iter/sequence.ml

(*
Copyright (c) 2013, Simon Cruanes
All rights reserved.

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modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this
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*)

(** {1 Transient iterators, that abstract on a finite sequence of elements. *)

(** Sequence abstract iterator type *)
type 'a t = ('a -> unit) -> unit

type (+'a, +'b) t2 = ('a -> 'b -> unit) -> unit
  (** Sequence of pairs of values of type ['a] and ['b]. *)

(** Build a sequence from a iter function *)
let from_iter f = f

let empty = fun k -> ()

let singleton x = fun k -> k x

(** Infinite sequence of the same element *)
let repeat x = fun k -> while true do k x done

(** [iterate f x] is the infinite sequence (x, f(x), f(f(x)), ...) *)
let iterate f x =
  let rec iterate k x = k x; iterate k (f x) in
  from_iter (fun k -> iterate k x)

(** Sequence that calls the given function to produce elements *)
let forever f =
  let rec forever k = k (f ()); forever k in
  from_iter forever

(** Cycle forever through the given sequence. O(n). *)
let cycle s = fun k -> while true do s k; done

(** Consume the sequence, passing all its arguments to the function *)
let iter f seq = seq f

(** Iterate on elements and their index in the sequence *)
let iteri f seq =
  let r = ref 0 in
  let k x =
    f !r x;
    incr r
  in seq k

(** Fold over elements of the sequence, consuming it *)
let fold f init seq =
  let r = ref init in
  seq (fun elt -> r := f !r elt);
  !r

(** Fold over elements of the sequence and their index, consuming it *)
let foldi f init seq =
  let i = ref 0 in
  let r = ref init in
  seq (fun elt ->
    r := f !r !i elt;
    incr i);
  !r
    
(** Map objects of the sequence into other elements, lazily *)
let map f seq =
  let seq_fun' k = seq (fun x -> k (f x)) in
  seq_fun'

(** Map objects, along with their index in the sequence *)
let mapi f seq =
  let seq_fun' k =
    let i = ref 0 in
    seq (fun x -> k (f !i x); incr i) in
  seq_fun'

(** Filter on elements of the sequence *)
let filter p seq =
  let seq_fun' k = seq (fun x -> if p x then k x) in
  seq_fun'

(** Append two sequences *)
let append s1 s2 =
  let seq_fun k = s1 k; s2 k in
  seq_fun

(** Concatenate a sequence of sequences into one sequence *)
let concat s =
  from_iter (fun k ->
    (* function that is called on every sub-sequence *)
    let k_seq seq = iter k seq in
    s k_seq)

(** Monadic bind. It applies the function to every element of the
    initial sequence, and calls [concat]. *)
let flatMap f seq =
  from_iter
    (fun k -> seq (fun x -> (f x) k))

(** Insert the second element between every element of the sequence *)
let intersperse seq elem =
  from_iter
    (fun k -> seq (fun x -> k x; k elem))

(** Mutable unrolled list to serve as intermediate storage *)
module MList = struct
  type 'a t = {
    content : 'a array;   (* elements of the node *)
    mutable len : int;    (* number of elements in content *)
    mutable tl : 'a t;    (* tail *)
  } (** A list that contains some elements, and may point to another list *)

  let _empty () : 'a t = Obj.magic 0
    (** Empty list, for the tl field *)

  let make n =
    assert (n > 0);
    { content = Array.make n (Obj.magic 0);
      len = 0;
      tl = _empty ();
    }

  let rec is_empty l =
    l.len = 0 && (l.tl == _empty () || is_empty l.tl)

  let rec iter f l =
    for i = 0 to l.len - 1 do f l.content.(i); done;
    if l.tl != _empty () then iter f l.tl

  let iteri f l =
    let rec iteri i f l =
      for j = 0 to l.len - 1 do f (i+j) l.content.(j); done;
      if l.tl != _empty () then iteri (i+l.len) f l.tl
    in iteri 0 f l

  let rec iter_rev f l =
    (if l.tl != _empty () then iter_rev f l.tl);
    for i = l.len - 1 downto 0 do f l.content.(i); done

  let length l =
    let rec len acc l =
      if l.tl == _empty () then acc+l.len else len (acc+l.len) l.tl
    in len 0 l

  (** Get element by index *)
  let rec get l i =
    if i < l.len then l.content.(i)
    else if i >= l.len && l.tl == _empty () then raise (Invalid_argument "MList.get")
    else get l.tl (i - l.len)

  (** Push [x] at the end of the list. It returns the block in which the
      element is inserted. *)
  let rec push x l =
    if l.len = Array.length l.content
      then begin (* insert in the next block *)
        (if l.tl == _empty () then l.tl <- make (Array.length l.content));
        push x l.tl
      end else begin  (* insert in l *)
        l.content.(l.len) <- x;
        l.len <- l.len + 1;
        l
      end

  (** Reverse list (in place), and returns the new head *)
  let rev l =
    let rec rev prev l =
      (* reverse array *)
      for i = 0 to (l.len-1) / 2 do
        let x = l.content.(i) in
        l.content.(i) <- l.content.(l.len - i - 1);
        l.content.(l.len - i - 1) <- x;
      done;
      (* reverse next block *)
      let l' = l.tl in
      l.tl <- prev;
      if l' == _empty () then l else rev l l'
    in
    rev (_empty ()) l

  (** Build a MList of elements of the Seq. The optional argument indicates
      the size of the blocks *)
  let of_seq ?(size=64) seq =
    (* read sequence into a MList.t *)
    let start = make size in
    let l = ref start in
    seq (fun x -> l := push x !l);
    start
end

(** Iterate on the sequence, storing elements in a data structure.
    The resulting sequence can be iterated on as many times as needed. *)
let persistent (seq : 'a t) : 'a t =
  let l = MList.of_seq seq in
  from_iter (fun k -> MList.iter k l)

(** Cartesian product of the sequences. *)
let product outer inner =
  let outer = persistent outer in
  from_iter
    (fun k ->
      outer (fun x ->
        inner (fun y -> k (x,y))))

(** [unfoldr f b] will apply [f] to [b]. If it
    yields [Some (x,b')] then [x] is returned
    and unfoldr recurses with [b']. *)
let unfoldr f b =
  let rec unfold k b = match f b with
    | None -> ()
    | Some (x, b') -> k x; unfold k b'
  in
  from_iter (fun k -> unfold k b)

(** Sequence of intermediate results *)
let scan f acc seq =
  from_iter
    (fun k ->
      k acc;
      let acc = ref acc in
      seq (fun elt -> let acc' = f !acc elt in k acc'; acc := acc'))

(** Max element of the sequence, using the given comparison
    function. A default element has to be provided. *)
let max ?(lt=fun x y -> x < y) seq m =
  fold (fun m x -> if lt m x then x else m) m seq

(** Min element of the sequence, using the given comparison function *)
let min ?(lt=fun x y -> x < y) seq m =
  fold (fun m x -> if lt x m then x else m) m seq

exception ExitSequence

(** Take at most [n] elements from the sequence *)
let take n seq =
  let count = ref 0 in
  fun k ->
    try
      seq
        (fun x -> if !count < n then begin incr count; k x end
                                else raise ExitSequence)
    with ExitSequence -> ()

(** Drop the [n] first elements of the sequence *)
let drop n seq =
  let count = ref 0 in
  fun k -> seq
    (fun x -> if !count >= n then k x else incr count)

(** Reverse the sequence. O(n) memory. *)
let rev seq =
  let l = MList.of_seq seq in
  from_iter (fun k -> MList.iter_rev k l)

(** Do all elements satisfy the predicate? *)
let for_all p seq =
  try
    seq (fun x -> if not (p x) then raise ExitSequence);
    true
  with ExitSequence -> false

(** Exists there some element satisfying the predicate? *)
let exists p seq =
  try
    seq (fun x -> if p x then raise ExitSequence);
    false
  with ExitSequence -> true

(** How long is the sequence? *)
let length seq =
  let r = ref 0 in
  seq (fun _ -> incr r);
  !r

(** Is the sequence empty? *)
let is_empty seq =
  try seq (fun _ -> raise ExitSequence); true
  with ExitSequence -> false

(** {2 Transform a sequence} *)

let empty2 =
  fun k -> ()

let is_empty2 seq2 =
  try ignore (seq2 (fun _ _ -> raise ExitSequence)); true
  with ExitSequence -> false

let length2 seq2 =
  let r = ref 0 in
  seq2 (fun _ _ -> incr r);
  !r

let zip seq2 =
  fun k -> seq2 (fun x y -> k (x,y))

let unzip seq =
  fun k -> seq (fun (x,y) -> k x y)

(** Zip elements of the sequence with their index in the sequence *)
let zip_i seq =
  fun k ->
    let r = ref 0 in
    seq (fun x -> let n = !r in incr r; k n x)

let fold2 f acc seq2 =
  let acc = ref acc in
  seq2 (fun x y -> acc := f !acc x y);
  !acc

let iter2 f seq2 =
  seq2 f

let map2 f seq2 =
  fun k -> seq2 (fun x y -> k (f x y))

(** [map2_2 f g seq2] maps each [x, y] of seq2 into [f x y, g x y] *)
let map2_2 f g seq2 =
  fun k -> seq2 (fun x y -> k (f x y) (g x y))

(** {2 Basic data structures converters} *)

let to_list seq = List.rev (fold (fun y x -> x::y) [] seq)

let to_rev_list seq = fold (fun y x -> x :: y) [] seq
  (** Get the list of the reversed sequence (more efficient) *)

let of_list l = from_iter (fun k -> List.iter k l)

let to_array seq =
  let l = MList.of_seq seq in
  let n = MList.length l in
  if n = 0
    then [||]
    else begin
      let a = Array.make n (MList.get l 0) in
      MList.iteri (fun i x -> a.(i) <- x) l;
      a
    end

let of_array a = from_iter (fun k -> Array.iter k a)

let of_array_i a =
  let seq k =
    for i = 0 to Array.length a - 1 do k (i, a.(i)) done
  in from_iter seq

(** [array_slice a i j] Sequence of elements whose indexes range
    from [i] to [j] *)
let array_slice a i j =
  assert (i >= 0 && j < Array.length a);
  fun k ->
    for idx = i to j do
      k a.(idx);  (* iterate on sub-array *)
    done

(** Sequence of elements of a stream (usable only once) *)
let of_stream s =
  let seq k = Stream.iter k s in
  from_iter seq

(** Convert to a stream. The sequence is made persistent. *)
let to_stream seq =
  let l = ref (MList.of_seq seq) in
  let i = ref 0 in
  let rec get_next () =
    if !l == MList._empty () then None
    else if (!l).MList.len = !i then (l := (!l).MList.tl; i := 0; get_next ())
    else let x = (!l).MList.content.(!i) in (incr i; Some x)
  in
  Stream.from (fun _ -> get_next ())

(** Push elements of the sequence on the stack *)
let to_stack s seq = iter (fun x -> Stack.push x s) seq

(** Sequence of elements of the stack (same order as [Stack.iter]) *)
let of_stack s = from_iter (fun k -> Stack.iter k s)

(** Push elements of the sequence into the queue *)
let to_queue q seq = iter (fun x -> Queue.push x q) seq

(** Sequence of elements contained in the queue, FIFO order *)
let of_queue q = from_iter (fun k -> Queue.iter k q)

let hashtbl_add h seq =
  iter (fun (k,v) -> Hashtbl.add h k v) seq

let hashtbl_replace h seq =
  iter (fun (k,v) -> Hashtbl.replace h k v) seq

let to_hashtbl seq =
  let h = Hashtbl.create 3 in
  hashtbl_replace h seq;
  h

let of_hashtbl h =
  from_iter (fun k -> Hashtbl.iter (fun a b -> k (a, b)) h)

let hashtbl_keys h =
  from_iter (fun k -> Hashtbl.iter (fun a b -> k a) h)

let hashtbl_values h =
  from_iter (fun k -> Hashtbl.iter (fun a b -> k b) h)

let of_str s = from_iter (fun k -> String.iter k s)
    
let to_str seq =
  let b = Buffer.create 64 in
  iter (fun c -> Buffer.add_char b c) seq;
  Buffer.contents b

let of_in_channel ic =
  from_iter (fun k ->
    try while true do
      let c = input_char ic in k c
    done with End_of_file -> ())

(** Copy content of the sequence into the buffer *)
let to_buffer seq buf =
  iter (fun c -> Buffer.add_char buf c) seq

(** Iterator on integers in [start...stop] by steps 1 *)
let int_range ~start ~stop =
  fun k ->
    for i = start to stop do k i done

(** Convert the given set to a sequence. The set module must be provided. *)
let of_set (type s) (type v) m set =
  let module S = (val m : Set.S with type t = s and type elt = v) in
  from_iter
    (fun k -> S.iter k set)

(** Convert the sequence to a set, given the proper set module *)
let to_set (type s) (type v) m seq =
  let module S = (val m : Set.S with type t = s and type elt = v) in
  fold
    (fun set x -> S.add x set)
    S.empty seq

(** {2 Functorial conversions between sets and sequences} *)

module Set = struct
  module type S = sig
    type set
    include Set.S with type t := set
    val of_seq : elt t -> set
    val to_seq : set -> elt t
  end

  (** Create an enriched Set module from the given one *)
  module Adapt(X : Set.S) : S with type elt = X.elt and type set = X.t = struct
    type set = X.t

    let to_seq set = from_iter (fun k -> X.iter k set)

    let of_seq seq = fold (fun set x -> X.add x set) X.empty seq

    include X
  end
    
  (** Functor to build an extended Set module from an ordered type *)
  module Make(X : Set.OrderedType) : S with type elt = X.t = struct
    module MySet = Set.Make(X)
    include Adapt(MySet)
  end
end

(** {2 Conversion between maps and sequences.} *)

module Map = struct
  module type S = sig
    type +'a map
    include Map.S with type 'a t := 'a map
    val to_seq : 'a map -> (key * 'a) t
    val of_seq : (key * 'a) t -> 'a map
    val keys : 'a map -> key t
    val values : 'a map -> 'a t
  end

  (** Adapt a pre-existing Map module to make it sequence-aware *)
  module Adapt(M : Map.S) : S with type key = M.key and type 'a map = 'a M.t = struct
    type 'a map = 'a M.t

    let to_seq m = from_iter (fun k -> M.iter (fun x y -> k (x,y)) m)

    let of_seq seq = fold (fun m (k,v) -> M.add k v m) M.empty seq

    let keys m = from_iter (fun k -> M.iter (fun x _ -> k x) m)

    let values m = from_iter (fun k -> M.iter (fun _ y -> k y) m)

    include M
  end

  (** Create an enriched Map module, with sequence-aware functions *)
  module Make(V : Map.OrderedType) : S with type key = V.t = struct
    module M = Map.Make(V)
    include Adapt(M)
  end
end

(** {2 Infinite sequences of random values} *)

let random_int bound = forever (fun () -> Random.int bound)

let random_bool = forever Random.bool

let random_float bound = forever (fun () -> Random.float bound)

(** Sequence of choices of an element in the array *)
let random_array a =
  assert (Array.length a > 0);
  let seq k =
    while true do
      let i = Random.int (Array.length a) in
      k a.(i);
    done in
  from_iter seq

let random_list l = random_array (Array.of_list l)

(** {2 Type-classes} *)

module TypeClass = struct
  (** {3 Classes} *)
  type ('a,'b) sequenceable = {
    to_seq : 'b -> 'a t;
    of_seq : 'a t -> 'b;
  }

  type ('a,'b) addable = {
    empty : 'b;
    add : 'b -> 'a -> 'b;
  }

  type 'a monoid = ('a,'a) addable

  type ('a,'b) iterable = {
    iter : ('a -> unit) -> 'b -> unit;
  }

  (** {3 Instances} *)

  let (sequenceable : ('a,'a t) sequenceable) = {
    to_seq = (fun seq -> seq);
    of_seq = (fun seq -> seq);
  }

  let (iterable : ('a, 'a t) iterable) = {
    iter = (fun f seq -> iter f seq);
  }

  let (monoid : 'a t monoid) = {
    empty = empty;
    add = (fun s1 s2 -> append s1 s2);
  }

  (** {3 Conversions} *)

  let of_iterable iterable x =
    from_iter (fun k -> iterable.iter k x)


  let to_addable addable seq =
    fold addable.add addable.empty seq
end


(** {2 Pretty printing of sequences} *)

(** Pretty print a sequence of ['a], using the given pretty printer
    to print each elements. An optional separator string can be provided. *)
let pp_seq ?(sep=", ") pp_elt formatter seq =
  let first = ref true in
  iter
    (fun x -> 
      (if !first then first := false else Format.pp_print_string formatter sep);
      pp_elt formatter x;
      Format.pp_print_cut formatter ())
    seq