Minor updates and added small examples

theories/channel.v

@@ -20,6 +20,7 @@ Definition new_chan : val :=
 
 Coercion side_to_bool (s : side) : bool :=
   match s with Left => true | Right => false end.
+Arguments side_to_bool : simpl never.
 Definition side_elim {A} (s : side) (l r : A) : A :=
   match s with Left => l | Right => r end.
 

theories/examples.v

+From iris.proofmode Require Import tactics.
+From iris.program_logic Require Export weakestpre.
+From iris.heap_lang Require Import proofmode notation.
+From osiris Require Import typing channel logrel.
+From iris.algebra Require Import list auth excl.
+From iris.base_logic Require Import invariants.
+
+Section Examples.
+  Context `{!heapG Σ} (N : namespace).
+  Context `{!logrelG Σ}.
+
+  Definition seq_example : expr :=
+    (let: "c" := new_chan #() in
+     send "c" #Left #5;;
+     recv "c" #Right)%E.
+
+  Notation "⟦ c @ s : sτ ⟧{ γ }" := (interp_st N γ sτ c s)
+    (at level 10, s at next level, sτ at next level, γ at next level,
+     format "⟦  c  @  s  :  sτ  ⟧{ γ }").
+
+  Lemma seq_proof :
+    {{{ True }}} seq_example {{{ v, RET v; ⌜v = #5⌝ }}}.
+  Proof.
+    iIntros (Φ H) "HΦ".
+    rewrite /seq_example.
+    wp_bind (new_chan _).
+    wp_apply (new_chan_st_spec N (TSR Send (λ v, ⌜v = #5⌝%I) (λ v, TEnd)))=> //.
+    iIntros (c γ) "[Hstl Hstr]"=> /=.
+    wp_pures.
+    wp_bind (send _ _ _).
+    wp_apply (send_st_spec N with "[Hstl]"). by iFrame.
+    iIntros "Hstl".
+    wp_pures.
+    wp_apply (recv_st_spec _ with "[Hstr]"). by iFrame.
+    iIntros (v) "[Hstr HP]".
+    by iApply "HΦ".
+  Qed.
+
+  Definition par_example : expr :=
+    (let: "c" := new_chan #() in
+     Fork(send "c" #Left #5);;
+     recv "c" #Right)%E.
+
+  Lemma par_proof :
+    {{{ True }}} par_example {{{ v, RET v; ⌜v = #5⌝ }}}.
+  Proof.
+    iIntros (Φ H) "HΦ".
+    rewrite /par_example.
+    wp_bind (new_chan _).
+    wp_apply (new_chan_st_spec N (TSR Send (λ v, ⌜v = #5⌝%I) (λ v, TEnd)))=> //.
+    iIntros (c γ) "[Hstl Hstr]"=> /=.
+    wp_pures.
+    wp_bind (Fork _).
+    wp_apply (wp_fork with "[Hstl]").
+    - iNext. wp_apply (send_st_spec N with "[Hstl]"). by iFrame. eauto.
+    - wp_apply (recv_st_spec _ with "[Hstr]"). by iFrame.
+      iIntros (v) "[Hstr HP]". by iApply "HΦ".
+  Qed.
+
+  Definition par_2_example : expr :=
+    (let: "c" := new_chan #() in
+     Fork(let: "v" := recv "c" #Right in send "c" #Right ("v"+#2));;
+     send "c" #Left #5;;recv "c" #Left)%E.
+
+  Lemma par_2_proof :
+    {{{ True }}}
+      par_2_example
+    {{{ v, RET v; ∃ w, ⌜v = LitV $ LitInt $ w ∧ w >= 7⌝ }}}.
+  Proof.
+    iIntros (Φ H) "HΦ".
+    rewrite /par_2_example.
+    wp_bind (new_chan _).
+    wp_apply (new_chan_st_spec N
+      (TSR Send
+           (λ v, ⌜v = #5⌝%I)
+           (λ v, TSR Receive
+                     (λ v',
+                      (∃ w, ⌜v = LitV $ LitInt $ w⌝ ∧
+                       ∃ w', ⌜v' = LitV $ LitInt $ w' ∧ w' >= w+2⌝)%I)
+                     (λ v', TEnd))))=> //.
+    iIntros (c γ) "[Hstl Hstr]"=> /=.
+    wp_pures.
+    wp_bind (Fork _).
+    wp_apply (wp_fork with "[Hstr]").
+    - iNext.
+      wp_apply (recv_st_spec _ with "[Hstr]"). by iFrame.
+      iIntros (v) "[Hstr HP]".
+      wp_pures.
+      iDestruct "HP" as %->.
+      wp_apply (send_st_spec N with "[Hstr]"). iFrame.
+      iExists _. iSplit=> //.
+      iExists _. iSplit=> //.
+      eauto.
+    - wp_apply (send_st_spec _ with "[Hstl]"). by iFrame.
+      iIntros "Hstl".
+      wp_apply (recv_st_spec _ with "[Hstl]"). by iFrame.
+      iIntros (v) "[Hstl HP]".
+      iApply "HΦ".
+      iDestruct "HP" as %[w [HP [w' [HQ HQ']]]].
+      iExists _.
+      iSplit=> //. iPureIntro.
+      inversion HP. rewrite -H1 in HQ'.
+      eauto.
+  Qed.
+
+End Examples.
\ No newline at end of file

theories/logrel.v

@@ -18,7 +18,7 @@ Instance subG_chanΣ {Σ} : subG logrelΣ Σ → logrelG Σ.
 Proof. intros [??%subG_auth_exclG]%subG_inv. constructor; apply _. Qed.
 
 Section logrel.
-  Context `{!heapG Σ, !lockG Σ} (N : namespace).
+  Context `{!heapG Σ} (N : namespace).
   Context `{!logrelG Σ}.
 
   Notation stype_iprop := (@stypeC (laterC (iProp Σ))).