Fix levels of `<=?` and `<?` in the stdlib

They were defined at level 70, no associativity in all but three places,
where they were instead declared at level 35.

Fixes #11890

4 files changed, 23 insertions, 4 deletions

diff --git a/doc/changelog/10-standard-library/11891-fix-order-notations.rst b/doc/changelog/10-standard-library/11891-fix-order-notations.rst
new file mode 100644
index 0000000000..d58d26244a
--- /dev/null
+++ b/doc/changelog/10-standard-library/11891-fix-order-notations.rst
@@ -0,0 +1,10 @@
+- **Changed:**
+  Notations :g:`<=?` and :g:`<?` from ``Coq.Structures.Orders`` and
+  ``Coq.Sorting.Mergesort.NatOrder`` are now at level 70 rather than
+  35, so as to be compatible with the notations defined everywhere
+  else in the standard library.  This may require re-parenthesizing
+  some expressions.  These notations were breaking the ability to
+  import modules from the standard library that were otherwise
+  compatible (fixes `#11890
+  <https://github.com/coq/coq/issues/11890>`_, `#11891
+  <https://github.com/coq/coq/pull/11891>`_, by Jason Gross).
diff --git a/test-suite/bugs/closed/bug_11890.v b/test-suite/bugs/closed/bug_11890.v
new file mode 100644
index 0000000000..c0426fcfda
--- /dev/null
+++ b/test-suite/bugs/closed/bug_11890.v
@@ -0,0 +1,10 @@
+Require Import Coq.Structures.Orders Coq.ZArith.ZArith Coq.Sorting.Mergesort.
+(* Note that this has always worked fine without the '; we are testing importing notations from the stdlib here *)
+Declare Module A : LeBool'.
+Declare Module B : LtBool'.
+Import A B NatOrder.
+(*
+Error: Notation "_ <=? _" is already defined at level 70 with arguments constr
+at next level, constr at next level while it is now required to be at level 35
+with arguments constr at next level, constr at next level.
+*)
diff --git a/theories/Sorting/Mergesort.v b/theories/Sorting/Mergesort.v
index a761dba62d..e9171cfdb3 100644
--- a/theories/Sorting/Mergesort.v
+++ b/theories/Sorting/Mergesort.v
@@ -259,7 +259,7 @@ Module NatOrder <: TotalLeBool.
     | _, 0 => false
     | S x', S y' => leb x' y'
     end.
-  Infix "<=?" := leb (at level 35).
+  Infix "<=?" := leb (at level 70, no associativity).
   Theorem leb_total : forall a1 a2, a1 <=? a2 \/ a2 <=? a1.
   Proof.
     induction a1; destruct a2; simpl; auto.
@@ -269,4 +269,3 @@ End NatOrder.
 Module Import NatSort := Sort NatOrder.
 
 Example SimpleMergeExample := Eval compute in sort [5;3;6;1;8;6;0].
-
diff --git a/theories/Structures/Orders.v b/theories/Structures/Orders.v
index 6a0e7397eb..94938c1d4d 100644
--- a/theories/Structures/Orders.v
+++ b/theories/Structures/Orders.v
@@ -192,11 +192,11 @@ Module Type HasLtb (Import T:Typ).
 End HasLtb.
 
 Module Type LebNotation (T:Typ)(E:HasLeb T).
- Infix "<=?" := E.leb (at level 35).
+ Infix "<=?" := E.leb (at level 70, no associativity).
 End LebNotation.
 
 Module Type LtbNotation (T:Typ)(E:HasLtb T).
- Infix "<?" := E.ltb (at level 35).
+ Infix "<?" := E.ltb (at level 70, no associativity).
 End LtbNotation.
 
 Module Type LebSpec (T:Typ)(X:HasLe T)(Y:HasLeb T).