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(************************************************************************)
(* * 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) *)
(************************************************************************)
module type OrderedType =
sig
type t
val compare : t -> t -> int
end
module type MonadS =
sig
type +'a t
val return : 'a -> 'a t
val (>>=) : 'a t -> ('a -> 'b t) -> 'b t
end
module type S = Map.S
module type ExtS =
sig
include CSig.MapS
module Set : CSig.SetS with type elt = key
val get : key -> 'a t -> 'a
val set : key -> 'a -> 'a t -> 'a t
val modify : key -> (key -> 'a -> 'a) -> 'a t -> 'a t
val domain : 'a t -> Set.t
val bind : (key -> 'a) -> Set.t -> 'a t
val fold_left : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val fold_right : (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val height : 'a t -> int
val filter_range : (key -> int) -> 'a t -> 'a t
val update: key -> ('a option -> 'a option) -> 'a t -> 'a t
module Smart :
sig
val map : ('a -> 'a) -> 'a t -> 'a t
val mapi : (key -> 'a -> 'a) -> 'a t -> 'a t
end
module Unsafe :
sig
val map : (key -> 'a -> key * 'b) -> 'a t -> 'b t
end
module Monad(M : MonadS) :
sig
val fold : (key -> 'a -> 'b -> 'b M.t) -> 'a t -> 'b -> 'b M.t
val fold_left : (key -> 'a -> 'b -> 'b M.t) -> 'a t -> 'b -> 'b M.t
val fold_right : (key -> 'a -> 'b -> 'b M.t) -> 'a t -> 'b -> 'b M.t
end
end
module MapExt (M : Map.OrderedType) :
sig
type 'a map = 'a Map.Make(M).t
val set : M.t -> 'a -> 'a map -> 'a map
val modify : M.t -> (M.t -> 'a -> 'a) -> 'a map -> 'a map
val domain : 'a map -> Set.Make(M).t
val bind : (M.t -> 'a) -> Set.Make(M).t -> 'a map
val fold_left : (M.t -> 'a -> 'b -> 'b) -> 'a map -> 'b -> 'b
val fold_right : (M.t -> 'a -> 'b -> 'b) -> 'a map -> 'b -> 'b
val height : 'a map -> int
val filter_range : (M.t -> int) -> 'a map -> 'a map
val update: M.t -> ('a option -> 'a option) -> 'a map -> 'a map
module Smart :
sig
val map : ('a -> 'a) -> 'a map -> 'a map
val mapi : (M.t -> 'a -> 'a) -> 'a map -> 'a map
end
module Unsafe :
sig
val map : (M.t -> 'a -> M.t * 'b) -> 'a map -> 'b map
end
module Monad(MS : MonadS) :
sig
val fold : (M.t -> 'a -> 'b -> 'b MS.t) -> 'a map -> 'b -> 'b MS.t
val fold_left : (M.t -> 'a -> 'b -> 'b MS.t) -> 'a map -> 'b -> 'b MS.t
val fold_right : (M.t -> 'a -> 'b -> 'b MS.t) -> 'a map -> 'b -> 'b MS.t
end
end =
struct
(** This unsafe module is a way to access to the actual implementations of
OCaml sets and maps without reimplementing them ourselves. It is quite
dubious that these implementations will ever be changed... Nonetheless,
if this happens, we can still implement a less clever version of [domain].
*)
module F = Map.Make(M)
type 'a map = 'a F.t
module S = Set.Make(M)
type set = S.t
type 'a _map =
| MEmpty
| MNode of {l:'a map; v:F.key; d:'a; r:'a map; h:int}
type _set =
| SEmpty
| SNode of set * M.t * set * int
let map_prj : 'a map -> 'a _map = Obj.magic
let map_inj : 'a _map -> 'a map = Obj.magic
let set_prj : set -> _set = Obj.magic
let set_inj : _set -> set = Obj.magic
let rec set k v (s : 'a map) : 'a map = match map_prj s with
| MEmpty -> raise Not_found
| MNode {l; v=k'; d=v'; r; h} ->
let c = M.compare k k' in
if c < 0 then
let l' = set k v l in
if l == l' then s
else map_inj (MNode {l=l'; v=k'; d=v'; r; h})
else if c = 0 then
if v' == v then s
else map_inj (MNode {l; v=k'; d=v; r; h})
else
let r' = set k v r in
if r == r' then s
else map_inj (MNode {l; v=k'; d=v'; r=r'; h})
let rec modify k f (s : 'a map) : 'a map = match map_prj s with
| MEmpty -> raise Not_found
| MNode {l; v; d; r; h} ->
let c = M.compare k v in
if c < 0 then
let l' = modify k f l in
if l == l' then s
else map_inj (MNode {l=l'; v; d; r; h})
else if c = 0 then
let d' = f v d in
if d' == d then s
else map_inj (MNode {l; v; d=d'; r; h})
else
let r' = modify k f r in
if r == r' then s
else map_inj (MNode {l; v; d; r=r'; h})
let rec domain (s : 'a map) : set = match map_prj s with
| MEmpty -> set_inj SEmpty
| MNode {l; v; r; h; _} ->
set_inj (SNode (domain l, v, domain r, h))
(** This function is essentially identity, but OCaml current stdlib does not
take advantage of the similarity of the two structures, so we introduce
this unsafe loophole. *)
let rec bind f (s : set) : 'a map = match set_prj s with
| SEmpty -> map_inj MEmpty
| SNode (l, k, r, h) ->
map_inj (MNode { l=bind f l; v=k; d=f k; r=bind f r; h})
(** Dual operation of [domain]. *)
let rec fold_left f (s : 'a map) accu = match map_prj s with
| MEmpty -> accu
| MNode {l; v=k; d=v; r; h} ->
let accu = f k v (fold_left f l accu) in
fold_left f r accu
let rec fold_right f (s : 'a map) accu = match map_prj s with
| MEmpty -> accu
| MNode {l; v=k; d=v; r; h} ->
let accu = f k v (fold_right f r accu) in
fold_right f l accu
let height s = match map_prj s with
| MEmpty -> 0
| MNode {h;_} -> h
(* Filter based on a range *)
let filter_range in_range m =
let rec aux m = function
| MEmpty -> m
| MNode {l; v; d; r; _} ->
let vr = in_range v in
(* the range is below the current value *)
if vr < 0 then aux m (map_prj l)
(* the range is above the current value *)
else if vr > 0 then aux m (map_prj r)
(* The current value is in the range *)
else
let m = aux m (map_prj l) in
let m = aux m (map_prj r) in
F.add v d m
in aux F.empty (map_prj m)
(* Imported from OCaml upstream until we can bump the version *)
let create l x d r =
let hl = height l and hr = height r in
map_inj @@ MNode{l; v=x; d; r; h=(if hl >= hr then hl + 1 else hr + 1)}
let bal l x d r =
let hl = match map_prj l with MEmpty -> 0 | MNode {h} -> h in
let hr = match map_prj r with MEmpty -> 0 | MNode {h} -> h in
if hl > hr + 2 then begin
match map_prj l with
| MEmpty -> invalid_arg "Map.bal"
| MNode{l=ll; v=lv; d=ld; r=lr} ->
if height ll >= height lr then
create ll lv ld (create lr x d r)
else begin
match map_prj lr with
| MEmpty -> invalid_arg "Map.bal"
| MNode{l=lrl; v=lrv; d=lrd; r=lrr}->
create (create ll lv ld lrl) lrv lrd (create lrr x d r)
end
end else if hr > hl + 2 then begin
match map_prj r with
| MEmpty -> invalid_arg "Map.bal"
| MNode{l=rl; v=rv; d=rd; r=rr} ->
if height rr >= height rl then
create (create l x d rl) rv rd rr
else begin
match map_prj rl with
| MEmpty -> invalid_arg "Map.bal"
| MNode{l=rll; v=rlv; d=rld; r=rlr} ->
create (create l x d rll) rlv rld (create rlr rv rd rr)
end
end else
map_inj @@ MNode{l; v=x; d; r; h=(if hl >= hr then hl + 1 else hr + 1)}
let rec remove_min_binding m = match map_prj m with
| MEmpty -> invalid_arg "Map.remove_min_elt"
| MNode {l;v;d;r;_} ->
match map_prj l with
| MEmpty -> r
| _ -> bal (remove_min_binding l) v d r
let merge t1 t2 =
match (map_prj t1, map_prj t2) with
(MEmpty, t) -> map_inj t
| (t, MEmpty) -> map_inj t
| (_, _) ->
let (x, d) = F.min_binding t2 in
bal t1 x d (remove_min_binding t2)
let rec update x f m = match map_prj m with
| MEmpty ->
begin match f None with
| None -> map_inj MEmpty
| Some data -> map_inj @@ MNode{l=map_inj MEmpty; v=x; d=data; r=map_inj MEmpty; h=1}
end
| MNode {l; v; d; r; h} as m ->
let c = M.compare x v in
if c = 0 then begin
match f (Some d) with
| None -> merge l r
| Some data ->
if d == data then map_inj m else
map_inj @@ MNode{l; v=x; d=data; r; h}
end else if c < 0 then
let ll = update x f l in
if l == ll then map_inj m else bal ll v d r
else
let rr = update x f r in
if r == rr then map_inj m else bal l v d rr
(* End of Imported OCaml *)
module Smart =
struct
let rec map f (s : 'a map) = match map_prj s with
| MEmpty -> map_inj MEmpty
| MNode {l; v=k; d=v; r; h} ->
let l' = map f l in
let r' = map f r in
let v' = f v in
if l == l' && r == r' && v == v' then s
else map_inj (MNode {l=l'; v=k; d=v'; r=r'; h})
let rec mapi f (s : 'a map) = match map_prj s with
| MEmpty -> map_inj MEmpty
| MNode {l; v=k; d=v; r; h} ->
let l' = mapi f l in
let r' = mapi f r in
let v' = f k v in
if l == l' && r == r' && v == v' then s
else map_inj (MNode {l=l'; v=k; d=v'; r=r'; h})
end
module Unsafe =
struct
let rec map f (s : 'a map) : 'b map = match map_prj s with
| MEmpty -> map_inj MEmpty
| MNode {l; v=k; d=v; r; h} ->
let (k, v) = f k v in
map_inj (MNode {l=map f l; v=k; d=v; r=map f r; h})
end
module Monad(M : MonadS) =
struct
open M
let rec fold_left f s accu = match map_prj s with
| MEmpty -> return accu
| MNode {l; v=k; d=v; r; h} ->
fold_left f l accu >>= fun accu ->
f k v accu >>= fun accu ->
fold_left f r accu
let rec fold_right f s accu = match map_prj s with
| MEmpty -> return accu
| MNode {l; v=k; d=v; r; h} ->
fold_right f r accu >>= fun accu ->
f k v accu >>= fun accu ->
fold_right f l accu
let fold = fold_left
end
end
module Make(M : Map.OrderedType) =
struct
include Map.Make(M)
include MapExt(M)
let get k m = try find k m with Not_found -> assert false
end
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