diff --git a/papers/CPP21.md b/papers/CPP21.md
index 5767a03366629243ed11503591e408869cf46fb9..c46167433a6211aa5e12dac43d50fd8607ac18d5 100644
--- a/papers/CPP21.md
+++ b/papers/CPP21.md
@@ -15,7 +15,7 @@ contains an overview of the files in that directory.
   Coq and the paper.
 - The typing rule for branching (`ltyped_branch`) is written as a function
   instead of an n-ary rule with multiple premises.
-- The disjunction of the compute client list invariant is encoded using a boolean
+- The disjunction of the compute client invariant is encoded using a boolean
   flag, as it makes mechanisation easier.
 - The mechanisation employs a typing judgement for values (`ltyped_val`),
   for technical reasons. More details on this is found in
@@ -23,6 +23,10 @@ contains an overview of the files in that directory.
 
 # Examples
 
+- The compute service example in Section 3 can be found in
+  [theories/logrel/examples/compute_service.v](../theories/logrel/examples/compute_service.v)
+  The program recursively receive computation requests, which it computes and
+  then send back. It is entirely type checked with the rules of the type system
 - The parallel receive example in Section 4 can be found in
   [theories/logrel/examples/par_recv.v](../theories/logrel/examples/par_recv.v):
   This program performs two "racy" parallel receives on the same channel from
@@ -36,3 +40,4 @@ contains an overview of the files in that directory.
   [theories/logrel/examples/compute_service.v](../theories/logrel/examples/compute_service.v).
   The definition of the list type and the weakest precondition for `llength`
   can be found in [theories/logrel/lib/list.v](../theories/logrel/lib/list.v)
+  It is type checked using a manual typing proof.
diff --git a/theories/logrel/examples/compute_service.v b/theories/logrel/examples/compute_service.v
index 79ac5fa5a7421f3587434cbb5c48e84233c2f716..1495297d181510da08ee99721930b156293e925b 100644
--- a/theories/logrel/examples/compute_service.v
+++ b/theories/logrel/examples/compute_service.v
@@ -4,7 +4,8 @@
              stop : end }
 
 It recursively receives computations, computes them, and then
-sends back the results. *)
+sends back the results.
+The example is type checked using only the rules of the type system. *)
 From iris.heap_lang Require Import metatheory.
 From actris.channel Require Import proofmode.
 From actris.logrel Require Import session_typing_rules.