diff --git a/crates/fayalite/src/ty.rs b/crates/fayalite/src/ty.rs
index ab69532..843aedb 100644
--- a/crates/fayalite/src/ty.rs
+++ b/crates/fayalite/src/ty.rs
@@ -1309,16 +1309,49 @@ trait TraceAsStringTrait: fmt::Debug + 'static + Send + Sync + SupportsPtrEqWith
     fn can_substitute_type(&self, new_type: CanonicalType) -> bool;
 }
 
-impl<T: Type> TraceAsStringTrait for T {
+#[derive(Clone, PartialEq, Eq, Hash)]
+struct TraceAsStringState<T: Type> {
+    ty: Interned<T>,
+    canonical_ty: CanonicalType,
+}
+
+impl<T: Type> TraceAsStringState<T> {
+    fn new(ty: Interned<T>) -> Interned<Self> {
+        #[derive(Copy, Clone, PartialEq, Eq, Hash)]
+        struct MyMemoize<T: Type>(PhantomData<T>);
+        impl<T: Type> Memoize for MyMemoize<T> {
+            type Input = Interned<T>;
+            type InputOwned = Interned<T>;
+            type Output = Interned<TraceAsStringState<T>>;
+
+            fn inner(self, input: &Self::Input) -> Self::Output {
+                TraceAsStringState {
+                    ty: *input,
+                    canonical_ty: input.canonical(),
+                }
+                .intern_sized()
+            }
+        }
+        MyMemoize(PhantomData).get_owned(ty)
+    }
+}
+
+impl<T: Type> fmt::Debug for TraceAsStringState<T> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        self.ty.fmt(f)
+    }
+}
+
+impl<T: Type> TraceAsStringTrait for TraceAsStringState<T> {
     fn trace_fmt(
         &self,
         opaque: OpaqueSimValueSlice<'_>,
         f: &mut fmt::Formatter<'_>,
     ) -> fmt::Result {
-        fmt::Debug::fmt(&Type::sim_value_from_opaque(self, opaque), f)
+        fmt::Debug::fmt(&Type::sim_value_from_opaque(&*self.ty, opaque), f)
     }
     fn can_substitute_type(&self, new_type: CanonicalType) -> bool {
-        self.canonical().is_layout_equivalent(new_type)
+        self.canonical_ty.is_layout_equivalent(new_type)
     }
 }
 
@@ -1374,7 +1407,7 @@ impl<T: Type> TraceAsString<T> {
         Self {
             inner_ty: LazyInterned::Interned(inner_ty),
             trace_as_string: LazyInterned::Interned(Interned::cast_unchecked(
-                inner_ty,
+                TraceAsStringState::new(inner_ty),
                 |v| -> &dyn TraceAsStringTrait { v },
             )),
         }
@@ -1548,7 +1581,10 @@ impl<T: StaticType> Default for TraceAsStringStaticTypeHelper<T> {
 
 impl<T: StaticType> From<TraceAsStringStaticTypeHelper<T>> for Interned<dyn TraceAsStringTrait> {
     fn from(_value: TraceAsStringStaticTypeHelper<T>) -> Self {
-        Interned::cast_unchecked(T::TYPE.intern_sized(), |v| -> &dyn TraceAsStringTrait { v })
+        Interned::cast_unchecked(
+            TraceAsStringState::new(T::TYPE.intern_sized()),
+            |v| -> &dyn TraceAsStringTrait { v },
+        )
     }
 }