diff -r 9226980e45a7 -r 848ecc05becf src/norms.rs
--- a/src/norms.rs	Tue Dec 31 08:30:02 2024 -0500
+++ b/src/norms.rs	Tue Dec 31 09:02:55 2024 -0500
@@ -119,7 +119,7 @@
 ///
 /// println!("{:?}, {:?}", x.proj_ball(1.0, L2), x.proj_ball(0.5, Linfinity));
 /// ```
-pub trait Projection<F : Num, Exponent : NormExponent> : Norm<F, Exponent> + Euclidean<F>
+pub trait Projection<F : Num, Exponent : NormExponent> : Norm<F, Exponent> + Sized
 where F : Float {
     /// Projection of `self` to the `q`-norm-ball of radius ρ.
     fn proj_ball(mut self, ρ : F, q : Exponent) -> Self {
@@ -128,7 +128,7 @@
     }
 
     /// In-place projection of `self` to the `q`-norm-ball of radius ρ.
-    fn proj_ball_mut(&mut self, ρ : F, _q : Exponent);
+    fn proj_ball_mut(&mut self, ρ : F, q : Exponent);
 }
 
 /*impl<F : Float, E : Euclidean<F>> Norm<F, L2> for E {
@@ -202,3 +202,65 @@
     }
 }
 
+pub trait Normed<F : Num = f64> : Space + Norm<F, Self::NormExp> {
+    type NormExp : NormExponent;
+
+    fn norm_exponent(&self) -> Self::NormExp;
+
+    #[inline]
+    fn norm_(&self) -> F {
+        self.norm(self.norm_exponent())
+    }
+
+    // fn similar_origin(&self) -> Self;
+
+    fn is_zero(&self) -> bool;
+}
+
+pub trait HasDual<F : Num = f64> : Normed<F> {
+    type DualSpace : Normed<F>;
+}
+
+pub trait Reflexive<F : Num = f64> : HasDual<F>
+where
+    Self::DualSpace : HasDual<F, DualSpace = Self>
+{ }
+
+
+pub trait HasDualExponent : NormExponent {
+    type DualExp : NormExponent;
+
+    fn dual_exponent(&self) -> Self::DualExp;
+}
+
+impl HasDualExponent for L2 {
+    type DualExp = L2;
+    
+    #[inline]
+    fn dual_exponent(&self) -> Self::DualExp {
+        L2
+    }
+}
+
+impl HasDualExponent for L1 {
+    type DualExp = Linfinity;
+    
+    #[inline]
+    fn dual_exponent(&self) -> Self::DualExp {
+        Linfinity
+    }
+}
+
+
+impl HasDualExponent for Linfinity {
+    type DualExp = L1;
+    
+    #[inline]
+    fn dual_exponent(&self) -> Self::DualExp {
+        L1
+    }
+}
+
+
+
+