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diff --git a/libs/mapext.ml b/libs/mapext.ml new file mode 100644 index 0000000..51f41ee --- /dev/null +++ b/libs/mapext.ml @@ -0,0 +1,741 @@ +(* + Cours "Sémantique et Application à la Vérification de programmes" + + Antoine Miné 2014 + 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] symbol. + Based on rev. 10468 2010-05-25 13:29:43Z + + 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 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 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 max_binding: 'a t -> (key * 'a) + val choose: 'a t -> (key * 'a) + val split: key -> 'a t -> 'a t * 'a option * 'a t + val find: key -> 'a t -> 'a + 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 + + type 'a t = + Empty + | Node of 'a t * key * 'a * 'a t * int + + 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, x, d, r, (if hl >= hr then hl + 1 else hr + 1)) + + let singleton x d = Node(Empty, x, d, Empty, 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 "Mapext.bal" + | Node(ll, lv, ld, lr, _) -> + if height ll >= height lr then + create ll lv ld (create lr x d r) + else begin + match lr with + Empty -> invalid_arg "Mapext.bal" + | Node(lrl, lrv, lrd, 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 "Mapext.bal" + | Node(rl, rv, rd, rr, _) -> + if height rr >= height rl then + create (create l x d rl) rv rd rr + else begin + match rl with + Empty -> invalid_arg "Mapext.bal" + | Node(rll, rlv, rld, rlr, _) -> + create (create l x d rll) rlv rld (create rlr rv rd rr) + end + end else + Node(l, x, d, r, (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(Empty, x, data, Empty, 1) + | Node(l, v, d, r, h) -> + let c = Ord.compare x v in + if c = 0 then + Node(l, x, data, r, h) + else if c < 0 then + bal (add x data l) v d r + else + bal l v d (add x data r) + + 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 mem x = function + Empty -> + false + | Node(l, v, d, 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(Empty, x, d, r, _) -> (x, d) + | Node(l, x, d, r, _) -> min_binding l + + let rec max_binding = function + Empty -> raise Not_found + | Node(l, x, d, Empty, _) -> (x, d) + | Node(l, x, d, r, _) -> max_binding r + + let rec remove_min_binding = function + Empty -> invalid_arg "Mapext.remove_min_elt" + | Node(Empty, x, d, r, _) -> r + | Node(l, x, d, r, _) -> bal (remove_min_binding l) x 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, h) -> + let c = Ord.compare x v in + if c = 0 then + merge l r + else if c < 0 then + bal (remove x l) v d r + else + bal l v d (remove x r) + + 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', v, d', 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', v, d', 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)) + + (* [AM] changed to call p in the key order *) + let rec for_all p = function + Empty -> true + | Node(l, v, d, r, _) -> for_all p l && p v d && for_all p r + + (* [AM] changed to call p in the key order *) + let rec exists p = function + Empty -> false + | Node(l, v, d, r, _) -> exists p l || p v d || exists p r + + (* [AM] changed to call p in the key order *) + let filter p s = + fold (fun k d a -> if p k d then add k d a else a) s Empty + + let partition p s = + let rec part (t, f as accu) = function + | Empty -> accu + | Node(l, v, d, r, _) -> + part (part (if p v d then (add v d t, f) else (t, add v d f)) l) r in + part (Empty, Empty) s + + (* 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 v d r + | (_, Empty) -> add v d l + | (Node(ll, lv, ld, lr, lh), Node(rl, rv, rd, rr, 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 (l1, v1, d1, r1, 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 (l2, v2, d2, r2, h2)) -> + 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 + + 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 + + + + (* [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 (l1,k1,d1,r1,h1) -> + let c = Ord.compare k k1 in + if c < 0 then + let l2,d2,r2 = cut k l1 in (l2,d2,Node (r2,k1,d1,r1,h1)) + else if c > 0 then + let l2,d2,r2 = cut k r1 in (Node (l1,k1,d1,l2,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 (l1,k,d1,r1,h1) -> + match cut k m2 with + | l2, Some d2, r2 -> + Node (map2 f l1 l2, k, f k d1 d2, map2 f r1 r2, 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + match cut k m2 with + | l2, Some d2, r2 -> + let d = if d1 == d2 then d1 else f k d1 d2 in + Node (map2z f l1 l2, k, d, map2z f r1 r2, 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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 (l1,k,d1,r1,h1) -> + 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,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,k,d,r,h) + + let rec iter_slice f m lo hi = + match m with + | Empty -> () + | Node (l,k,d,r,_) -> + 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,k,d,r,_) -> + 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,k,d,r,_) -> + 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,k,d,r,_) -> + 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 (l1, k, _, r1, _) -> + 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 (l1, k, _, r1, _) -> + 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, kk, d, r, _) -> + 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, kk, d, r, _) -> + 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, kk, d, r, _) -> + 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, kk, d, r, _) -> + 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) |