Merge PR #8764: Add parsing of decimal constants (e.g., 1.02e+01)

Reviewed-by: Zimmi48
Reviewed-by: ejgallego
Ack-by: gares
Ack-by: herbelin
Ack-by: ppedrot
Ack-by: proux01

9 files changed, 208 insertions, 70 deletions

diff --git a/interp/constrexpr.ml b/interp/constrexpr.ml
index 757d186c8b..7a14a4e708 100644
--- a/interp/constrexpr.ml
+++ b/interp/constrexpr.ml
@@ -48,16 +48,26 @@ type abstraction_kind = AbsLambda | AbsPi
 
 type proj_flag = int option (** [Some n] = proj of the n-th visible argument *)
 
-(** Representation of integer literals that appear in Coq scripts.
-    We now use raw strings of digits in base 10 (big-endian), and a separate
-    sign flag. Note that this representation is not unique, due to possible
-    multiple leading zeros, and -0 = +0 *)
-
-type sign = bool
-type raw_natural_number = string
+(** Representation of decimal literals that appear in Coq scripts.
+   We now use raw strings following the format defined by
+   [NumTok.t] and a separate sign flag.
+
+   Note that this representation is not unique, due to possible
+   multiple leading or trailing zeros, and -0 = +0, for instances.
+   The reason to keep the numeral exactly as it was parsed is that
+   specific notations can be declared for specific numerals
+   (e.g. [Notation "0" := False], or [Notation "00" := (nil,nil)], or
+   [Notation "2e1" := ...]). Those notations, which override the
+   generic interpretation as numeral, use the same representation of
+   numeral using the Numeral constructor. So the latter should be able
+   to record the form of the numeral which exactly matches the
+   notation. *)
+
+type sign = SPlus | SMinus
+type raw_numeral = NumTok.t
 
 type prim_token =
-  | Numeral of raw_natural_number * sign
+  | Numeral of sign * raw_numeral
   | String of string
 
 type instance_expr = Glob_term.glob_level list
diff --git a/interp/constrexpr_ops.ml b/interp/constrexpr_ops.ml
index 95a0039b0a..60610b92b8 100644
--- a/interp/constrexpr_ops.ml
+++ b/interp/constrexpr_ops.ml
@@ -50,13 +50,14 @@ let names_of_local_binders bl =
 (**********************************************************************)
 (* Functions on constr_expr *)
 
-(* Note: redundant Numeral representations such as -0 and +0 (or different
-   numbers of leading zeros) are considered different here. *)
+(* Note: redundant Numeral representations, such as -0 and +0 (and others),
+   are considered different here. *)
 
 let prim_token_eq t1 t2 = match t1, t2 with
-| Numeral (n1,s1), Numeral (n2,s2) -> String.equal n1 n2 && s1 == s2
+| Numeral (SPlus,n1), Numeral (SPlus,n2)
+| Numeral (SMinus,n1), Numeral (SMinus,n2) -> NumTok.equal n1 n2
 | String s1, String s2 -> String.equal s1 s2
-| _ -> false
+| (Numeral ((SPlus|SMinus),_) | String _), _ -> false
 
 let explicitation_eq ex1 ex2 = match ex1, ex2 with
 | ExplByPos (i1, id1), ExplByPos (i2, id2) ->
diff --git a/interp/constrextern.ml b/interp/constrextern.ml
index c2afa097bb..24b1362e6d 100644
--- a/interp/constrextern.ml
+++ b/interp/constrextern.ml
@@ -318,29 +318,28 @@ let drop_implicits_in_patt cst nb_expl args =
 let destPrim = function { CAst.v = CPrim t } -> Some t | _ -> None
 let destPatPrim = function { CAst.v = CPatPrim t } -> Some t | _ -> None
 
-let is_number s =
-  let rec aux i =
-    Int.equal (String.length s) i ||
-    match s.[i] with '0'..'9' -> aux (i+1) | _ -> false
-  in aux 0
-
 let is_zero s =
   let rec aux i =
     Int.equal (String.length s) i || (s.[i] == '0' && aux (i+1))
   in aux 0
+let is_zero n = is_zero n.NumTok.int && is_zero n.NumTok.frac
 
 let make_notation_gen loc ntn mknot mkprim destprim l bl =
   match snd ntn,List.map destprim l with
     (* Special case to avoid writing "- 3" for e.g. (Z.opp 3) *)
-    | "- _", [Some (Numeral (p,true))] when not (is_zero p) ->
+    | "- _", [Some (Numeral (SPlus,p))] when not (is_zero p) ->
         assert (bl=[]);
         mknot (loc,ntn,([mknot (loc,(InConstrEntrySomeLevel,"( _ )"),l,[])]),[])
     | _ ->
 	match decompose_notation_key ntn, l with
-        | (InConstrEntrySomeLevel,[Terminal "-"; Terminal x]), [] when is_number x ->
-	   mkprim (loc, Numeral (x,false))
-        | (InConstrEntrySomeLevel,[Terminal x]), [] when is_number x ->
-	   mkprim (loc, Numeral (x,true))
+        | (InConstrEntrySomeLevel,[Terminal "-"; Terminal x]), [] ->
+           begin match NumTok.of_string x with
+           | Some n -> mkprim (loc, Numeral (SMinus,n))
+           | None -> mknot (loc,ntn,l,bl) end
+        | (InConstrEntrySomeLevel,[Terminal x]), [] ->
+           begin match NumTok.of_string x with
+           | Some n -> mkprim (loc, Numeral (SPlus,n))
+           | None -> mknot (loc,ntn,l,bl) end
         | _ -> mknot (loc,ntn,l,bl)
 
 let make_notation loc ntn (terms,termlists,binders,binderlists as subst) =
@@ -969,7 +968,7 @@ let rec extern inctx (custom,scopes as allscopes) vars r =
       CCast (sub_extern true scopes vars c,
              map_cast_type (extern_typ scopes vars) c')
   | GInt i ->
-     CPrim(Numeral (Uint63.to_string i,true))
+     CPrim(Numeral (SPlus, NumTok.int (Uint63.to_string i)))
 
   in insert_coercion coercion (CAst.make ?loc c)
 
diff --git a/interp/constrintern.ml b/interp/constrintern.ml
index 7a3e9881ea..59feb46dc1 100644
--- a/interp/constrintern.ml
+++ b/interp/constrintern.ml
@@ -1487,8 +1487,9 @@ let alias_of als = match als.alias_ids with
 
 let is_zero s =
   let rec aux i =
-    Int.equal (String.length s) i || (s.[i] == '0' && aux (i+1))
+    Int.equal (String.length s) i || ((s.[i] == '0' || s.[i] == '_') && aux (i+1))
   in aux 0
+let is_zero n = is_zero n.NumTok.int && is_zero n.NumTok.frac
 
 let merge_subst s1 s2 = Id.Map.fold Id.Map.add s1 s2
 
@@ -1513,11 +1514,11 @@ let rec subst_pat_iterator y t = DAst.(map (function
   | RCPatOr pl -> RCPatOr (List.map (subst_pat_iterator y t) pl)))
 
 let is_non_zero c = match c with
-| { CAst.v = CPrim (Numeral (p, true)) } -> not (is_zero p)
+| { CAst.v = CPrim (Numeral (SPlus, p)) } -> not (is_zero p)
 | _ -> false
 
 let is_non_zero_pat c = match c with
-| { CAst.v = CPatPrim (Numeral (p, true)) } -> not (is_zero p)
+| { CAst.v = CPatPrim (Numeral (SPlus, p)) } -> not (is_zero p)
 | _ -> false
 
 let get_asymmetric_patterns = Goptions.declare_bool_option_and_ref
@@ -1628,8 +1629,8 @@ let drop_notations_pattern looked_for genv =
         let (argscs1,_) = find_remaining_scopes expl_pl pl g in
         DAst.make ?loc @@ RCPatCstr (g, List.map2 (in_pat_sc scopes) argscs1 expl_pl @ List.map (in_pat false scopes) pl, [])
     | CPatNotation ((InConstrEntrySomeLevel,"- _"),([a],[]),[]) when is_non_zero_pat a ->
-      let p = match a.CAst.v with CPatPrim (Numeral (p, _)) -> p | _ -> assert false in
-      let pat, _df = Notation.interp_prim_token_cases_pattern_expr ?loc (ensure_kind false loc) (Numeral (p,false)) scopes in
+      let p = match a.CAst.v with CPatPrim (Numeral (_, p)) -> p | _ -> assert false in
+      let pat, _df = Notation.interp_prim_token_cases_pattern_expr ?loc (ensure_kind false loc) (Numeral (SMinus,p)) scopes in
       rcp_of_glob scopes pat
     | CPatNotation ((InConstrEntrySomeLevel,"( _ )"),([a],[]),[]) ->
       in_pat top scopes a
@@ -1944,8 +1945,8 @@ let internalize globalenv env pattern_mode (_, ntnvars as lvar) c =
         GLetIn (na.CAst.v, inc1, int,
           intern (push_name_env ntnvars (impls_term_list inc1) env na) c2)
     | CNotation ((InConstrEntrySomeLevel,"- _"), ([a],[],[],[])) when is_non_zero a ->
-      let p = match a.CAst.v with CPrim (Numeral (p, _)) -> p | _ -> assert false in
-       intern env (CAst.make ?loc @@ CPrim (Numeral (p,false)))
+      let p = match a.CAst.v with CPrim (Numeral (_, p)) -> p | _ -> assert false in
+       intern env (CAst.make ?loc @@ CPrim (Numeral (SMinus,p)))
     | CNotation ((InConstrEntrySomeLevel,"( _ )"),([a],[],[],[])) -> intern env a
     | CNotation (ntn,args) ->
         intern_notation intern env ntnvars loc ntn args
diff --git a/interp/interp.mllib b/interp/interp.mllib
index 147eaf20dc..1262dbb181 100644
--- a/interp/interp.mllib
+++ b/interp/interp.mllib
@@ -1,3 +1,4 @@
+NumTok
 Constrexpr
 Tactypes
 Stdarg
diff --git a/interp/notation.ml b/interp/notation.ml
index 2765661749..b9aca82cf4 100644
--- a/interp/notation.ml
+++ b/interp/notation.ml
@@ -476,7 +476,7 @@ let notation_constr_key = function (* Rem: NApp(NRef ref,[]) stands for @ref *)
 (* Interpreting numbers (not in summary because functional objects)   *)
 
 type required_module = full_path * string list
-type rawnum = Constrexpr.raw_natural_number * Constrexpr.sign
+type rawnum = Constrexpr.sign * Constrexpr.raw_numeral
 
 type prim_token_uid = string
 
@@ -499,15 +499,20 @@ module InnerPrimToken = struct
     | StringInterp f, StringInterp f' -> f == f'
     | _ -> false
 
-  let ofNumeral n s =
-    if s then Bigint.of_string n else Bigint.neg (Bigint.of_string n)
+  let ofNumeral s n =
+    let n = String.(concat "" (split_on_char '_' n)) in
+    match s with
+    | SPlus -> Bigint.of_string n
+    | SMinus -> Bigint.neg (Bigint.of_string n)
 
   let do_interp ?loc interp primtok =
     match primtok, interp with
-    | Numeral (n,s), RawNumInterp interp -> interp ?loc (n,s)
-    | Numeral (n,s), BigNumInterp interp -> interp ?loc (ofNumeral n s)
+    | Numeral (s,n), RawNumInterp interp -> interp ?loc (s,n)
+    | Numeral (s,{ NumTok.int = n; frac = ""; exp = "" }),
+      BigNumInterp interp -> interp ?loc (ofNumeral s n)
     | String s, StringInterp interp -> interp ?loc s
-    | _ -> raise Not_found
+    | (Numeral _ | String _),
+      (RawNumInterp _ | BigNumInterp _ | StringInterp _) -> raise Not_found
 
   type uninterpreter =
     | RawNumUninterp of (any_glob_constr -> rawnum option)
@@ -521,15 +526,17 @@ module InnerPrimToken = struct
     | _ -> false
 
   let mkNumeral n =
-    if Bigint.is_pos_or_zero n then Numeral (Bigint.to_string n, true)
-    else Numeral (Bigint.to_string (Bigint.neg n), false)
+    if Bigint.is_pos_or_zero n then
+      Numeral (SPlus,NumTok.int (Bigint.to_string n))
+    else
+      Numeral (SMinus,NumTok.int (Bigint.to_string (Bigint.neg n)))
 
   let mkString = function
     | None -> None
     | Some s -> if Unicode.is_utf8 s then Some (String s) else None
 
   let do_uninterp uninterp g = match uninterp with
-    | RawNumUninterp u -> Option.map (fun (n,s) -> Numeral (n,s)) (u g)
+    | RawNumUninterp u -> Option.map (fun (s,n) -> Numeral (s,n)) (u g)
     | BigNumUninterp u -> Option.map mkNumeral (u g)
     | StringUninterp u -> mkString (u g)
 
@@ -559,8 +566,8 @@ exception PrimTokenNotationError of string * Environ.env * Evd.evar_map * prim_t
 
 type numnot_option =
   | Nop
-  | Warning of raw_natural_number
-  | Abstract of raw_natural_number
+  | Warning of string
+  | Abstract of string
 
 type int_ty =
   { uint : Names.inductive;
@@ -570,11 +577,16 @@ type z_pos_ty =
   { z_ty : Names.inductive;
     pos_ty : Names.inductive }
 
+type decimal_ty =
+  { int : int_ty;
+    decimal : Names.inductive }
+
 type target_kind =
   | Int of int_ty (* Coq.Init.Decimal.int + uint *)
   | UInt of Names.inductive (* Coq.Init.Decimal.uint *)
   | Z of z_pos_ty (* Coq.Numbers.BinNums.Z and positive *)
   | Int63 (* Coq.Numbers.Cyclic.Int63.Int63.int *)
+  | Decimal of decimal_ty (* Coq.Init.Decimal.decimal + uint + int *)
 
 type string_target_kind =
   | ListByte
@@ -760,15 +772,29 @@ let coquint_of_rawnum uint str =
   let nil = mkConstruct (uint,1) in
   let rec do_chars s i acc =
     if i < 0 then acc
-    else
+    else if s.[i] == '_' then do_chars s (i-1) acc else
       let dg = mkConstruct (uint, digit_of_char s.[i]) in
       do_chars s (i-1) (mkApp(dg,[|acc|]))
   in
   do_chars str (String.length str - 1) nil
 
-let coqint_of_rawnum inds (str,sign) =
+let coqint_of_rawnum inds sign str =
   let uint = coquint_of_rawnum inds.uint str in
-  mkApp (mkConstruct (inds.int, if sign then 1 else 2), [|uint|])
+  let pos_neg = match sign with SPlus -> 1 | SMinus -> 2 in
+  mkApp (mkConstruct (inds.int, pos_neg), [|uint|])
+
+let coqdecimal_of_rawnum inds sign n =
+  let i, f, e = NumTok.(n.int, n.frac, n.exp) in
+  let i = coqint_of_rawnum inds.int sign i in
+  let f = coquint_of_rawnum inds.int.uint f in
+  if e = "" then mkApp (mkConstruct (inds.decimal, 1), [|i; f|])  (* Decimal *)
+  else
+    let sign, e = match e.[1] with
+      | '-' -> SMinus, String.sub e 2 (String.length e - 2)
+      | '+' -> SPlus, String.sub e 2 (String.length e - 2)
+      | _ -> SPlus, String.sub e 1 (String.length e - 1) in
+    let e = coqint_of_rawnum inds.int sign e in
+    mkApp (mkConstruct (inds.decimal, 2), [|i; f; e|])  (* DecimalExp *)
 
 let rawnum_of_coquint c =
   let rec of_uint_loop c buf =
@@ -788,17 +814,30 @@ let rawnum_of_coquint c =
     (* To avoid ambiguities between Nil and (D0 Nil), we choose
        to not display Nil alone as "0" *)
     raise NotAValidPrimToken
-  else Buffer.contents buf
+  else NumTok.int (Buffer.contents buf)
 
 let rawnum_of_coqint c =
   match Constr.kind c with
   | App (c,[|c'|]) ->
      (match Constr.kind c with
-      | Construct ((_,1), _) (* Pos *) -> (rawnum_of_coquint c', true)
-      | Construct ((_,2), _) (* Neg *) -> (rawnum_of_coquint c', false)
+      | Construct ((_,1), _) (* Pos *) -> (SPlus, rawnum_of_coquint c')
+      | Construct ((_,2), _) (* Neg *) -> (SMinus, rawnum_of_coquint c')
       | _ -> raise NotAValidPrimToken)
   | _ -> raise NotAValidPrimToken
 
+let rawnum_of_decimal c =
+  let of_ife i f e =
+    let sign, n = rawnum_of_coqint i in
+    let f =
+      try (rawnum_of_coquint f).NumTok.int with NotAValidPrimToken -> "" in
+    let e = match e with None -> "" | Some e -> match rawnum_of_coqint e with
+      | SPlus, e -> "e+" ^ e.NumTok.int
+      | SMinus, e -> "e-" ^ e.NumTok.int in
+    sign,{ n with NumTok.frac = f; exp = e } in
+  match Constr.kind c with
+  | App (_,[|i; f|]) -> of_ife i f None
+  | App (_,[|i; f; e|]) -> of_ife i f (Some e)
+  | _ -> raise NotAValidPrimToken
 
 (***********************************************************************)
 
@@ -885,31 +924,42 @@ let bigint_of_int63 c =
   | _ -> raise NotAValidPrimToken
 
 let big2raw n =
-  if Bigint.is_pos_or_zero n then (Bigint.to_string n, true)
-  else (Bigint.to_string (Bigint.neg n), false)
+  if Bigint.is_pos_or_zero n then
+    (SPlus, NumTok.int (Bigint.to_string n))
+  else
+    (SMinus, NumTok.int (Bigint.to_string (Bigint.neg n)))
 
-let raw2big (n,s) =
-  if s then Bigint.of_string n else Bigint.neg (Bigint.of_string n)
+let raw2big s n = match s with
+  | SPlus -> Bigint.of_string n
+  | SMinus -> Bigint.neg (Bigint.of_string n)
 
 let interp o ?loc n =
-  begin match o.warning with
-  | Warning threshold when snd n && rawnum_compare (fst n) threshold >= 0 ->
+  begin match o.warning, n with
+  | Warning threshold, (SPlus, { NumTok.int = n; frac = ""; exp = "" })
+       when rawnum_compare n threshold >= 0 ->
      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_prim_token "number" ?loc o.ty_name
-    | Z z_pos_ty -> z_of_bigint z_pos_ty (raw2big n)
-    | Int63 -> interp_int63 ?loc (raw2big n)
+  let c = match fst o.to_kind, n with
+    | Int int_ty, (s, { NumTok.int = n; frac = ""; exp = "" }) ->
+       coqint_of_rawnum int_ty s n
+    | UInt uint_ty, (SPlus, { NumTok.int = n; frac = ""; exp = "" }) ->
+       coquint_of_rawnum uint_ty n
+    | Z z_pos_ty, (s, { NumTok.int = n; frac = ""; exp = "" }) ->
+       z_of_bigint z_pos_ty (raw2big s n)
+    | Int63, (s, { NumTok.int = n; frac = ""; exp = "" }) ->
+       interp_int63 ?loc (raw2big s n)
+    | (Int _ | UInt _ | Z _ | Int63), _ ->
+       no_such_prim_token "number" ?loc o.ty_name
+    | Decimal decimal_ty, (s,n) -> coqdecimal_of_rawnum decimal_ty s n
   in
   let env = Global.env () in
   let sigma = Evd.from_env env in
   let sigma,to_ty = Evd.fresh_global env sigma o.to_ty in
   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 ->
+  | Abstract threshold, Direct
+       when rawnum_compare (snd n).NumTok.int threshold >= 0 ->
      warn_abstract_large_num (o.ty_name,o.to_ty);
      glob_of_constr "numeral" ?loc env sigma (mkApp (to_ty,[|c|]))
   | _ ->
@@ -922,9 +972,10 @@ let uninterp o n =
   PrimTokenNotation.uninterp
     begin function
       | (Int _, c) -> rawnum_of_coqint c
-      | (UInt _, c) -> (rawnum_of_coquint c, true)
+      | (UInt _, c) -> (SPlus, rawnum_of_coquint c)
       | (Z _, c) -> big2raw (bigint_of_z c)
       | (Int63, c) -> big2raw (bigint_of_int63 c)
+      | (Decimal _, c) -> rawnum_of_decimal c
     end o n
 end
 
@@ -1249,8 +1300,8 @@ let find_notation ntn sc =
   (n.not_interp, n.not_location)
 
 let notation_of_prim_token = function
-  | Numeral (n,true) -> InConstrEntrySomeLevel, n
-  | Numeral (n,false) -> InConstrEntrySomeLevel, "- "^n
+  | Numeral (SPlus,n) -> InConstrEntrySomeLevel, NumTok.to_string n
+  | Numeral (SMinus,n) -> InConstrEntrySomeLevel, "- "^NumTok.to_string n
   | String _ -> raise Not_found
 
 let find_prim_token check_allowed ?loc p sc =
diff --git a/interp/notation.mli b/interp/notation.mli
index 5dcc96dc29..57e2be16b9 100644
--- a/interp/notation.mli
+++ b/interp/notation.mli
@@ -70,14 +70,14 @@ val find_delimiters_scope : ?loc:Loc.t -> delimiters -> scope_name
 
 (** {6 Declare and uses back and forth an interpretation of primitive token } *)
 
-(** A numeral interpreter is the pair of an interpreter for **integer**
+(** A numeral interpreter is the pair of an interpreter for **decimal**
    numbers in terms and an optional interpreter in pattern, if
-   negative numbers are not supported, the interpreter must fail with
-   an appropriate error message *)
+   non integer or negative numbers are not supported, the interpreter
+   must fail with an appropriate error message *)
 
 type notation_location = (DirPath.t * DirPath.t) * string
 type required_module = full_path * string list
-type rawnum = Constrexpr.raw_natural_number * Constrexpr.sign
+type rawnum = Constrexpr.sign * Constrexpr.raw_numeral
 
 (** The unique id string below will be used to refer to a particular
     registered interpreter/uninterpreter of numeral or string notation.
@@ -112,8 +112,8 @@ exception PrimTokenNotationError of string * Environ.env * Evd.evar_map * prim_t
 
 type numnot_option =
   | Nop
-  | Warning of raw_natural_number
-  | Abstract of raw_natural_number
+  | Warning of string
+  | Abstract of string
 
 type int_ty =
   { uint : Names.inductive;
@@ -123,11 +123,16 @@ type z_pos_ty =
   { z_ty : Names.inductive;
     pos_ty : Names.inductive }
 
+type decimal_ty =
+  { int : int_ty;
+    decimal : Names.inductive }
+
 type target_kind =
   | Int of int_ty (* Coq.Init.Decimal.int + uint *)
   | UInt of Names.inductive (* Coq.Init.Decimal.uint *)
   | Z of z_pos_ty (* Coq.Numbers.BinNums.Z and positive *)
   | Int63 (* Coq.Numbers.Cyclic.Int63.Int63.int *)
+  | Decimal of decimal_ty (* Coq.Init.Decimal.decimal + uint + int *)
 
 type string_target_kind =
   | ListByte
diff --git a/interp/numTok.ml b/interp/numTok.ml
new file mode 100644
index 0000000000..8f2004b889
--- /dev/null
+++ b/interp/numTok.ml
@@ -0,0 +1,52 @@
+type t = {
+  int : string;
+  frac : string;
+  exp : string
+}
+
+let equal n1 n2 =
+  String.(equal n1.int n2.int && equal n1.frac n2.frac && equal n1.exp n2.exp)
+
+let int s = { int = s; frac = ""; exp = "" }
+
+let to_string n = n.int ^ (if n.frac = "" then "" else "." ^ n.frac) ^ n.exp
+
+let parse =
+  let buff = ref (Bytes.create 80) in
+  let store len x =
+    let open Bytes in
+    if len >= length !buff then
+      buff := cat !buff (create (length !buff));
+    set !buff len x;
+    succ len in
+  let get_buff len = Bytes.sub_string !buff 0 len in
+  (* reads [0-9_]* *)
+  let rec number len s = match Stream.peek s with
+    | Some (('0'..'9' | '_') as c) -> Stream.junk s; number (store len c) s
+    | _ -> len in
+  fun s ->
+  let i = get_buff (number 0 s) in
+  let f =
+    match Stream.npeek 2 s with
+    | '.' :: (('0'..'9' | '_') as c) :: _ ->
+       Stream.junk s; Stream.junk s; get_buff (number (store 0 c) s)
+    | _ -> "" in
+  let e =
+    match (Stream.npeek 2 s) with
+    | (('e'|'E') as e) :: ('0'..'9' as c) :: _ ->
+       Stream.junk s; Stream.junk s; get_buff (number (store (store 0 e) c) s)
+    | (('e'|'E') as e) :: (('+'|'-') as sign) :: _ ->
+       begin match Stream.npeek 3 s with
+       | _ :: _ :: ('0'..'9' as c) :: _ ->
+          Stream.junk s; Stream.junk s; Stream.junk s;
+          get_buff (number (store (store (store 0 e) sign) c) s)
+       | _ -> ""
+       end
+    | _ -> "" in
+  { int = i; frac = f; exp = e }
+
+let of_string s =
+  if s = "" || s.[0] < '0' || s.[0] > '9' then None else
+    let strm = Stream.of_string (s ^ "  ") in
+    let n = parse strm in
+    if Stream.count strm >= String.length s then Some n else None
diff --git a/interp/numTok.mli b/interp/numTok.mli
new file mode 100644
index 0000000000..0b6a877cbd
--- /dev/null
+++ b/interp/numTok.mli
@@ -0,0 +1,18 @@
+type t = {
+  int : string;  (** \[0-9\]\[0-9_\]* *)
+  frac : string;  (** empty or \[0-9_\]+ *)
+  exp : string  (** empty or \[eE\]\[+-\]?\[0-9\]\[0-9_\]* *)
+}
+
+val equal : t -> t -> bool
+
+(** [int s] amounts to [\{ int = s; frac = ""; exp = "" \}] *)
+val int : string -> t
+
+val to_string : t -> string
+
+val of_string : string -> t option
+
+(** Precondition: the first char on the stream is a digit (\[0-9\]).
+    Precondition: at least two extra chars after the numeral to parse. *)
+val parse : char Stream.t -> t