diff --git a/src/model_03.rs b/src/model_03.rs
index b0ed681..832e345 100644
--- a/src/model_03.rs
+++ b/src/model_03.rs
@@ -10,12 +10,12 @@ use pin_project::pin_project;
 pub trait Trait {
     type Associated: ?Sized + Trait;
     type In<'out: 'tmp, 'tmp, I: 'tmp>;
-    type Out<'out, A>;
+    type Out<'out, I: Impl<Self>>;
 }
 
 pub trait Impl<T: ?Sized + Trait>: Sized {
     type Associated: Impl<T::Associated>;
-    fn method<'out: 'tmp, 'tmp>(_: T::In<'out, 'tmp, Self>) -> T::Out<'out, Self::Associated>
+    fn method<'out: 'tmp, 'tmp>(_: T::In<'out, 'tmp, Self>) -> T::Out<'out, Self>
     where
         Self: 'tmp;
 }
@@ -45,7 +45,7 @@ pub struct Is<That, T: ?Sized>(That, T);
 impl<That, T: ?Sized + Trait> Trait for Is<That, T> {
     type Associated = T;
     type In<'out: 'tmp, 'tmp, I: 'tmp> = I;
-    type Out<'out, A> = That;
+    type Out<'out, I: Impl<Self>> = That;
 }
 
 impl<That: Impl<T>, T: ?Sized + Trait> Impl<Is<Self, T>> for That {
@@ -66,7 +66,7 @@ pub struct To<T: ?Sized>(T);
 impl<T: ?Sized + Trait> Trait for To<T> {
     type Associated = T;
     type In<'out: 'tmp, 'tmp, I: 'tmp> = I;
-    type Out<'out, A> = A;
+    type Out<'out, I: Impl<Self>> = I::Associated;
 }
 
 impl<I: FnOnce() -> Output, Output: Impl<T>, T: ?Sized + Trait> Impl<To<T>> for I {
@@ -74,7 +74,7 @@ impl<I: FnOnce() -> Output, Output: Impl<T>, T: ?Sized + Trait> Impl<To<T>> for
 
     fn method<'out: 'tmp, 'tmp>(
         this: <To<T> as Trait>::In<'out, 'tmp, Self>,
-    ) -> <To<T> as Trait>::Out<'out, Self::Associated>
+    ) -> <To<T> as Trait>::Out<'out, Self>
     where
         Self: 'tmp,
     {
@@ -282,7 +282,7 @@ pub struct FutureTo<T: ?Sized>(T);
 impl<T: ?Sized + Trait> Trait for FutureTo<T> {
     type Associated = T;
     type In<'out: 'tmp, 'tmp, I: 'tmp> = (Pin<&'tmp mut I>, &'tmp mut Context<'out>);
-    type Out<'out, A> = Poll<A>;
+    type Out<'out, I: Impl<Self>> = Poll<I::Associated>;
 }
 
 impl<T: ?Sized + Trait, Output: Impl<T>, F: Future<Output = Output>> Impl<FutureTo<T>> for F {
@@ -290,7 +290,7 @@ impl<T: ?Sized + Trait, Output: Impl<T>, F: Future<Output = Output>> Impl<Future
 
     fn method<'out: 'tmp, 'tmp>(
         (this, cx): <FutureTo<T> as Trait>::In<'out, 'tmp, Self>,
-    ) -> <FutureTo<T> as Trait>::Out<'out, Self::Associated>
+    ) -> <FutureTo<T> as Trait>::Out<'out, Self>
     where
         Self: 'tmp,
     {
@@ -368,3 +368,151 @@ fn doubly_futures() {
     let x = futures::executor::block_on(Futures::flatten(x).into_future_()).into_::<i32>();
     assert_eq!(x, 10);
 }
+
+struct TracePure;
+
+struct TraceMap<T>(T);
+
+struct TraceJoin<T0, T1>(T0, T1);
+
+struct TraceFlatten<T0, T1>(T0, T1);
+
+pub trait AsTrace {
+    fn as_trace(&self) -> Trace;
+}
+
+pub enum Trace<'trace> {
+    Pure,
+    Flatten(&'trace dyn AsTrace, &'trace dyn AsTrace),
+    Map(&'trace dyn AsTrace),
+    Join(&'trace dyn AsTrace, &'trace dyn AsTrace),
+}
+
+impl AsTrace for TracePure {
+    fn as_trace(&self) -> Trace {
+        Trace::Pure
+    }
+}
+
+impl<T: AsTrace> AsTrace for TraceMap<T> {
+    fn as_trace(&self) -> Trace {
+        Trace::Map(&self.0)
+    }
+}
+
+impl<T0: AsTrace, T1: AsTrace> AsTrace for TraceJoin<T0, T1> {
+    fn as_trace(&self) -> Trace {
+        Trace::Join(&self.0, &self.1)
+    }
+}
+
+impl<T0: AsTrace, T1: AsTrace> AsTrace for TraceFlatten<T0, T1> {
+    fn as_trace(&self) -> Trace {
+        Trace::Flatten(&self.0, &self.1)
+    }
+}
+
+struct DynTrace<I>(I, fn(&I) -> Trace);
+
+impl<I> AsTrace for DynTrace<I> {
+    fn as_trace(&self) -> Trace {
+        self.1(&self.0)
+    }
+}
+
+struct WithTrace<A, T> {
+    value: Option<A>,
+    trace: T,
+}
+
+impl<A, T: AsTrace> AsTrace for WithTrace<A, T> {
+    fn as_trace(&self) -> Trace {
+        self.trace.as_trace()
+    }
+}
+
+pub struct Traced<Etc: ?Sized>(Etc);
+
+impl<Etc: ?Sized + Trait> Trait for Traced<Etc> {
+    type Associated = Etc;
+    type In<'out: 'tmp, 'tmp, I: 'tmp> = I;
+    type Out<'out, I: Impl<Self>> = (I::Associated, I, fn(&I) -> Trace);
+}
+
+impl<Etc: ?Sized + Trait, T: AsTrace, A: Impl<Etc>> Impl<Traced<Etc>> for WithTrace<A, T> {
+    type Associated = A;
+
+    fn method<'out: 'tmp, 'tmp>(
+        mut this: <Traced<Etc> as Trait>::In<'out, 'tmp, Self>,
+    ) -> <Traced<Etc> as Trait>::Out<'out, Self>
+    where
+        Self: 'tmp,
+    {
+        let value = this.value.take().expect("duplicate tracing extraction");
+        (value, this, Self::as_trace)
+    }
+}
+
+trait SplitTrace<T: ?Sized> {
+    type Value;
+    fn split_trace(self) -> (Self::Value, impl AsTrace);
+}
+
+impl<T: ?Sized + Trait, I: Impl<Traced<T>>> SplitTrace<T> for I {
+    type Value = I::Associated;
+
+    fn split_trace(self) -> (Self::Value, impl AsTrace) {
+        let (value, this, method) = I::method(self);
+        (value, DynTrace(this, method))
+    }
+}
+
+pub struct Traces;
+
+impl Functor for Traces {
+    type W<T: ?Sized + Trait> = Traced<T>;
+
+    fn pure<A: ?Sized + Trait>(a: impl Impl<A>) -> impl Impl<Self::W<A>> {
+        WithTrace {
+            value: Some(a),
+            trace: TracePure,
+        }
+    }
+
+    fn map<A: ?Sized + Trait, F: TraitFn<A>>(
+        a: impl Impl<Self::W<A>>,
+        f: F,
+    ) -> impl Impl<Self::W<F::Out>> {
+        let (a, ta) = a.split_trace();
+        WithTrace {
+            value: Some(f.run(a)),
+            trace: TraceMap(ta),
+        }
+    }
+}
+
+impl Applicative for Traces {
+    fn map2<A: ?Sized + Trait, B: ?Sized + Trait, F: TraitFn2<A, B>>(
+        a: impl Impl<Self::W<A>>,
+        b: impl Impl<Self::W<B>>,
+        f: F,
+    ) -> impl Impl<Self::W<F::Out>> {
+        let (a, ta) = a.split_trace();
+        let (b, tb) = b.split_trace();
+        WithTrace {
+            value: Some(f.run(a, b)),
+            trace: TraceJoin(ta, tb),
+        }
+    }
+}
+
+impl Monad for Traces {
+    fn flatten<A: ?Sized + Trait>(a: impl Impl<Self::W<Self::W<A>>>) -> impl Impl<Self::W<A>> {
+        let (a, to) = a.split_trace();
+        let (a, ti) = a.split_trace();
+        WithTrace {
+            value: Some(a),
+            trace: TraceFlatten(to, ti),
+        }
+    }
+}