In recursive notations, accept partial application over the recursive pattern.

This allows e.g. to support a notation of the form "x <== y <== z <= t"
standing for "x <= y /\ y <= z /\ z <= t".

4 files changed, 26 insertions, 1 deletions

diff --git a/interp/notation.ml b/interp/notation.ml
index 948ebe9640..1a361dc1a6 100644
--- a/interp/notation.ml
+++ b/interp/notation.ml
@@ -391,6 +391,10 @@ let notation_constr_key = function (* Rem: NApp(NRef ref,[]) stands for @ref *)
   | NBinderList (_,_,NApp (NRef ref,args),_,_) ->
       RefKey (canonical_gr ref), AppBoundedNotation (List.length args)
   | NRef ref -> RefKey(canonical_gr ref), NotAppNotation
+  | NApp (NList (_,_,NApp (NRef ref,args),_,_), args') ->
+      RefKey (canonical_gr ref), AppBoundedNotation (List.length args + List.length args')
+  | NApp (NList (_,_,NApp (_,args),_,_), args') ->
+      Oth, AppBoundedNotation (List.length args + List.length args')
   | NApp (_,args) -> Oth, AppBoundedNotation (List.length args)
   | NList (_,_,NApp (NVar x,_),_,_) when x = Notation_ops.ldots_var -> Oth, AppUnboundedNotation
   | _ -> Oth, NotAppNotation
diff --git a/interp/notation_ops.ml b/interp/notation_ops.ml
index 2e3fa0aa0e..7cb3ca25ee 100644
--- a/interp/notation_ops.ml
+++ b/interp/notation_ops.ml
@@ -275,6 +275,12 @@ type found_variables = {
 let add_id r id = r := { !r with vars = id :: (!r).vars }
 let add_name r = function Anonymous -> () | Name id -> add_id r id
 
+let mkNApp1 (g,a) =
+  match g with
+  (* Ensure flattening of nested applicative nodes *)
+  | NApp (g,args') -> NApp (g,args'@[a])
+  | _ -> NApp (g,[a])
+
 let is_gvar id c = match DAst.get c with
 | GVar id' -> Id.equal id id'
 | _ -> false
@@ -443,7 +449,10 @@ let notation_constr_and_vars_of_glob_constr recvars a =
         aux' c
   and aux' x = DAst.with_val (function
   | GVar id -> if not (Id.equal id ldots_var) then add_id found id; NVar id
-  | GApp (g,args) -> NApp (aux g, List.map aux args)
+  | GApp (g,[]) -> NApp (aux g,[]) (* Encoding @foo *)
+  | GApp (g,args) ->
+     (* Treat applicative notes as binary nodes *)
+     let a,args = List.sep_last args in mkNApp1 (aux (DAst.make (GApp (g, args))), aux a)
   | GLambda (na,bk,ty,c) -> add_name found na; NLambda (na,aux ty,aux c)
   | GProd (na,bk,ty,c) -> add_name found na; NProd (na,aux ty,aux c)
   | GLetIn (na,b,t,c) -> add_name found na; NLetIn (na,aux b,Option.map aux t, aux c)
diff --git a/test-suite/output/Notations3.out b/test-suite/output/Notations3.out
index bd22d45059..623ca316c9 100644
--- a/test-suite/output/Notations3.out
+++ b/test-suite/output/Notations3.out
@@ -249,3 +249,5 @@ myfoo01 tt
      : nat
 myfoo01 tt
      : nat
+1 ⪯ 2 ⪯ 3 ⪯ 4
+     : Prop
diff --git a/test-suite/output/Notations3.v b/test-suite/output/Notations3.v
index 839df99ea7..ce97d909a7 100644
--- a/test-suite/output/Notations3.v
+++ b/test-suite/output/Notations3.v
@@ -410,3 +410,13 @@ Check myfoo0 1 tt. (* was printing [myfoo0 1 HI], but should print [myfoo01 HI]
 Check myfoo01 tt. (* was printing [myfoo0 1 HI], but should print [myfoo01 HI]  *)
 
 End Issue8126.
+
+Module RecursiveNotationPartialApp.
+
+(* Discussed on Coq Club, 28 July 2020 *)
+Notation "x  ⪯ y  ⪯ ..  ⪯ z  ⪯ t" :=
+  ((fun b A a => a <= b /\ A b) y .. ((fun b A a => a <= b /\ A b) z (fun b => b <= t)) .. x)
+  (at level 70, y at next level, z at next level, t at next level).
+Check 1 ⪯ 2 ⪯ 3 ⪯ 4.
+
+End RecursiveNotationPartialApp.