Factor out common code in numeral/string notations

As per https://github.com/coq/coq/pull/8965#issuecomment-441440779

2 files changed, 124 insertions, 206 deletions

diff --git a/interp/notation.ml b/interp/notation.ml
index b6322c7441..6a305c24af 100644
--- a/interp/notation.ml
+++ b/interp/notation.ml
@@ -395,12 +395,11 @@ let prim_token_uninterpreters =
 
 (*******************************************************)
 (* Numeral notation interpretation                     *)
-type numeral_or_string_notation_error =
+type prim_token_notation_error =
   | UnexpectedTerm of Constr.t
   | UnexpectedNonOptionTerm of Constr.t
 
-exception NumeralNotationError of Environ.env * Evd.evar_map * numeral_or_string_notation_error
-exception StringNotationError of Environ.env * Evd.evar_map * numeral_or_string_notation_error
+exception PrimTokenNotationError of string * Environ.env * Evd.evar_map * prim_token_notation_error
 
 type numnot_option =
   | Nop
@@ -425,27 +424,21 @@ type string_target_kind =
   | Byte
 
 type option_kind = Option | Direct
-type conversion_kind = target_kind * option_kind
-type string_conversion_kind = string_target_kind * option_kind
+type 'target conversion_kind = 'target * option_kind
 
-type numeral_notation_obj =
-  { to_kind : conversion_kind;
+type ('target, 'warning) prim_token_notation_obj =
+  { to_kind : 'target conversion_kind;
     to_ty : GlobRef.t;
-    of_kind : conversion_kind;
+    of_kind : 'target conversion_kind;
     of_ty : GlobRef.t;
-    num_ty : Libnames.qualid; (* for warnings / error messages *)
-    warning : numnot_option }
+    ty_name : Libnames.qualid; (* for warnings / error messages *)
+    warning : 'warning }
 
-type string_notation_obj =
-  { sto_kind : string_conversion_kind;
-    sto_ty : GlobRef.t;
-    sof_kind : string_conversion_kind;
-    sof_ty : GlobRef.t;
-    string_ty : Libnames.qualid (* for warnings / error messages *) }
-
-module Numeral = struct
-(** * Numeral notation *)
+type numeral_notation_obj = (target_kind, numnot_option) prim_token_notation_obj
+type string_notation_obj = (string_target_kind, unit) prim_token_notation_obj
 
+module PrimTokenNotation = struct
+(** * Code shared between Numeral notation and String notation *)
 (** Reduction
 
     The constr [c] below isn't necessarily well-typed, since we
@@ -474,7 +467,69 @@ let eval_constr env sigma (c : Constr.t) =
 let eval_constr_app env sigma c1 c2 =
   eval_constr env sigma (mkApp (c1,[| c2 |]))
 
-exception NotANumber
+exception NotAValidPrimToken
+
+(** The uninterp function below work at the level of [glob_constr]
+    which is too low for us here. So here's a crude conversion back
+    to [constr] for the subset that concerns us. *)
+
+let rec constr_of_glob env sigma g = match DAst.get g with
+  | Glob_term.GRef (ConstructRef c, _) ->
+      let sigma,c = Evd.fresh_constructor_instance env sigma c in
+      sigma,mkConstructU c
+  | Glob_term.GApp (gc, gcl) ->
+      let sigma,c = constr_of_glob env sigma gc in
+      let sigma,cl = List.fold_left_map (constr_of_glob env) sigma gcl in
+      sigma,mkApp (c, Array.of_list cl)
+  | _ ->
+      raise NotAValidPrimToken
+
+let rec glob_of_constr token_kind ?loc env sigma c = match Constr.kind c with
+  | App (c, ca) ->
+      let c = glob_of_constr token_kind ?loc env sigma c in
+      let cel = List.map (glob_of_constr token_kind ?loc env sigma) (Array.to_list ca) in
+      DAst.make ?loc (Glob_term.GApp (c, cel))
+  | Construct (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstructRef c, None))
+  | Const (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstRef c, None))
+  | Ind (ind, _) -> DAst.make ?loc (Glob_term.GRef (IndRef ind, None))
+  | Var id -> DAst.make ?loc (Glob_term.GRef (VarRef id, None))
+  | _ -> Loc.raise ?loc (PrimTokenNotationError(token_kind,env,sigma,UnexpectedTerm c))
+
+let no_such_prim_token uninterpreted_token_kind ?loc ty =
+  CErrors.user_err ?loc
+   (str ("Cannot interpret this "^uninterpreted_token_kind^" as a value of type ") ++
+    pr_qualid ty)
+
+let interp_option uninterpreted_token_kind token_kind ty ?loc env sigma c =
+  match Constr.kind c with
+  | App (_Some, [| _; c |]) -> glob_of_constr token_kind ?loc env sigma c
+  | App (_None, [| _ |]) -> no_such_prim_token uninterpreted_token_kind ?loc ty
+  | x -> Loc.raise ?loc (PrimTokenNotationError(token_kind,env,sigma,UnexpectedNonOptionTerm c))
+
+let uninterp_option c =
+  match Constr.kind c with
+  | App (_Some, [| _; x |]) -> x
+  | _ -> raise NotAValidPrimToken
+
+let uninterp to_raw o (Glob_term.AnyGlobConstr n) =
+  let env = Global.env () in
+  let sigma = Evd.from_env env in
+  let sigma,of_ty = Evd.fresh_global env sigma o.of_ty in
+  let of_ty = EConstr.Unsafe.to_constr of_ty in
+  try
+    let sigma,n = constr_of_glob env sigma n in
+    let c = eval_constr_app env sigma of_ty n in
+    let c = if snd o.of_kind == Direct then c else uninterp_option c in
+    Some (to_raw (fst o.of_kind, c))
+  with
+  | Type_errors.TypeError _ | Pretype_errors.PretypeError _ -> None (* cf. eval_constr_app *)
+  | NotAValidPrimToken -> None (* all other functions except big2raw *)
+
+end
+
+module Numeral = struct
+(** * Numeral notation *)
+open PrimTokenNotation
 
 let warn_large_num =
   CWarnings.create ~name:"large-number" ~category:"numbers"
@@ -548,15 +603,15 @@ let rawnum_of_coquint c =
         | Construct ((_,n), _) (* D0 to D9 *) ->
            let () = Buffer.add_char buf (char_of_digit n) in
            of_uint_loop a buf
-        | _ -> raise NotANumber)
-    | _ -> raise NotANumber
+        | _ -> raise NotAValidPrimToken)
+    | _ -> raise NotAValidPrimToken
   in
   let buf = Buffer.create 64 in
   let () = of_uint_loop c buf in
   if Int.equal (Buffer.length buf) 0 then
     (* To avoid ambiguities between Nil and (D0 Nil), we choose
        to not display Nil alone as "0" *)
-    raise NotANumber
+    raise NotAValidPrimToken
   else Buffer.contents buf
 
 let rawnum_of_coqint c =
@@ -565,8 +620,8 @@ let rawnum_of_coqint c =
      (match Constr.kind c with
       | Construct ((_,1), _) (* Pos *) -> (rawnum_of_coquint c', true)
       | Construct ((_,2), _) (* Neg *) -> (rawnum_of_coquint c', false)
-      | _ -> raise NotANumber)
-  | _ -> raise NotANumber
+      | _ -> raise NotAValidPrimToken)
+  | _ -> raise NotAValidPrimToken
 
 
 (***********************************************************************)
@@ -596,9 +651,9 @@ let rec bigint_of_pos c = match Constr.kind c with
           | 2 -> (* xO *) Bigint.mult_2 (bigint_of_pos d)
           | n -> assert false (* no other constructor of type positive *)
           end
-      | x -> raise NotANumber
+      | x -> raise NotAValidPrimToken
       end
-  | x -> raise NotANumber
+  | x -> raise NotAValidPrimToken
 
 (** Now, [Z] from/to bigint *)
 
@@ -623,51 +678,9 @@ let bigint_of_z z = match Constr.kind z with
           | 3 -> (* Zneg *) Bigint.neg (bigint_of_pos d)
           | n -> assert false (* no other constructor of type Z *)
           end
-      | _ -> raise NotANumber
+      | _ -> raise NotAValidPrimToken
       end
-  | _ -> raise NotANumber
-
-(** The uninterp function below work at the level of [glob_constr]
-    which is too low for us here. So here's a crude conversion back
-    to [constr] for the subset that concerns us. *)
-
-let rec constr_of_glob env sigma g = match DAst.get g with
-  | Glob_term.GRef (ConstructRef c, _) ->
-      let sigma,c = Evd.fresh_constructor_instance env sigma c in
-      sigma,mkConstructU c
-  | Glob_term.GApp (gc, gcl) ->
-      let sigma,c = constr_of_glob env sigma gc in
-      let sigma,cl = List.fold_left_map (constr_of_glob env) sigma gcl in
-      sigma,mkApp (c, Array.of_list cl)
-  | _ ->
-      raise NotANumber
-
-let rec glob_of_constr ?loc env sigma c = match Constr.kind c with
-  | App (c, ca) ->
-      let c = glob_of_constr ?loc env sigma c in
-      let cel = List.map (glob_of_constr ?loc env sigma) (Array.to_list ca) in
-      DAst.make ?loc (Glob_term.GApp (c, cel))
-  | Construct (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstructRef c, None))
-  | Const (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstRef c, None))
-  | Ind (ind, _) -> DAst.make ?loc (Glob_term.GRef (IndRef ind, None))
-  | Var id -> DAst.make ?loc (Glob_term.GRef (VarRef id, None))
-  | _ -> Loc.raise ?loc (NumeralNotationError(env,sigma,UnexpectedTerm c))
-
-let no_such_number ?loc ty =
-  CErrors.user_err ?loc
-   (str "Cannot interpret this number as a value of type " ++
-    pr_qualid ty)
-
-let interp_option ty ?loc env sigma c =
-  match Constr.kind c with
-  | App (_Some, [| _; c |]) -> glob_of_constr ?loc env sigma c
-  | App (_None, [| _ |]) -> no_such_number ?loc ty
-  | x -> Loc.raise ?loc (NumeralNotationError(env,sigma,UnexpectedNonOptionTerm c))
-
-let uninterp_option c =
-  match Constr.kind c with
-  | App (_Some, [| _; x |]) -> x
-  | _ -> raise NotANumber
+  | _ -> raise NotAValidPrimToken
 
 let big2raw n =
   if Bigint.is_pos_or_zero n then (Bigint.to_string n, true)
@@ -679,13 +692,13 @@ let raw2big (n,s) =
 let interp o ?loc n =
   begin match o.warning with
   | Warning threshold when snd n && rawnum_compare (fst n) threshold >= 0 ->
-     warn_large_num o.num_ty
+     warn_large_num o.ty_name
   | _ -> ()
   end;
   let c = match fst o.to_kind with
     | Int int_ty -> coqint_of_rawnum int_ty n
     | UInt uint_ty when snd n -> coquint_of_rawnum uint_ty (fst n)
-    | UInt _ (* n <= 0 *) -> no_such_number ?loc o.num_ty
+    | UInt _ (* n <= 0 *) -> no_such_prim_token "number" ?loc o.ty_name
     | Z z_pos_ty -> z_of_bigint z_pos_ty (raw2big n)
   in
   let env = Global.env () in
@@ -694,64 +707,26 @@ let interp o ?loc n =
   let to_ty = EConstr.Unsafe.to_constr to_ty in
   match o.warning, snd o.to_kind with
   | Abstract threshold, Direct when rawnum_compare (fst n) threshold >= 0 ->
-     warn_abstract_large_num (o.num_ty,o.to_ty);
-     glob_of_constr ?loc env sigma (mkApp (to_ty,[|c|]))
+     warn_abstract_large_num (o.ty_name,o.to_ty);
+     glob_of_constr "numeral" ?loc env sigma (mkApp (to_ty,[|c|]))
   | _ ->
      let res = eval_constr_app env sigma to_ty c in
      match snd o.to_kind with
-     | Direct -> glob_of_constr ?loc env sigma res
-     | Option -> interp_option o.num_ty ?loc env sigma res
-
-let uninterp o (Glob_term.AnyGlobConstr n) =
-  let env = Global.env () in
-  let sigma = Evd.from_env env in
-  let sigma,of_ty = Evd.fresh_global env sigma o.of_ty in
-  let of_ty = EConstr.Unsafe.to_constr of_ty in
-  try
-    let sigma,n = constr_of_glob env sigma n in
-    let c = eval_constr_app env sigma of_ty n in
-    let c = if snd o.of_kind == Direct then c else uninterp_option c in
-    match fst o.of_kind with
-    | Int _ -> Some (rawnum_of_coqint c)
-    | UInt _ -> Some (rawnum_of_coquint c, true)
-    | Z _ -> Some (big2raw (bigint_of_z c))
-  with
-  | Type_errors.TypeError _ | Pretype_errors.PretypeError _ -> None (* cf. eval_constr_app *)
-  | NotANumber -> None (* all other functions except big2raw *)
+     | Direct -> glob_of_constr "numeral" ?loc env sigma res
+     | Option -> interp_option "number" "numeral" o.ty_name ?loc env sigma res
+
+let uninterp o n =
+  PrimTokenNotation.uninterp
+    begin function
+      | (Int _, c) -> rawnum_of_coqint c
+      | (UInt _, c) -> (rawnum_of_coquint c, true)
+      | (Z _, c) -> big2raw (bigint_of_z c)
+    end o n
 end
 
 module Strings = struct
 (** * String notation *)
-
-(** Reduction
-
-    The constr [c] below isn't necessarily well-typed, since we
-    built it via an [mkApp] of a conversion function on a term
-    that starts with the right constructor but might be partially
-    applied.
-
-    At least [c] is known to be evar-free, since it comes from
-    our own ad-hoc [constr_of_glob] or from conversions such
-    as [coqint_of_rawnum].
-*)
-
-let eval_constr env sigma (c : Constr.t) =
-  let c = EConstr.of_constr c in
-  let sigma,t = Typing.type_of env sigma c in
-  let c' = Vnorm.cbv_vm env sigma c t in
-  EConstr.Unsafe.to_constr c'
-
-(* For testing with "compute" instead of "vm_compute" :
-let eval_constr env sigma (c : Constr.t) =
-  let c = EConstr.of_constr c in
-  let c' = Tacred.compute env sigma c in
-  EConstr.Unsafe.to_constr c'
-*)
-
-let eval_constr_app env sigma c1 c2 =
-  eval_constr env sigma (mkApp (c1,[| c2 |]))
-
-exception NotAString
+open PrimTokenNotation
 
 let qualid_of_ref n =
   n |> Coqlib.lib_ref |> Nametab.shortest_qualid_of_global Id.Set.empty
@@ -794,7 +769,7 @@ let make_ascii_string n =
 let char_code_of_coqbyte c =
   match Constr.kind c with
   | Construct ((_,c), _) -> c - 1
-  | _ -> raise NotAString
+  | _ -> raise NotAValidPrimToken
 
 let string_of_coqbyte c = make_ascii_string (char_code_of_coqbyte c)
 
@@ -818,85 +793,34 @@ let string_of_coqlist_byte c =
     | App (_cons, [|_ty;b;c|]) ->
       let () = Buffer.add_char buf (Char.chr (char_code_of_coqbyte b)) in
       of_coqlist_byte_loop c buf
-    | _ -> raise NotAString
+    | _ -> raise NotAValidPrimToken
   in
   let buf = Buffer.create 64 in
   let () = of_coqlist_byte_loop c buf in
   Buffer.contents buf
 
-(** The uninterp function below work at the level of [glob_constr]
-    which is too low for us here. So here's a crude conversion back
-    to [constr] for the subset that concerns us. *)
-
-let rec constr_of_glob env sigma g = match DAst.get g with
-  | Glob_term.GRef (ConstructRef c, _) ->
-      let sigma,c = Evd.fresh_constructor_instance env sigma c in
-      sigma,mkConstructU c
-  | Glob_term.GApp (gc, gcl) ->
-      let sigma,c = constr_of_glob env sigma gc in
-      let sigma,cl = List.fold_left_map (constr_of_glob env) sigma gcl in
-      sigma,mkApp (c, Array.of_list cl)
-  | _ ->
-      raise NotAString
-
-let rec glob_of_constr ?loc env sigma c = match Constr.kind c with
-  | App (c, ca) ->
-      let c = glob_of_constr ?loc env sigma c in
-      let cel = List.map (glob_of_constr ?loc env sigma) (Array.to_list ca) in
-      DAst.make ?loc (Glob_term.GApp (c, cel))
-  | Construct (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstructRef c, None))
-  | Const (c, _) -> DAst.make ?loc (Glob_term.GRef (ConstRef c, None))
-  | Ind (ind, _) -> DAst.make ?loc (Glob_term.GRef (IndRef ind, None))
-  | Var id -> DAst.make ?loc (Glob_term.GRef (VarRef id, None))
-  | _ -> Loc.raise ?loc (StringNotationError(env,sigma,UnexpectedTerm c))
-
-let no_such_string ?loc ty =
-  CErrors.user_err ?loc
-   (str "Cannot interpret this string as a value of type " ++
-    pr_qualid ty)
-
-let interp_option ty ?loc env sigma c =
-  match Constr.kind c with
-  | App (_Some, [| _; c |]) -> glob_of_constr ?loc env sigma c
-  | App (_None, [| _ |]) -> no_such_string ?loc ty
-  | x -> Loc.raise ?loc (StringNotationError(env,sigma,UnexpectedNonOptionTerm c))
-
-let uninterp_option c =
-  match Constr.kind c with
-  | App (_Some, [| _; x |]) -> x
-  | _ -> raise NotAString
-
 let interp o ?loc n =
   let byte_ty = locate_byte () in
   let list_ty = locate_list () in
-  let c = match fst o.sto_kind with
+  let c = match fst o.to_kind with
     | ListByte -> coqlist_byte_of_string byte_ty list_ty n
     | Byte -> coqbyte_of_string ?loc byte_ty n
   in
   let env = Global.env () in
   let sigma = Evd.from_env env in
-  let sigma,to_ty = Evd.fresh_global env sigma o.sto_ty in
+  let sigma,to_ty = Evd.fresh_global env sigma o.to_ty in
   let to_ty = EConstr.Unsafe.to_constr to_ty in
   let res = eval_constr_app env sigma to_ty c in
-  match snd o.sto_kind with
-  | Direct -> glob_of_constr ?loc env sigma res
-  | Option -> interp_option o.string_ty ?loc env sigma res
-
-let uninterp o (Glob_term.AnyGlobConstr n) =
-  let env = Global.env () in
-  let sigma = Evd.from_env env in
-  let sigma,of_ty = Evd.fresh_global env sigma o.sof_ty in
-  let of_ty = EConstr.Unsafe.to_constr of_ty in
-  try
-    let sigma,n = constr_of_glob env sigma n in
-    let c = eval_constr_app env sigma of_ty n in
-    let c = if snd o.sof_kind == Direct then c else uninterp_option c in
-    match fst o.sof_kind with
-    | ListByte -> Some (string_of_coqlist_byte c)
-    | Byte -> Some (string_of_coqbyte c)
-  with
-  | Type_errors.TypeError _ | Pretype_errors.PretypeError _ -> None (* cf. eval_constr_app *)
-  | NotAString -> None (* all other functions except big2raw *)
+  match snd o.to_kind with
+  | Direct -> glob_of_constr "string" ?loc env sigma res
+  | Option -> interp_option "string" "string" o.ty_name ?loc env sigma res
+
+let uninterp o n =
+  PrimTokenNotation.uninterp
+    begin function
+      | (ListByte, c) -> string_of_coqlist_byte c
+      | (Byte, c) -> string_of_coqbyte c
+    end o n
 end
 
 (* A [prim_token_infos], which is synchronized with the document
diff --git a/interp/notation.mli b/interp/notation.mli
index 6880b9a2cd..c0ff1a1ac3 100644
--- a/interp/notation.mli
+++ b/interp/notation.mli
@@ -104,12 +104,11 @@ val register_string_interpretation :
 
 (** * Numeral notation *)
 
-type numeral_or_string_notation_error =
+type prim_token_notation_error =
   | UnexpectedTerm of Constr.t
   | UnexpectedNonOptionTerm of Constr.t
 
-exception NumeralNotationError of Environ.env * Evd.evar_map * numeral_or_string_notation_error
-exception StringNotationError of Environ.env * Evd.evar_map * numeral_or_string_notation_error
+exception PrimTokenNotationError of string * Environ.env * Evd.evar_map * prim_token_notation_error
 
 type numnot_option =
   | Nop
@@ -134,23 +133,18 @@ type string_target_kind =
   | Byte
 
 type option_kind = Option | Direct
-type conversion_kind = target_kind * option_kind
-type string_conversion_kind = string_target_kind * option_kind
+type 'target conversion_kind = 'target * option_kind
 
-type numeral_notation_obj =
-  { to_kind : conversion_kind;
+type ('target, 'warning) prim_token_notation_obj =
+  { to_kind : 'target conversion_kind;
     to_ty : GlobRef.t;
-    of_kind : conversion_kind;
+    of_kind : 'target conversion_kind;
     of_ty : GlobRef.t;
-    num_ty : Libnames.qualid; (* for warnings / error messages *)
-    warning : numnot_option }
-
-type string_notation_obj =
-  { sto_kind : string_conversion_kind;
-    sto_ty : GlobRef.t;
-    sof_kind : string_conversion_kind;
-    sof_ty : GlobRef.t;
-    string_ty : Libnames.qualid (* for warnings / error messages *) }
+    ty_name : Libnames.qualid; (* for warnings / error messages *)
+    warning : 'warning }
+
+type numeral_notation_obj = (target_kind, numnot_option) prim_token_notation_obj
+type string_notation_obj = (string_target_kind, unit) prim_token_notation_obj
 
 type prim_token_interp_info =
     Uid of prim_token_uid