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