diff -r 9226980e45a7 -r 848ecc05becf src/convex.rs
--- a/src/convex.rs	Tue Dec 31 08:30:02 2024 -0500
+++ b/src/convex.rs	Tue Dec 31 09:02:55 2024 -0500
@@ -2,8 +2,10 @@
 Some convex analysis basics
 */
 
+use std::marker::PhantomData;
 use crate::types::*;
 use crate::mapping::{Mapping, Space};
+use crate::linops::IdOp;
 use crate::instance::{Instance, InstanceMut, DecompositionMut};
 use crate::norms::*;
 
@@ -11,16 +13,15 @@
 ///
 /// TODO: should constrain `Mapping::Codomain` to implement a partial order,
 /// but this makes everything complicated with little benefit.
-pub trait ConvexMapping<Domain : Space> : Mapping<Domain>
+pub trait ConvexMapping<Domain : Space, F : Num = f64> : Mapping<Domain, Codomain = F>
 {}
 
 /// Trait for mappings with a Fenchel conjugate
 ///
 /// The conjugate type has to implement [`ConvexMapping`], but a `Conjugable` mapping need
 /// not be convex.
-pub trait Conjugable<Domain : Space> : Mapping<Domain> {
-    type DualDomain : Space;
-    type Conjugate<'a> : ConvexMapping<Self::DualDomain> where Self : 'a;
+pub trait Conjugable<Domain : HasDual<F>, F : Num = f64> : Mapping<Domain> {
+    type Conjugate<'a> : ConvexMapping<Domain::DualSpace, F> where Self : 'a;
 
     fn conjugate(&self) -> Self::Conjugate<'_>;
 }
@@ -28,10 +29,13 @@
 /// Trait for mappings with a Fenchel preconjugate
 ///
 /// In contrast to [`Conjugable`], the preconjugate need not implement [`ConvexMapping`],
-/// but a `Preconjugable` mapping has be convex.
-pub trait Preconjugable<Domain : Space> : ConvexMapping<Domain> {
-    type PredualDomain : Space;
-    type Preconjugate<'a> : Mapping<Self::PredualDomain> where Self : 'a;
+/// but a `Preconjugable` mapping has to be convex.
+pub trait Preconjugable<Domain, Predual, F : Num = f64> : ConvexMapping<Domain, F>
+where
+    Domain : Space,
+    Predual : HasDual<F>
+{
+    type Preconjugate<'a> : Mapping<Predual> where Self : 'a;
 
     fn preconjugate(&self) -> Self::Preconjugate<'_>;
 }
@@ -65,20 +69,13 @@
 
 pub struct NormConjugate<F : Float, E : NormExponent>(NormMapping<F, E>);
 
-impl<Domain, E, F> ConvexMapping<Domain> for NormMapping<F, E>
+impl<Domain, E, F> ConvexMapping<Domain, F> for NormMapping<F, E>
 where
     Domain : Space,
     E : NormExponent,
     F : Float,
-    Self : Mapping<Domain, Codomain=F> {}
-
-
-impl<Domain, E, F> ConvexMapping<Domain> for NormConjugate<F, E>
-where
-    Domain : Space,
-    E : NormExponent,
-    F : Float,
-    Self : Mapping<Domain, Codomain=F> {}
+    Self : Mapping<Domain, Codomain=F>
+{}
 
 
 impl<F, E, Domain> Mapping<Domain> for NormConjugate<F, E>
@@ -98,20 +95,121 @@
     }
 }
 
+impl<Domain, E, F> ConvexMapping<Domain, F> for NormConjugate<F, E>
+where
+    Domain : Space,
+    E : NormExponent,
+    F : Float,
+    Self : Mapping<Domain, Codomain=F>
+{}
+
+
+impl<E, F, Domain> Conjugable<Domain, F> for NormMapping<F, E>
+where
+    E : HasDualExponent,
+    F : Float,
+    Domain : HasDual<F> + Norm<F, E> + Space,
+    <Domain as HasDual<F>>::DualSpace : Norm<F, E::DualExp>
+{
+    type Conjugate<'a> = NormConjugate<F, E::DualExp> where Self : 'a;
+
+    fn conjugate(&self) -> Self::Conjugate<'_> {
+        NormConjugate(self.exponent.dual_exponent().as_mapping())
+    }
+}
 
 
-impl<E, F, Domain> Conjugable<Domain> for NormMapping<F, E>
-where
-    E : NormExponent + Clone,
-    F : Float,
-    Domain : Norm<F, E> + Space,
-{
+/// The zero mapping
+pub struct Zero<Domain : Space, F : Num>(PhantomData<(Domain, F)>);
+
+impl<Domain : Space, F : Num> Zero<Domain, F> {
+    pub fn new() -> Self {
+        Zero(PhantomData)
+    }
+}
+
+impl<Domain : Space, F : Num> Mapping<Domain> for Zero<Domain, F> {
+    type Codomain = F;
 
-    type DualDomain = Domain;
-    type Conjugate<'a> = NormConjugate<F, E> where Self : 'a;
+    /// Compute the value of `self` at `x`.
+    fn apply<I : Instance<Domain>>(&self, _x : I) -> Self::Codomain {
+        F::ZERO
+    }
+}
+
+impl<Domain : Space, F : Num> ConvexMapping<Domain, F> for Zero<Domain, F> { }
 
+
+impl<Domain : HasDual<F>, F : Float> Conjugable<Domain, F> for Zero<Domain, F> {
+    type Conjugate<'a> = ZeroIndicator<Domain::DualSpace, F> where Self : 'a;
+
+    #[inline]
     fn conjugate(&self) -> Self::Conjugate<'_> {
-        NormConjugate(self.clone())
+        ZeroIndicator::new()
     }
 }
 
+impl<Domain, Predual, F : Float> Preconjugable<Domain, Predual, F> for Zero<Domain, F>
+where
+    Domain : Space,
+    Predual : HasDual<F>
+{
+    type Preconjugate<'a> = ZeroIndicator<Predual, F> where Self : 'a;
+
+    #[inline]
+    fn preconjugate(&self) -> Self::Preconjugate<'_> {
+        ZeroIndicator::new()
+    }
+}
+
+impl<Domain : Space + Clone, F : Num> Prox<Domain> for Zero<Domain, F> {
+    type Prox<'a> = IdOp<Domain> where Self : 'a;
+
+    #[inline]
+    fn prox_mapping(&self, _τ : Self::Codomain) -> Self::Prox<'_> {
+        IdOp::new()
+    }
+}
+
+
+/// The zero indicator
+pub struct ZeroIndicator<Domain : Space, F : Num>(PhantomData<(Domain, F)>);
+
+impl<Domain : Space, F : Num> ZeroIndicator<Domain, F> {
+    pub fn new() -> Self {
+        ZeroIndicator(PhantomData)
+    }
+}
+
+impl<Domain : Normed<F>, F : Float> Mapping<Domain> for ZeroIndicator<Domain, F> {
+    type Codomain = F;
+
+    /// Compute the value of `self` at `x`.
+    fn apply<I : Instance<Domain>>(&self, x : I) -> Self::Codomain {
+        x.eval(|x̃| if x̃.is_zero() { F::ZERO } else { F::INFINITY })
+    }
+}
+
+impl<Domain : Normed<F>, F : Float> ConvexMapping<Domain, F> for ZeroIndicator<Domain, F> { }
+
+impl<Domain : HasDual<F>, F : Float> Conjugable<Domain, F> for ZeroIndicator<Domain, F> {
+    type Conjugate<'a> = Zero<Domain::DualSpace, F> where Self : 'a;
+
+    #[inline]
+    fn conjugate(&self) -> Self::Conjugate<'_> {
+        Zero::new()
+    }
+}
+
+impl<Domain, Predual, F : Float> Preconjugable<Domain, Predual, F> for ZeroIndicator<Domain, F>
+where
+    Domain : Normed<F>,
+    Predual : HasDual<F>
+{
+    type Preconjugate<'a> = Zero<Predual, F> where Self : 'a;
+
+    #[inline]
+    fn preconjugate(&self) -> Self::Preconjugate<'_> {
+        Zero::new()
+    }
+}