path: root/lib/util.ml

(***********************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
(*   \VV/  *************************************************************)
(*    //   *      This file is distributed under the terms of the      *)
(*         *       GNU Lesser General Public License Version 2.1       *)
(***********************************************************************)

(* Mapping under pairs *)

let on_fst f (a,b) = (f a,b)
let on_snd f (a,b) = (a,f b)
let map_pair f (a,b) = (f a,f b)

(* Mapping under pairs *)

let on_pi1 f (a,b,c) = (f a,b,c)
let on_pi2 f (a,b,c) = (a,f b,c)
let on_pi3 f (a,b,c) = (a,b,f c)

(* Projections from triplets *)

let pi1 (a,_,_) = a
let pi2 (_,a,_) = a
let pi3 (_,_,a) = a

(* Projection operator *)

let down_fst f x = f (fst x)
let down_snd f x = f (snd x)

(* Characters *)

let is_letter c = (c >= 'a' && c <= 'z') or (c >= 'A' && c <= 'Z')
let is_digit c = (c >= '0' && c <= '9')
let is_ident_tail c =
  is_letter c or is_digit c or c = '\'' or c = '_'
let is_blank = function
  | ' ' | '\r' | '\t' | '\n' -> true
  | _ -> false

(* Strings *)

let explode s =
  let rec explode_rec n =
    if n >= String.length s then
      []
    else
      String.make 1 (String.get s n) :: explode_rec (succ n)
  in
  explode_rec 0

let implode sl = String.concat "" sl

let strip s =
  let n = String.length s in
  let rec lstrip_rec i =
    if i < n && is_blank s.[i] then
      lstrip_rec (i+1)
    else i
  in
  let rec rstrip_rec i =
    if i >= 0 && is_blank s.[i] then
      rstrip_rec (i-1)
    else i
  in
  let a = lstrip_rec 0 and b = rstrip_rec (n-1) in
  String.sub s a (b-a+1)

let drop_simple_quotes s =
  let n = String.length s in
  if n > 2 & s.[0] = '\'' & s.[n-1] = '\'' then String.sub s 1 (n-2) else s

(* substring searching... *)

(* gdzie = where, co = what *)
(* gdzie=gdzie(string) gl=gdzie(length) gi=gdzie(index) *)
let rec is_sub gdzie gl gi co cl ci =
  (ci>=cl) ||
  ((String.unsafe_get gdzie gi = String.unsafe_get co ci) &&
   (is_sub gdzie gl (gi+1) co cl (ci+1)))

let rec raw_str_index i gdzie l c co cl =
  (* First adapt to ocaml 3.11 new semantics of index_from *)
  if (i+cl > l) then raise Not_found;
  (* Then proceed as in ocaml < 3.11 *)
  let i' = String.index_from gdzie i c in
    if (i'+cl <= l) && (is_sub gdzie l i' co cl 0) then i' else
      raw_str_index (i'+1) gdzie l c co cl

let string_index_from gdzie i co =
  if co="" then i else
    raw_str_index i gdzie (String.length gdzie)
      (String.unsafe_get co 0) co (String.length co)

let string_string_contains ~where ~what =
  try
    let _ = string_index_from where 0 what in true
  with
      Not_found -> false

let plural n s = if n<>1 then s^"s" else s

let ordinal n =
  let s = match n mod 10 with 1 -> "st" | 2 -> "nd" | 3 -> "rd" | _ -> "th" in
  string_of_int n ^ s

(* string parsing *)

let split_string_at c s =
  let len = String.length s in
  let rec split n =
    try
      let pos = String.index_from s n c in
      let dir = String.sub s n (pos-n) in
      dir :: split (succ pos)
    with
      | Not_found -> [String.sub s n (len-n)]
  in
  if len = 0 then [] else split 0

let parse_loadpath s =
  let l = split_string_at '/' s in
  if List.mem "" l then
    invalid_arg "parse_loadpath: find an empty dir in loadpath";
  l

module Stringset = Set.Make(struct type t = string let compare = compare end)

module Stringmap = Map.Make(struct type t = string let compare = compare end)

type utf8_status = UnicodeLetter | UnicodeIdentPart | UnicodeSymbol

exception UnsupportedUtf8

(* The following table stores classes of Unicode characters that
   are used by the lexer. There are 3 different classes so 2 bits are
   allocated for each character. We only use 16 bits over the 31 bits
   to simplify the masking process. (This choice seems to be a good
   trade-off between speed and space after some benchmarks.) *)

(* A 256ko table, initially filled with zeros. *)
let table = Array.create (1 lsl 17) 0

(* Associate a 2-bit pattern to each status at position [i]. 
   Only the 3 lowest bits of [i] are taken into account to 
   define the position of the pattern in the word. 
   Notice that pattern "00" means "undefined". *)
let mask i = function
  | UnicodeLetter    -> 1 lsl ((i land 7) lsl 1) (* 01 *)
  | UnicodeIdentPart -> 2 lsl ((i land 7) lsl 1) (* 10 *)
  | UnicodeSymbol    -> 3 lsl ((i land 7) lsl 1) (* 11 *)

(* Helper to reset 2 bits in a word. *)
let reset_mask i =
  lnot (3 lsl ((i land 7) lsl 1))

(* Initialize the lookup table from a list of segments, assigning
   a status to every character of each segment. The order of these
   assignments is relevant: it is possible to assign status [s] to
   a segment [(c1, c2)] and later assign [s'] to [c] even if [c] is
   between [c1] and [c2]. *)
let mk_lookup_table_from_unicode_tables_for status tables =
  List.iter
    (List.iter
       (fun (c1, c2) ->
          for i = c1 to c2 do
            table.(i lsr 3) <-
              (table.(i lsr 3) land (reset_mask i)) lor (mask i status)
          done))
    tables

(* Look up into the table and interpret the found pattern. *)
let lookup x =
  let v = (table.(x lsr 3) lsr ((x land 7) lsl 1)) land 3 in
    if      v = 1 then UnicodeLetter
    else if v = 2 then UnicodeIdentPart
    else if v = 3 then UnicodeSymbol
    else raise UnsupportedUtf8

(* [classify_unicode] discriminates between 3 different kinds of
   symbols based on the standard unicode classification (extracted from
   Camomile). *)
let classify_unicode =
  let single c = [ (c, c) ] in
    (* General tables. *)
    mk_lookup_table_from_unicode_tables_for UnicodeSymbol
      [
        Unicodetable.sm;           (* Symbol, maths.             *)
        Unicodetable.sc;           (* Symbol, currency.          *)
        Unicodetable.so;           (* Symbol, modifier.          *)
        Unicodetable.pd;           (* Punctation, dash.          *)
        Unicodetable.pc;           (* Punctation, connector.     *)
        Unicodetable.pe;           (* Punctation, open.          *)
        Unicodetable.ps;           (* Punctation, close.         *)
        Unicodetable.pi;           (* Punctation, initial quote. *)
        Unicodetable.pf;           (* Punctation, final quote.   *)
        Unicodetable.po;           (* Punctation, other.         *)
      ];
    mk_lookup_table_from_unicode_tables_for UnicodeLetter
      [
        Unicodetable.lu;           (* Letter, uppercase.         *)
        Unicodetable.ll;           (* Letter, lowercase.         *)
        Unicodetable.lt;           (* Letter, titlecase.         *)
        Unicodetable.lo;           (* Letter, others.            *)
      ];
    mk_lookup_table_from_unicode_tables_for UnicodeIdentPart
      [
        Unicodetable.nd;           (* Number, decimal digits.    *)
        Unicodetable.nl;           (* Number, letter.            *)
        Unicodetable.no;           (* Number, other.             *)
      ];
    (* Exceptions (from a previous version of this function). *)
    mk_lookup_table_from_unicode_tables_for UnicodeSymbol
      [
        single 0x000B2;            (* Squared.                   *)
        single 0x0002E;            (* Dot.                       *)
      ];
    mk_lookup_table_from_unicode_tables_for UnicodeLetter
      [
        single 0x005F;             (* Underscore.                *)
        single 0x00A0;             (* Non breaking space.        *)
      ];
    mk_lookup_table_from_unicode_tables_for UnicodeIdentPart
      [
        single 0x0027;             (* Special space.             *)
      ];
    (* Lookup *)
    lookup

exception End_of_input

let utf8_of_unicode n =
  if n < 128 then
    String.make 1 (Char.chr n)
  else if n < 2048 then
    let s = String.make 2 (Char.chr (128 + n mod 64)) in
    begin
      s.[0] <- Char.chr (192 + n / 64);
      s
    end
  else if n < 65536 then
    let s = String.make 3 (Char.chr (128 + n mod 64)) in
    begin
      s.[1] <- Char.chr (128 + (n / 64) mod 64);
      s.[0] <- Char.chr (224 + n / 4096);
      s
    end
  else
    let s = String.make 4 (Char.chr (128 + n mod 64)) in
    begin
      s.[2] <- Char.chr (128 + (n / 64) mod 64);
      s.[1] <- Char.chr (128 + (n / 4096) mod 64);
      s.[0] <- Char.chr (240 + n / 262144);
      s
    end

let next_utf8 s i =
  let err () = invalid_arg "utf8" in
  let l = String.length s - i in
  if l = 0 then raise End_of_input
  else let a = Char.code s.[i] in if a <= 0x7F then
    1, a
  else if a land 0x40 = 0 or l = 1 then err ()
  else let b = Char.code s.[i+1] in if b land 0xC0 <> 0x80 then err ()
  else if a land 0x20 = 0 then
    2, (a land 0x1F) lsl 6 + (b land 0x3F)
  else if l = 2 then err ()
  else let c = Char.code s.[i+2] in if c land 0xC0 <> 0x80 then err ()
  else if a land 0x10 = 0 then
    3, (a land 0x0F) lsl 12 + (b land 0x3F) lsl 6 + (c land 0x3F)
  else if l = 3 then err ()
  else let d = Char.code s.[i+3] in if d land 0xC0 <> 0x80 then err ()
  else if a land 0x08 = 0 then
    4, (a land 0x07) lsl 18 + (b land 0x3F) lsl 12 +
       (c land 0x3F) lsl 6 + (d land 0x3F)
  else err ()

(* Check the well-formedness of an identifier *)

let initial_refutation j n s =
  match classify_unicode n with
  | UnicodeLetter -> None
  | _ ->
      let c = String.sub s 0 j in
      Some ("Invalid character '"^c^"' at beginning of identifier \""^s^"\".")

let trailing_refutation i j n s =
  match classify_unicode n with
  | UnicodeLetter | UnicodeIdentPart -> None
  | _ ->
      let c = String.sub s i j in
      Some ("Invalid character '"^c^"' in identifier \""^s^"\".")

let ident_refutation s =
  if s = ".." then None else try
    let j, n = next_utf8 s 0 in
      match initial_refutation j n s with
	|None ->
	   begin try
	     let rec aux i =
	       let j, n = next_utf8 s i in
		 match trailing_refutation i j n s with
		   |None -> aux (i + j)
		   |x -> x
	     in aux j
	   with End_of_input -> None
	   end
	|x -> x
  with
  | End_of_input -> Some "The empty string is not an identifier."
  | UnsupportedUtf8 -> Some (s^": unsupported character in utf8 sequence.")
  | Invalid_argument _ -> Some (s^": invalid utf8 sequence.")

let lowercase_unicode =
  let tree = Segmenttree.make Unicodetable.to_lower in
  fun unicode ->
    try
      match Segmenttree.lookup unicode tree with
	| `Abs c -> c
	| `Delta d -> unicode + d
    with Not_found -> unicode

let lowercase_first_char_utf8 s =
  assert (s <> "");
  let j, n = next_utf8 s 0 in
  utf8_of_unicode (lowercase_unicode n)

(** For extraction, we need to encode unicode character into ascii ones *)

let ascii_of_ident s =
  let check_ascii s =
    let ok = ref true in
    String.iter (fun c -> if Char.code c >= 128 then ok := false) s;
    !ok
  in
  if check_ascii s then s else
    let i = ref 0 and out = ref "" in
    begin try while true do
      let j, n = next_utf8 s !i in
      out :=
	if n >= 128
	then Printf.sprintf "%s__U%04x_" !out n
	else Printf.sprintf "%s%c" !out s.[!i];
      i := !i + j
    done with End_of_input -> () end;
    !out

(* Lists *)

let rec list_compare cmp l1 l2 =
  match l1,l2 with
      [], [] -> 0
    | _::_, [] -> 1
    | [], _::_ -> -1
    | x1::l1, x2::l2 ->
	(match cmp x1 x2 with
	   | 0 -> list_compare cmp l1 l2
	   | c -> c)

let rec list_equal cmp l1 l2 =
  match l1, l2 with
    | [], [] -> true
    | x1 :: l1, x2 :: l2 ->
      cmp x1 x2 && list_equal cmp l1 l2
    | _ -> false

let list_intersect l1 l2 =
  List.filter (fun x -> List.mem x l2) l1

let list_union l1 l2 =
  let rec urec = function
    | [] -> l2
    | a::l -> if List.mem a l2 then urec l else a::urec l
  in
  urec l1

let list_unionq l1 l2 =
  let rec urec = function
    | [] -> l2
    | a::l -> if List.memq a l2 then urec l else a::urec l
  in
  urec l1

let list_subtract l1 l2 =
  if l2 = [] then l1 else List.filter (fun x -> not (List.mem x l2)) l1

let list_subtractq l1 l2 =
  if l2 = [] then l1 else List.filter (fun x -> not (List.memq x l2)) l1

let list_tabulate f len =
  let rec tabrec n =
    if n = len then [] else (f n)::(tabrec (n+1))
  in
  tabrec 0

let list_addn n v =
  let rec aux n l =
    if n = 0 then l
    else aux (pred n) (v::l)
  in
    if n < 0 then invalid_arg "list_addn"
    else aux n

let list_make n v = list_addn n v []

let list_assign l n e =
  let rec assrec stk = function
    | ((h::t), 0) -> List.rev_append stk (e::t)
    | ((h::t), n) -> assrec (h::stk) (t, n-1)
    | ([], _) -> failwith "list_assign"
  in
  assrec [] (l,n)

let rec list_smartmap f l = match l with
    [] -> l
  | h::tl ->
      let h' = f h and tl' = list_smartmap f tl in
	if h'==h && tl'==tl then l
	else h'::tl'

let list_map_left f = (* ensures the order in case of side-effects *)
  let rec map_rec = function
    | [] -> []
    | x::l -> let v = f x in v :: map_rec l
  in
  map_rec

let list_map_i f =
  let rec map_i_rec i = function
    | [] -> []
    | x::l -> let v = f i x in v :: map_i_rec (i+1) l
  in
  map_i_rec

let list_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 list_map3 f l1 l2 l3 =
  let rec map = function
    | ([], [], []) -> []
    | ((h1::t1), (h2::t2), (h3::t3)) -> let v = f h1 h2 h3 in v::map (t1,t2,t3)
    | (_, _, _) -> invalid_arg "map3"
  in
  map (l1,l2,l3)

let list_map4 f l1 l2 l3 l4 =
  let rec map = function
    | ([], [], [], []) -> []
    | ((h1::t1), (h2::t2), (h3::t3), (h4::t4)) -> let v = f h1 h2 h3 h4 in v::map (t1,t2,t3,t4)
    | (_, _, _, _) -> invalid_arg "map4"
  in
  map (l1,l2,l3,l4)

let rec list_smartfilter f l = match l with
    [] -> l
  | h::tl ->
      let tl' = list_smartfilter f tl in
	if f h then
	  if tl' == tl then l
	  else h :: tl'
	else tl'
	  
let list_index_f f x =
  let rec index_x n = function
    | y::l -> if f x y then n else index_x (succ n) l
    | [] -> raise Not_found
  in
  index_x 1

let list_index0_f f x l = list_index_f f x l - 1

let list_index x =
  let rec index_x n = function
    | y::l -> if x = y then n else index_x (succ n) l
    | [] -> raise Not_found
  in
  index_x 1

let list_index0 x l = list_index x l - 1

let list_unique_index x =
  let rec index_x n = function
    | y::l ->
	if x = y then
	  if List.mem x l then raise Not_found
	  else n
	else index_x (succ n) l
    | [] -> raise Not_found
  in index_x 1

let list_fold_right_i f i l =
  let rec it_list_f i l a = match l with
    | [] -> a
    | b::l -> f (i-1) b (it_list_f (i-1) l a)
  in
  it_list_f (List.length l + i) l

let list_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 list_fold_left3 f accu l1 l2 l3 =
  match (l1, l2, l3) with
    ([], [], []) -> accu
  | (a1::l1, a2::l2, a3::l3) -> list_fold_left3 f (f accu a1 a2 a3) l1 l2 l3
  | (_, _, _) -> invalid_arg "list_fold_left3"

(* [list_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 rec list_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

let list_iter3 f l1 l2 l3 =
  let rec iter = function
    | ([], [], []) -> ()
    | ((h1::t1), (h2::t2), (h3::t3)) -> f h1 h2 h3; iter (t1,t2,t3)
    | (_, _, _) -> invalid_arg "map3"
  in
  iter (l1,l2,l3)

let list_iter_i f l = list_fold_left_i (fun i _ x -> f i x) 0 () l

let list_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 list_except x l = List.filter (fun y -> not (x = y)) l

let list_remove = list_except (* Alias *)

let rec list_remove_first a = function
  | b::l when a = b -> l
  | b::l -> b::list_remove_first a l
  | [] -> raise Not_found

let rec list_remove_assoc_in_triple x = function
  | [] -> []
  | (y,_,_ as z)::l -> if x = y then l else z::list_remove_assoc_in_triple x l

let rec list_assoc_snd_in_triple x = function
    [] -> raise Not_found
  | (a,b,_)::l -> if compare a x = 0 then b else list_assoc_snd_in_triple x l

let list_add_set x l = if List.mem x l then l else x::l

let list_eq_set l1 l2 =
  let rec aux l1 = function
  | [] -> l1 = []
  | a::l2 -> aux (list_remove_first a l1) l2 in
  try aux l1 l2 with Not_found -> false

let list_for_all2eq f l1 l2 =
  try List.for_all2 f l1 l2 with Invalid_argument _ -> false

let list_filter_i 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 list_sep_last = function
  | [] -> failwith "sep_last"
  | hd::[] -> (hd,[])
  | hd::tl -> let (l,tl) = list_sep_last tl in (l,hd::tl)

let list_try_find_i f =
  let rec try_find_f n = function
    | [] -> failwith "try_find_i"
    | h::t -> try f n h with Failure _ -> try_find_f (n+1) t
  in
  try_find_f

let list_try_find f =
  let rec try_find_f = function
    | [] -> failwith "try_find"
    | h::t -> try f h with Failure _ -> try_find_f t
  in
  try_find_f

let list_uniquize l =
  let visited = Hashtbl.create 23 in
  let rec aux acc = function
    | h::t -> if Hashtbl.mem visited h then aux acc t else
	  begin
	    Hashtbl.add visited h h;
	    aux (h::acc) t
	  end
    | [] -> List.rev acc
  in aux [] l

let rec list_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 rec list_merge_uniq cmp l1 l2 =
  match l1, l2 with
  | [], l2 -> l2
  | l1, [] -> l1
  | h1 :: t1, h2 :: t2 ->
      let c = cmp h1 h2 in
      if c = 0
      then h1 :: list_merge_uniq cmp t1 t2
      else if c <= 0
      then h1 :: list_merge_uniq cmp t1 l2
      else h2 :: list_merge_uniq cmp l1 t2

let rec list_duplicates = function
  | [] -> []
  | x::l ->
      let l' = list_duplicates l in
      if List.mem x l then list_add_set x l' else l'

let rec list_filter2 f = function
  | [], [] as p -> p
  | d::dp, l::lp ->
     let (dp',lp' as p) = list_filter2 f (dp,lp) in
      if f d l then d::dp', l::lp' else p
  | _ -> invalid_arg "list_filter2"

let rec list_map_filter f = function
  | [] -> []
  | x::l ->
      let l' = list_map_filter f l in
      match f x with None -> l' | Some y -> y::l'

let list_map_filter_i f =
  let rec aux i = function
    | [] -> []
    | x::l ->
      let l' = aux (succ i) l in
	match f i x with None -> l' | Some y -> y::l'
  in aux 0

let list_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

(* [list_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 list_chop n l =
  let rec chop_aux i acc = function
    | tl when i=0 -> (List.rev acc, tl)
    | h::t -> chop_aux (pred i) (h::acc) t
    | [] -> failwith "list_chop"
  in
  chop_aux n [] l

(* [list_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 list_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 []

(* [list_split_by p l] splits [l] into two lists [(l1,l2)] such that elements of
   [l1] satisfy [p] and elements of [l2] do not *)
let list_split_by p =
  let rec split_by_loop = function
  | []   -> ([],[])
  | a::l ->
      let (l1,l2) = split_by_loop l in if p a then (a::l1,l2) else (l1,a::l2)
  in
  split_by_loop

let rec list_split3 = function
  | [] -> ([], [], [])
  | (x,y,z)::l ->
      let (rx, ry, rz) = list_split3 l in (x::rx, y::ry, z::rz)

let rec list_insert_in_class f a = function
  | [] -> [[a]]
  | (b::_ as l)::classes when f a b -> (a::l)::classes
  | l::classes -> l :: list_insert_in_class f a classes

let list_partition_by f l =
  List.fold_right (list_insert_in_class f) l []

let list_firstn n l =
  let rec aux acc = function
    | (0, l) -> List.rev acc
    | (n, (h::t)) -> aux (h::acc) (pred n, t)
    | _ -> failwith "firstn"
  in
  aux [] (n,l)

let rec list_last = function
  | [] -> failwith "list_last"
  | [x] -> x
  | _ :: l -> list_last l

let list_lastn n l =
  let len = List.length l in
  let rec aux m l =
    if m = n then l else aux (m - 1) (List.tl l)
  in
  if len < n then failwith "lastn" else aux len l

let rec list_skipn n l = match n,l with
  | 0, _ -> l
  | _, [] -> failwith "list_skipn"
  | n, _::l -> list_skipn (pred n) l

let rec list_skipn_at_least n l =
  try list_skipn n l with Failure _ -> []

let list_prefix_of prefl l =
  let rec prefrec = function
    | (h1::t1, h2::t2) -> h1 = h2 && prefrec (t1,t2)
    | ([], _) -> true
    | (_, _) -> false
  in
    prefrec (prefl,l)

let list_drop_prefix p l =
(* if l=p++t then return t else l *)
  let rec list_drop_prefix_rec = function
    | ([], tl) -> Some tl
    | (_, []) -> None
    | (h1::tp, h2::tl) ->
	if h1 = h2 then list_drop_prefix_rec (tp,tl) else None
  in
    match list_drop_prefix_rec (p,l) with
      | Some r -> r
      | None -> l

let list_map_append f l = List.flatten (List.map f l)
let list_join_map = list_map_append   (* Alias *)

let list_map_append2 f l1 l2 = List.flatten (List.map2 f l1 l2)

let list_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)

let rec list_fold_map f e = function
  |  []  -> (e,[])
  |  h::t ->
       let e',h' = f e h in
       let e'',t' = list_fold_map f e' t in
         e'',h'::t'

(* (* tail-recursive version of the above function *)
let list_fold_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 list_fold_map' f l e =
  List.fold_right (fun x (l,e) -> let (y,e) = f x e in (y::l,e)) l ([],e)

let list_map_assoc f = List.map (fun (x,a) -> (x,f a))

let rec list_assoc_f f a = function
  | (x, e) :: xs -> if f a x then e else list_assoc_f f a xs
  | [] -> raise Not_found

(* Specification:
   - =p= is set equality (double inclusion)
   - f such that \forall l acc, (f l acc) =p= append (f l []) acc
   - let g = fun x -> f x [] in
   - union_map f l acc =p= append (flatten (map g l)) acc
 *)
let list_union_map f l acc =
  List.fold_left
    (fun x y -> f y x)
    acc
    l

(* A generic cartesian product: for any operator (**),
   [list_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 rec list_cartesian op l1 l2 =
  list_map_append (fun x -> List.map (op x) l2) l1

(* [list_cartesians] is an n-ary cartesian product: it iterates
   [list_cartesian] over a list of lists.  *)

let list_cartesians op init ll =
  List.fold_right (list_cartesian op) ll [init]

(* list_combinations [[a;b];[c;d]] gives [[a;c];[a;d];[b;c];[b;d]] *)

let list_combinations l = list_cartesians (fun x l -> x::l) [] l

let rec list_combine3 x y z = 
  match x, y, z with
  | [], [], [] -> []
  | (x :: xs), (y :: ys), (z :: zs) ->
      (x, y, z) :: list_combine3 xs ys zs
  | _, _, _ -> raise (Invalid_argument "list_combine3")
  
(* Keep only those products that do not return None *)

let rec list_cartesian_filter op l1 l2 =
  list_map_append (fun x -> list_map_filter (op x) l2) l1

(* Keep only those products that do not return None *)

let rec list_cartesians_filter op init ll =
  List.fold_right (list_cartesian_filter op) ll [init]

(* Drop the last element of a list *)

let rec list_drop_last = function [] -> assert false | hd :: [] -> [] | hd :: tl -> hd :: list_drop_last tl

(* Arrays *)

let array_compare item_cmp v1 v2 =
  let c = compare (Array.length v1) (Array.length v2) in
  if c<>0 then c else
    let rec cmp = function
	-1 -> 0
      | i ->
	  let c' = item_cmp v1.(i) v2.(i) in
	  if c'<>0 then c'
	  else cmp (i-1) in
    cmp (Array.length v1 - 1)

let array_equal cmp t1 t2 =
  Array.length t1 = Array.length t2 &&
  let rec aux i =
    (i = Array.length t1) || (cmp t1.(i) t2.(i) && aux (i + 1))
  in aux 0

let array_exists f v =
  let rec exrec = function
    | -1 -> false
    | n -> (f v.(n)) || (exrec (n-1))
  in
  exrec ((Array.length v)-1)

let array_for_all f v =
  let rec allrec = function
    | -1 -> true
    | n -> (f v.(n)) && (allrec (n-1))
  in
  allrec ((Array.length v)-1)

let array_for_all2 f v1 v2 =
  let rec allrec = function
    | -1 -> true
    | n -> (f v1.(n) v2.(n)) && (allrec (n-1))
  in
  let lv1 = Array.length v1 in
  lv1 = Array.length v2 && allrec (pred lv1)

let array_for_all3 f v1 v2 v3 =
  let rec allrec = function
    | -1 -> true
    | n -> (f v1.(n) v2.(n) v3.(n)) && (allrec (n-1))
  in
  let lv1 = Array.length v1 in
  lv1 = Array.length v2 && lv1 = Array.length v3 && allrec (pred lv1)

let array_for_all4 f v1 v2 v3 v4 =
  let rec allrec = function
    | -1 -> true
    | n -> (f v1.(n) v2.(n) v3.(n) v4.(n)) && (allrec (n-1))
  in
  let lv1 = Array.length v1 in
  lv1 = Array.length v2 &&
  lv1 = Array.length v3 &&
  lv1 = Array.length v4 &&
    allrec (pred lv1)

let array_for_all_i f i v =
  let rec allrec i n = n = Array.length v || f i v.(n) && allrec (i+1) (n+1) in
  allrec i 0

exception Found of int

let array_find_i (pred: int -> 'a -> bool) (arr: 'a array) : int option =
  try
    for i=0 to Array.length arr - 1 do if pred i (arr.(i)) then raise (Found i) done;
    None
  with Found i -> Some i

let array_hd v =
  match Array.length v with
    | 0 -> failwith "array_hd"
    | _ -> v.(0)

let array_tl v =
  match Array.length v with
    | 0 -> failwith "array_tl"
    | n -> Array.sub v 1 (pred n)

let array_last v =
  match Array.length v with
    | 0 -> failwith "array_last"
    | n -> v.(pred n)

let array_cons e v = Array.append [|e|] v

let array_rev t =
  let n=Array.length t in
    if n <=0 then ()
    else
      let tmp=ref t.(0) in
      for i=0 to pred (n/2) do
	tmp:=t.((pred n)-i);
	t.((pred n)-i)<- t.(i);
	t.(i)<- !tmp
      done

let array_fold_right_i f v a =
  let rec fold a n =
    if n=0 then a
    else
      let k = n-1 in
      fold (f k v.(k) a) k in
  fold a (Array.length v)

let array_fold_left_i f v a =
  let n = Array.length a in
  let rec fold i v = if i = n then v else fold (succ i) (f i v a.(i)) in
  fold 0 v

let array_fold_right2 f v1 v2 a =
  let lv1 = Array.length v1 in
  let rec fold a n =
    if n=0 then a
    else
      let k = n-1 in
      fold (f v1.(k) v2.(k) a) k in
  if Array.length v2 <> lv1 then invalid_arg "array_fold_right2";
  fold a lv1

let array_fold_left2 f a v1 v2 =
  let lv1 = Array.length v1 in
  let rec fold a n =
    if n >= lv1 then a else fold (f a v1.(n) v2.(n)) (succ n)
  in
  if Array.length v2 <> lv1 then invalid_arg "array_fold_left2";
  fold a 0

let array_fold_left2_i f a v1 v2 =
  let lv1 = Array.length v1 in
  let rec fold a n =
    if n >= lv1 then a else fold (f n a v1.(n) v2.(n)) (succ n)
  in
  if Array.length v2 <> lv1 then invalid_arg "array_fold_left2";
  fold a 0

let array_fold_left3 f a v1 v2 v3 =
  let lv1 = Array.length v1 in
  let rec fold a n =
    if n >= lv1 then a else fold (f a v1.(n) v2.(n) v3.(n)) (succ n)
  in
  if Array.length v2 <> lv1 || Array.length v3 <> lv1 then
    invalid_arg "array_fold_left2";
  fold a 0

let array_fold_left_from n f a v =
  let rec fold a n =
    if n >= Array.length v then a else fold (f a v.(n)) (succ n)
  in
  fold a n

let array_fold_right_from n f v a =
  let rec fold n =
    if n >= Array.length v then a else f v.(n) (fold (succ n))
  in
  fold n

let array_app_tl v l =
  if Array.length v = 0 then invalid_arg "array_app_tl";
  array_fold_right_from 1 (fun e l -> e::l) v l

let array_list_of_tl v =
  if Array.length v = 0 then invalid_arg "array_list_of_tl";
  array_fold_right_from 1 (fun e l -> e::l) v []

let array_map_to_list f v =
  List.map f (Array.to_list v)

let array_chop n v =
  let vlen = Array.length v in
  if n > vlen then failwith "array_chop";
  (Array.sub v 0 n, Array.sub v n (vlen-n))

exception Local of int

(* If none of the elements is changed by f we return ar itself.
   The for loop looks for the first such an element.
   If found it is temporarily stored in a ref and the new array is produced,
   but f is not re-applied to elements that are already checked *)
let array_smartmap f ar =
  let ar_size = Array.length ar in
  let aux = ref None in
  try
    for i = 0 to ar_size-1 do
      let a = ar.(i) in
      let a' = f a in
	if a != a' then (* pointer (in)equality *) begin
	  aux := Some a';
	  raise (Local i)
	end
    done;
    ar
  with
      Local i ->
	let copy j =
	  if j<i then ar.(j)
	  else if j=i then
	    match !aux with Some a' -> a' | None -> failwith "Error"
	  else f (ar.(j))
	in
	  Array.init ar_size copy

let array_map2 f v1 v2 =
  if Array.length v1 <> Array.length v2 then invalid_arg "array_map2";
  if Array.length v1 == 0 then
    [| |]
  else begin
    let res = Array.create (Array.length v1) (f v1.(0) v2.(0)) in
    for i = 1 to pred (Array.length v1) do
      res.(i) <- f v1.(i) v2.(i)
    done;
    res
  end

let array_map2_i f v1 v2 =
  if Array.length v1 <> Array.length v2 then invalid_arg "array_map2";
  if Array.length v1 == 0 then
    [| |]
  else begin
    let res = Array.create (Array.length v1) (f 0 v1.(0) v2.(0)) in
    for i = 1 to pred (Array.length v1) do
      res.(i) <- f i v1.(i) v2.(i)
    done;
    res
  end

let array_map3 f v1 v2 v3 =
  if Array.length v1 <> Array.length v2 ||
     Array.length v1 <> Array.length v3 then invalid_arg "array_map3";
  if Array.length v1 == 0 then
    [| |]
  else begin
    let res = Array.create (Array.length v1) (f v1.(0) v2.(0) v3.(0)) in
    for i = 1 to pred (Array.length v1) do
      res.(i) <- f v1.(i) v2.(i) v3.(i)
    done;
    res
  end

let array_map_left f a = (* Ocaml does not guarantee Array.map is LR *)
  let l = Array.length a in (* (even if so), then we rewrite it *)
  if l = 0 then [||] else begin
    let r = Array.create l (f a.(0)) in
    for i = 1 to l - 1 do
      r.(i) <- f a.(i)
    done;
    r
  end

let array_map_left_pair f a g b =
  let l = Array.length a in
  if l = 0 then [||],[||] else begin
    let r = Array.create l (f a.(0)) in
    let s = Array.create l (g b.(0)) in
    for i = 1 to l - 1 do
      r.(i) <- f a.(i);
      s.(i) <- g b.(i)
    done;
    r, s
  end

let array_iter2 f v1 v2 =
  let n = Array.length v1 in
  if Array.length v2 <> n then invalid_arg "array_iter2"
  else for i = 0 to n - 1 do f v1.(i) v2.(i) done

let pure_functional = false

let array_fold_map' f v e =
if pure_functional then
  let (l,e) =
    Array.fold_right
      (fun x (l,e) -> let (y,e) = f x e in (y::l,e))
      v ([],e) in
  (Array.of_list l,e)
else
  let e' = ref e in
  let v' = Array.map (fun x -> let (y,e) = f x !e' in e' := e; y) v in
  (v',!e')

let array_fold_map f e v =
  let e' = ref e in
  let v' = Array.map (fun x -> let (e,y) = f !e' x in e' := e; y) v in
  (!e',v')

let array_fold_map2' f v1 v2 e =
  let e' = ref e in
  let v' =
    array_map2 (fun x1 x2 -> let (y,e) = f x1 x2 !e' in e' := e; y) v1 v2
  in
  (v',!e')

let array_distinct v =
  let visited = Hashtbl.create 23 in
  try
    Array.iter
      (fun x ->
        if Hashtbl.mem visited x then raise Exit
        else Hashtbl.add visited x x)
      v;
    true
  with Exit -> false

let array_union_map f a acc =
  Array.fold_left
    (fun x y -> f y x)
    acc
    a

let array_rev_to_list a =
  let rec tolist i res =
    if i >= Array.length a then res else tolist (i+1) (a.(i) :: res) in
  tolist 0 []

(* Stream *)

let stream_nth n st =
  try List.nth (Stream.npeek (n+1) st) n
  with Failure _ -> raise Stream.Failure

let stream_njunk n st =
  for i = 1 to n do Stream.junk st done

(* Matrices *)

let matrix_transpose mat =
  List.fold_right (List.map2 (fun p c -> p::c)) mat
    (if mat = [] then [] else List.map (fun _ -> []) (List.hd mat))

(* Functions *)

let identity x = x

let compose f g x = f (g x)

let const x _ = x

let iterate f =
  let rec iterate_f n x =
    if n <= 0 then x else iterate_f (pred n) (f x)
  in
  iterate_f

let repeat n f x =
  for i = 1 to n do f x done

let iterate_for a b f x =
  let rec iterate i v = if i > b then v else iterate (succ i) (f i v) in
  iterate a x

(* Delayed computations *)

type 'a delayed = unit -> 'a

let delayed_force f = f ()

(* Misc *)

type ('a,'b) union = Inl of 'a | Inr of 'b

module Intset = Set.Make(struct type t = int let compare = compare end)

module Intmap = Map.Make(struct type t = int let compare = compare end)

let intmap_in_dom x m =
  try let _ = Intmap.find x m in true with Not_found -> false

let intmap_to_list m = Intmap.fold (fun n v l -> (n,v)::l) m []

let intmap_inv m b = Intmap.fold (fun n v l -> if v = b then n::l else l) m []

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 map_succeed f =
  let rec map_f = function
    | [] -> []
    |  h::t -> try (let x = f h in x :: map_f t) with Failure _ -> map_f t
  in
  map_f

(*s Memoization *)

let memo1_eq eq f =
  let m = ref None in
  fun x ->
    match !m with
        Some(x',y') when eq x x' -> y'
      | _ -> let y = f x in m := Some(x,y); y

let memo1_1 f = memo1_eq (==) f
let memo1_2 f =
  let f' =
    memo1_eq (fun (x,y) (x',y') -> x==x' && y==y') (fun (x,y) -> f x y) in
  (fun x y -> f'(x,y))

(* Memorizes the last n distinct calls to f. Since there is no hash,
   Efficient only for small n. *)
let memon_eq eq n f =
  let cache = ref [] in (* the cache: a stack *)
  let m = ref 0 in      (* usage of the cache *)
  let rec find x = function
    | (x',y')::l when eq x x' -> y', l (* cell is moved to the top *)
    | [] -> (* we assume n>0, so creating one memo cell is OK *)
        incr m; (f x, [])
    | [_] when !m>=n -> f x,[] (* cache is full: dispose of last cell *)
    | p::l (* not(eq x (fst p)) *) -> let (y,l') = find x l in (y, p::l')
  in
  (fun x ->
    let (y,l) = find x !cache in
    cache := (x,y)::l;
    y)


(*s Size of ocaml values. *)

module Size = struct

  (*s Pointers already visited are stored in a hash-table, where
      comparisons are done using physical equality. *)

  module H = Hashtbl.Make(
    struct
      type t = Obj.t
      let equal = (==)
      let hash o = Hashtbl.hash (Obj.magic o : int)
    end)

  let node_table = (H.create 257 : unit H.t)

  let in_table o = try H.find node_table o; true with Not_found -> false

  let add_in_table o = H.add node_table o ()

  let reset_table () = H.clear node_table

  (*s Objects are traversed recursively, as soon as their tags are less than
      [no_scan_tag]. [count] records the numbers of words already visited. *)

  let size_of_double = Obj.size (Obj.repr 1.0)

  let count = ref 0

  let rec traverse t =
    if not (in_table t) then begin
      add_in_table t;
      if Obj.is_block t then begin
	let n = Obj.size t in
	let tag = Obj.tag t in
	if tag < Obj.no_scan_tag then begin
	  count := !count + 1 + n;
	  for i = 0 to n - 1 do
      	    let f = Obj.field t i in
	    if Obj.is_block f then traverse f
	  done
	end else if tag = Obj.string_tag then
	  count := !count + 1 + n
	else if tag = Obj.double_tag then
	  count := !count + size_of_double
	else if tag = Obj.double_array_tag then
	  count := !count + 1 + size_of_double * n
	else
	  incr count
      end
    end

  (*s Sizes of objects in words and in bytes. The size in bytes is computed
      system-independently according to [Sys.word_size]. *)

  let size_w o =
    reset_table ();
    count := 0;
    traverse (Obj.repr o);
    !count

  let size_b o = (size_w o) * (Sys.word_size / 8)

  let size_kb o = (size_w o) / (8192 / Sys.word_size)

end

let size_w = Size.size_w
let size_b = Size.size_b
let size_kb = Size.size_kb

(*s Total size of the allocated ocaml heap. *)

let heap_size () =
  let stat = Gc.stat ()
  and control = Gc.get () in
  let max_words_total = stat.Gc.heap_words + control.Gc.minor_heap_size in
  (max_words_total * (Sys.word_size / 8))

let heap_size_kb () = (heap_size () + 1023) / 1024

(*s interruption *)

let interrupt = ref false
let check_for_interrupt () =
  if !interrupt then begin interrupt := false; raise Sys.Break end