|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
type 'a cmp = 'a -> 'a -> int
type 'a eq = 'a -> 'a -> bool
module type S = module type of List
module type ExtS =
sig
include S
val compare : 'a cmp -> 'a list cmp
val equal : 'a eq -> 'a list eq
val is_empty : 'a list -> bool
val mem_f : 'a eq -> 'a -> 'a list -> bool
val for_all_i : (int -> 'a -> bool) -> int -> 'a list -> bool
val for_all2eq : ('a -> 'b -> bool) -> 'a list -> 'b list -> bool
val prefix_of : 'a eq -> 'a list -> 'a list -> bool
val interval : int -> int -> int list
val make : int -> 'a -> 'a list
val addn : int -> 'a -> 'a list -> 'a list
val init : int -> (int -> 'a) -> 'a list
val append : 'a list -> 'a list -> 'a list
val concat : 'a list list -> 'a list
val flatten : 'a list list -> 'a list
val assign : 'a list -> int -> 'a -> 'a list
val filter : ('a -> bool) -> 'a list -> 'a list
val filter2 : ('a -> 'b -> bool) -> 'a list -> 'b list -> 'a list * 'b list
val filteri :
(int -> 'a -> bool) -> 'a list -> 'a list
val filter_with : bool list -> 'a list -> 'a list
val map_filter : ('a -> 'b option) -> 'a list -> 'b list
val map_filter_i : (int -> 'a -> 'b option) -> 'a list -> 'b list
val partitioni :
(int -> 'a -> bool) -> 'a list -> 'a list * 'a list
val map : ('a -> 'b) -> 'a list -> 'b list
val map2 : ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
val map_left : ('a -> 'b) -> 'a list -> 'b list
val map_i : (int -> 'a -> 'b) -> int -> 'a list -> 'b list
val map2_i :
(int -> 'a -> 'b -> 'c) -> int -> 'a list -> 'b list -> 'c list
val map3 :
('a -> 'b -> 'c -> 'd) -> 'a list -> 'b list -> 'c list -> 'd list
val map4 :
('a -> 'b -> 'c -> 'd -> 'e) -> 'a list -> 'b list -> 'c list -> 'd list -> 'e list
val map_of_array : ('a -> 'b) -> 'a array -> 'b list
val map_append : ('a -> 'b list) -> 'a list -> 'b list
val map_append2 : ('a -> 'b -> 'c list) -> 'a list -> 'b list -> 'c list
val extend : bool list -> 'a -> 'a list -> 'a list
val count : ('a -> bool) -> 'a list -> int
val index : 'a eq -> 'a -> 'a list -> int
val safe_index : 'a eq -> 'a -> 'a list -> int option
val index0 : 'a eq -> 'a -> 'a list -> int
val fold_left_until : ('c -> 'a -> 'c CSig.until) -> 'c -> 'a list -> 'c
val fold_right_i : (int -> 'a -> 'b -> 'b) -> int -> 'a list -> 'b -> 'b
val fold_left_i : (int -> 'a -> 'b -> 'a) -> int -> 'a -> 'b list -> 'a
val fold_right_and_left :
('a -> 'b -> 'b list -> 'a) -> 'b list -> 'a -> 'a
val fold_left3 : ('a -> 'b -> 'c -> 'd -> 'a) -> 'a -> 'b list -> 'c list -> 'd list -> 'a
val fold_left2_set : exn -> ('a -> 'b -> 'c -> 'b list -> 'c list -> 'a) -> 'a -> 'b list -> 'c list -> 'a
val fold_left_map : ('a -> 'b -> 'a * 'c) -> 'a -> 'b list -> 'a * 'c list
val fold_right_map : ('b -> 'a -> 'c * 'a) -> 'b list -> 'a -> 'c list * 'a
val fold_left2_map : ('a -> 'b -> 'c -> 'a * 'd) -> 'a -> 'b list -> 'c list -> 'a * 'd list
val fold_right2_map : ('b -> 'c -> 'a -> 'd * 'a) -> 'b list -> 'c list -> 'a -> 'd list * 'a
val fold_left3_map : ('a -> 'b -> 'c -> 'd -> 'a * 'e) -> 'a -> 'b list -> 'c list -> 'd list -> 'a * 'e list
val fold_left4_map : ('a -> 'b -> 'c -> 'd -> 'e -> 'a * 'r) -> 'a -> 'b list -> 'c list -> 'd list -> 'e list -> 'a * 'r list
val except : 'a eq -> 'a -> 'a list -> 'a list
val remove : 'a eq -> 'a -> 'a list -> 'a list
val remove_first : ('a -> bool) -> 'a list -> 'a list
val extract_first : ('a -> bool) -> 'a list -> 'a list * 'a
val find_map : ('a -> 'b option) -> 'a list -> 'b
exception IndexOutOfRange
val goto : int -> 'a list -> 'a list * 'a list
val split_when : ('a -> bool) -> 'a list -> 'a list * 'a list
val sep_last : 'a list -> 'a * 'a list
val drop_last : 'a list -> 'a list
val last : 'a list -> 'a
val lastn : int -> 'a list -> 'a list
val chop : int -> 'a list -> 'a list * 'a list
val firstn : int -> 'a list -> 'a list
val skipn : int -> 'a list -> 'a list
val skipn_at_least : int -> 'a list -> 'a list
val drop_prefix : 'a eq -> 'a list -> 'a list -> 'a list
val insert : ('a -> 'a -> bool) -> 'a -> 'a list -> 'a list
val share_tails : 'a list -> 'a list -> 'a list * 'a list * 'a list
val map_assoc : ('a -> 'b) -> ('c * 'a) list -> ('c * 'b) list
val assoc_f : 'a eq -> 'a -> ('a * 'b) list -> 'b
val remove_assoc_f : 'a eq -> 'a -> ('a * 'b) list -> ('a * 'b) list
val mem_assoc_f : 'a eq -> 'a -> ('a * 'b) list -> bool
val factorize_left : 'a eq -> ('a * 'b) list -> ('a * 'b list) list
val split : ('a * 'b) list -> 'a list * 'b list
val combine : 'a list -> 'b list -> ('a * 'b) list
val split3 : ('a * 'b * 'c) list -> 'a list * 'b list * 'c list
val split4 : ('a * 'b * 'c * 'd) list -> 'a list * 'b list * 'c list * 'd list
val combine3 : 'a list -> 'b list -> 'c list -> ('a * 'b * 'c) list
val add_set : 'a eq -> 'a -> 'a list -> 'a list
val eq_set : 'a eq -> 'a list -> 'a list -> bool
val subset : 'a list -> 'a list -> bool
val merge_set : 'a cmp -> 'a list -> 'a list -> 'a list
val intersect : 'a eq -> 'a list -> 'a list -> 'a list
val union : 'a eq -> 'a list -> 'a list -> 'a list
val unionq : 'a list -> 'a list -> 'a list
val subtract : 'a eq -> 'a list -> 'a list -> 'a list
val subtractq : 'a list -> 'a list -> 'a list
val distinct : 'a list -> bool
val distinct_f : 'a cmp -> 'a list -> bool
val duplicates : 'a eq -> 'a list -> 'a list
val uniquize : 'a list -> 'a list
val sort_uniquize : 'a cmp -> 'a list -> 'a list
val min : 'a cmp -> 'a list -> 'a
val cartesian : ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list
val cartesians : ('a -> 'b -> 'b) -> 'b -> 'a list list -> 'b list
val combinations : 'a list list -> 'a list list
val cartesians_filter :
('a -> 'b -> 'b option) -> 'b -> 'a list list -> 'b list
module Smart :
sig
val map : ('a -> 'a) -> 'a list -> 'a list
end
module type MonoS = sig
type elt
val equal : elt list -> elt list -> bool
val mem : elt -> elt list -> bool
val assoc : elt -> (elt * 'a) list -> 'a
val mem_assoc : elt -> (elt * 'a) list -> bool
val remove_assoc : elt -> (elt * 'a) list -> (elt * 'a) list
val mem_assoc_sym : elt -> ('a * elt) list -> bool
end
end
include List
(** Tail-rec implementation of usual functions. This is a well-known trick used
in, for instance, ExtLib and Batteries. *)
type 'a cell = {
head : 'a;
mutable tail : 'a list;
}
external cast : 'a cell -> 'a list = "%identity"
(** Extensions and redefinitions of OCaml Stdlib *)
(** {6 Equality, testing} *)
let rec compare cmp l1 l2 =
if l1 == l2 then 0 else
match l1,l2 with
| [], [] -> 0
| _::_, [] -> 1
| [], _::_ -> -1
| x1::l1, x2::l2 ->
match cmp x1 x2 with
| 0 -> compare cmp l1 l2
| c -> c
let rec equal cmp l1 l2 =
l1 == l2 ||
match l1, l2 with
| [], [] -> true
| x1 :: l1, x2 :: l2 -> cmp x1 x2 && equal cmp l1 l2
| _ -> false
let is_empty = function
| [] -> true
| _ -> false
let mem_f cmp x l =
List.exists (cmp x) l
let for_all_i p =
let rec for_all_p i = function
| [] -> true
| a::l -> p i a && for_all_p (i+1) l
in
for_all_p
let for_all2eq f l1 l2 =
try List.for_all2 f l1 l2 with Invalid_argument _ -> false
let prefix_of cmp prefl l =
let rec prefrec = function
| (h1::t1, h2::t2) -> cmp h1 h2 && prefrec (t1,t2)
| ([], _) -> true
| _ -> false
in
prefrec (prefl,l)
(** {6 Creating lists} *)
let interval n m =
let rec interval_n (l,m) =
if n > m then l else interval_n (m::l, pred m)
in
interval_n ([], m)
let addn n v =
let rec aux n l =
if Int.equal n 0 then l
else aux (pred n) (v :: l)
in
if n < 0 then invalid_arg "List.addn"
else aux n
let make n v =
addn n v []
let rec init_loop len f p i =
if Int.equal i len then ()
else
let c = { head = f i; tail = [] } in
p.tail <- cast c;
init_loop len f c (succ i)
let init len f =
if len < 0 then invalid_arg "List.init"
else if Int.equal len 0 then []
else
let c = { head = f 0; tail = [] } in
init_loop len f c 1;
cast c
let rec append_loop p tl = function
| [] -> p.tail <- tl
| x :: l ->
let c = { head = x; tail = [] } in
p.tail <- cast c;
append_loop c tl l
let append l1 l2 = match l1 with
| [] -> l2
| x :: l ->
let c = { head = x; tail = [] } in
append_loop c l2 l;
cast c
let rec copy p = function
| [] -> p
| x :: l ->
let c = { head = x; tail = [] } in
p.tail <- cast c;
copy c l
let rec concat_loop p = function
| [] -> ()
| x :: l -> concat_loop (copy p x) l
let concat l =
let dummy = { head = Obj.magic 0; tail = [] } in
concat_loop dummy l;
dummy.tail
let flatten = concat
(** {6 Lists as arrays} *)
let assign l n e =
let rec assrec stk l i = match l, i with
| (h :: t, 0) -> List.rev_append stk (e :: t)
| (h :: t, n) -> assrec (h :: stk) t (pred n)
| ([], _) -> failwith "List.assign"
in
assrec [] l n
(** {6 Filtering} *)
let rec filter_loop f p = function
| [] -> ()
| x :: l' as l ->
let b = f x in
filter_loop f p l';
if b then if p.tail == l' then p.tail <- l else p.tail <- x :: p.tail
let rec filter f = function
| [] -> []
| x :: l' as l ->
if f x then
let c = { head = x; tail = [] } in
filter_loop f c l';
if c.tail == l' then l else cast c
else
filter f l'
let rec filter2_loop f p q l1 l2 = match l1, l2 with
| [], [] -> ()
| x :: l1', y :: l2' ->
let b = f x y in
filter2_loop f p q l1' l2';
if b then
if p.tail == l1' then begin
p.tail <- l1;
q.tail <- l2
end
else begin
p.tail <- x :: p.tail;
q.tail <- y :: q.tail
end
| _ -> invalid_arg "List.filter2"
let rec filter2 f l1 l2 = match l1, l2 with
| [], [] -> ([],[])
| x1 :: l1', x2 :: l2' ->
let b = f x1 x2 in
if b then
let c1 = { head = x1; tail = [] } in
let c2 = { head = x2; tail = [] } in
filter2_loop f c1 c2 l1' l2';
if c1.tail == l1' then (l1, l2) else (cast c1, cast c2)
else
filter2 f l1' l2'
| _ -> invalid_arg "List.filter2"
let filteri p =
let rec filter_i_rec i = function
| [] -> []
| x :: l -> let l' = filter_i_rec (succ i) l in if p i x then x :: l' else l'
in
filter_i_rec 0
let rec filter_with_loop filter p l = match filter, l with
| [], [] -> ()
| b :: filter, x :: l' ->
filter_with_loop filter p l';
if b then if p.tail == l' then p.tail <- l else p.tail <- x :: p.tail
| _ -> invalid_arg "List.filter_with"
let rec filter_with filter l = match filter, l with
| [], [] -> []
| b :: filter, x :: l' ->
if b then
let c = { head = x; tail = [] } in
filter_with_loop filter c l';
if c.tail == l' then l else cast c
else filter_with filter l'
| _ -> invalid_arg "List.filter_with"
let rec map_filter_loop f p = function
| [] -> ()
| x :: l ->
match f x with
| None -> map_filter_loop f p l
| Some y ->
let c = { head = y; tail = [] } in
p.tail <- cast c;
map_filter_loop f c l
let rec map_filter f = function
| [] -> []
| x :: l' ->
match f x with
| None -> map_filter f l'
| Some y ->
let c = { head = y; tail = [] } in
map_filter_loop f c l';
cast c
let rec map_filter_i_loop f i p = function
| [] -> ()
| x :: l ->
match f i x with
| None -> map_filter_i_loop f (succ i) p l
| Some y ->
let c = { head = y; tail = [] } in
p.tail <- cast c;
map_filter_i_loop f (succ i) c l
let rec map_filter_i_loop' f i = function
| [] -> []
| x :: l' ->
match f i x with
| None -> map_filter_i_loop' f (succ i) l'
| Some y ->
let c = { head = y; tail = [] } in
map_filter_i_loop f (succ i) c l';
cast c
let map_filter_i f l =
map_filter_i_loop' f 0 l
let partitioni p =
let rec aux i = function
| [] -> [], []
| x :: l ->
let (l1, l2) = aux (succ i) l in
if p i x then (x :: l1, l2)
else (l1, x :: l2)
in
aux 0
(** {6 Applying functorially} *)
let rec map_loop f p = function
| [] -> ()
| x :: l ->
let c = { head = f x; tail = [] } in
p.tail <- cast c;
map_loop f c l
let map f = function
| [] -> []
| x :: l ->
let c = { head = f x; tail = [] } in
map_loop f c l;
cast c
let rec map2_loop f p l1 l2 = match l1, l2 with
| [], [] -> ()
| x :: l1, y :: l2 ->
let c = { head = f x y; tail = [] } in
p.tail <- cast c;
map2_loop f c l1 l2
| _ -> invalid_arg "List.map2"
let map2 f l1 l2 = match l1, l2 with
| [], [] -> []
| x :: l1, y :: l2 ->
let c = { head = f x y; tail = [] } in
map2_loop f c l1 l2;
cast c
| _ -> invalid_arg "List.map2"
(** Like OCaml [List.mapi] but tail-recursive *)
let rec map_i_loop f i p = function
| [] -> ()
| x :: l ->
let c = { head = f i x; tail = [] } in
p.tail <- cast c;
map_i_loop f (succ i) c l
let map_i f i = function
| [] -> []
| x :: l ->
let c = { head = f i x; tail = [] } in
map_i_loop f (succ i) c l;
cast c
let map_left = map
let map2_i f i l1 l2 =
let rec map_i i = function
| ([], []) -> []
| (h1 :: t1, h2 :: t2) -> let v = f i h1 h2 in v :: map_i (succ i) (t1,t2)
| (_, _) -> invalid_arg "map2_i"
in
map_i i (l1,l2)
let rec map3_loop f p l1 l2 l3 = match l1, l2, l3 with
| [], [], [] -> ()
| x :: l1, y :: l2, z :: l3 ->
let c = { head = f x y z; tail = [] } in
p.tail <- cast c;
map3_loop f c l1 l2 l3
| _ -> invalid_arg "List.map3"
let map3 f l1 l2 l3 = match l1, l2, l3 with
| [], [], [] -> []
| x :: l1, y :: l2, z :: l3 ->
let c = { head = f x y z; tail = [] } in
map3_loop f c l1 l2 l3;
cast c
| _ -> invalid_arg "List.map3"
let rec map4_loop f p l1 l2 l3 l4 = match l1, l2, l3, l4 with
| [], [], [], [] -> ()
| x :: l1, y :: l2, z :: l3, t :: l4 ->
let c = { head = f x y z t; tail = [] } in
p.tail <- cast c;
map4_loop f c l1 l2 l3 l4
| _ -> invalid_arg "List.map4"
let map4 f l1 l2 l3 l4 = match l1, l2, l3, l4 with
| [], [], [], [] -> []
| x :: l1, y :: l2, z :: l3, t :: l4 ->
let c = { head = f x y z t; tail = [] } in
map4_loop f c l1 l2 l3 l4;
cast c
| _ -> invalid_arg "List.map4"
let rec map_of_array_loop f p a i l =
if Int.equal i l then ()
else
let c = { head = f (Array.unsafe_get a i); tail = [] } in
p.tail <- cast c;
map_of_array_loop f c a (i + 1) l
let map_of_array f a =
let l = Array.length a in
if Int.equal l 0 then []
else
let c = { head = f (Array.unsafe_get a 0); tail = [] } in
map_of_array_loop f c a 1 l;
cast c
let map_append f l = flatten (map f l)
let map_append2 f l1 l2 = flatten (map2 f l1 l2)
let rec extend l a l' = match l,l' with
| true :: l, b :: l' -> b :: extend l a l'
| false :: l, l' -> a :: extend l a l'
| [], [] -> []
| _ -> invalid_arg "extend"
let count f l =
let rec aux acc = function
| [] -> acc
| h :: t -> if f h then aux (acc + 1) t else aux acc t
in
aux 0 l
(** {6 Finding position} *)
let rec index_f f x l n = match l with
| [] -> raise Not_found
| y :: l -> if f x y then n else index_f f x l (succ n)
let index f x l = index_f f x l 1
let safe_index f x l = try Some (index f x l) with Not_found -> None
let index0 f x l = index_f f x l 0
(** {6 Folding} *)
let fold_left_until f accu s =
let rec aux accu = function
| [] -> accu
| x :: xs -> match f accu x with CSig.Stop x -> x | CSig.Cont i -> aux i xs
in
aux accu s
let fold_right_i f i l =
let rec it_f i l a = match l with
| [] -> a
| b :: l -> f (i-1) b (it_f (i-1) l a)
in
it_f (List.length l + i) l
let fold_left_i f =
let rec it_list_f i a = function
| [] -> a
| b :: l -> it_list_f (i+1) (f i a b) l
in
it_list_f
let rec fold_left3 f accu l1 l2 l3 =
match (l1, l2, l3) with
| ([], [], []) -> accu
| (a1 :: l1, a2 :: l2, a3 :: l3) -> fold_left3 f (f accu a1 a2 a3) l1 l2 l3
| (_, _, _) -> invalid_arg "List.fold_left3"
let rec fold_left4 f accu l1 l2 l3 l4 =
match (l1, l2, l3, l4) with
| ([], [], [], []) -> accu
| (a1 :: l1, a2 :: l2, a3 :: l3, a4 :: l4) -> fold_left4 f (f accu a1 a2 a3 a4) l1 l2 l3 l4
| (_,_, _, _) -> invalid_arg "List.fold_left4"
(* [fold_right_and_left f [a1;...;an] hd =
f (f (... (f (f hd
an
[an-1;...;a1])
an-1
[an-2;...;a1])
...)
a2
[a1])
a1
[]] *)
let fold_right_and_left f l hd =
let rec aux tl = function
| [] -> hd
| a :: l -> let hd = aux (a :: tl) l in f hd a tl
in
aux [] l
(* Match sets as lists according to a matching function, also folding a side effect *)
let rec fold_left2_set e f x l1 l2 =
match l1 with
| a1 :: l1 ->
let rec find seen = function
| [] -> raise e
| a2 :: l2 ->
try fold_left2_set e f (f x a1 a2 l1 l2) l1 (List.rev_append seen l2)
with e' when e' = e -> find (a2 :: seen) l2 in
find [] l2
| [] ->
if l2 = [] then x else raise e
(* Poor man's monadic map *)
let rec fold_left_map f e = function
| [] -> (e,[])
| h :: t ->
let e',h' = f e h in
let e'',t' = fold_left_map f e' t in
e'',h' :: t'
(* (* tail-recursive version of the above function *)
let fold_left_map f e l =
let g (e,b') h =
let (e',h') = f e h in
(e',h'::b')
in
let (e',lrev) = List.fold_left g (e,[]) l in
(e',List.rev lrev)
*)
(* The same, based on fold_right, with the effect accumulated on the right *)
let fold_right_map f l e =
List.fold_right (fun x (l,e) -> let (y,e) = f x e in (y::l,e)) l ([],e)
let on_snd f (x,y) = (x,f y)
let fold_left2_map f e l l' =
on_snd List.rev @@
List.fold_left2 (fun (e,l) x x' ->
let (e,y) = f e x x' in
(e, y::l)
) (e, []) l l'
let fold_right2_map f l l' e =
List.fold_right2 (fun x x' (l,e) -> let (y,e) = f x x' e in (y::l,e)) l l' ([],e)
let fold_left3_map f e l l' l'' =
on_snd List.rev @@
fold_left3 (fun (e,l) x x' x'' -> let (e,y) = f e x x' x'' in (e,y::l)) (e,[]) l l' l''
let fold_left4_map f e l1 l2 l3 l4 =
on_snd List.rev @@
fold_left4 (fun (e,l) x1 x2 x3 x4 -> let (e,y) = f e x1 x2 x3 x4 in (e,y::l)) (e,[]) l1 l2 l3 l4
(** {6 Splitting} *)
let except cmp x l =
List.filter (fun y -> not (cmp x y)) l
let remove = except (* Alias *)
let rec remove_first p = function
| b :: l when p b -> l
| b :: l -> b :: remove_first p l
| [] -> raise Not_found
let extract_first p li =
let rec loop rev_left = function
| [] -> raise Not_found
| x :: right ->
if p x then List.rev_append rev_left right, x
else loop (x :: rev_left) right
in
loop [] li
let insert p v l =
let rec insrec = function
| [] -> [v]
| h :: tl -> if p v h then v :: h :: tl else h :: insrec tl
in
insrec l
let rec find_map f = function
| [] -> raise Not_found
| x :: l ->
match f x with
| None -> find_map f l
| Some y -> y
(* FIXME: again, generic hash function *)
let subset l1 l2 =
let t2 = Hashtbl.create 151 in
List.iter (fun x -> Hashtbl.add t2 x ()) l2;
let rec look = function
| [] -> true
| x :: ll -> try Hashtbl.find t2 x; look ll with Not_found -> false
in
look l1
(** [goto i l] splits [l] into two lists [(l1,l2)] such that
[(List.rev l1)++l2=l] and [l1] has length [i]. It raises
[IndexOutOfRange] when [i] is negative or greater than the
length of [l]. *)
exception IndexOutOfRange
let goto n l =
let rec goto i acc = function
| tl when Int.equal i 0 -> (acc, tl)
| h :: t -> goto (pred i) (h :: acc) t
| [] -> raise IndexOutOfRange
in
goto n [] l
(* [chop i l] splits [l] into two lists [(l1,l2)] such that
[l1++l2=l] and [l1] has length [i].
It raises [Failure] when [i] is negative or greater than the length of [l] *)
let chop n l =
try let (h,t) = goto n l in (List.rev h,t)
with IndexOutOfRange -> failwith "List.chop"
(* spiwack: should raise [IndexOutOfRange] but I'm afraid of missing
a try/with when replacing the exception. *)
(* [split_when p l] splits [l] into two lists [(l1,a::l2)] such that
[l1++(a::l2)=l], [p a=true] and [p b = false] for every element [b] of [l1].
If there is no such [a], then it returns [(l,[])] instead *)
let split_when p =
let rec split_when_loop x y =
match y with
| [] -> (List.rev x,[])
| (a :: l) -> if (p a) then (List.rev x,y) else split_when_loop (a :: x) l
in
split_when_loop []
let firstn n l =
let rec aux acc n l =
match n, l with
| 0, _ -> List.rev acc
| n, h :: t -> aux (h :: acc) (pred n) t
| _ -> failwith "firstn"
in
aux [] n l
let rec sep_last = function
| [] -> failwith "sep_last"
| hd :: [] -> (hd,[])
| hd :: tl -> let (l,tl) = sep_last tl in (l,hd :: tl)
(* Drop the last element of a list *)
let rec drop_last = function
| [] -> failwith "drop_last"
| hd :: [] -> []
| hd :: tl -> hd :: drop_last tl
let rec last = function
| [] -> failwith "List.last"
| hd :: [] -> hd
| _ :: tl -> last tl
let lastn n l =
let len = List.length l in
let rec aux m l =
if Int.equal m n then l else aux (m - 1) (List.tl l)
in
if len < n then failwith "lastn" else aux len l
let rec skipn n l = match n,l with
| 0, _ -> l
| _, [] -> failwith "List.skipn"
| n, _ :: l -> skipn (pred n) l
let skipn_at_least n l =
try skipn n l with Failure _ when n >= 0 -> []
(** if [l=p++t] then [drop_prefix p l] is [t] else [l] *)
let drop_prefix cmp p l =
let rec drop_prefix_rec = function
| (h1 :: tp, h2 :: tl) when cmp h1 h2 -> drop_prefix_rec (tp,tl)
| ([], tl) -> tl
| _ -> l
in
drop_prefix_rec (p,l)
let share_tails l1 l2 =
let rec shr_rev acc = function
| (x1 :: l1, x2 :: l2) when x1 == x2 -> shr_rev (x1 :: acc) (l1,l2)
| (l1, l2) -> (List.rev l1, List.rev l2, acc)
in
shr_rev [] (List.rev l1, List.rev l2)
(** {6 Association lists} *)
let map_assoc f = map (fun (x,a) -> (x,f a))
let rec assoc_f f a = function
| (x, e) :: xs -> if f a x then e else assoc_f f a xs
| [] -> raise Not_found
let remove_assoc_f f a l =
try remove_first (fun (x,_) -> f a x) l with Not_found -> l
let mem_assoc_f f a l = List.exists (fun (x,_) -> f a x) l
(** {6 Operations on lists of tuples} *)
let rec split_loop p q = function
| [] -> ()
| (x, y) :: l ->
let cl = { head = x; tail = [] } in
let cr = { head = y; tail = [] } in
p.tail <- cast cl;
q.tail <- cast cr;
split_loop cl cr l
let split = function
| [] -> [], []
| (x, y) :: l ->
let cl = { head = x; tail = [] } in
let cr = { head = y; tail = [] } in
split_loop cl cr l;
(cast cl, cast cr)
let rec combine_loop p l1 l2 = match l1, l2 with
| [], [] -> ()
| x :: l1, y :: l2 ->
let c = { head = (x, y); tail = [] } in
p.tail <- cast c;
combine_loop c l1 l2
| _ -> invalid_arg "List.combine"
let combine l1 l2 = match l1, l2 with
| [], [] -> []
| x :: l1, y :: l2 ->
let c = { head = (x, y); tail = [] } in
combine_loop c l1 l2;
cast c
| _ -> invalid_arg "List.combine"
let rec split3_loop p q r = function
| [] -> ()
| (x, y, z) :: l ->
let cp = { head = x; tail = [] } in
let cq = { head = y; tail = [] } in
let cr = { head = z; tail = [] } in
p.tail <- cast cp;
q.tail <- cast cq;
r.tail <- cast cr;
split3_loop cp cq cr l
let split3 = function
| [] -> [], [], []
| (x, y, z) :: l ->
let cp = { head = x; tail = [] } in
let cq = { head = y; tail = [] } in
let cr = { head = z; tail = [] } in
split3_loop cp cq cr l;
(cast cp, cast cq, cast cr)
(** XXX TODO tailrec *)
let rec split4 = function
| [] -> ([], [], [], [])
| (a,b,c,d)::l ->
let (ra, rb, rc, rd) = split4 l in (a::ra, b::rb, c::rc, d::rd)
let rec combine3_loop p l1 l2 l3 = match l1, l2, l3 with
| [], [], [] -> ()
| x :: l1, y :: l2, z :: l3 ->
let c = { head = (x, y, z); tail = [] } in
p.tail <- cast c;
combine3_loop c l1 l2 l3
| _ -> invalid_arg "List.combine3"
let combine3 l1 l2 l3 = match l1, l2, l3 with
| [], [], [] -> []
| x :: l1, y :: l2, z :: l3 ->
let c = { head = (x, y, z); tail = [] } in
combine3_loop c l1 l2 l3;
cast c
| _ -> invalid_arg "List.combine3"
(** {6 Operations on lists seen as sets, preserving uniqueness of elements} *)
(** Add an element, preserving uniqueness of elements *)
let add_set cmp x l =
if mem_f cmp x l then l else x :: l
(** List equality up to permutation (but considering multiple occurrences) *)
let eq_set cmp l1 l2 =
let rec aux l1 = function
| [] -> is_empty l1
| a :: l2 -> aux (remove_first (cmp a) l1) l2
in
try aux l1 l2 with Not_found -> false
let rec merge_set cmp l1 l2 = match l1, l2 with
| [], l2 -> l2
| l1, [] -> l1
| h1 :: t1, h2 :: t2 ->
let c = cmp h1 h2 in
if Int.equal c 0
then h1 :: merge_set cmp t1 t2
else if c <= 0
then h1 :: merge_set cmp t1 l2
else h2 :: merge_set cmp l1 t2
let intersect cmp l1 l2 =
filter (fun x -> mem_f cmp x l2) l1
let union cmp l1 l2 =
let rec urec = function
| [] -> l2
| a :: l -> if mem_f cmp a l2 then urec l else a :: urec l
in
urec l1
let subtract cmp l1 l2 =
if is_empty l2 then l1
else List.filter (fun x -> not (mem_f cmp x l2)) l1
let unionq l1 l2 = union (==) l1 l2
let subtractq l1 l2 = subtract (==) l1 l2
(** {6 Uniqueness and duplication} *)
(* FIXME: we should avoid relying on the generic hash function,
just as we'd better avoid Pervasives.compare *)
let distinct l =
let visited = Hashtbl.create 23 in
let rec loop = function
| h :: t ->
if Hashtbl.mem visited h then false
else
begin
Hashtbl.add visited h h;
loop t
end
| [] -> true
in
loop l
let distinct_f cmp l =
let rec loop = function
| a :: b :: _ when Int.equal (cmp a b) 0 -> false
| a :: l -> loop l
| [] -> true
in loop (List.sort cmp l)
(* FIXME: again, generic hash function *)
let uniquize l =
let visited = Hashtbl.create 23 in
let rec aux acc changed = function
| h :: t -> if Hashtbl.mem visited h then aux acc true t else
begin
Hashtbl.add visited h h;
aux (h :: acc) changed t
end
| [] -> if changed then List.rev acc else l
in
aux [] false l
(** [sort_uniquize] might be an alternative to the hashtbl-based
[uniquize], when the order of the elements is irrelevant *)
let rec uniquize_sorted cmp = function
| a :: b :: l when Int.equal (cmp a b) 0 -> uniquize_sorted cmp (a :: l)
| a :: l -> a :: uniquize_sorted cmp l
| [] -> []
let sort_uniquize cmp l =
uniquize_sorted cmp (List.sort cmp l)
let min cmp l =
let rec aux cur = function
| [] -> cur
| x :: l -> if cmp x cur < 0 then aux x l else aux cur l
in
match l with
| x :: l -> aux x l
| [] -> raise Not_found
let rec duplicates cmp = function
| [] -> []
| x :: l ->
let l' = duplicates cmp l in
if mem_f cmp x l then add_set cmp x l' else l'
(** {6 Cartesian product} *)
(* A generic cartesian product: for any operator (**),
[cartesian (**) [x1;x2] [y1;y2] = [x1**y1; x1**y2; x2**y1; x2**y1]],
and so on if there are more elements in the lists. *)
let cartesian op l1 l2 =
map_append (fun x -> map (op x) l2) l1
(* [cartesians] is an n-ary cartesian product: it iterates
[cartesian] over a list of lists. *)
let cartesians op init ll =
List.fold_right (cartesian op) ll [init]
(* combinations [[a;b];[c;d]] gives [[a;c];[a;d];[b;c];[b;d]] *)
let combinations l =
cartesians (fun x l -> x :: l) [] l
(* Keep only those products that do not return None *)
let cartesian_filter op l1 l2 =
map_append (fun x -> map_filter (op x) l2) l1
(* Keep only those products that do not return None *)
let cartesians_filter op init ll =
List.fold_right (cartesian_filter op) ll [init]
(* Factorize lists of pairs according to the left argument *)
let rec factorize_left cmp = function
| (a,b) :: l ->
let al,l' = partition (fun (a',_) -> cmp a a') l in
(a,(b :: map snd al)) :: factorize_left cmp l'
| [] -> []
module Smart =
struct
let rec map_loop f p = function
| [] -> ()
| x :: l' as l ->
let x' = f x in
map_loop f p l';
if x' == x && !p == l' then p := l else p := x' :: !p
let map f = function
| [] -> []
| x :: l' as l ->
let p = ref [] in
let x' = f x in
map_loop f p l';
if x' == x && !p == l' then l else x' :: !p
end
module type MonoS = sig
type elt
val equal : elt list -> elt list -> bool
val mem : elt -> elt list -> bool
val assoc : elt -> (elt * 'a) list -> 'a
val mem_assoc : elt -> (elt * 'a) list -> bool
val remove_assoc : elt -> (elt * 'a) list -> (elt * 'a) list
val mem_assoc_sym : elt -> ('a * elt) list -> bool
end
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