diff --git a/stdlib/bytes.ml b/stdlib/bytes.ml
index 092f8c8f0..cfcd1ec05 100644
--- a/stdlib/bytes.ml
+++ b/stdlib/bytes.ml
@@ -164,7 +164,15 @@ let map f s =
   let l = length s in
   if l = 0 then s else begin
     let r = create l in
-    for i = 0 to l - 1 do unsafe_set r i (f(unsafe_get s i)) done;
+    for i = 0 to l - 1 do unsafe_set r i (f (unsafe_get s i)) done;
+    r
+  end
+
+let mapi f s =
+  let l = length s in
+  if l = 0 then s else begin
+    let r = create l in
+    for i = 0 to l - 1 do unsafe_set r i (f i (unsafe_get s i)) done;
     r
   end
 
diff --git a/stdlib/bytes.mli b/stdlib/bytes.mli
index 99c2af033..d9c104674 100644
--- a/stdlib/bytes.mli
+++ b/stdlib/bytes.mli
@@ -67,8 +67,9 @@ val make : int -> char -> bytes
     Raise [Invalid_argument] if [n < 0] or [n > ]{!Sys.max_string_length}. *)
 
 val init : int -> (int -> char) -> bytes
-(** [Bytes.init n f] returns a fresh byte sequence of length [n],
-    with character [i] initialized to the result of [f i].
+(** [Bytes.init n f] returns a fresh byte sequence of length [n], with
+    character [i] initialized to the result of [f i] (in increasing
+    index order).
 
     Raise [Invalid_argument] if [n < 0] or [n > ]{!Sys.max_string_length}. *)
 
@@ -132,9 +133,14 @@ val iteri : (int -> char -> unit) -> bytes -> unit
     argument. *)
 
 val map : (char -> char) -> bytes -> bytes
-(** [map f s] applies function [f] in turn to all the bytes of [s] and
-    stores the resulting bytes in a new sequence that is returned as
-    the result. *)
+(** [map f s] applies function [f] in turn to all the bytes of [s]
+    (in increasing index order) and stores the resulting bytes in
+    a new sequence that is returned as the result. *)
+
+val mapi : (int -> char -> char) -> bytes -> bytes
+(** [mapi f s] calls [f] with each character of [s] and its
+    index (in increasing index order) and stores the resulting bytes
+    in a new sequence that is returned as the result. *)
 
 val trim : bytes -> bytes
 (** Return a copy of the argument, without leading and trailing
diff --git a/stdlib/string.ml b/stdlib/string.ml
index 741ca2af1..44e9c4898 100644
--- a/stdlib/string.ml
+++ b/stdlib/string.ml
@@ -37,6 +37,7 @@ let concat = (Obj.magic B.concat : string -> string list -> string)
 let iter = (Obj.magic B.iter : (char -> unit) -> string -> unit)
 let iteri = (Obj.magic B.iteri : (int -> char -> unit) -> string -> unit)
 let map = (Obj.magic B.map : (char -> char) -> string -> string)
+let mapi = (Obj.magic B.mapi : (int -> char -> char) -> string -> string)
 
 (* Beware: we cannot use B.trim or B.escape because they always make a
    copy, but String.mli spells out some cases where we are not allowed
diff --git a/stdlib/string.mli b/stdlib/string.mli
index 3cfccd1f2..da6d8351a 100644
--- a/stdlib/string.mli
+++ b/stdlib/string.mli
@@ -81,10 +81,14 @@ val make : int -> char -> string
    Raise [Invalid_argument] if [n < 0] or [n > ]{!Sys.max_string_length}. *)
 
 val init : int -> (int -> char) -> string
-(** [String.init n f] returns a string of length [n],
-    with character [i] initialized to the result of [f i].
+(** [String.init n f] returns a string of length [n], with character
+    [i] initialized to the result of [f i] (called in increasing
+    index order).
 
-   Raise [Invalid_argument] if [n < 0] or [n > ]{!Sys.max_string_length}. *)
+    Raise [Invalid_argument] if [n < 0] or [n > ]{!Sys.max_string_length}.
+
+    @since 4.02.0
+*)
 
 val copy : string -> string
 (** Return a copy of the given string. *)
@@ -131,10 +135,16 @@ val iteri : (int -> char -> unit) -> string -> unit
    @since 4.00.0 *)
 
 val map : (char -> char) -> string -> string
-(** [String.map f s] applies function [f] in turn to all
-   the characters of [s] and stores the results in a new string that
-   is returned.
-   @since 4.00.0 *)
+(** [String.map f s] applies function [f] in turn to all the
+    characters of [s] (in increasing index order) and stores the
+    results in a new string that is returned.
+    @since 4.00.0 *)
+
+val mapi : (int -> char -> char) -> string -> string
+(** [String.mapi f s] calls [f] with each character of [s] and its
+    index (in increasing index order) and stores the results in a new
+    string that is returned.
+    @since 4.02.0 *)
 
 val trim : string -> string
 (** Return a copy of the argument, without leading and trailing