);
+    }
 }