Port to latest Iris.

opam

@@ -9,5 +9,5 @@ build: [make "-j%{jobs}%"]
 install: [make "install"]
 remove: [ "sh" "-c" "rm -rf '%{lib}%/coq/user-contrib/actris" ]
 depends: [
-  "coq-iris" { (= "dev.2020-04-01.4.6b759b62") | (= "dev") }
+  "coq-iris" { (= "dev.2020-04-02.4.739cc004") | (= "dev") }
 ]

theories/utils/cofe_solver_2.v

 From iris.algebra Require Import cofe_solver.
 
-(** Composition of [oFunctor]. Move to Iris. Fix name [oFunctor_compose] which
-is already in use. *)
-Program Definition oFunctor_compose (F1 F2 : oFunctor)
-  `{!∀ `{Cofe A, Cofe B}, Cofe (oFunctor_car F2 A B)} : oFunctor := {|
-  oFunctor_car A _ B _ := oFunctor_car F1 (oFunctor_car F2 B A) (oFunctor_car F2 A B);
-  oFunctor_map A1 _ A2 _ B1 _ B2 _ 'fg :=
-    oFunctor_map F1 (oFunctor_map F2 (fg.2,fg.1),oFunctor_map F2 fg)
-|}.
-Next Obligation.
-  intros F1 F2 ? A1 ? A2 ? B1 ? B2 ? n [f1 g1] [f2 g2] [??]; simpl in *.
-  apply oFunctor_ne; split; apply oFunctor_ne; by split.
-Qed.
-Next Obligation.
-  intros F1 F2 ? A ? B ? x; simpl in *. rewrite -{2}(oFunctor_id F1 x).
-  apply equiv_dist=> n. apply oFunctor_ne. split=> y /=; by rewrite !oFunctor_id.
-Qed.
-Next Obligation.
-  intros F1 F2 ? A1 ? A2 ? A3 ? B1 ? B2 ? B3 ? f g f' g' x; simpl in *.
-  rewrite -oFunctor_compose. apply equiv_dist=> n. apply oFunctor_ne.
-  split=> y /=; by rewrite !oFunctor_compose.
-Qed.
-Instance oFunctor_compose_contractive1 (F1 F2 : oFunctor)
-  `{!∀ `{Cofe A, Cofe B}, Cofe (oFunctor_car F2 A B)} :
-  oFunctorContractive F1 → oFunctorContractive (oFunctor_compose F1 F2).
-Proof.
-  intros ? A1 ? A2 ? B1 ? B2 ? n [f1 g1] [f2 g2] Hfg; simpl in *.
-  f_contractive; destruct Hfg; split; simpl in *; apply oFunctor_ne; by split.
-Qed.
-
 (** Version of the cofe_solver for a parametrized functor. Generalize and move
 to Iris. *)
 Record solution_2 (F : ofeT → oFunctor) := Solution2 {
   solution_2_car :> ∀ An `{!Cofe An} A `{!Cofe A}, ofeT;
   solution_2_cofe `{!Cofe An, !Cofe A} : Cofe (solution_2_car An A);
   solution_2_iso `{!Cofe An, !Cofe A} :>
-    ofe_iso (F A (solution_2_car A An) _) (solution_2_car An A);
+    ofe_iso (oFunctor_apply (F A) (solution_2_car A An)) (solution_2_car An A);
 }.
 Existing Instance solution_2_cofe.
 
@@ -47,7 +18,7 @@ Section cofe_solver_2.
   Notation map := (oFunctor_map (F _)).
 
   Definition F_2 (An : ofeT) `{!Cofe An} (A : ofeT) `{!Cofe A} : oFunctor :=
-    oFunctor_compose (F A) (F An).
+    oFunctor_oFunctor_compose (F A) (F An).
 
   Definition T_result `{!Cofe An, !Cofe A} : solution (F_2 An A) := solver.result _.
   Definition T (An : ofeT) `{!Cofe An} (A : ofeT) `{!Cofe A} : ofeT :=
@@ -57,16 +28,20 @@ Section cofe_solver_2.
     populate (ofe_iso_1 T_result inhabitant).
 
   Definition T_iso_fun_aux `{!Cofe An, !Cofe A}
-      (rec : prodO (F An (T An A) _ -n> T A An) (T A An -n> F An (T An A) _)) :
-      prodO (F A (T A An) _ -n> T An A) (T An A -n> F A (T A An) _) :=
+      (rec : prodO (oFunctor_apply (F An) (T An A) -n> T A An)
+                   (T A An -n> oFunctor_apply (F An) (T An A))) :
+      prodO (oFunctor_apply (F A) (T A An) -n> T An A)
+            (T An A -n> oFunctor_apply (F A) (T A An)) :=
     (ofe_iso_1 T_result ◎ map (rec.1,rec.2), map (rec.2,rec.1) ◎ ofe_iso_2 T_result).
   Instance T_iso_aux_fun_contractive `{!Cofe An, !Cofe A} :
     Contractive (T_iso_fun_aux (An:=An) (A:=A)).
   Proof. solve_contractive. Qed.
 
   Definition T_iso_fun_aux_2 `{!Cofe An, !Cofe A}
-      (rec : prodO (F A (T A An) _ -n> T An A) (T An A -n> F A (T A An) _)) :
-      prodO (F A (T A An) _ -n> T An A) (T An A -n> F A (T A An) _) :=
+      (rec : prodO (oFunctor_apply (F A) (T A An) -n> T An A)
+                   (T An A -n> oFunctor_apply (F A) (T A An))) :
+      prodO (oFunctor_apply (F A) (T A An) -n> T An A)
+            (T An A -n> oFunctor_apply (F A) (T A An)) :=
     T_iso_fun_aux (T_iso_fun_aux rec).
   Instance T_iso_fun_aux_2_contractive `{!Cofe An, !Cofe A} :
     Contractive (T_iso_fun_aux_2 (An:=An) (A:=A)).
@@ -76,7 +51,8 @@ Section cofe_solver_2.
   Qed.
 
   Definition T_iso_fun `{!Cofe An, !Cofe A} :
-      prodO (F A (T A An) _ -n> T An A) (T An A -n> F A (T A An) _) :=
+      prodO (oFunctor_apply (F A) (T A An) -n> T An A)
+            (T An A -n> oFunctor_apply (F A) (T A An)) :=
     fixpoint T_iso_fun_aux_2.
   Definition T_iso_fun_unfold_1 `{!Cofe An, !Cofe A} y :
     T_iso_fun (An:=An) (A:=A).1 y ≡ (T_iso_fun_aux (T_iso_fun_aux T_iso_fun)).1 y.
@@ -93,17 +69,19 @@ Section cofe_solver_2.
       induction (lt_wf n) as [n _ IH]; intros An ? A ? y.
       rewrite T_iso_fun_unfold_1 T_iso_fun_unfold_2 /=.
       rewrite -{2}(ofe_iso_12 T_result y). f_equiv.
-      rewrite -(oFunctor_id (F _) (ofe_iso_2 T_result y)) -!ofe.oFunctor_compose.
+      rewrite -(oFunctor_map_id (F _) (ofe_iso_2 T_result y))
+              -!oFunctor_map_compose.
       f_equiv; apply Fcontr; destruct n as [|n]; simpl; [done|].
-      split => x /=; rewrite ofe_iso_21 -{2}(oFunctor_id (F _) x)
-        -!ofe.oFunctor_compose; do 2 f_equiv; split=> z /=; auto.
+      split => x /=; rewrite ofe_iso_21 -{2}(oFunctor_map_id (F _) x)
+        -!oFunctor_map_compose; do 2 f_equiv; split=> z /=; auto.
     - intros y. apply equiv_dist=> n. revert An Hcn A Hc y.
       induction (lt_wf n) as [n _ IH]; intros An ? A ? y.
       rewrite T_iso_fun_unfold_1 T_iso_fun_unfold_2 /= ofe_iso_21.
-      rewrite -(oFunctor_id (F _) y) -!ofe.oFunctor_compose.
+      rewrite -(oFunctor_map_id (F _) y) -!oFunctor_map_compose.
       f_equiv; apply Fcontr; destruct n as [|n]; simpl; [done|].
       split => x /=; rewrite -{2}(ofe_iso_12 T_result x); f_equiv;
-        rewrite -{2}(oFunctor_id (F _) (ofe_iso_2 T_result x)) -!ofe.oFunctor_compose;
+        rewrite -{2}(oFunctor_map_id (F _) (ofe_iso_2 T_result x))
+                -!oFunctor_map_compose;
         do 2 f_equiv; split=> z /=; auto.
   Qed.
 End cofe_solver_2.