fix warnings about missing Global

.gitlab-ci.yml

@@ -32,6 +32,7 @@ build-coq.8.14.1:
   variables:
     OPAM_PINS: "coq version 8.14.1"
     MANGLE_NAMES: "1"
+    DENY_WARNINGS: "1"
 
 build-coq.8.13.2:
   <<: *template

theories/simulang/behavior.v

@@ -33,11 +33,11 @@ Fixpoint obs_val (v_t v_s : val) {struct v_s} : Prop :=
 (** The simulang instance of [prog_ref]. *)
 Definition prog_ref := prog_ref init_state "main" #() obs_val.
 
-Instance obs_val_refl : Reflexive obs_val.
+Global Instance obs_val_refl : Reflexive obs_val.
 Proof.
   intros v. induction v as [ [ | | | | | ] | | | ]; naive_solver.
 Qed.
-Instance obs_val_trans : Transitive obs_val.
+Global Instance obs_val_trans : Transitive obs_val.
 Proof.
   intros v1 v2 v3 H1 H2.
   induction v3 as [ [ | | | | | ] | v31 IH1 v32 IH2 | v3 IH | v3 IH] in v1, v2, H1, H2 |-*.

theories/simulang/locations.v

@@ -29,10 +29,10 @@ Qed.
 Global Instance loc_countable : Countable loc.
 Proof. by apply (inj_countable' (λ l, (loc_block l, loc_idx l)) (λ '(i, j), {| loc_block := i; loc_idx := j |})); intros []. Qed.
 
-Program Instance block_infinite : Infinite block :=
+Global Program Instance block_infinite : Infinite block :=
   inj_infinite DynBlock (λ b, if b is DynBlock b then Some b else None) _.
 Next Obligation. done. Qed.
-Program Instance loc_infinite : Infinite loc :=
+Global Program Instance loc_infinite : Infinite loc :=
   inj_infinite (λ '(i, j), {| loc_block := i; loc_idx := j |}) (λ l, Some ((loc_block l, loc_idx l))) _.
 Next Obligation. done. Qed.
 

theories/simulang/logical_heap.v

@@ -94,8 +94,8 @@ Section definitions.
 End definitions.
 
 Typeclasses Opaque heap_mapsto heap_block_size heap_mapsto_vec.
-Instance: Params (@heap_mapsto) 4 := {}.
-Instance: Params (@heap_block_size) 5 := {}.
+Global Instance: Params (@heap_mapsto) 4 := {}.
+Global Instance: Params (@heap_block_size) 5 := {}.
 
 (* Notation "l ↦{ q } v" := (heap_mapsto l q v) *)
 (*   (at level 20, q at level 50, format "l  ↦{ q }  v") : bi_scope. *)

theories/simulation/language.v

@@ -1136,7 +1136,7 @@ End safe_reach.
 
 (* discrete OFE instance for expr and thread_id *)
 Definition exprO {Λ : language} := leibnizO (expr Λ).
-Instance expr_equiv {Λ} : Equiv (expr Λ). apply exprO. Defined.
+Global Instance expr_equiv {Λ} : Equiv (expr Λ). apply exprO. Defined.
 
 Definition thread_idO := leibnizO thread_id.
-Instance thread_id_equiv : Equiv thread_id. apply thread_idO. Defined.
+Global Instance thread_id_equiv : Equiv thread_id. apply thread_idO. Defined.

theories/stacked_borrows/bor_semantics.v

@@ -29,7 +29,7 @@ Definition grants (perm: permission) (access: access_kind) : bool :=
 
 Definition matched_grant (access: access_kind) (bor: tag) (it: item) :=
   grants it.(perm) access ∧ it.(tg) = bor.
-Instance matched_grant_dec (access: access_kind) (bor: tag) (it : item) :
+Global Instance matched_grant_dec (access: access_kind) (bor: tag) (it : item) :
   Decision (matched_grant access bor it) := _.
 
 (** Difference from the paper/Miri in indexing of stacks: *)
@@ -54,7 +54,7 @@ Definition is_active_protector cids (it: item) :=
   | Some c => Is_true (is_active cids c) ∧ it.(perm) ≠ Disabled
   | _ => False
   end.
-Instance is_active_protector_dec cids it : Decision (is_active_protector cids it).
+Global Instance is_active_protector_dec cids it : Decision (is_active_protector cids it).
 Proof. rewrite /is_active_protector. case_match; solve_decision. Qed.
 
 (* Find the top active protector *)
@@ -381,9 +381,9 @@ Definition tag_values_included (v: value) nxtp :=
   ∀ l tg, ScPtr l tg ∈ v → tg <t nxtp.
 Infix "<<t" := tag_values_included (at level 60, no associativity).
 
-Instance tag_included_dec tg nxtp : Decision (tag_included tg nxtp).
+Global Instance tag_included_dec tg nxtp : Decision (tag_included tg nxtp).
 Proof. destruct tg; cbn; apply _. Qed.
-Instance tag_values_included_dec v nxtp : Decision (tag_values_included v nxtp).
+Global Instance tag_values_included_dec v nxtp : Decision (tag_values_included v nxtp).
 Proof.
   rewrite /tag_values_included. induction v as [ | sc v IH].
   - left; intros l tg Ha. exfalso. by eapply not_elem_of_nil.

theories/stacked_borrows/defs.v

@@ -24,7 +24,7 @@ Definition stack_item_included (stk: stack) (nxtp: ptr_id) (nxtc: call_id) :=
 
 Definition is_tagged (it: item) :=
   match it.(tg) with Tagged _ => True | _ => False end.
-Instance is_tagged_dec it: Decision (is_tagged it).
+Global Instance is_tagged_dec it: Decision (is_tagged it).
 Proof. intros. rewrite /is_tagged. case tg; solve_decision. Defined.
 Definition stack_item_tagged_NoDup (stk : stack) :=
   NoDup (fmap tg (filter is_tagged stk)).

theories/stacked_borrows/helpers.v

@@ -85,34 +85,34 @@ Proof.
 Qed.
 
 (** SqSubsetEq for option *)
-Instance option_sqsubseteq `{SqSubsetEq A} : SqSubsetEq (option A) :=
+Global Instance option_sqsubseteq `{SqSubsetEq A} : SqSubsetEq (option A) :=
   λ o1 o2, if o1 is Some x1 return _ then
               if o2 is Some x2 return _ then x1 ⊑ x2 else False
            else True.
-Instance option_sqsubseteq_preorder `{SqSubsetEq A} `{!@PreOrder A (⊑)} :
+Global Instance option_sqsubseteq_preorder `{SqSubsetEq A} `{!@PreOrder A (⊑)} :
   @PreOrder (option A) (⊑).
 Proof.
   split.
   - move=>[x|] //. apply (@reflexivity A (⊑) _).
   - move=>[x|] [y|] [z|] //. apply (@transitivity A (⊑) _).
 Qed.
-Instance option_sqsubseteq_antisymm `{SqSubsetEq A} `{!@AntiSymm A eq (⊑)} :
+Global Instance option_sqsubseteq_antisymm `{SqSubsetEq A} `{!@AntiSymm A eq (⊑)} :
   @AntiSymm (option A) eq (⊑).
 Proof.
   intros [a|] [b|] Ha Hb; [|done|done|done]. f_equal. by apply : anti_symm.
 Qed.
-Instance option_sqsubseteq_po `{SqSubsetEq A} `{!@PartialOrder A (⊑)} :
+Global Instance option_sqsubseteq_po `{SqSubsetEq A} `{!@PartialOrder A (⊑)} :
   @PartialOrder (option A) (⊑).
 Proof. split; apply _. Qed.
 
-Instance nat_sqsubseteq : SqSubsetEq nat := le.
-Instance nat_sqsubseteq_po : @PartialOrder nat (⊑) := _.
+Global Instance nat_sqsubseteq : SqSubsetEq nat := le.
+Global Instance nat_sqsubseteq_po : @PartialOrder nat (⊑) := _.
 
-Instance elem_of_list_suffix_proper {A : Type} (x:A) :
+Global Instance elem_of_list_suffix_proper {A : Type} (x:A) :
   Proper ((suffix) ==> impl) (x ∈.).
 Proof. intros l1 l2 [? ->] ?. rewrite elem_of_app. by right. Qed.
 
-Instance elem_of_list_sublist_proper {A : Type} (x:A) :
+Global Instance elem_of_list_sublist_proper {A : Type} (x:A) :
   Proper ((sublist) ==> impl) (x ∈.).
 Proof.
   intros l1 l2 SUB. induction SUB; [done|..].
@@ -172,7 +172,7 @@ Proof.
   - move => /NoDup_cons [NI /IH //].
 Qed.
 
-Instance NoDup_sublist_proper {A: Type} :
+Global Instance NoDup_sublist_proper {A: Type} :
   Proper (sublist ==> flip impl) (@NoDup A).
 Proof. intros ????. by eapply NoDup_sublist. Qed.
 

theories/stacked_borrows/lang.v

@@ -59,7 +59,7 @@ Lemma to_of_result v : to_result (of_result v) = Some v.
 Proof. by destruct v as [[]|]. Qed.
 Lemma of_to_result e v : to_result e = Some v → of_result v = e.
 Proof. destruct e=>//=; intros; by simplify_eq. Qed.
-Instance of_result_inj : Inj (=) (=) of_result.
+Global Instance of_result_inj : Inj (=) (=) of_result.
 Proof. by intros ?? Hv; apply (inj Some); rewrite -2!to_of_result Hv /=. Qed.
 Lemma is_closed_to_result X e v : to_result e = Some v → is_closed X e.
 Proof. intros <-%of_to_result. apply is_closed_of_result. Qed.
@@ -77,9 +77,9 @@ Proof. induction vl as [|v vl IH]; [done|]. by rewrite 3!fmap_cons IH. Qed.
 
 (** Equality and other typeclass stuff *)
 
-Instance bin_op_eq_dec : EqDecision bin_op.
+Global Instance bin_op_eq_dec : EqDecision bin_op.
 Proof. solve_decision. Defined.
-Instance bin_op_countable : Countable bin_op.
+Global Instance bin_op_countable : Countable bin_op.
 Proof.
   refine (inj_countable'
     (λ o, match o with AddOp => 0 | SubOp => 1 | LeOp => 2 |
@@ -88,9 +88,9 @@ Proof.
                   3 => LtOp | 4 => EqOp | _ => OffsetOp end) _); by intros [].
 Qed.
 
-Instance scalar_eq_dec : EqDecision scalar.
+Global Instance scalar_eq_dec : EqDecision scalar.
 Proof. solve_decision. Defined.
-Instance scalar_countable : Countable scalar.
+Global Instance scalar_countable : Countable scalar.
 Proof.
   refine (inj_countable
           (λ v, match v with
@@ -109,9 +109,9 @@ Proof.
               end) _); by intros [].
 Qed.
 
-Instance retag_kind_eq_dec : EqDecision retag_kind.
+Global Instance retag_kind_eq_dec : EqDecision retag_kind.
 Proof. solve_decision. Defined.
-Instance retag_kind_countable : Countable retag_kind.
+Global Instance retag_kind_countable : Countable retag_kind.
 Proof.
   refine (inj_countable
           (λ k, match k with
@@ -186,11 +186,11 @@ Proof.
     clear FIX. naive_solver.
 Qed.
 
-Instance expr_dec_eq : EqDecision expr.
+Global Instance expr_dec_eq : EqDecision expr.
 Proof.
   refine (λ e1 e2, cast_if (decide (expr_beq e1 e2))); by rewrite -expr_beq_correct.
 Defined.
-Instance expr_countable : Countable expr.
+Global Instance expr_countable : Countable expr.
 Proof.
   refine (inj_countable'
     (fix go e := match e with
@@ -263,11 +263,11 @@ Proof.
   - fix FIX_INNER 1. intros []; [done|]. by simpl; f_equal.
 Qed.
 
-Instance result_dec_eq : EqDecision result.
+Global Instance result_dec_eq : EqDecision result.
 Proof.
   refine (λ v1 v2, cast_if (decide (of_result v1 = of_result v2))); abstract naive_solver.
 Defined.
-Instance result_countable : Countable result.
+Global Instance result_countable : Countable result.
 Proof.
   refine (inj_countable
     (λ v, match v with
@@ -281,10 +281,10 @@ Proof.
   by intros [].
 Qed.
 
-Instance scalar_inhabited : Inhabited scalar := populate ScPoison.
-Instance expr_inhabited : Inhabited expr := populate (#[☠])%E.
-Instance result_inhabited : Inhabited result := populate (ValR [☠]%S).
-Instance state_Inhabited : Inhabited state.
+Global Instance scalar_inhabited : Inhabited scalar := populate ScPoison.
+Global Instance expr_inhabited : Inhabited expr := populate (#[☠])%E.
+Global Instance result_inhabited : Inhabited result := populate (ValR [☠]%S).
+Global Instance state_Inhabited : Inhabited state.
 Proof. do 2!econstructor; exact: inhabitant. Qed.
 
 Canonical Structure locO := leibnizO loc.
@@ -296,7 +296,7 @@ Canonical Structure stateO := leibnizO state.
 (** Basic properties about the language *)
 
 
-Instance fill_item_inj Ki : Inj (=) (=) (fill_item Ki).
+Global Instance fill_item_inj Ki : Inj (=) (=) (fill_item Ki).
 Proof. destruct Ki; intros ???; simplify_eq/=; auto with f_equal. Qed.
 Global Instance fill_inj K : Inj (=) (=) (fill K).
 Proof. induction K; intros ???; by simplify_eq/=. Qed.

theories/stacked_borrows/lang_base.v

@@ -33,9 +33,9 @@ Inductive tag :=
   | Tagged (t: ptr_id)
   | Untagged.
 
-Instance tag_eq_dec : EqDecision tag.
+Global Instance tag_eq_dec : EqDecision tag.
 Proof. solve_decision. Defined.
-Instance tag_countable : Countable tag.
+Global Instance tag_countable : Countable tag.
 Proof.
   refine (inj_countable
           (λ tg, match tg with
@@ -49,9 +49,9 @@ Proof.
 Qed.
 
 Inductive permission := Unique | SharedReadWrite | SharedReadOnly | Disabled.
-Instance permission_eq_dec : EqDecision permission.
+Global Instance permission_eq_dec : EqDecision permission.
 Proof. solve_decision. Defined.
-Instance permission_countable : Countable permission.
+Global Instance permission_countable : Countable permission.
 Proof.
   refine (inj_countable
     (λ p,
@@ -71,7 +71,7 @@ Record item := mkItem {
   tg        : tag;
   protector : option call_id;
 }.
-Instance item_eq_dec : EqDecision item.
+Global Instance item_eq_dec : EqDecision item.
 Proof. solve_decision. Defined.
 
 Definition stack := list item.
@@ -208,9 +208,9 @@ Fixpoint is_closed (X : list string) (e : expr) : bool :=
 Class Closed (X : list string) (e : expr) := closed : is_closed X e.
 #[global]
 Hint Mode Closed + + : typeclass_instances.
-Instance closed_proof_irrel env e : ProofIrrel (Closed env e).
+Global Instance closed_proof_irrel env e : ProofIrrel (Closed env e).
 Proof. rewrite /Closed. apply _. Qed.
-Instance closed_decision env e : Decision (Closed env e).
+Global Instance closed_decision env e : Decision (Closed env e).
 Proof. rewrite /Closed. apply _. Qed.
 
 (** Irreducible (language values) *)

theories/stacked_borrows/locations.v

@@ -22,7 +22,7 @@ Proof. solve_decision. Qed.
 Global Instance loc_inhabited : Inhabited loc := populate (1%positive, 0).
 Global Instance loc_countable : Countable loc.
 Proof. by apply (inj_countable' (λ l, l) (λ '(i, j), (i, j))); intros []. Qed.
-Program Instance loc_infinite : Infinite loc :=
+Global Program Instance loc_infinite : Infinite loc :=
   inj_infinite (λ '(i, j), (i, j)) (λ l, Some l) _.
 Next Obligation. intros []. done. Qed.
 
@@ -42,7 +42,7 @@ Proof. rewrite /shift_loc /=. f_equal. lia. Qed.
 Lemma shift_loc_0_nat l : l +ₗ 0%nat = l.
 Proof. destruct l as [b o]. rewrite /shift_loc /=. f_equal. lia. Qed.
 
-Instance shift_loc_inj l : Inj (=) (=) (shift_loc l).
+Global Instance shift_loc_inj l : Inj (=) (=) (shift_loc l).
 Proof. destruct l as [b o]; intros n n' [=?]; lia. Qed.
 
 Lemma shift_loc_block l n : (l +ₗ n).1 = l.1.

theories/stacked_borrows/steps_list.v

@@ -11,7 +11,7 @@ Definition tagged_sublist (stk1 stk2: stack) :=
   ∀ it1, it1 ∈ stk1 → ∃ it2,
   it2 ∈ stk2 ∧ it1.(tg) = it2.(tg) ∧ it1.(protector) = it2.(protector) ∧
   (it1.(perm) ≠ Disabled → it2.(perm) = it1.(perm)).
-Instance tagged_sublist_preorder : PreOrder tagged_sublist.
+Global Instance tagged_sublist_preorder : PreOrder tagged_sublist.
 Proof.
   constructor.
   - intros ??. naive_solver.
@@ -20,7 +20,7 @@ Proof.
     intros ND3. specialize (ND ND3). rewrite ND2 // ND //.
 Qed.
 
-Instance tagged_sublist_proper stk : Proper ((⊆) ==> impl) (tagged_sublist stk).
+Global Instance tagged_sublist_proper stk : Proper ((⊆) ==> impl) (tagged_sublist stk).
 Proof. move => ?? SUB H1 ? /H1 [? [/SUB ? ?]]. naive_solver. Qed.
 
 Lemma tagged_sublist_app l1 l2 k1 k2 :
@@ -176,7 +176,7 @@ Lemma stack_item_tagged_NoDup_app stk1 stk2 :
   stack_item_tagged_NoDup stk1 ∧ stack_item_tagged_NoDup stk2.
 Proof. rewrite /stack_item_tagged_NoDup filter_app fmap_app NoDup_app. naive_solver. Qed.
 
-Instance stack_item_tagged_NoDup_proper :
+Global Instance stack_item_tagged_NoDup_proper :
   Proper (Permutation ==> iff) stack_item_tagged_NoDup.
 Proof. intros stk1 stk2 PERM. by rewrite /stack_item_tagged_NoDup PERM. Qed.
 

theories/stacked_borrows/steps_retag.v

@@ -12,7 +12,7 @@ Definition tag_on_top (stks: stacks) l t pm : Prop :=
 Definition active_preserving (cids: call_id_set) (stk stk': stack) :=
   ∀ pm t c, c ∈ cids → mkItem pm t (Some c) ∈ stk → mkItem pm t (Some c) ∈ stk'.
 
-Instance active_preserving_preorder cids : PreOrder (active_preserving cids).
+Global Instance active_preserving_preorder cids : PreOrder (active_preserving cids).
 Proof.
   constructor.
   - intros ??. done.

theories/stacked_borrows/type.v

@@ -174,20 +174,20 @@ End type_general_ind.
 
 (** Decidability *)
 
-Instance type_inhabited : Inhabited type := populate (FixedSize 0).
+Global Instance type_inhabited : Inhabited type := populate (FixedSize 0).
 
-Instance mutability_eq_dec : EqDecision mutability.
+Global Instance mutability_eq_dec : EqDecision mutability.
 Proof. solve_decision. Defined.
-Instance mutability_countable : Countable mutability.
+Global Instance mutability_countable : Countable mutability.
 Proof.
   refine (inj_countable'
     (λ m, match m with Mutable => 0 | Immutable => 1 end)
     (λ x, match x with 0 => Mutable | _ => Immutable end) _); by intros [].
 Qed.
 
-Instance pointer_kind_eq_dec : EqDecision pointer_kind.
+Global Instance pointer_kind_eq_dec : EqDecision pointer_kind.
 Proof. solve_decision. Defined.
-Instance pointer_kind_countable : Countable pointer_kind.
+Global Instance pointer_kind_countable : Countable pointer_kind.
 Proof.
   refine (inj_countable
           (λ k, match k with
@@ -239,11 +239,11 @@ Proof.
       specialize (FIX Ts1h). naive_solver. }
     clear FIX. naive_solver.
 Qed.
-Instance type_eq_dec : EqDecision type.
+Global Instance type_eq_dec : EqDecision type.
 Proof.
   refine (λ T1 T2, cast_if (decide (type_beq T1 T2))); by rewrite -type_beq_correct.
 Defined.
-Instance type_countable : Countable type.
+Global Instance type_countable : Countable type.
 Proof.
   refine (inj_countable'
     (fix go T := match T with