+let list_mapi f l =
+ let rec aux k = function
+ | [] -> []
+ | h::tl -> f h k :: aux (k+1) tl
+ in
+ aux 0 l
+;;
+
+let list_mapi_acc f a l =
+ let rec aux k a res = function
+ | [] -> a, List.rev res
+ | h::tl -> let a,h = f h k a in aux (k+1) a (h::res) tl
+ in
+ aux 0 a [] l
+;;
+
+let list_index p =
+ let rec aux n =
+ function
+ [] -> None
+ | he::_ when p he -> Some (n,he)
+ | _::tl -> aux (n + 1) tl
+ in
+ aux 0
+;;
+
+let rec list_iter_default2 f l1 def l2 =
+ match l1,l2 with
+ | [], _ -> ()
+ | a::ta, b::tb -> f a b; list_iter_default2 f ta def tb
+ | a::ta, [] -> f a def; list_iter_default2 f ta def []
+;;
+
+let rec list_forall_default3 f l1 l2 def l3 =
+ match l1,l2,l3 with
+ | [], [], _ -> true
+ | [], _, _
+ | _, [], _ -> raise (Invalid_argument "list_forall_default3")
+ | a::ta, b::tb, c::tc -> f a b c && list_forall_default3 f ta tb def tc
+ | a::ta, b::tb, [] -> f a b def && list_forall_default3 f ta tb def []
+;;
+
+exception FailureAt of int;;
+
+let list_forall_default3_var f l1 l2 def l3 =
+ let rec aux f l1 l2 def l3 i =
+ match l1,l2,l3 with
+ | [], [], _ -> true
+ | [], _, _
+ | _, [], _ -> raise (Invalid_argument "list_forall_default3")
+ | a::ta, b::tb, c::tc ->
+ if f a b c then aux f ta tb def tc (i+1)
+ else raise (FailureAt i)
+ | a::ta, b::tb, [] ->
+ if f a b def then aux f ta tb def [] (i+1)
+ else raise (FailureAt i)
+ in aux f l1 l2 def l3 0
+;;
+
+let sharing_map f l =
+ let unchanged = ref true in
+ let rec aux b = function
+ | [] as t -> unchanged := b; t
+ | he::tl ->
+ let he1 = f he in
+ he1 :: aux (b && he1 == he) tl
+ in
+ let l1 = aux true l in
+ if !unchanged then l else l1
+;;
+