diff --git a/Makefile.coq.local b/Makefile.coq.local
index 00c3e49a688c2b0e7fb9a0f93c8bf4fa5dd164c0..e623454d6ddb3e74c2742f40f0ff232567ffffce 100644
--- a/Makefile.coq.local
+++ b/Makefile.coq.local
@@ -13,9 +13,10 @@ NORMALIZER:=test-normalizer.sed
 
 test: $(TESTFILES:.v=.vo)
 # Make sure everything imports the options, and all Instance/Argument/Hint are qualified.
+	$(SHOW)"Performing some style checks..."
 	$(HIDE)for FILE in $(VFILES); do \
 	  if ! fgrep -q 'From stdpp Require Import options.' "$$FILE"; then echo "ERROR: $$FILE does not import 'options'."; echo; exit 1; fi ; \
-	  if egrep '^\s*(Instance|Arguments|Remove|Hint (Extern|Constructors|Resolve|Immediate|Mode|Opaque|Transparent|Unfold))\s' "$$FILE"; then echo "ERROR: $$FILE contains unqualified 'Instance'/'Arguments'/'Hint'."; echo "Please add 'Global' or 'Local' as appropriate."; echo; exit 1; fi \
+	  if egrep '^\s*(Instance|Arguments|Remove|Hint\s+(Extern|Constructors|Resolve|Immediate|Mode|Opaque|Transparent|Unfold)|(Open|Close)\s+Scope)\s' "$$FILE"; then echo "ERROR: $$FILE contains unqualified 'Instance'/'Arguments'/'Hint'/'Scope' (see above)."; echo "Please add 'Global' or 'Local' as appropriate."; echo; exit 1; fi \
 	done
 .PHONY: test
 
diff --git a/theories/streams.v b/theories/streams.v
index 3c2736a2df09337e5c29f5cc6ddf6a48a31b7dc7..32baa73d56f087596a49bbc57b1e1c02c60dfcf6 100644
--- a/theories/streams.v
+++ b/theories/streams.v
@@ -3,7 +3,7 @@ From stdpp Require Import options.
 
 Declare Scope stream_scope.
 Delimit Scope stream_scope with stream.
-Open Scope stream_scope.
+Global Open Scope stream_scope.
 
 CoInductive stream (A : Type) : Type := scons : A → stream A → stream A.
 Global Arguments scons {_} _ _ : assert.
diff --git a/theories/strings.v b/theories/strings.v
index f41aa1fbf11d57377610fe87acdf5ad31e91ce43..5cf255a6d3959dd1aeb39cb11c30e8acaf76106b 100644
--- a/theories/strings.v
+++ b/theories/strings.v
@@ -9,10 +9,10 @@ imported hereditarily somewhere. *)
 Notation length := List.length.
 
 (** * Fix scopes *)
-Open Scope string_scope.
+Global Open Scope string_scope.
 (* Make sure [list_scope] has priority over [string_scope], so that
    the "++" notation designates list concatenation. *)
-Open Scope list_scope.
+Global Open Scope list_scope.
 Infix "+:+" := String.append (at level 60, right associativity) : stdpp_scope.
 Global Arguments String.append : simpl never.
 
diff --git a/theories/vector.v b/theories/vector.v
index 6cff743f2a285fd61bde6c4ff69f7e9c9a43e811..c95ffd1f49167b475d32b47cd57c4716adae8565 100644
--- a/theories/vector.v
+++ b/theories/vector.v
@@ -5,7 +5,7 @@ naming conventions in this development. *)
 From stdpp Require Import countable.
 From stdpp Require Export fin list.
 From stdpp Require Import options.
-Open Scope vector_scope.
+Global Open Scope vector_scope.
 
 (** The type [vec n] represents lists of consisting of exactly [n] elements.
 Whereas the standard library declares exactly the same notations for vectors as