AStat/libs/mapext.ml

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(*
Cours "Semantics and applications to verification"
Antoine Miné 2014
Marc Chevalier 2018
Ecole normale supérieure, Paris, France / CNRS / INRIA
*)
(*
This file is derived from the map.ml file from the OCaml distribution.
Changes are marked with the [AM] or [MC] symbol.
Based on rev. 10468 2010-05-25 13:29:43Z
[MC] Updated to follow map.ml as in
Based on rev. 2d6ed01bd89099e93b3a8dd7cad941156f70bce5
Thu Feb 22 14:01:15 2018 +0100
Original copyright follows.
*)
(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* en Automatique. All rights reserved. This file is distributed *)
(* under the terms of the GNU Library General Public License, with *)
(* the special exception on linking described in file ../LICENSE. *)
(* *)
(***********************************************************************)
module type OrderedType =
sig
type t
val compare: t -> t -> int
end
module type S =
sig
type key
type +'a t
val empty: 'a t
val is_empty: 'a t -> bool
val mem: key -> 'a t -> bool
val add: key -> 'a -> 'a t -> 'a t
val update: key -> ('a option -> 'a option) -> 'a t -> 'a t
val singleton: key -> 'a -> 'a t
val remove: key -> 'a t -> 'a t
val merge:
(key -> 'a option -> 'b option -> 'c option) -> 'a t -> 'b t -> 'c t
val union: (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
val compare: ('a -> 'a -> int) -> 'a t -> 'a t -> int
val equal: ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
val iter: (key -> 'a -> unit) -> 'a t -> unit
val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
val for_all: (key -> 'a -> bool) -> 'a t -> bool
val exists: (key -> 'a -> bool) -> 'a t -> bool
val filter: (key -> 'a -> bool) -> 'a t -> 'a t
val partition: (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
val cardinal: 'a t -> int
val bindings: 'a t -> (key * 'a) list
val min_binding: 'a t -> (key * 'a)
val min_binding_opt: 'a t -> (key * 'a) option
val max_binding: 'a t -> (key * 'a)
val max_binding_opt: 'a t -> (key * 'a) option
val choose: 'a t -> (key * 'a)
val choose_opt: 'a t -> (key * 'a) option
val split: key -> 'a t -> 'a t * 'a option * 'a t
val find: key -> 'a t -> 'a
val find_opt: key -> 'a t -> 'a option
val find_first: (key -> bool) -> 'a t -> key * 'a
val find_first_opt: (key -> bool) -> 'a t -> (key * 'a) option
val find_last: (key -> bool) -> 'a t -> key * 'a
val find_last_opt: (key -> bool) -> 'a t -> (key * 'a) option
val map: ('a -> 'b) -> 'a t -> 'b t
val mapi: (key -> 'a -> 'b) -> 'a t -> 'b t
(* [AM] additions by Antoine Mine' *)
val of_list: (key * 'a) list -> 'a t
val map2: (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val iter2: (key -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit
val fold2: (key -> 'a -> 'b -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c
val for_all2: (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val exists2: (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val map2z: (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
val iter2z: (key -> 'a -> 'a -> unit) -> 'a t -> 'a t -> unit
val fold2z: (key -> 'a -> 'a -> 'b -> 'b) -> 'a t -> 'a t -> 'b -> 'b
val for_all2z: (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
val exists2z: (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
val map2o: (key -> 'a -> 'c) -> (key -> 'b -> 'c) -> (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
val iter2o: (key -> 'a -> unit) -> (key -> 'b -> unit) -> (key -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit
val fold2o: (key -> 'a -> 'c -> 'c) -> (key -> 'b -> 'c -> 'c) -> (key -> 'a -> 'b -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c
val for_all2o: (key -> 'a -> bool) -> (key -> 'b -> bool) -> (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val exists2o: (key -> 'a -> bool) -> (key -> 'b -> bool) -> (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
val map2zo: (key -> 'a -> 'a) -> (key -> 'a -> 'a) -> (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
val iter2zo: (key -> 'a -> unit) -> (key -> 'a -> unit) -> (key -> 'a -> 'a -> unit) -> 'a t -> 'a t -> unit
val fold2zo: (key -> 'a -> 'b -> 'b) -> (key -> 'a -> 'b -> 'b) -> (key -> 'a -> 'a -> 'b -> 'b) -> 'a t -> 'a t -> 'b -> 'b
val for_all2zo: (key -> 'a -> bool) -> (key -> 'a -> bool) -> (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
val exists2zo: (key -> 'a -> bool) -> (key -> 'a -> bool) -> (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
val map_slice: (key -> 'a -> 'a) -> 'a t -> key -> key -> 'a t
val iter_slice: (key -> 'a -> unit) -> 'a t -> key -> key -> unit
val fold_slice: (key -> 'a -> 'b -> 'b) -> 'a t -> key -> key -> 'b -> 'b
val for_all_slice: (key -> 'a -> bool) -> 'a t -> key -> key -> bool
val exists_slice: (key -> 'a -> bool) -> 'a t -> key -> key -> bool
val key_equal: 'a t -> 'a t -> bool
val key_subset: 'a t -> 'a t -> bool
val find_greater: key -> 'a t -> key * 'a
val find_less: key -> 'a t -> key * 'a
val find_greater_equal: key -> 'a t -> key * 'a
val find_less_equal: key -> 'a t -> key * 'a
end
module Make(Ord: OrderedType) = (struct
type key = Ord.t
(* BEGIN [MC] compatibility with ocaml < 4.03.0 *)
type 'a node_type = {l:'a t; v:key; d:'a; r:'a t; h:int}
and 'a t =
Empty
| Node of 'a node_type
(* END [MC] *)
let height = function
Empty -> 0
| Node {h;_ } -> h
let create l x d r =
let hl = height l and hr = height r in
Node{l; v=x; d; r; h=(if hl >= hr then hl + 1 else hr + 1)}
let singleton x d = Node{l=Empty; v=x; d; r=Empty; h=1}
let bal l x d r =
let hl = match l with Empty -> 0 | Node {h; _} -> h in
let hr = match r with Empty -> 0 | Node {h; _} -> h in
if hl > hr + 2 then begin
match l with
Empty -> invalid_arg "Map.bal"
| Node{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 lr with
Empty -> invalid_arg "Map.bal"
| Node{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 r with
Empty -> invalid_arg "Map.bal"
| Node{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 rl with
Empty -> invalid_arg "Map.bal"
| Node{l=rll; v=rlv; d=rld; r=rlr; _} ->
create (create l x d rll) rlv rld (create rlr rv rd rr)
end
end else
Node{l; v=x; d; r; h=(if hl >= hr then hl + 1 else hr + 1)}
let empty = Empty
let is_empty = function Empty -> true | _ -> false
let rec add x data = function
Empty ->
Node{l=Empty; v=x; d=data; r=Empty; h=1}
| Node {l; v; d; r; h} as m ->
let c = Ord.compare x v in
if c = 0 then
if d == data then m else Node{l; v=x; d=data; r; h}
else if c < 0 then
let ll = add x data l in
if l == ll then m else bal ll v d r
else
let rr = add x data r in
if r == rr then m else bal l v d rr
let rec find x = function
Empty ->
raise Not_found
| Node {l; v; d; r; _} ->
let c = Ord.compare x v in
if c = 0 then d
else find x (if c < 0 then l else r)
let rec find_first_aux v0 d0 f = function
Empty ->
(v0, d0)
| Node {l; v; d; r; _} ->
if f v then
find_first_aux v d f l
else
find_first_aux v0 d0 f r
let rec find_first f = function
Empty ->
raise Not_found
| Node {l; v; d; r; _} ->
if f v then
find_first_aux v d f l
else
find_first f r
let rec find_first_opt_aux v0 d0 f = function
Empty ->
Some (v0, d0)
| Node {l; v; d; r; _} ->
if f v then
find_first_opt_aux v d f l
else
find_first_opt_aux v0 d0 f r
let rec find_first_opt f = function
Empty ->
None
| Node {l; v; d; r; _} ->
if f v then
find_first_opt_aux v d f l
else
find_first_opt f r
let rec find_last_aux v0 d0 f = function
Empty ->
(v0, d0)
| Node {l; v; d; r; _} ->
if f v then
find_last_aux v d f r
else
find_last_aux v0 d0 f l
let rec find_last f = function
Empty ->
raise Not_found
| Node {l; v; d; r; _} ->
if f v then
find_last_aux v d f r
else
find_last f l
let rec find_last_opt_aux v0 d0 f = function
Empty ->
Some (v0, d0)
| Node {l; v; d; r; _} ->
if f v then
find_last_opt_aux v d f r
else
find_last_opt_aux v0 d0 f l
let rec find_last_opt f = function
Empty ->
None
| Node {l; v; d; r; _} ->
if f v then
find_last_opt_aux v d f r
else
find_last_opt f l
let rec find_opt x = function
Empty ->
None
| Node {l; v; d; r; _} ->
let c = Ord.compare x v in
if c = 0 then Some d
else find_opt x (if c < 0 then l else r)
let rec mem x = function
Empty ->
false
| Node {l; v; r; _} ->
let c = Ord.compare x v in
c = 0 || mem x (if c < 0 then l else r)
let rec min_binding = function
Empty -> raise Not_found
| Node {l=Empty; v; d; _} -> (v, d)
| Node {l; _} -> min_binding l
let rec min_binding_opt = function
Empty -> None
| Node {l=Empty; v; d; _} -> Some (v, d)
| Node {l; _}-> min_binding_opt l
let rec max_binding = function
Empty -> raise Not_found
| Node {v; d; r=Empty; _} -> (v, d)
| Node {r; _} -> max_binding r
let rec max_binding_opt = function
Empty -> None
| Node {v; d; r=Empty; _} -> Some (v, d)
| Node {r; _} -> max_binding_opt r
let rec remove_min_binding = function
Empty -> invalid_arg "Map.remove_min_elt"
| Node {l=Empty; r; _} -> r
| Node {l; v; d; r; _} -> bal (remove_min_binding l) v d r
let merge t1 t2 =
match (t1, t2) with
(Empty, t) -> t
| (t, Empty) -> t
| (_, _) ->
let (x, d) = min_binding t2 in
bal t1 x d (remove_min_binding t2)
let rec remove x = function
Empty ->
Empty
| (Node {l; v; d; r; _} as m) ->
let c = Ord.compare x v in
if c = 0 then merge l r
else if c < 0 then
let ll = remove x l in if l == ll then m else bal ll v d r
else
let rr = remove x r in if r == rr then m else bal l v d rr
let rec update x f = function
Empty ->
begin match f None with
| None -> Empty
| Some data -> Node{l=Empty; v=x; d=data; r=Empty; h=1}
end
| Node {l; v; d; r; h} as m ->
let c = Ord.compare x v in
if c = 0 then begin
match f (Some d) with
| None -> merge l r
| Some data ->
if d == data then m else Node{l; v=x; d=data; r; h}
end else if c < 0 then
let ll = update x f l in
if l == ll then m else bal ll v d r
else
let rr = update x f r in
if r == rr then m else bal l v d rr
let rec iter f = function
Empty -> ()
| Node {l; v; d; r; _} ->
iter f l; f v d; iter f r
let rec map f = function
Empty ->
Empty
| Node {l; v; d; r; h} ->
let l' = map f l in
let d' = f d in
let r' = map f r in
Node{l=l'; v; d=d'; r=r'; h}
let rec mapi f = function
Empty ->
Empty
| Node {l; v; d; r; h} ->
let l' = mapi f l in
let d' = f v d in
let r' = mapi f r in
Node{l=l'; v; d=d'; r=r'; h}
let rec fold f m accu =
match m with
Empty -> accu
| Node {l; v; d; r; _} ->
fold f r (f v d (fold f l accu))
let rec for_all p = function
Empty -> true
| Node {l; v; d; r; _} -> p v d && for_all p l && for_all p r
let rec exists p = function
Empty -> false
| Node {l; v; d; r; _} -> p v d || exists p l || exists p r
(* Beware: those two functions assume that the added k is *strictly*
smaller (or bigger) than all the present keys in the tree; it
does not test for equality with the current min (or max) key.
Indeed, they are only used during the "join" operation which
respects this precondition.
*)
let rec add_min_binding k x = function
| Empty -> singleton k x
| Node {l; v; d; r; _} ->
bal (add_min_binding k x l) v d r
let rec add_max_binding k x = function
| Empty -> singleton k x
| Node {l; v; d; r; _} ->
bal l v d (add_max_binding k x r)
(* Same as create and bal, but no assumptions are made on the
relative heights of l and r. *)
let rec join l v d r =
match (l, r) with
(Empty, _) -> add_min_binding v d r
| (_, Empty) -> add_max_binding v d l
| (Node{l=ll; v=lv; d=ld; r=lr; h=lh}, Node{l=rl; v=rv; d=rd; r=rr; h=rh}) ->
if lh > rh + 2 then bal ll lv ld (join lr v d r) else
if rh > lh + 2 then bal (join l v d rl) rv rd rr else
create l v d r
(* Merge two trees l and r into one.
All elements of l must precede the elements of r.
No assumption on the heights of l and r. *)
let concat t1 t2 =
match (t1, t2) with
(Empty, t) -> t
| (t, Empty) -> t
| (_, _) ->
let (x, d) = min_binding t2 in
join t1 x d (remove_min_binding t2)
let concat_or_join t1 v d t2 =
match d with
| Some d -> join t1 v d t2
| None -> concat t1 t2
let rec split x = function
Empty ->
(Empty, None, Empty)
| Node {l; v; d; r; _} ->
let c = Ord.compare x v in
if c = 0 then (l, Some d, r)
else if c < 0 then
let (ll, pres, rl) = split x l in (ll, pres, join rl v d r)
else
let (lr, pres, rr) = split x r in (join l v d lr, pres, rr)
let rec merge f s1 s2 =
match (s1, s2) with
(Empty, Empty) -> Empty
| (Node {l=l1; v=v1; d=d1; r=r1; h=h1}, _) when h1 >= height s2 ->
let (l2, d2, r2) = split v1 s2 in
concat_or_join (merge f l1 l2) v1 (f v1 (Some d1) d2) (merge f r1 r2)
| (_, Node {l=l2; v=v2; d=d2; r=r2; _}) ->
let (l1, d1, r1) = split v2 s1 in
concat_or_join (merge f l1 l2) v2 (f v2 d1 (Some d2)) (merge f r1 r2)
| _ ->
assert false
let rec union f s1 s2 =
match (s1, s2) with
| (Empty, s) | (s, Empty) -> s
| (Node {l=l1; v=v1; d=d1; r=r1; h=h1}, Node {l=l2; v=v2; d=d2; r=r2; h=h2}) ->
if h1 >= h2 then
let (l2, d2, r2) = split v1 s2 in
let l = union f l1 l2 and r = union f r1 r2 in
match d2 with
| None -> join l v1 d1 r
| Some d2 -> concat_or_join l v1 (f v1 d1 d2) r
else
let (l1, d1, r1) = split v2 s1 in
let l = union f l1 l2 and r = union f r1 r2 in
match d1 with
| None -> join l v2 d2 r
| Some d1 -> concat_or_join l v2 (f v2 d1 d2) r
let rec filter p = function
Empty -> Empty
| Node {l; v; d; r; _} as m ->
(* call [p] in the expected left-to-right order *)
let l' = filter p l in
let pvd = p v d in
let r' = filter p r in
if pvd then if l==l' && r==r' then m else join l' v d r'
else concat l' r'
let rec partition p = function
Empty -> (Empty, Empty)
| Node {l; v; d; r; _} ->
(* call [p] in the expected left-to-right order *)
let (lt, lf) = partition p l in
let pvd = p v d in
let (rt, rf) = partition p r in
if pvd
then (join lt v d rt, concat lf rf)
else (concat lt rt, join lf v d rf)
type 'a enumeration = End | More of key * 'a * 'a t * 'a enumeration
let rec cons_enum m e =
match m with
Empty -> e
| Node {l; v; d; r; _} -> cons_enum l (More(v, d, r, e))
let compare cmp m1 m2 =
let rec compare_aux e1 e2 =
match (e1, e2) with
(End, End) -> 0
| (End, _) -> -1
| (_, End) -> 1
| (More(v1, d1, r1, e1), More(v2, d2, r2, e2)) ->
let c = Ord.compare v1 v2 in
if c <> 0 then c else
let c = cmp d1 d2 in
if c <> 0 then c else
compare_aux (cons_enum r1 e1) (cons_enum r2 e2)
in compare_aux (cons_enum m1 End) (cons_enum m2 End)
let equal cmp m1 m2 =
let rec equal_aux e1 e2 =
match (e1, e2) with
(End, End) -> true
| (End, _) -> false
| (_, End) -> false
| (More(v1, d1, r1, e1), More(v2, d2, r2, e2)) ->
Ord.compare v1 v2 = 0 && cmp d1 d2 &&
equal_aux (cons_enum r1 e1) (cons_enum r2 e2)
in equal_aux (cons_enum m1 End) (cons_enum m2 End)
let rec cardinal = function
Empty -> 0
| Node {l; r; _} -> cardinal l + 1 + cardinal r
let rec bindings_aux accu = function
Empty -> accu
| Node {l; v; d; r; _} -> bindings_aux ((v, d) :: bindings_aux accu r) l
let bindings s =
bindings_aux [] s
let choose = min_binding
let choose_opt = min_binding_opt
(* [AM] additions by Antoine Mine' *)
(* ******************************* *)
let of_list l =
List.fold_left (fun acc (k,x) -> add k x acc) empty l
(* similar to split, but returns unbalanced trees *)
let rec cut k = function
Empty -> Empty,None,Empty
| Node {l=l1;v=k1;d=d1;r=r1;h=h1} ->
let c = Ord.compare k k1 in
if c < 0 then
let l2,d2,r2 = cut k l1 in (l2,d2,Node {l=r2;v=k1;d=d1;r=r1;h=h1})
else if c > 0 then
let l2,d2,r2 = cut k r1 in (Node {l=l1;v=k1;d=d1;r=l2;h=h1},d2,r2)
else (l1,Some d1,r1)
(* binary operations that fail on maps with different keys *)
(* functions are called in increasing key order *)
let rec map2 f m1 m2 =
match m1 with
| Empty -> if m2 = Empty then Empty else invalid_arg "Mapext.map2"
| Node {l=l1;v=k;d=d1;r=r1;h=h1} ->
match cut k m2 with
| l2, Some d2, r2 ->
Node {l=map2 f l1 l2; v=k; d=f k d1 d2; r=map2 f r1 r2; h=h1}
| _, None, _ -> invalid_arg "Mapext.map2"
let rec iter2 f m1 m2 =
match m1 with
| Empty -> if m2 = Empty then () else invalid_arg "Mapext.iter2"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 -> iter2 f l1 l2; f k d1 d2; iter2 f r1 r2
| _, None, _ -> invalid_arg "Mapext.iter2"
let rec fold2 f m1 m2 acc =
match m1 with
| Empty -> if m2 = Empty then acc else invalid_arg "Mapext.fold2"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 ->
fold2 f r1 r2 (f k d1 d2 (fold2 f l1 l2 acc))
| _, None, _ -> invalid_arg "Mapext.fold2"
let rec for_all2 f m1 m2 =
match m1 with
| Empty -> if m2 = Empty then true else invalid_arg "Mapext.for_all2"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 ->
for_all2 f l1 l2 && f k d1 d2 && for_all2 f r1 r2
| _, None, _ -> invalid_arg "Mapext.for_all2"
let rec exists2 f m1 m2 =
match m1 with
| Empty -> if m2 = Empty then false else invalid_arg "Mapext.exists2"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 ->
exists2 f l1 l2 || f k d1 d2 || exists2 f r1 r2
| _, None, _ -> invalid_arg "Mapext.exists2"
(* as above, but ignore physically equal subtrees
- for map, assumes: f k d d = d
- for iter, assumes: f k d d has no effect
- for fold, assumes: k f d d acc = acc
- for for_all, assumes: f k d d = true
- for exists, assumes: f k d d = false
*)
let rec map2z f m1 m2 =
if m1 == m2 then m1 else
match m1 with
| Empty -> if m2 = Empty then Empty else invalid_arg "Mapext.map2z"
| Node {l=l1;v=k;d=d1;r=r1;h=h1} ->
match cut k m2 with
| l2, Some d2, r2 ->
let d = if d1 == d2 then d1 else f k d1 d2 in
Node {l=map2z f l1 l2; v=k; d=d; r=map2z f r1 r2; h=h1}
| _, None, _ -> invalid_arg "Mapext.map2z"
let rec iter2z f m1 m2 =
if m1 == m2 then () else
match m1 with
| Empty -> if m2 = Empty then () else invalid_arg "Mapext.iter2z"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 ->
iter2z f l1 l2; (if d1 != d2 then f k d1 d2); iter2z f r1 r2
| _, None, _ -> invalid_arg "Mapext.iter2z"
let rec fold2z f m1 m2 acc =
if m1 == m2 then acc else
match m1 with
| Empty -> if m2 = Empty then acc else invalid_arg "Mapext.fold2z"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 ->
let acc = fold2z f l1 l2 acc in
let acc = if d1 == d2 then acc else f k d1 d2 acc in
fold2z f r1 r2 acc
| _, None, _ -> invalid_arg "Mapext.fold2z"
let rec for_all2z f m1 m2 =
(m1 == m2) ||
(match m1 with
| Empty -> if m2 = Empty then true else invalid_arg "Mapext.for_all2z"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 ->
(for_all2z f l1 l2) &&
(d1 == d2 || f k d1 d2) &&
(for_all2z f r1 r2)
| _, None, _ -> invalid_arg "Mapext.for_all2z"
)
let rec exists2z f m1 m2 =
(m1 != m2) &&
(match m1 with
| Empty -> if m2 = Empty then false else invalid_arg "Mapext.exists2z"
| Node {l=l1;v=k;d=d1;r=r1;_} ->
match cut k m2 with
| l2, Some d2, r2 ->
(exists2z f l1 l2) ||
(d1 != d2 && f k d1 d2) ||
(exists2z f r1 r2)
| _, None, _ -> invalid_arg "Mapext.exists2z"
)
(* as above, but allow maps with different keys *)
let rec map2o f1 f2 f m1 m2 =
match m1 with
| Empty -> mapi f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
let l = map2o f1 f2 f l1 l2 in
let d = match d2 with None -> f1 k d1 | Some d2 -> f k d1 d2 in
let r = map2o f1 f2 f r1 r2 in
join l k d r
let rec iter2o f1 f2 f m1 m2 =
match m1 with
| Empty -> iter f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
iter2o f1 f2 f l1 l2;
(match d2 with None -> f1 k d1 | Some d2 -> f k d1 d2);
iter2o f1 f2 f r1 r2
let rec fold2o f1 f2 f m1 m2 acc =
match m1 with
| Empty -> fold f2 m2 acc
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
let acc = fold2o f1 f2 f l1 l2 acc in
let acc = match d2 with
| None -> f1 k d1 acc | Some d2 -> f k d1 d2 acc
in
fold2o f1 f2 f r1 r2 acc
let rec for_all2o f1 f2 f m1 m2 =
match m1 with
| Empty -> for_all f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
(for_all2o f1 f2 f l1 l2) &&
(match d2 with None -> f1 k d1 | Some d2 -> f k d1 d2) &&
(for_all2o f1 f2 f r1 r2)
let rec exists2o f1 f2 f m1 m2 =
match m1 with
| Empty -> exists f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
(exists2o f1 f2 f l1 l2) ||
(match d2 with None -> f1 k d1 | Some d2 -> f k d1 d2) ||
(exists2o f1 f2 f r1 r2)
(* all together now *)
let rec map2zo f1 f2 f m1 m2 =
if m1 == m2 then m1 else
match m1 with
| Empty -> mapi f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
let l = map2zo f1 f2 f l1 l2 in
let d = match d2 with
| None -> f1 k d1
| Some d2 -> if d1 == d2 then d1 else f k d1 d2
in
let r = map2zo f1 f2 f r1 r2 in
join l k d r
let rec iter2zo f1 f2 f m1 m2 =
if m1 == m2 then () else
match m1 with
| Empty -> iter f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
iter2zo f1 f2 f l1 l2;
(match d2 with
| None -> f1 k d1
| Some d2 -> if d1 != d2 then f k d1 d2);
iter2zo f1 f2 f r1 r2
let rec fold2zo f1 f2 f m1 m2 acc =
if m1 == m2 then acc else
match m1 with
| Empty -> fold f2 m2 acc
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
let acc = fold2zo f1 f2 f l1 l2 acc in
let acc = match d2 with
| None -> f1 k d1 acc
| Some d2 -> if d1 == d2 then acc else f k d1 d2 acc
in
fold2zo f1 f2 f r1 r2 acc
let rec for_all2zo f1 f2 f m1 m2 =
(m1 == m2) ||
(match m1 with
| Empty -> for_all f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
(for_all2zo f1 f2 f l1 l2) &&
(match d2 with None -> f1 k d1 | Some d2 -> d1 == d2 || f k d1 d2) &&
(for_all2zo f1 f2 f r1 r2)
)
let rec exists2zo f1 f2 f m1 m2 =
(m1 != m2) &&
(match m1 with
| Empty -> exists f2 m2
| Node {l=l1;v=k;d=d1;r=r1;_} ->
let l2, d2, r2 = cut k m2 in
(exists2zo f1 f2 f l1 l2) ||
(match d2 with None -> f1 k d1 | Some d2 -> d1 != d2 && f k d1 d2) ||
(exists2zo f1 f2 f r1 r2)
)
(* iterators limited to keys between two bounds *)
let rec map_slice f m lo hi =
match m with
| Empty -> Empty
| Node {l;v=k;d;r;h} ->
let c1, c2 = Ord.compare k lo, Ord.compare k hi in
let l = if c1 > 0 then map_slice f l lo k else l in
let d = if c1 >= 0 && c2 <= 0 then f k d else d in
let r = if c2 < 0 then map_slice f r k hi else r in
Node {l;v=k;d;r;h}
let rec iter_slice f m lo hi =
match m with
| Empty -> ()
| Node {l=l;v=k;d=d;r=r;h=_} ->
let c1, c2 = Ord.compare k lo, Ord.compare k hi in
if c1 > 0 then iter_slice f l lo k;
if c1 >= 0 && c2 <= 0 then f k d;
if c2 < 0 then iter_slice f r k hi
let rec fold_slice f m lo hi acc =
match m with
| Empty -> acc
| Node {l=l;v=k;d=d;r=r;h=_} ->
let c1, c2 = Ord.compare k lo, Ord.compare k hi in
let acc = if c1 > 0 then fold_slice f l lo k acc else acc in
let acc = if c1 >= 0 && c2 <= 0 then f k d acc else acc in
if c2 < 0 then fold_slice f r k hi acc else acc
let rec for_all_slice f m lo hi =
match m with
| Empty -> true
| Node {l=l;v=k;d=d;r=r;h=_} ->
let c1, c2 = Ord.compare k lo, Ord.compare k hi in
(c1 <= 0 || for_all_slice f l lo k) &&
(c1 < 0 || c2 > 0 || f k d) &&
(c2 >= 0 || for_all_slice f r k hi)
let rec exists_slice f m lo hi =
match m with
| Empty -> false
| Node {l=l;v=k;d=d;r=r;h=_} ->
let c1, c2 = Ord.compare k lo, Ord.compare k hi in
(c1 > 0 && exists_slice f l lo k) ||
(c1 >= 0 && c2 <= 0 && f k d) ||
(c2 < 0 && exists_slice f r k hi)
(* key set comparison *)
let rec key_equal m1 m2 =
(m1 == m2) ||
(match m1 with
| Empty -> m2 = Empty
| Node {l=l1;v=k;d=_;r=r1;h=_} ->
match cut k m2 with
| _, None, _ -> false
| l2, Some _, r2 -> key_equal l1 l2 && key_equal r1 r2
)
let rec key_subset m1 m2 =
(m1 == m2) ||
(match m1 with
| Empty -> true
| Node {l=l1;v=k;d=_;r=r1;h=_} ->
match cut k m2 with
| _, None, _ -> false
| l2, Some _, r2 -> key_subset l1 l2 && key_subset r1 r2
)
(* nagivation *)
let find_greater_equal k m =
let rec aux m found = match m with
| Empty -> (match found with None -> raise Not_found | Some x -> x)
| Node {l=l;v=kk;d=d;r=r;h=_} ->
let c = Ord.compare k kk in
if c = 0 then kk, d else
if c > 0 then aux r found else
aux l (Some (kk, d))
in
aux m None
let find_greater k m =
let rec aux m found = match m with
| Empty -> (match found with None -> raise Not_found | Some x -> x)
| Node {l=l;v=kk;d=d;r=r;h=_} ->
let c = Ord.compare k kk in
if c >= 0 then aux r found else
aux l (Some (kk, d))
in
aux m None
let find_less_equal k m =
let rec aux m found = match m with
| Empty -> (match found with None -> raise Not_found | Some x -> x)
| Node {l=l;v=kk;d=d;r=r;h=_} ->
let c = Ord.compare k kk in
if c = 0 then kk, d else
if c < 0 then aux l found else
aux r (Some (kk, d))
in
aux m None
let find_less k m =
let rec aux m found = match m with
| Empty -> (match found with None -> raise Not_found | Some x -> x)
| Node {l=l;v=kk;d=d;r=r;h=_} ->
let c = Ord.compare k kk in
if c <= 0 then aux l found else
aux r (Some (kk, d))
in
aux m None
end: S with type key = Ord.t)