Make make work.

exercises/compatibility.v

@@ -58,29 +58,21 @@ Section compatibility.
     iDestruct 1 as (w1 w2 ->) "[??]". by wp_pures.
   Qed.
   Lemma Snd_sem_typed Γ e A1 A2 : Γ ⊨ e : A1 * A2 -∗ Γ ⊨ Snd e : A2.
-  Proof.
-    iIntros "#H" (vs) "!# #HΓ /=".
-    wp_apply (wp_wand with "(H [//])"); iIntros (w).
-    iDestruct 1 as (w1 w2 ->) "[??]". by wp_pures.
-  Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   Lemma InjL_sem_typed Γ e A1 A2 : Γ ⊨ e : A1 -∗ Γ ⊨ InjL e : A1 + A2.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
-  (* REMOVE *) Lemma InjR_sem_typed Γ e A1 A2 : Γ ⊨ e : A2 -∗ Γ ⊨ InjR e : A1 + A2.
-  Proof.
-    iIntros "#H" (vs) "!# #HΓ /=".
-    wp_apply (wp_wand with "(H [//])"); iIntros (w) "#HA".
-    wp_pures. iRight. iExists w. auto.
-  Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
+  Lemma InjR_sem_typed Γ e A1 A2 : Γ ⊨ e : A2 -∗ Γ ⊨ InjR e : A1 + A2.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
   Lemma Case_sem_typed Γ e e1 e2 A1 A2 B :
     Γ ⊨ e : A1 + A2 -∗ Γ ⊨ e1 : (A1 → B) -∗ Γ ⊨ e2 : (A2 → B) -∗
     Γ ⊨ Case e e1 e2 : B.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** * Functions *)
   Lemma Rec_sem_typed Γ f x e A1 A2 :
     binder_insert f (A1 → A2)%sem_ty (binder_insert x A1 Γ) ⊨ e : A2 -∗
-    Γ ⊨ (rec: f x. (* FILL IN HERE *) Admitted.
+    Γ ⊨ (rec: f x := e) : (A1 → A2).
   Proof.
     iIntros "#H" (vs) "!# #HΓ /=". wp_pures. iLöb as "IH".
     iIntros "!#" (v) "#HA1". wp_pures. set (r := RecV f x _).
@@ -109,11 +101,11 @@ Section compatibility.
   Qed.
 
   Lemma Pack_sem_typed Γ e C A : Γ ⊨ e : C A -∗ Γ ⊨ (pack: e) : ∃ A, C A.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
   Lemma Unpack_sem_typed Γ x e1 e2 C B :
     (Γ ⊨ e1 : ∃ A, C A) -∗ (∀ A, binder_insert x (C A) Γ ⊨ e2 : B) -∗
     Γ ⊨ (unpack: x := e1 in e2) : B.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** ** Heap operations *)
   Lemma Alloc_sem_typed Γ e A : Γ ⊨ e : A -∗ Γ ⊨ ref e : ref A.
@@ -134,15 +126,15 @@ Section compatibility.
   Qed.
   Lemma Store_sem_typed Γ e1 e2 A :
     Γ ⊨ e1 : ref A -∗ Γ ⊨ e2 : A -∗ Γ ⊨ (e1 <- e2) : ().
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
   Lemma FAA_sem_typed Γ e1 e2 :
     Γ ⊨ e1 : ref sem_ty_int -∗ Γ ⊨ e2 : sem_ty_int -∗ Γ ⊨ FAA e1 e2 : sem_ty_int.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
   Lemma CmpXchg_sem_typed Γ A e1 e2 e3 :
     SemTyUnboxed A →
     Γ ⊨ e1 : ref A -∗ Γ ⊨ e2 : A -∗ Γ ⊨ e3 : A -∗
     Γ ⊨ CmpXchg e1 e2 e3 : A * sem_ty_bool.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** ** Operators *)
   Lemma UnOp_sem_typed Γ e op A B :
@@ -154,16 +146,16 @@ Section compatibility.
   Qed.
   Lemma BinOp_sem_typed Γ e1 e2 op A1 A2 B :
     SemTyBinOp op A1 A2 B → Γ ⊨ e1 : A1 -∗ Γ ⊨ e2 : A2 -∗ Γ ⊨ BinOp op e1 e2 : B.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   Lemma If_sem_typed Γ e e1 e2 B :
     Γ ⊨ e : sem_ty_bool -∗ Γ ⊨ e1 : B -∗ Γ ⊨ e2 : B -∗
     Γ ⊨ (if: e then e1 else e2) : B.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** ** Fork *)
   Lemma Fork_sem_typed Γ e : Γ ⊨ e : () -∗ Γ ⊨ Fork e : ().
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** * Compatibility rules for value typing *)
   (** ** Base types *)
@@ -172,7 +164,7 @@ Section compatibility.
   Lemma BoolV_sem_typed (b : bool) : (⊨ᵥ #b : sem_ty_bool)%I.
   Proof. by iExists b. Qed.
   Lemma IntV_sem_typed (n : Z) : (⊨ᵥ #n : sem_ty_int)%I.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** ** Products and sums *)
   Lemma PairV_sem_typed v1 v2 τ1 τ2 :

exercises/language.v

@@ -233,7 +233,7 @@ You should prove this lemma.
 
 Hint: [wp_pures] also executes the [+] operator. Carefully check how it affects
 the embedded [#] and convince yourself why that makes sense. *)
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 (** ** Reasoning about higher-order functions *)
 (** For the next example, let us consider the higher-order function [twice].
@@ -336,7 +336,7 @@ Lemma wp_add_two_ref `{!heapG Σ} l (x : Z) :
 about addition on [Z] (or the [replace] or [rewrite (_ : x = y)] tactic with
 [lia]) to turn [2 + x] into [1 + (1 + x)]. Tactics like [replace] and [rewrite]
 work operate both on the MoSeL proof goal and the MoSeL proof context. *)
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 (** ** Reasoning about higher-order state *)
 (** To see how Iris can be used to reason about higher-order state---that is,
@@ -407,7 +407,7 @@ Definition add_two_fancy : val := λ: "x",
 
 Lemma wp_add_two_fancy `{!heapG Σ} (x : Z) :
   WP add_two_fancy #x {{ w, ⌜ w = #(2 + x) ⌝ }}%I.
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 (** * Reasoning about "unsafe" programs *)
 (** Since HeapLang is an untyped language, we can write down arbitrary
@@ -438,4 +438,4 @@ Definition unsafe_ref : val := λ: <>,
 
 Lemma wp_unsafe_ref `{!heapG Σ} :
   WP unsafe_ref #() {{ v, ⌜ v = #true ⌝ }}%I.
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.

exercises/parametricity.v

@@ -27,20 +27,20 @@ Section parametricity.
     (∀ `{!heapG Σ}, (∅ ⊨ e : ∀ A, A)%I) →
     rtc erased_step ([e <_>]%E, σ) (of_val w :: es, σ') →
     False.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** * Exercise (boolean_param, moderate) *)
   Lemma boolean_param `{!heapPreG Σ} e (v1 v2 : val) σ w es σ' :
     (∀ `{!heapG Σ}, (∅ ⊨ e : ∀ A, A → A → A)%I) →
     rtc erased_step ([e <_> v1 v2]%E, σ) (of_val w :: es, σ') → w = v1 ∨ w = v2.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** * Exercise (nat_param, hard) *)
   Lemma nat_param `{!heapPreG Σ} e σ w es σ' :
     (∀ `{!heapG Σ}, (∅ ⊨ e : ∀ A, (A → A) → A → A)%I) →
     rtc erased_step ([e <_> (λ: "n", "n" + #1)%V #0]%E, σ)
       (of_val w :: es, σ') → ∃ n : nat, w = #n.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 
   (** * Exercise (strong_nat_param, hard) *)
   Lemma strong_nat_param `{!heapPreG Σ} e σ w es σ' (vf vz : val) φ :
@@ -50,5 +50,5 @@ Section parametricity.
       (Φ vz)%I ∧
       (∀ w, Φ w -∗ ⌜φ w⌝)%I) →
     rtc erased_step ([e <_> vf vz]%E, σ) (of_val w :: es, σ') → φ w.
-  Proof. (* FILL IN YOUR PROOF *) Qed.
+  Proof. (* FILL IN YOUR PROOF *) Admitted.
 End parametricity.

exercises/polymorphism.v

@@ -44,4 +44,4 @@ Lemma wp_swap_poly `{!heapG Σ} l1 l2 v1 v2 :
   l1 ↦ v1 -∗
   l2 ↦ v2 -∗
   WP swap_poly <_> #l1 #l2 {{ v, ⌜ v = #() ⌝ ∗ l1 ↦ v2 ∗ l2 ↦ v1 }}.
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.

exercises/typed.v

@@ -267,47 +267,47 @@ of them for both the expression construct and their value counterpart. *)
 Lemma Lam_typed Γ x e τ1 τ2 :
   binder_insert x τ1 Γ ⊢ₜ e : τ2 →
   Γ ⊢ₜ (λ: x, e) : TArr τ1 τ2.
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 Lemma LamV_typed x e τ1 τ2 :
   binder_insert x τ1 ∅ ⊢ₜ e : τ2 →
   ⊢ᵥ (λ: x, e) : TArr τ1 τ2.
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 Lemma Let_typed Γ x e1 e2 τ1 τ2 :
   Γ ⊢ₜ e1 : τ1 →
   binder_insert x τ1 Γ ⊢ₜ e2 : τ2 →
   Γ ⊢ₜ (let: x := e1 in e2) : τ2.
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 Lemma Seq_typed Γ e1 e2 τ1 τ2 :
   Γ ⊢ₜ e1 : τ1 →
   Γ ⊢ₜ e2 : τ2 →
   Γ ⊢ₜ (e1;; e2) : τ2.
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 Lemma Skip_typed Γ :
   Γ ⊢ₜ Skip : ().
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 (** * Typing of concrete programs *)
 (** ** Exercise (swap_typed, easy) *)
 (** Prove that the non-polymorphic swap function [swap] can be given the type
 [ref τ → ref τ → ()] for any [τ]. *)
 Lemma swap_typed τ : ⊢ᵥ swap : (ref τ → ref τ → ()).
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 (** ** Exercise (swap_poly_typed, easy) *)
 (** Prove that [swap_poly] can be typed using the polymorphic type
 [∀ X, ref X → ref X → ())], i.e. [∀: ref #0 → ref #0 → ())] in De Bruijn style. *)
 Lemma swap_poly_typed : ⊢ᵥ swap_poly : (∀: ref #0 → ref #0 → ()).
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 (** ** Exercise (not_typed, easy) *)
 (** Prove that the programs [unsafe_pure] and [unsafe_ref] from [language.v]
 cannot be typed using the syntactic type system. *)
 Lemma unsafe_pure_not_typed τ : ¬ (⊢ᵥ unsafe_pure : τ).
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.
 
 Lemma unsafe_ref_not_typed τ : ¬ (⊢ᵥ unsafe_ref : τ).
-Proof. (* FILL IN YOUR PROOF *) Qed.
+Proof. (* FILL IN YOUR PROOF *) Admitted.

mk-exercises.sh

@@ -3,7 +3,7 @@ set -e
 
 # config
 REPLACE="perl -0pe"
-REMOVEPRF_RE='s/\(\*\s*REMOVE\s*\*\)\s*Proof.\s*.*?\s*Qed\.\R/Proof. (* FILL IN YOUR PROOF *) Qed.\n/gms'
+REMOVEPRF_RE='s/\(\*\s*REMOVE\s*\*\)\s*Proof.\s*.*?\s*Qed\.\R/Proof. (* FILL IN YOUR PROOF *) Admitted.\n/gms'
 REMOVE_RE='s/\(\*\s*REMOVE\s*\*\)\s*(.*?)\s*:=.*?\.\R/\1. (* FILL IN HERE *) Admitted.\n/gms'
 STRONGHIDE_RE='s/\(\*\s*STRONGHIDE\s*\*\)\s*(.*?)\(\*\s*ENDSTRONGHIDE\s*\*\)\R?//gms'
 HIDE_RE='s/\(\*\s*HIDE\s*\*\)\s*(.*?)\(\*\s*ENDHIDE\s*\*\)/Definition hole := remove_this_line.\n(* ANSWER THE QUESTION AND REMOVE THE LINE ABOVE *)/gms'

solutions/compatibility.v

@@ -57,8 +57,8 @@ Section compatibility.
     wp_apply (wp_wand with "(H [//])"); iIntros (w).
     iDestruct 1 as (w1 w2 ->) "[??]". by wp_pures.
   Qed.
-  (* REMOVE *) Lemma Snd_sem_typed Γ e A1 A2 : Γ ⊨ e : A1 * A2 -∗ Γ ⊨ Snd e : A2.
-  Proof.
+  Lemma Snd_sem_typed Γ e A1 A2 : Γ ⊨ e : A1 * A2 -∗ Γ ⊨ Snd e : A2.
+  (* REMOVE *) Proof.
     iIntros "#H" (vs) "!# #HΓ /=".
     wp_apply (wp_wand with "(H [//])"); iIntros (w).
     iDestruct 1 as (w1 w2 ->) "[??]". by wp_pures.
@@ -70,8 +70,8 @@ Section compatibility.
     wp_apply (wp_wand with "(H [//])"); iIntros (w) "#HA".
     wp_pures. iLeft. iExists w. auto.
   Qed.
-  (* REMOVE *) Lemma InjR_sem_typed Γ e A1 A2 : Γ ⊨ e : A2 -∗ Γ ⊨ InjR e : A1 + A2.
-  Proof.
+  Lemma InjR_sem_typed Γ e A1 A2 : Γ ⊨ e : A2 -∗ Γ ⊨ InjR e : A1 + A2.
+  (* REMOVE *) Proof.
     iIntros "#H" (vs) "!# #HΓ /=".
     wp_apply (wp_wand with "(H [//])"); iIntros (w) "#HA".
     wp_pures. iRight. iExists w. auto.