fix a bunch of Coq 8.8 warnings

theories/algebra/irelations.v

@@ -132,10 +132,10 @@ Section definitions.
   Proof.
     unfold al_enabled'.
     split.
-    - revert x e i. cofix.
+    - revert x e i. cofix COFIX.
       intros x e i Hae. 
       destruct Hae. econstructor; eauto.
-    - revert x e i. cofix.
+    - revert x e i. cofix COFIX.
       intros x e i Hae. 
       destruct Hae. econstructor; eauto.
   Qed.
@@ -228,11 +228,11 @@ Section definitions.
   Proof.
     unfold ae_taken'.
     split.
-    - revert x e i. cofix.
+    - revert x e i. cofix COFIX.
       intros x e i Hae. 
       destruct Hae. econstructor; eauto.
       apply ev_taken_equiv; auto.
-    - revert x e i. cofix.
+    - revert x e i. cofix COFIX.
       intros x e i Hae. 
       destruct Hae. econstructor; eauto.
       apply ev_taken_equiv; auto.
@@ -320,11 +320,11 @@ Section definitions.
         simpl; auto.
       * intros. destruct Hae.
         simpl. eapply IHk. eauto.
-    - revert x e. cofix.
+    - revert x e. cofix COFIX.
       intros x e Hf. destruct e. 
       econstructor.
       * eapply (Hf 0).
-      * eapply tr2fun_al; eauto.
+      * eapply COFIX; eauto.
         intros k. specialize (Hf (S k)); auto.
   Qed.
 
@@ -344,11 +344,11 @@ Section definitions.
         edestruct IHk as (k'&?&?); eauto.
         exists (S k'); split; auto.
         omega.
-    - revert x e. cofix.
+    - revert x e. cofix COFIX.
       intros x e Hf. destruct e. econstructor.
       * edestruct (Hf O) as (k'&?&?).
         eapply tr2fun_ev. exists k'. eauto.
-      * eapply tr2fun_al_ev.
+      * eapply COFIX.
         intros k.
         edestruct (Hf (S k)) as (k'&?&?).
         destruct k' as [| k']; [omega|].
@@ -404,11 +404,11 @@ Section definitions.
         simpl; destruct e;auto.
       * intros. destruct Hae.
         simpl. eapply IHk. eauto.
-    - revert x e. cofix.
+    - revert x e. cofix COFIX.
       intros x e Hf. destruct e. 
       econstructor.
       * simpl in Hf. specialize (Hf 0). simpl in Hf. destruct e; auto.
-      * eapply tr2fun_al_2; eauto.
+      * eapply COFIX; eauto.
         intros k. specialize (Hf (S k)); auto.
   Qed.
 
@@ -428,11 +428,11 @@ Section definitions.
         edestruct IHk as (k'&?&?); eauto.
         exists (S k'); split; auto.
         omega.
-    - revert x e. cofix.
+    - revert x e. cofix COFIX.
       intros x e Hf. destruct e. econstructor.
       * edestruct (Hf O) as (k'&?&?).
         eapply tr2fun_ev_2. exists k'. eauto.
-      * eapply tr2fun_al_ev_2.
+      * eapply COFIX.
         intros k.
         edestruct (Hf (S k)) as (k'&?&?).
         destruct k' as [| k']; [omega|].
@@ -658,7 +658,7 @@ Section definitions.
       induction i.
       * intros; destruct Heq; auto.
       * intros. destruct Heq; eauto.
-    - revert x e e'. cofix. 
+    - revert x e e'. cofix COFIX. 
       intros x e e' Hf. 
       destruct e as [i x y r e]. 
       destruct e' as [i' x y' r' e']. 
@@ -668,7 +668,7 @@ Section definitions.
       generalize (Hf 1); intros Hf1; simpl in Hf1.
       destruct e, e'. simpl in *. 
       inversion Hf1. subst. econstructor.
-      eapply eq_ext_tr2fun. eauto.
+      eapply COFIX. eauto.
       intros. specialize (Hf (S i)); eauto.
   Qed.
       
@@ -879,12 +879,12 @@ Section cofair.
     ∀ {x y} (e: trace R1 x) (e': trace R2 y) i, 
       enabled_reflecting e e' → al_enabled e' i → al_enabled e i.
   Proof.
-    cofix. intros x y e e' i Hco Hale.
+    cofix COFIX. intros x y e e' i Hco Hale.
     destruct Hco.
     inversion Hale; subst.
     econstructor. 
     * auto.
-    * eapply enabled_reflecting_al_enabled; eauto.
+    * eapply COFIX; eauto.
       existT_eq_elim; subst; auto.
   Qed.
 
@@ -924,13 +924,13 @@ Section cofair.
     ∀ {x y} (e: trace R1 x) (e': trace R2 y) i, 
       co_step e e' → ae_taken e i → ae_taken e' i.
   Proof.
-    cofix. intros x y e e' i Hco Hae.
+    cofix COFIX. intros x y e e' i Hco Hae.
     destruct Hco.
     inversion Hae; repeat (existT_eq_elim; subst).
     econstructor. 
     * eapply co_step_ev_taken; eauto.
       econstructor; eauto.
-    * eapply co_step_ae_taken; eauto.
+    * eapply COFIX; eauto.
   Qed.
                    
   Lemma co_se_fair_pres:
@@ -967,7 +967,7 @@ Section cofair.
     co_se e1 e2 → co_step e1 e2 ∧ enabled_reflecting e1 e2.
   Proof.
     intros Hcose.
-    split; revert x1 x2 e1 e2 Hcose; cofix.
+    split; revert x1 x2 e1 e2 Hcose; cofix COFIX.
     - intros. destruct Hcose. econstructor; eauto.
     - intros. destruct Hcose. econstructor; eauto.
   Qed.
@@ -1050,7 +1050,7 @@ Section cofair.
      (∀ x e, ∃ i', ev_estep x e i') →
      (∀ x e, ae_ev_estep x e).
   Proof.
-    cofix. intros. destruct e; econstructor; [| | eauto]; eauto.
+    cofix COFIX. intros. destruct e; econstructor; [| | eauto]; eauto.
   Qed.
     
   Lemma ae_ev_estep_destr_clean x e:
@@ -1859,4 +1859,4 @@ simpl. destruct e. simpl in *.
     Qed.
     End block.
   
-End cofair.
\ No newline at end of file
+End cofair.

theories/chan2heap/refine_protocol.v

@@ -518,8 +518,8 @@ Section proof.
 
   Lemma dual_involutive (p: protocol): p ≡ dual (dual p).
   Proof.
-    revert p. cofix; intros p. rewrite (unfold_prot (dual _)). 
-    destruct p; simpl; econstructor; try eapply dual_involutive.
+    revert p. cofix COFIX; intros p. rewrite (unfold_prot (dual _)).
+    destruct p; simpl; econstructor; try eapply COFIX.
   Qed.
 
   Lemma prot_inv_left_orient Θ p Φ c pl pr s:

theories/chan2heap/simple_reln.v

@@ -4,6 +4,10 @@ From fri.chan_lang Require Export lang refine_heap_proofmode.
 From fri.chan2heap Require Export refine_protocol.
 From fri.chan_lang Require Export simple_types substitution.
 From fri.heap_lang Require Import lang heap proofmode substitution.
+From iris.proofmode Require coq_tactics.
+From fri.heap_lang Require notation proofmode.
+From fri.chan_lang Require lang derived refine refine_heap refine_heap_proofmode protocol.
+
 Section lr.
   Definition Kd := 200%nat.
   (* A hack to be able to ignore delay constants during the logical relations argument *)
@@ -27,10 +31,9 @@ Section lr.
   Local Notation cexprC := (leibnizC (chan_lang.expr)).
   Local Notation hvalC := (leibnizC (heap_lang.val)).
   Local Notation cvalC := (leibnizC (chan_lang.val)).
-  From iris.proofmode Require Import coq_tactics.
   
 
-  Import uPred.
+  Import uPred coq_tactics.
   (*
   Notation ownT := (λ i ec K, ownT i ec K (dK ec)).
    *)
@@ -68,7 +71,7 @@ Section lr.
   Definition lift3 (f: typC → hvalC → cvalC → iProp) : typC -n> hvalC -n> cvalC -n> iProp :=
     CofeMor(λ x, CofeMor(λ y, CofeMor (λ z, f x y z))).
 
-  From fri.heap_lang Require Import notation.
+  Import heap_lang.notation.
   
   Fixpoint val_equiv_pre 
              (ve: typC -n> hvalC -n> cvalC -n> iProp)
@@ -237,7 +240,7 @@ Section lr.
   (* At type 2, expr_equiv in empty context implies 
      safe_refinement using bool_refine *)
 
-  From fri.heap_lang Require Import proofmode notation.
+  Import heap_lang.notation heap_lang.proofmode.
   Lemma subst2typ_inv Γ S x ty: 
     Γ !! x = Some ty → 
     subst2typ S = Γ →
@@ -355,7 +358,7 @@ Section lr.
     - inversion 1.
   Qed.
 
-  From fri.chan_lang Require Export lang derived refine refine_heap refine_heap_proofmode protocol.
+  Import chan_lang.lang chan_lang.derived chan_lang.refine chan_lang.refine_heap chan_lang.refine_heap_proofmode chan_lang.protocol.
 
   Lemma tac_refine_bind Δ Δ' k t e K K' P:
     envs_lookup k Δ = Some (false, ownT t (fill K' e) K (dK K (fill K' e))) →

theories/chan_lang/protocol.v

@@ -114,11 +114,11 @@ Instance dual_proper T: Proper ((≡) ==> (≡)) (@dual T).
 Proof.
   intros p p' Heq.
   revert p p' Heq.
-  cofix. intros p p' Heq.
+  cofix COFIX. intros p p' Heq.
   rewrite (unfold_prot (dual p)).
   rewrite (unfold_prot (dual p')).
   destruct p, p'; simpl; try inversion Heq; subst;
-  econstructor; eapply dual_proper; eauto.
+  econstructor; eapply COFIX; eauto.
 Qed.
 
 

theories/chan_lang/refine_heap.v

@@ -3,6 +3,7 @@ From fri.algebra Require Import list frac dec_agree base_logic.
 From fri.program_logic Require Export invariants ghost_ownership.
 From fri.program_logic Require Import ownership auth.
 From iris.proofmode Require Import tactics.
+From iris.proofmode Require coq_tactics.
 Import uPred.
 
 Definition scheapN : namespace := nroot .@ "scheap".
@@ -145,8 +146,6 @@ Section heap.
     rewrite option_validI excl_validI /op /excl_op //=.
     apply affinely_elim.
   Qed.
-
-  From iris.proofmode Require Import coq_tactics tactics.
   
   Context (d d': nat).
   Context (Hd_le: (d ≤ Kd)%nat).

theories/heap_lang/refine_heap.v

@@ -3,6 +3,7 @@ From fri.algebra Require Import base_logic frac dec_agree.
 From fri.program_logic Require Export invariants ghost_ownership.
 From fri.program_logic Require Import ownership auth.
 From iris.proofmode Require Import tactics.
+From fri.heap_lang Require wp_tactics heap.
 Import uPred.
 
 Definition sheapN : namespace := nroot .@ "sheap".
@@ -113,7 +114,7 @@ Section heap.
   Lemma sheap_mapsto_op_split l q v : l ↦s{q} v ⊣⊢ (l ↦s{q/2} v ★ l ↦s{q/2} v).
   Proof. by rewrite sheap_mapsto_op_eq Qp_div_2. Qed.
 
-  From fri.heap_lang Require Export wp_tactics heap.
+  Import heap_lang.wp_tactics heap_lang.heap.
 
   Context (d d': nat).
   Context (Hd_le: (d ≤ Kd)%nat).
@@ -589,4 +590,4 @@ Section heap.
     split; omega.
   Qed.
   
-End heap.
\ No newline at end of file
+End heap.

theories/locks/lock_reln.v

@@ -2,6 +2,7 @@ From fri.algebra Require Import base_logic.
 From fri.heap_lang Require Export lang notation.
 From stdpp Require Import gmap stringmap mapset list.
 Global Set Bullet Behavior "Strict Subproofs".
+From fri.heap_lang Require heap proofmode notation refine_proofmode substitution.
 
 Section lock_reln. 
 
@@ -138,7 +139,7 @@ Arguments type_trans _ _%E _%E _.
 Hint Constructors type_trans.
 
 Section lr.
-  From fri.heap_lang Require Import heap proofmode notation refine_proofmode.
+  Import heap proofmode notation refine_proofmode.
   Context (dinit : nat) (Σ: gFunctors) (N: namespace).
   Context (Hdisj1: N ## heapN).
   Context (Hdisj2: N ## sheapN).
@@ -329,7 +330,7 @@ Section lr.
     stuple { styp : typ ; sval : expr; tval : expr }.
   Definition subst_ctx := gmap string subst_tuple.
 
-  From fri.heap_lang Require Import substitution.
+  Import substitution.
   Definition subst2typ (S: subst_ctx) : typ_ctx := styp <$> S.
   Definition subst2s (S: subst_ctx) : subst_map := sval <$> S.
   Definition subst2t (S: subst_ctx) : subst_map := tval <$> S.
@@ -382,7 +383,7 @@ Section lr.
       inversion 1.
   Qed.
 
-  From iris.proofmode Require Import coq_tactics environments.
+  Import coq_tactics environments.
   Lemma tac_refine_bind Δ Δ' k t e K K' P:
     envs_lookup k Δ = Some (false, ownT t (fill K' e) K (dK K (fill K' e))) →
     envs_simple_replace k false (Esnoc Enil k (ownT t e (comp_ectx K K') (dK (comp_ectx K K') e))) Δ
@@ -1409,4 +1410,4 @@ Qed.
 End lr.
 
 
-End lock_reln.
\ No newline at end of file
+End lock_reln.

theories/program_logic/adequacy_inf.v

+Require ClassicalEpsilon.
 From fri.algebra Require Export irelations.
 From fri.prelude Require Import list set_finite_setoid.
 From fri.program_logic Require Export hoare.
@@ -420,7 +421,7 @@ Section bounded_nondet_hom2.
        * eapply Forall_app; auto.
   Qed.
   
-  Require Import ClassicalEpsilon.
+  Import ClassicalEpsilon.
   
   Lemma trace_wptp_hom2 (tσ: cfg Λ) (e: trace (idx_step) tσ) b: 
     (∀ n,
@@ -432,7 +433,7 @@ Section bounded_nondet_hom2.
     trace (B_idx_step) (Some b).
   Proof.
     revert tσ e b.
-    cofix.
+    cofix COFIX.
     intros tσ e b Hex.
     inversion e; subst.
     intros.
@@ -445,7 +446,7 @@ Section bounded_nondet_hom2.
     - destruct (Hwptp 2) as (robs1&rs1&Φs&Hwptp').
       specialize (Hwptp' 2). edestruct Hwptp' as (?&?&?&?&?&?&?&?&?&?&?&?); eauto.
       
-    - eapply trace_wptp_hom2; eauto.
+    - eapply COFIX; eauto.
       intros. 
       destruct (Hwptp (S (S n))) as (robs1&rs1&Φs&Hwptp').
       specialize (Hwptp' n). edestruct Hwptp' as (?&?&?&?&?&?&?&?&?&?&?&?); eauto.
@@ -470,7 +471,7 @@ Section bounded_nondet_hom2.
     co_se_trace _ B_idx_step e (Some b).
   Proof.
     revert tσ e b.
-    cofix.
+    cofix COFIX.
     intros tσ e b Hex.
     destruct e as [? tσ1 tσ2 ? ]; subst.
     assert (idx_step i tσ1 tσ2) as Hi by auto.
@@ -491,7 +492,7 @@ Section bounded_nondet_hom2.
     - destruct (Hwptp 2) as (robs1&rs1&Φs&Hwptp').
       specialize (Hwptp' 2). edestruct Hwptp' as (?&?&?&?&?&?&?&?&?&?&?&?); eauto.
       
-    - eapply trace_wptp_co_se_hom2; eauto.
+    - eapply COFIX; eauto.
       intros. 
       destruct (Hwptp (S (S n))) as (robs1&rs1&Φs&Hwptp').
       specialize (Hwptp' n). edestruct Hwptp' as (?&?&?&?&?&?&?&?&?&?&?&?); eauto.

theories/program_logic/delayed_language.v

+Require ClassicalEpsilon.
+Require Wellfounded.Lexicographic_Product.
 From fri.program_logic Require Import language.
 From stdpp Require Import set.
 From fri.algebra Require Import irelations.
@@ -80,7 +82,6 @@ Section delayed_lang.
               (∀ p', plt p' p → minimal p') → 
               delayed_atomic' (of_val v, p).
  
- Require ClassicalEpsilon.
  Definition delayed_atomic: delayed_expr → bool.
  Proof.
    intros e.
@@ -470,7 +471,6 @@ Section delayed_lang.
     intros. eapply IH. eapply Hequiv. eauto.
   Qed.
 
-  Require Wellfounded.Lexicographic_Product.
   Lemma pow_plt_wf (n: nat): wf (pow_plt n).
   Proof.
     induction n.

theories/program_logic/nat_delayed_language.v

+Require Wellfounded.Lexicographic_Product.
 From fri.program_logic Require Import language.
 From stdpp Require Import set.
 From fri.algebra Require Import irelations.
@@ -389,7 +390,6 @@ Section delayed_lang.
     intros. eapply IH. eapply Hequiv. eauto.
   Qed.
 
-  Require Wellfounded.Lexicographic_Product.
   Lemma pow_plt_wf (n: nat): wf (pow_plt n).
   Proof.
     induction n.

theories/program_logic/refine_ectx.v

@@ -2,6 +2,8 @@ From fri.algebra Require Import upred dra cmra_tactics.
 From fri.program_logic Require Import 
      language ectx_language wsat refine_raw refine_raw_adequacy hoare ownership.
 From iris.proofmode Require Import tactics.
+Require fri.program_logic.refine.
+From fri.program_logic Require refine.
 Import uPred.
 
 
@@ -26,7 +28,6 @@ Context `{refineG Λ Σ (@ectx_lang expr val ectx state sΛ) Kd}.
 
 (* All the other monoids used must have a trivial step relation *)
 
-Require fri.program_logic.refine.
 
 (* Asserts ownership of physical state sσ in source language *)
 Definition ownSP (sσ: state) := refine.ownSP _ sσ.
@@ -134,7 +135,6 @@ Context (PrimDet: ∀ (e: expr) σ e1' σ1' ef1' e2' σ2' ef2',
 Context (PrimDec: ∀ (e: expr) σ, { t | prim_step e σ (fst (fst t)) (snd (fst t)) (snd t)} +
                                     {¬ ∃ e' σ' ef', prim_step e σ e' σ' ef'}).
 
-From fri.program_logic Require refine.
 
 
 Lemma ht_equiv_ectx (E: expr) e (sσ: state) σ Φ:

theories/program_logic/refine_ectx_delay.v

@@ -3,6 +3,8 @@ From fri.program_logic Require Import
      language nat_delayed_language ectx_language wsat refine_raw refine_raw_adequacy 
      hoare ownership.
 From iris.proofmode Require Import tactics.
+Require fri.program_logic.refine.
+From fri.program_logic Require refine.
 Import uPred.
 
 
@@ -20,7 +22,6 @@ Context {expr val ectx state} {sΛ : EctxLanguage expr val ectx state}.
 
 Context `{refineG Λ Σ (delayed_lang (ectx_lang expr) Kd Fd) (S Kd * (Kd + 3))}.
 
-Require fri.program_logic.refine.
 
 (* Asserts ownership of physical state sσ in source language *)
 Definition ownSP (sσ: delayed_state _) := refine.ownSP _ sσ.
@@ -274,7 +275,6 @@ Context (PrimDet: ∀ (e: expr) σ e1' σ1' ef1' e2' σ2' ef2',
 Context (PrimDec: ∀ (e: expr) σ, { t | prim_step e σ (fst (fst t)) (snd (fst t)) (snd t)} +
                                     {¬ ∃ e' σ' ef', prim_step e σ e' σ' ef'}).
 
-From fri.program_logic Require refine.
 
 
 Lemma ht_equiv_ectx (E: expr) d e (sσ: state) σ Φ:

theories/program_logic/refine_raw_adequacy.v

@@ -432,7 +432,7 @@ Qed.
     - intros; apply excluded_middle_informative.
     - intros; apply excluded_middle_informative.
     - remember (Some x) as mx. revert mx e x Heqmx.
-      cofix. 
+      cofix COFIX.
       intros mx e x.
       destruct e as [i mx y Hstep]. intros ->. destruct y as [y|].
       * exists y. intros i' Henabled. destruct Henabled as (y'&?).