Addressing issues with PR#873: performance and use of abbreviation for printing.

We do a couple of changes:

- Splitting notation keys into more categories to make table smaller.
  This should (a priori) make printing faster (see #6416).

- Abbreviations are treated for printing like single notations: they
  are pushed to the scope stack, so that in a situation such as

  Open Scope foo_scope.
  Notation foo := term.
  Open Scope bar_scope.

  one looks for notations first in scope bar_scope, then try to use
  foo, they try for notations in scope foo_scope.

- We seize the opportunity of this commit to simplify
  availability_of_notation which is now integrated to
  uninterp_notation and which does not have to be called explicitly
  anymore.

3 files changed, 159 insertions, 93 deletions

diff --git a/interp/constrextern.ml b/interp/constrextern.ml
index faff0d71e0..f1d8d858a1 100644
--- a/interp/constrextern.ml
+++ b/interp/constrextern.ml
@@ -110,13 +110,13 @@ let deactivate_notation nr =
      (* shouldn't we check wether it is well defined? *)
      inactive_notations_table := IRuleSet.add nr !inactive_notations_table
   | NotationRule (scopt, ntn) ->
-     match availability_of_notation (scopt, ntn) (scopt, []) with
-     | None -> user_err ~hdr:"Notation"
+     if not (exists_notation_interpretation_in_scope scopt ntn) then
+       user_err ~hdr:"Notation"
                         (pr_notation ntn ++ spc () ++ str "does not exist"
                          ++ (match scopt with
                              | None -> spc () ++ str "in the empty scope."
                              | Some _ -> show_scope scopt ++ str "."))
-     | Some _ ->
+     else
         if IRuleSet.mem nr !inactive_notations_table then
           Feedback.msg_warning
             (str "Notation" ++ spc () ++ pr_notation ntn ++ spc ()
@@ -443,16 +443,12 @@ let rec extern_cases_pattern_in_scope (custom,scopes as allscopes) vars pat =
 and apply_notation_to_pattern ?loc gr ((subst,substlist),(nb_to_drop,more_args))
     (custom, (tmp_scope, scopes) as allscopes) vars =
   function
-    | NotationRule (sc,ntn) ->
+    | NotationRule (sc,ntn),key ->
       begin
         match availability_of_entry_coercion custom (fst ntn) with
         | None -> raise No_match
         | Some coercion ->
-        match availability_of_notation (sc,ntn) (tmp_scope,scopes) with
-	  (* Uninterpretation is not allowed in current context *)
-	  | None -> raise No_match
-	  (* Uninterpretation is allowed in current context *)
-	  | Some (scopt,key) ->
+            let scopt = match key with Some _ -> sc | _ -> None in
 	    let scopes' = Option.List.cons scopt scopes in
 	    let l =
               List.map (fun (c,(subentry,(scopt,scl))) ->
@@ -474,7 +470,8 @@ and apply_notation_to_pattern ?loc gr ((subst,substlist),(nb_to_drop,more_args))
               (insert_pat_delimiters ?loc
                  (make_pat_notation ?loc ntn (l,ll) l2') key)
       end
-    | SynDefRule kn ->
+    | SynDefRule kn,key ->
+      assert (key = None);
       match availability_of_entry_coercion custom InConstrEntrySomeLevel with
       | None -> raise No_match
       | Some coercion ->
@@ -494,7 +491,7 @@ and apply_notation_to_pattern ?loc gr ((subst,substlist),(nb_to_drop,more_args))
       insert_pat_coercion ?loc coercion (mkPat ?loc qid (List.rev_append l1 l2'))
 and extern_notation_pattern allscopes vars t = function
   | [] -> raise No_match
-  | (keyrule,pat,n as _rule)::rules ->
+  | (keyrule,pat,n as _rule,key)::rules ->
     try
       if is_inactive_rule keyrule then raise No_match;
       let loc = t.loc in
@@ -502,7 +499,7 @@ and extern_notation_pattern allscopes vars t = function
         | PatCstr (cstr,args,na) ->
           let t = if na = Anonymous then t else DAst.make ?loc (PatCstr (cstr,args,Anonymous)) in
 	  let p = apply_notation_to_pattern ?loc (ConstructRef cstr)
-	    (match_notation_constr_cases_pattern t pat) allscopes vars keyrule in
+            (match_notation_constr_cases_pattern t pat) allscopes vars (keyrule,key) in
 	  insert_pat_alias ?loc p na
 	| PatVar Anonymous -> CAst.make ?loc @@ CPatAtom None
         | PatVar (Name id) -> CAst.make ?loc @@ CPatAtom (Some (qualid_of_ident ?loc id))
@@ -511,11 +508,11 @@ and extern_notation_pattern allscopes vars t = function
 
 let rec extern_notation_ind_pattern allscopes vars ind args = function
   | [] -> raise No_match
-  | (keyrule,pat,n as _rule)::rules ->
+  | (keyrule,pat,n as _rule,key)::rules ->
     try
       if is_inactive_rule keyrule then raise No_match;
       apply_notation_to_pattern (IndRef ind)
-	(match_notation_constr_ind_pattern ind args pat) allscopes vars keyrule
+        (match_notation_constr_ind_pattern ind args pat) allscopes vars (keyrule,key)
     with
 	No_match -> extern_notation_ind_pattern allscopes vars ind args rules
 
@@ -1058,7 +1055,7 @@ and extern_eqn inctx scopes vars {CAst.loc;v=(ids,pll,c)} =
 
 and extern_notation (custom,scopes as allscopes) vars t = function
   | [] -> raise No_match
-  | (keyrule,pat,n as _rule)::rules ->
+  | (keyrule,pat,n as _rule,key)::rules ->
       let loc = Glob_ops.loc_of_glob_constr t in
       try
         if is_inactive_rule keyrule then raise No_match;
@@ -1106,11 +1103,7 @@ and extern_notation (custom,scopes as allscopes) vars t = function
              (match availability_of_entry_coercion custom (fst ntn) with
              | None -> raise No_match
              | Some coercion ->
-               match availability_of_notation (sc,ntn) scopes with
-                  (* Uninterpretation is not allowed in current context *)
-              | None -> raise No_match
-                  (* Uninterpretation is allowed in current context *)
-	      | Some (scopt,key) ->
+                  let scopt = match key with Some _ -> sc | None -> None in
                   let scopes' = Option.List.cons scopt (snd scopes) in
 	          let l =
                     List.map (fun (c,(subentry,(scopt,scl))) ->
diff --git a/interp/notation.ml b/interp/notation.ml
index 49403c6e34..d5b43860c1 100644
--- a/interp/notation.ml
+++ b/interp/notation.ml
@@ -156,6 +156,8 @@ let scope_eq s1 s2 = match s1, s2 with
 | Scope _, SingleNotation _
 | SingleNotation _, Scope _ -> false
 
+(* Scopes for interpretation *)
+
 let scope_stack = ref []
 
 let current_scopes () = !scope_stack
@@ -165,14 +167,56 @@ let scope_is_open_in_scopes sc l =
 
 let scope_is_open sc = scope_is_open_in_scopes sc (!scope_stack)
 
+(* Uninterpretation tables *)
+
+type interp_rule =
+  | NotationRule of scope_name option * notation
+  | SynDefRule of KerName.t
+
+type notation_rule_core = interp_rule * interpretation * int option
+type notation_rule = notation_rule_core * delimiters option
+
+(* Scopes for uninterpretation: includes abbreviations (i.e. syntactic definitions) and  *)
+
+type uninterp_scope_elem =
+  | UninterpScope of scope_name
+  | UninterpSingle of notation_rule_core
+
+let uninterp_scope_eq_weak s1 s2 = match s1, s2 with
+| UninterpScope s1, UninterpScope s2 -> String.equal s1 s2
+| UninterpSingle s1, UninterpSingle s2 -> false
+| (UninterpSingle _ | UninterpScope _), _ -> false
+
+module ScopeOrd =
+  struct
+    type t = scope_name option
+    let compare = Pervasives.compare
+  end
+
+module ScopeMap = CMap.Make(ScopeOrd)
+
+let uninterp_scope_stack = ref []
+
+let push_uninterp_scope sc scopes = UninterpScope sc :: scopes
+
+let push_uninterp_scopes = List.fold_right push_uninterp_scope
+
+let make_current_uninterp_scopes (tmp_scope,scopes) =
+  Option.fold_right push_uninterp_scope tmp_scope
+    (push_uninterp_scopes scopes !uninterp_scope_stack)
+
 (* TODO: push nat_scope, z_scope, ... in scopes summary *)
 
 (* Exportation of scopes *)
 let open_scope i (_,(local,op,sc)) =
-  if Int.equal i 1 then
+  if Int.equal i 1 then begin
     scope_stack :=
-      if op then sc :: !scope_stack
-      else List.except scope_eq sc !scope_stack
+      if op then Scope sc :: !scope_stack
+      else List.except scope_eq (Scope sc) !scope_stack;
+    uninterp_scope_stack :=
+      if op then UninterpScope sc :: !uninterp_scope_stack
+      else List.except uninterp_scope_eq_weak (UninterpScope sc) !uninterp_scope_stack
+    end
 
 let cache_scope o =
   open_scope 1 o
@@ -187,7 +231,7 @@ let discharge_scope (_,(local,_,_ as o)) =
 let classify_scope (local,_,_ as o) =
   if local then Dispose else Substitute o
 
-let inScope : bool * bool * scope_elem -> obj =
+let inScope : bool * bool * scope_name -> obj =
   declare_object {(default_object "SCOPE") with
       cache_function = cache_scope;
       open_function = open_scope;
@@ -196,7 +240,7 @@ let inScope : bool * bool * scope_elem -> obj =
       classify_function = classify_scope }
 
 let open_close_scope (local,opening,sc) =
-  Lib.add_anonymous_leaf (inScope (local,opening,Scope (normalize_scope sc)))
+  Lib.add_anonymous_leaf (inScope (local,opening,normalize_scope sc))
 
 let empty_scope_stack = []
 
@@ -250,40 +294,55 @@ let find_delimiters_scope ?loc key =
     user_err ?loc ~hdr:"find_delimiters"
       (str "Unknown scope delimiting key " ++ str key ++ str ".")
 
-(* Uninterpretation tables *)
-
-type interp_rule =
-  | NotationRule of scope_name option * notation
-  | SynDefRule of KerName.t
-
 (* We define keys for glob_constr and aconstr to split the syntax entries
    according to the key of the pattern (adapted from Chet Murthy by HH) *)
 
 type key =
   | RefKey of GlobRef.t
+  | LambdaKey
+  | ProdKey
   | Oth
 
 let key_compare k1 k2 = match k1, k2 with
 | RefKey gr1, RefKey gr2 -> GlobRef.Ordered.compare gr1 gr2
-| RefKey _, Oth -> -1
-| Oth, RefKey _ -> 1
-| Oth, Oth -> 0
+| RefKey _, _ -> -1
+| _, RefKey _ -> 1
+| k1, k2 -> Pervasives.compare k1 k2
 
 module KeyOrd = struct type t = key let compare = key_compare end
 module KeyMap = Map.Make(KeyOrd)
 
-type notation_rule = interp_rule * interpretation * int option
+let keymap_add key sc interp map =
+  let oldkeymap = try ScopeMap.find sc map with Not_found -> KeyMap.empty in
+  let oldscmap = try KeyMap.find key oldkeymap with Not_found -> [] in
+  let newscmap = KeyMap.add key (interp :: oldscmap) oldkeymap in
+  ScopeMap.add sc newscmap map
 
-let keymap_add key interp map =
-  let old = try KeyMap.find key map with Not_found -> [] in
-  KeyMap.add key (interp :: old) map
+let keymap_extract keys sc map =
+  let keymap, map =
+    try ScopeMap.find sc map, ScopeMap.remove sc map
+    with Not_found -> KeyMap.empty, map in
+  let add_scope rule = (rule,None) in
+  List.map_append (fun key -> try List.map add_scope (KeyMap.find key keymap) with Not_found -> []) keys, map
 
-let keymap_find key map =
-  try KeyMap.find key map
-  with Not_found -> []
+let find_with_delimiters = function
+  | None -> None
+  | Some scope ->
+      match (String.Map.find scope !scope_map).delimiters with
+        | Some key -> Some (Some key)
+        | None -> None
+
+let keymap_extract_remainder keys map =
+  ScopeMap.fold (fun sc keymap acc ->
+      match find_with_delimiters sc with
+      | None -> acc
+      | Some delim ->
+         let add_scope rule = (rule,delim) in
+         let l = List.map_append (fun key -> try List.map add_scope (KeyMap.find key keymap) with Not_found -> []) keys in
+      l @ acc) map []
 
 (* Scopes table : interpretation -> scope_name *)
-let notations_key_table = ref (KeyMap.empty : notation_rule list KeyMap.t)
+let notations_key_table = ref (ScopeMap.empty : notation_rule_core list KeyMap.t ScopeMap.t)
 
 let glob_prim_constr_key c = match DAst.get c with
   | GRef (ref, _) -> Some (canonical_gr ref)
@@ -295,12 +354,14 @@ let glob_prim_constr_key c = match DAst.get c with
   | _ -> None
 
 let glob_constr_keys c = match DAst.get c with
+  | GRef (ref,_) -> [RefKey (canonical_gr ref)]
   | GApp (c, _) ->
     begin match DAst.get c with
     | GRef (ref, _) -> [RefKey (canonical_gr ref); Oth]
     | _ -> [Oth]
     end
-  | GRef (ref,_) -> [RefKey (canonical_gr ref)]
+  | GLambda _ -> [LambdaKey]
+  | GProd _ -> [ProdKey]
   | _ -> [Oth]
 
 let cases_pattern_key c = match DAst.get c with
@@ -314,6 +375,8 @@ let notation_constr_key = function (* Rem: NApp(NRef ref,[]) stands for @ref *)
       RefKey (canonical_gr ref), Some (List.length args)
   | NRef ref -> RefKey(canonical_gr ref), None
   | NApp (_,args) -> Oth, Some (List.length args)
+  | NLambda _ | NBinderList (_,_,NLambda _,_,_) | NList (_,_,NLambda _,_,_) -> LambdaKey, None
+  | NProd _ | NBinderList (_,_,NProd _,_,_) | NList (_,_,NProd _,_,_) -> ProdKey, None
   | _ -> Oth, None
 
 (**********************************************************************)
@@ -839,19 +902,12 @@ let check_required_module ?loc sc (sp,d) =
 (* Look if some notation or numeral printer in [scope] can be used in
    the scope stack [scopes], and if yes, using delimiters or not *)
 
-let find_with_delimiters = function
-  | None -> None
-  | Some scope ->
-      match (String.Map.find scope !scope_map).delimiters with
-	| Some key -> Some (Some scope, Some key)
-	| None -> None
-
 let rec find_without_delimiters find (ntn_scope,ntn) = function
-  | Scope scope :: scopes ->
+  | UninterpScope scope :: scopes ->
       (* Is the expected ntn/numpr attached to the most recently open scope? *)
       begin match ntn_scope with
       | Some scope' when String.equal scope scope' ->
-	Some (None,None)
+        Some None
       | _ ->
 	(* If the most recently open scope has a notation/numeral printer
     	   but not the expected one then we need delimiters *)
@@ -860,13 +916,14 @@ let rec find_without_delimiters find (ntn_scope,ntn) = function
 	else
 	  find_without_delimiters find (ntn_scope,ntn) scopes
       end
-  | SingleNotation ntn' :: scopes ->
+  | UninterpSingle (NotationRule (_,ntn'),_,_) :: scopes ->
       begin match ntn_scope, ntn with
       | None, Some ntn when notation_eq ntn ntn' ->
-	Some (None, None)
+        Some None
       | _ ->
 	find_without_delimiters find (ntn_scope,ntn) scopes
       end
+  | UninterpSingle (SynDefRule _,_,_) :: scopes -> find_without_delimiters find (ntn_scope,ntn) scopes
   | [] ->
       (* Can we switch to [scope]? Yes if it has defined delimiters *)
       find_with_delimiters ntn_scope
@@ -902,9 +959,19 @@ let declare_notation_interpretation ntn scopt pat df ~onlyprint =
   | Some _ -> ()
   end
 
+let scope_of_rule = function
+  | NotationRule (None,_) | SynDefRule _ -> None
+  | NotationRule (Some sc as sco,_) -> sco
+
+let uninterp_scope_to_add pat n = function
+  | NotationRule (None,_) | SynDefRule _ as rule -> Some (UninterpSingle (rule,pat,n))
+  | NotationRule (Some sc,_) -> None
+
 let declare_uninterpretation rule (metas,c as pat) =
   let (key,n) = notation_constr_key c in
-  notations_key_table := keymap_add key (rule,pat,n) !notations_key_table
+  let sc = scope_of_rule rule in
+  notations_key_table := keymap_add key sc (rule,pat,n) !notations_key_table;
+  uninterp_scope_stack := Option.List.cons (uninterp_scope_to_add pat n rule) !uninterp_scope_stack
 
 let rec find_interpretation ntn find = function
   | [] -> raise Not_found
@@ -982,43 +1049,27 @@ let interp_notation ?loc ntn local_scopes =
     user_err ?loc 
     (str "Unknown interpretation for notation " ++ pr_notation ntn ++ str ".")
 
-let sort_notations scopes l =
-  let extract_scope l = function
-    | Scope sc -> List.partitioni (fun _i x ->
-                      match x with
-                      | NotationRule (Some sc',_),_,_ -> String.equal sc sc'
-                      | _ -> false) l
-    | SingleNotation ntn -> List.partitioni (fun _i x ->
-                      match x with
-                      | NotationRule (None,ntn'),_,_ -> notation_eq ntn ntn'
-                      | _ -> false) l in
-  let rec aux l scopes =
-    if l == [] then [] (* shortcut *) else
-    match scopes with
-    | sc :: scopes -> let ntn_in_sc,l = extract_scope l sc in ntn_in_sc @ aux l scopes
-    | [] -> l in
-  aux l scopes
+let extract_notations scopes keys =
+  if keys == [] then [] (* shortcut *) else
+  let rec aux scopes map =
+  match scopes with
+  | UninterpScope sc :: scopes ->
+      let l, map = keymap_extract keys (Some sc) map in l @ aux scopes map
+  | UninterpSingle rule :: scopes -> (rule,None) :: aux scopes map
+  | [] -> keymap_extract_remainder keys map
+  in aux scopes !notations_key_table
 
 let uninterp_notations scopes c =
-  let scopes = make_current_scopes scopes in
-  let keys = glob_constr_keys c in
-  let maps = List.map_append (fun key -> keymap_find key !notations_key_table) keys in
-  sort_notations scopes maps
+  let scopes = make_current_uninterp_scopes scopes in
+  extract_notations scopes (glob_constr_keys c)
 
 let uninterp_cases_pattern_notations scopes c =
-  let scopes = make_current_scopes scopes in
-  let maps = keymap_find (cases_pattern_key c) !notations_key_table in
-  sort_notations scopes maps
+  let scopes = make_current_uninterp_scopes scopes in
+  extract_notations scopes [cases_pattern_key c]
 
 let uninterp_ind_pattern_notations scopes ind =
-  let scopes = make_current_scopes scopes in
-  let maps = keymap_find (RefKey (canonical_gr (IndRef ind))) !notations_key_table in
-  sort_notations scopes maps
-
-let availability_of_notation (ntn_scope,ntn) scopes =
-  let f scope =
-    NotationMap.mem ntn (String.Map.find scope !scope_map).notations in
-  find_without_delimiters f (ntn_scope,Some ntn) (make_current_scopes scopes)
+  let scopes = make_current_uninterp_scopes scopes in
+  extract_notations scopes [RefKey (canonical_gr (IndRef ind))]
 
 (* We support coercions from a custom entry at some level to an entry
    at some level (possibly the same), and from and to the constr entry. E.g.:
@@ -1172,8 +1223,8 @@ let availability_of_prim_token n printer_scope local_scopes =
         | _ -> false
     with Not_found -> false
   in
-  let scopes = make_current_scopes local_scopes in
-  Option.map snd (find_without_delimiters f (Some printer_scope,None) scopes)
+  let scopes = make_current_uninterp_scopes local_scopes in
+  find_without_delimiters f (Some printer_scope,None) scopes
 
 (* Miscellaneous *)
 
@@ -1209,6 +1260,14 @@ let exists_notation_in_scope scopt ntn onlyprint r =
     interpretation_eq n.not_interp r
   with Not_found -> false
 
+let exists_notation_interpretation_in_scope scopt ntn =
+  let scope = match scopt with Some s -> s | None -> default_scope in
+  try
+    let sc = String.Map.find scope !scope_map in
+    let _ = NotationMap.find ntn sc.notations in
+    true
+  with Not_found -> false
+
 let isNVar_or_NHole = function NVar _ | NHole _ -> true | _ -> false
 
 (**********************************************************************)
@@ -1690,17 +1749,18 @@ let pr_visibility prglob = function
 (* Synchronisation with reset *)
 
 let freeze _ =
- (!scope_map, !scope_stack, !arguments_scope,
+ (!scope_map, !scope_stack, !uninterp_scope_stack, !arguments_scope,
   !delimiters_map, !notations_key_table, !scope_class_map,
   !prim_token_interp_infos, !prim_token_uninterp_infos,
   !entry_coercion_map, !entry_has_global_map,
   !entry_has_ident_map)
 
-let unfreeze (scm,scs,asc,dlm,fkm,clsc,ptii,ptui,coe,globs,ids) =
+let unfreeze (scm,scs,uscs,asc,dlm,fkm,clsc,ptii,ptui,coe,globs,ids) =
   scope_map := scm;
   scope_stack := scs;
-  delimiters_map := dlm;
+  uninterp_scope_stack := uscs;
   arguments_scope := asc;
+  delimiters_map := dlm;
   notations_key_table := fkm;
   scope_class_map := clsc;
   prim_token_interp_infos := ptii;
@@ -1711,8 +1771,9 @@ let unfreeze (scm,scs,asc,dlm,fkm,clsc,ptii,ptui,coe,globs,ids) =
 
 let init () =
   init_scope_map ();
+  uninterp_scope_stack := [];
   delimiters_map := String.Map.empty;
-  notations_key_table := KeyMap.empty;
+  notations_key_table := ScopeMap.empty;
   scope_class_map := initial_scope_class_map;
   prim_token_interp_infos := String.Map.empty;
   prim_token_uninterp_infos := GlobRef.Map.empty
diff --git a/interp/notation.mli b/interp/notation.mli
index 40b7f2c2c9..8cc69f4d1b 100644
--- a/interp/notation.mli
+++ b/interp/notation.mli
@@ -211,18 +211,27 @@ val declare_uninterpretation : interp_rule -> interpretation -> unit
 val interp_notation : ?loc:Loc.t -> notation -> subscopes ->
       interpretation * (notation_location * scope_name option)
 
-type notation_rule = interp_rule * interpretation * int option
+type notation_rule_core =
+    interp_rule (* kind of notation *)
+  * interpretation (* pattern associated to the notation *)
+  * int option (* number of expected arguments *)
+
+type notation_rule =
+    notation_rule_core
+  * delimiters option (* delimiter to possibly add *)
 
 (** Return the possible notations for a given term *)
 val uninterp_notations : subscopes -> 'a glob_constr_g -> notation_rule list
 val uninterp_cases_pattern_notations : subscopes -> 'a cases_pattern_g -> notation_rule list
 val uninterp_ind_pattern_notations : subscopes -> inductive -> notation_rule list
 
+(*
 (** Test if a notation is available in the scopes 
    context [scopes]; if available, the result is not None; the first 
    argument is itself not None if a delimiters is needed *)
 val availability_of_notation : scope_name option * notation -> subscopes ->
   (scope_name option * delimiters option) option
+ *)
 
 (** {6 Miscellaneous} *)
 
@@ -233,6 +242,9 @@ val interp_notation_as_global_reference : ?loc:Loc.t -> (GlobRef.t -> bool) ->
 val exists_notation_in_scope : scope_name option -> notation ->
       bool -> interpretation -> bool
 
+(** Checks for already existing notations *)
+val exists_notation_interpretation_in_scope : scope_name option -> notation -> bool
+
 (** Declares and looks for scopes associated to arguments of a global ref *)
 val declare_arguments_scope :
   bool (** true=local *) -> GlobRef.t -> scope_name option list -> unit