Bump Iris (Z_scope).

exercises/ex_04_parallel_add.v

@@ -108,14 +108,14 @@ Section proof2.
     { (* exercise *)
       admit. }
     iIntros (l) "#Hl". wp_let.
-    wp_apply (wp_par (λ _, own γ1 (◯E 2)) (λ _, own γ2 (◯E 2))
+    wp_apply (wp_par (λ _, own γ1 (◯E 2%Z)) (λ _, own γ2 (◯E 2%Z))
                 with "[Hγ1◯] [Hγ2◯]").
     - wp_apply (acquire_spec with "Hl"). iDestruct 1 as (n1 n2) "(Hr & Hγ1● & Hγ2●)".
       wp_seq. wp_load. wp_op. wp_store.
       iDestruct (ghost_var_agree with "Hγ1● Hγ1◯") as %->.
       iMod (ghost_var_update γ1 2 with "Hγ1● Hγ1◯") as "[Hγ1● Hγ1◯]".
       wp_apply (release_spec with "[- $Hl Hγ1◯]"); [|by auto].
-      iExists _, _. iFrame "Hγ1● Hγ2●". rewrite (_ : 2 + n2 = 0 + n2 + 2); [done|ring].
+      iExists _, _. iFrame "Hγ1● Hγ2●". rewrite (_ : 2 + n2 = 0 + n2 + 2)%Z; [done|ring].
     - (* exercise *)
       admit.
     - (* exercise *)
@@ -137,19 +137,19 @@ Section proof3.
   Proof.
     iIntros (Φ) "_ Post".
     unfold parallel_add. wp_alloc r as "Hr". wp_let.
-    iMod (own_alloc (●F 0%nat ⋅ ◯F 0%nat)) as (γ) "[Hγ● [Hγ1◯ Hγ2◯]]".
+    iMod (own_alloc (●F 0 ⋅ ◯F 0)) as (γ) "[Hγ● [Hγ1◯ Hγ2◯]]".
     { by apply auth_both_valid. }
     wp_apply (newlock_spec (parallel_add_inv_3 r γ) with "[Hr Hγ●]").
     { (* exercise *)
       admit. }
     iIntros (l) "#Hl". wp_let.
-    wp_apply (wp_par (λ _, own γ (◯F{1/2} 2%nat)) (λ _, own γ (◯F{1/2} 2%nat))
+    wp_apply (wp_par (λ _, own γ (◯F{1/2} 2)) (λ _, own γ (◯F{1/2} 2))
                 with "[Hγ1◯] [Hγ2◯]").
     - wp_apply (acquire_spec with "Hl"). iDestruct 1 as (n) "[Hr Hγ●]".
       wp_seq. wp_load. wp_op. wp_store.
-      iMod (own_update_2 _ _ _ (●F (n+2) ⋅ ◯F{1/2}2)%nat with "Hγ● Hγ1◯") as "[Hγ● Hγ1◯]".
+      iMod (own_update_2 _ _ _ (●F (n+2) ⋅ ◯F{1/2}2) with "Hγ● Hγ1◯") as "[Hγ● Hγ1◯]".
       { rewrite (comm plus).
-        by apply frac_auth_update, (op_local_update_discrete n 0 2)%nat. }
+        by apply frac_auth_update, (op_local_update_discrete n 0 2). }
       wp_apply (release_spec with "[$Hl Hr Hγ●]"); [|by auto].
       iExists _. iFrame. by rewrite Nat2Z.inj_add.
     - (* exercise *)

opam

@@ -9,7 +9,7 @@ dev-repo: "git+https://gitlab.mpi-sws.org/iris/tutorial-popl18.git"
 synopsis: "The Iris tutorial at POPL 2018"
 
 depends: [
-  "coq-iris" { (= "dev.2020-03-16.0.62be0a86") | (= "dev") }
+  "coq-iris" { (= "dev.2020-05-29.0.d5f678ee") | (= "dev") }
 ]
 
 build: [make "-j%{jobs}%"]

solutions/ex_04_parallel_add.v

@@ -111,14 +111,14 @@ Section proof2.
     wp_apply (newlock_spec (parallel_add_inv_2 r γ1 γ2) with "[Hr Hγ1● Hγ2●]").
     { (* exercise *) iExists 0, 0. iFrame. }
     iIntros (l) "#Hl". wp_let.
-    wp_apply (wp_par (λ _, own γ1 (◯E 2)) (λ _, own γ2 (◯E 2))
+    wp_apply (wp_par (λ _, own γ1 (◯E 2%Z)) (λ _, own γ2 (◯E 2%Z))
                 with "[Hγ1◯] [Hγ2◯]").
     - wp_apply (acquire_spec with "Hl"). iDestruct 1 as (n1 n2) "(Hr & Hγ1● & Hγ2●)".
       wp_seq. wp_load. wp_op. wp_store.
       iDestruct (ghost_var_agree with "Hγ1● Hγ1◯") as %->.
       iMod (ghost_var_update γ1 2 with "Hγ1● Hγ1◯") as "[Hγ1● Hγ1◯]".
       wp_apply (release_spec with "[- $Hl Hγ1◯]"); [|by auto].
-      iExists _, _. iFrame "Hγ1● Hγ2●". rewrite (_ : 2 + n2 = 0 + n2 + 2); [done|ring].
+      iExists _, _. iFrame "Hγ1● Hγ2●". rewrite (_ : 2 + n2 = 0 + n2 + 2)%Z; [done|ring].
     - (* exercise *)
       wp_apply (acquire_spec with "Hl"). iDestruct 1 as (n1 n2) "(Hr & Hγ1● & Hγ2●)".
       wp_seq. wp_load. wp_op. wp_store.
@@ -150,26 +150,26 @@ Section proof3.
   Proof.
     iIntros (Φ) "_ Post".
     unfold parallel_add. wp_alloc r as "Hr". wp_let.
-    iMod (own_alloc (●F 0%nat ⋅ ◯F 0%nat)) as (γ) "[Hγ● [Hγ1◯ Hγ2◯]]".
+    iMod (own_alloc (●F 0 ⋅ ◯F 0)) as (γ) "[Hγ● [Hγ1◯ Hγ2◯]]".
     { by apply auth_both_valid. }
     wp_apply (newlock_spec (parallel_add_inv_3 r γ) with "[Hr Hγ●]").
-    { (* exercise *) iExists 0%nat. iFrame. }
+    { (* exercise *) iExists 0. iFrame. }
     iIntros (l) "#Hl". wp_let.
-    wp_apply (wp_par (λ _, own γ (◯F{1/2} 2%nat)) (λ _, own γ (◯F{1/2} 2%nat))
+    wp_apply (wp_par (λ _, own γ (◯F{1/2} 2)) (λ _, own γ (◯F{1/2} 2))
                 with "[Hγ1◯] [Hγ2◯]").
     - wp_apply (acquire_spec with "Hl"). iDestruct 1 as (n) "[Hr Hγ●]".
       wp_seq. wp_load. wp_op. wp_store.
-      iMod (own_update_2 _ _ _ (●F (n+2) ⋅ ◯F{1/2}2)%nat with "Hγ● Hγ1◯") as "[Hγ● Hγ1◯]".
+      iMod (own_update_2 _ _ _ (●F (n+2) ⋅ ◯F{1/2}2) with "Hγ● Hγ1◯") as "[Hγ● Hγ1◯]".
       { rewrite (comm plus).
-        by apply frac_auth_update, (op_local_update_discrete n 0 2)%nat. }
+        by apply frac_auth_update, (op_local_update_discrete n 0 2). }
       wp_apply (release_spec with "[$Hl Hr Hγ●]"); [|by auto].
       iExists _. iFrame. by rewrite Nat2Z.inj_add.
     - (* exercise *)
       wp_apply (acquire_spec with "Hl"). iDestruct 1 as (n) "[Hr Hγ●]".
       wp_seq. wp_load. wp_op. wp_store.
-      iMod (own_update_2 _ _ _ (●F (n+2) ⋅ ◯F{1/2}2)%nat with "Hγ● Hγ2◯") as "[Hγ● Hγ2◯]".
+      iMod (own_update_2 _ _ _ (●F (n+2) ⋅ ◯F{1/2}2) with "Hγ● Hγ2◯") as "[Hγ● Hγ2◯]".
       { rewrite (comm plus).
-        by apply frac_auth_update, (op_local_update_discrete n 0 2)%nat. }
+        by apply frac_auth_update, (op_local_update_discrete n 0 2). }
       wp_apply (release_spec with "[- $Hl Hγ2◯]"); [|by auto].
       iExists _. iFrame. by rewrite Nat2Z.inj_add.
     - (* exercise *)

solutions/ex_05_parallel_add_mul.v

@@ -68,7 +68,7 @@ Section proof.
         end⌝)%I.
 
   Lemma parallel_add_mul_spec :
-    {{{ True }}} parallel_add_mul {{{ z, RET #z; ⌜ z = 2 ∨ z = 4 ⌝ }}}.
+    {{{ True }}} parallel_add_mul {{{ z, RET #z; ⌜ z = 2%Z ∨ z = 4%Z ⌝ }}}.
   Proof.
     iIntros (Φ) "_ Post".
     unfold parallel_add_mul. wp_alloc r as "Hr". wp_let.

talks/demo/part2.v

@@ -48,7 +48,7 @@ Proof.
   iIntros "Hl". wp_lam.
   wp_apply (strange_inc_spec with "Hl"); iIntros "Hl"; wp_seq.
   wp_apply (strange_inc_spec with "Hl"); iIntros "Hl".
-  rewrite (_ : 2 + x = 1 + (1 + x)); last lia. auto.
+  rewrite (_ : 2 + x = 1 + (1 + x))%Z; last lia. auto.
 Qed.
 
 Lemma strange_inc_twice_spec `{heapG Σ} l (x : Z) :
@@ -57,5 +57,5 @@ Proof.
   iIntros (Φ) "Hl Post". wp_lam.
   wp_apply (strange_inc_spec with "Hl"); iIntros "Hl"; wp_seq.
   wp_apply (strange_inc_spec with "Hl"); iIntros "Hl".
-  iApply "Post". rewrite (_ : 2 + x = 1 + (1 + x)); last lia. done.
+  iApply "Post". rewrite (_ : 2 + x = 1 + (1 + x))%Z; last lia. done.
 Qed.

talks/demo/part3.v

@@ -9,7 +9,7 @@ Definition coin_flip : val := λ: <>,
   !"l".
 
 Lemma test2_spec `{heapG Σ, spawnG Σ} :
-  {{{ True }}} coin_flip #() {{{ n, RET #n; ⌜ n = 0 ∨ n = 1 ⌝ }}}.
+  {{{ True }}} coin_flip #() {{{ n, RET #n; ⌜ n = 0%Z ∨ n = 1%Z ⌝ }}}.
 Proof.
   iIntros (Φ) "_ Post". wp_lam. wp_alloc l as "Hl". wp_let.
   iMod (inv_alloc N _

talks/demo/part4.v

@@ -63,7 +63,7 @@ Section proof2.
   Lemma frac_auth_update n n1 n2 q γ :
     own γ (●F n1) -∗
     own γ (◯F{q} n2) -∗ |==>
-    own γ (●F (n1 + n)%nat) ∗ own γ (◯F{q} (n2 + n)%nat).
+    own γ (●F (n1 + n)) ∗ own γ (◯F{q} (n2 + n)).
   Proof.
     iIntros "H H'". iMod (own_update_2 with "H H'") as "[$ $]"; last done.
     apply frac_auth_update, nat_local_update. lia.
@@ -84,27 +84,27 @@ Section proof2.
   Lemma par_inc_FAA_spec n n' γ l q :
     {{{ inv N (proof2_inv γ l) ∗ own γ (◯F{q} n) }}}
       FAA #l #n'
-    {{{ m, RET #m; own γ (◯F{q} (n + n'))%nat }}}.
+    {{{ m, RET #m; own γ (◯F{q} (n + n')) }}}.
   Proof.
     iIntros (Φ) "[#Hinv Hγ] Post". iInv N as (m) ">[Hauth Hl]" "Hclose".
     wp_faa.
     iMod (frac_auth_update n' with "Hauth Hγ") as "[Hauth Hγ]".
     iMod ("Hclose" with "[Hauth Hl]") as "_".
-    { iNext; iExists (m + n')%nat. rewrite Nat2Z.inj_add. iFrame. }
+    { iNext; iExists (m + n'). rewrite Nat2Z.inj_add. iFrame. }
     by iApply "Post".
   Qed.
 
   (* Proof of the whole program *)
   Lemma par_inc_spec :
-    {{{ True }}} par_inc #() {{{ RET #4%nat; True }}}.
+    {{{ True }}} par_inc #() {{{ RET #4; True }}}.
   Proof.
     iIntros (Φ) "_ Post". wp_lam. wp_alloc l as "Hl". wp_let.
     iMod (frac_auth_alloc 0) as (γ) "[Hauth Hγ]".
     iDestruct "Hγ" as "[Hγ1 Hγ2]".
     iMod (inv_alloc _ _ (proof2_inv γ l) with "[Hl Hauth]") as "#Hinv".
-    { iNext. iExists 0%nat. iFrame. }
-    wp_apply (wp_par (λ _, own γ (◯F{1/2} 2%nat))
-                     (λ _, own γ (◯F{1/2} 2%nat)) with "[Hγ1] [Hγ2]").
+    { iNext. iExists 0. iFrame. }
+    wp_apply (wp_par (λ _, own γ (◯F{1/2} 2))
+                     (λ _, own γ (◯F{1/2} 2)) with "[Hγ1] [Hγ2]").
     - iApply (par_inc_FAA_spec 0 2 with "[$]"); auto.
     - iApply (par_inc_FAA_spec 0 2 with "[$]"); auto.
     - iIntros (v1 v2) "[Hγ1 Hγ2] !>". iCombine "Hγ1 Hγ2" as "Hγ". simpl.
@@ -112,14 +112,14 @@ Section proof2.
       iDestruct (frac_auth_agree with "Hauth Hγ") as %->.
       wp_load.
       iMod ("Hclose" with "[Hauth Hx]") as "_".
-      { iNext. iExists 4%nat. iFrame. }
+      { iNext. iExists 4. iFrame. }
       by iApply "Post".
   Qed.
 
   Lemma par_incN_helper_spec n γ l q :
-    {{{ inv N (proof2_inv γ l) ∗ own γ (◯F{q} 0%nat) }}}
+    {{{ inv N (proof2_inv γ l) ∗ own γ (◯F{q} 0) }}}
       par_incN_helper #n #l
-    {{{ v, RET v; own γ (◯F{q} (n * 2))%nat }}}.
+    {{{ v, RET v; own γ (◯F{q} (n * 2)) }}}.
   Proof.
     iIntros (Φ) "[#? Hγ] Post /=".
     iInduction n as [|n] "IH" forall (q Φ).
@@ -127,8 +127,8 @@ Section proof2.
     rewrite Nat2Z.inj_succ. wp_lam. wp_pures.
     case_bool_decide; first (simplify_eq/=; lia). wp_if.
     iDestruct "Hγ" as "[Hγ1 Hγ2]".
-    wp_apply (wp_par (λ _, own γ (◯F{q/2} 2%nat))
-                     (λ _, own γ (◯F{q/2} (n * 2)%nat)) with "[Hγ1] [Hγ2]").
+    wp_apply (wp_par (λ _, own γ (◯F{q/2} 2))
+                     (λ _, own γ (◯F{q/2} (n * 2))) with "[Hγ1] [Hγ2]").
     - iApply (par_inc_FAA_spec 0 2 with "[$]"); auto.
     - wp_op. rewrite (_ : Z.succ n - 1 = n)%Z; last lia.
       iApply ("IH" with "Hγ2"); auto.
@@ -142,14 +142,14 @@ Section proof2.
     iIntros (Φ) "_ Post". wp_lam. wp_alloc l as "Hl". wp_let.
     iMod (frac_auth_alloc 0) as (γ) "[Hauth Hγ]".
     iMod (inv_alloc _ _ (proof2_inv γ l) with "[Hl Hauth]") as "#Hinv".
-    { iNext. iExists 0%nat. iFrame. }
+    { iNext. iExists 0. iFrame. }
     wp_apply (par_incN_helper_spec with "[$]").
     iIntros (v) "Hγ". wp_seq.
     iInv N as (m) ">[Hauth Hx]" "Hclose".
     iDestruct (frac_auth_agree with "Hauth Hγ") as %->.
     wp_load.
     iMod ("Hclose" with "[Hauth Hx]") as "_".
-    { iNext. iExists (n * 2)%nat. iFrame. }
+    { iNext. iExists (n * 2). iFrame. }
     by iApply "Post".
   Qed.
 End proof2.