A heuristic to add parentheses in the presence of rules such as

Notation "## c" := (S c) (at level 0, c at level 100).

which break the stratification of precedences. This works for the case
of infix or suffix operators which occur in only one grammar rule,
such as +, *, etc. This solves the "constr" part of #3709, even though
this example is artificial.

The fix is not complete. It puts extra parenthesese even when it is
end of sentence, as in

Notation "# c % d" := (c+d) (at level 3).
Check fun x => # ## x % ## (x * 2).
(* fun x : nat => # ## x % (## x * 2) *)

The fix could be improved by not always using 100 for the printing
level of "## c", but 100 only when not the end of the sentence.

The fix does not solve the general problem with symbols occurring in
more than one rule, as e.g. in:

Notation "# c % d" := (c+d) (at level 1).
Notation "## c" := (S c) (at level 0, c at level 5).
Check fun x => # ## x % 0.
(* Parentheses are necessary only if "0 % 0" is also parsable *)

I don't see in this case what better approach to follow than
restarting the parser to check reversibility of the printing.

1 files changed, 7 insertions, 0 deletions

diff --git a/test-suite/output/Notations2.v b/test-suite/output/Notations2.v
index 4e0d135d7..d32758375 100644
--- a/test-suite/output/Notations2.v
+++ b/test-suite/output/Notations2.v
@@ -106,3 +106,10 @@ Check fun x (H:le x 0) => exist (le x) 0 H.
 
 Parameters (A : Set) (x y : A) (Q : A -> A -> Prop) (conj : Q x y).
 Check (exist (Q x) y conj).
+
+(* Check printing of notations that have arguments at higher level
+   than the notation itself *)
+
+Notation "## a" := (S a) (at level 0, a at level 100).
+Check fun x => (S x) + x.
+Check fun x => S (x + x).