update

2023-05-11-bound.md

@@ -605,7 +605,7 @@ data ExpTransF i m f a
   | ExpTransFLam (m f a)
 ```
 
-The `Bound` instance for `ExpTransF` then becomes [^7]:
+The `Bound` instance for `ExpTransF` then becomes[^7]:
 
 ```haskell
 instance
@@ -625,6 +625,26 @@ Now, we have the following isomorphisms:
 - `ExpTransF IdentityT MaybeT` is isomorphic to `ExpF`.
 - `FreeF (ExpTransF IdentityT MaybeT)` is isomorphic to both `FreeF ExpF` and `Exp`.
 
+Alternatively, you can actually define `Bound` instances for `MaybeT` and
+`IdentityT`, and call out to them in the implementation of the `Bound` instance
+for `ExpTransF`:
+
+```haskell
+instance Bound IdentityT where
+  (>>>=) :: Monad h => IdentityT h a -> (a -> h b) -> IdentityT h b
+  (IdentityT m) >>>= f = IdentityT $ m >>= f
+
+instance Bound MaybeT where
+  (>>>=) :: Monad h => MaybeT h a -> (a -> h b) -> MaybeT h b
+  (MaybeT m) >>>= f = MaybeT $ m >>= traverse f
+
+instance (Bound i, Bound m) => Bound (ExpF i m) where
+  (>>>=) :: Monad h => ExpF i m h a -> (a -> h b) -> ExpF i m h b
+  ex >>>= f = case ex of
+    ExpFApp ida idb -> ExpFApp (ida >>>= f) (idb >>>= f)
+    ExpFLam l -> ExpFLam $ l >>>= f
+```
+
 ## Conclusion
 
 In practice, is this `FFree`, `Bound`, and `ExpF` approach good?