Added example of program reuse with a mapping service

theories/examples/subprotocols.v

 From actris.channel Require Import proofmode proto channel.
 From actris.logrel Require Import subtyping_rules.
 From iris.proofmode Require Import tactics.
+From actris.utils Require Import llist.
 
 Section basics.
   Context `{heapG Σ, chanG Σ}.
@@ -10,4 +11,33 @@ Section basics.
     (<! (l1 l2 : loc)> MSG (#l1, #l2) {{ l1 ↦ #20 ∗ l2 ↦ #22 }}; END) ⊑
     (<! (l1 : loc)> MSG (#l1, #l2') {{ l1 ↦ #20 }}; END).
   Proof. iIntros "Hl2'" (l1) "Hl1". iExists l1, l2'. by iFrame "Hl1 Hl2'". Qed.
+
+  Section program_reuse.
+    Context {T U R : Type}.
+    Context (IT : T -> val -> iProp Σ).
+    Context (ITR : (T * R) -> val -> iProp Σ).
+    Context (IU : U -> val -> iProp Σ).
+    Context (IUR : (U * R) -> val -> iProp Σ).
+    Context (IR : R -> iProp Σ).
+
+    Axiom HIT : ∀ v t r, ITR (t,r) v -∗ IT t v ∗ IR r.
+    Axiom HIU : ∀ v u r, (IU u v ∗ IR r) -∗ IUR (u,r) v.
+
+    Lemma example :
+      ⊢ (<! (v : val) (t : T)> MSG v {{ IT t v }};
+         <? (w : val) (u : U)> MSG w {{ IU u w }}; END) ⊑
+        (<! (v : val) (t : T) (r: R)> MSG v {{ ITR (t,r) v }};
+         <? (w : val) (u : U)> MSG w {{ IUR (u,r) w }}; END).
+    Proof.
+      iIntros (v t r) "HTR".
+      iDestruct (HIT with "HTR") as "[HT HR]".
+      iExists v, t. iFrame "HT".
+      iModIntro.
+      iIntros (w u) "HU".
+      iDestruct (HIU with "[$HR $HU]") as "HUR".
+      iExists w, u. iFrame "HUR".
+      eauto.
+    Qed.
+  End program_reuse.
+
 End basics.