package bap-std

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The Interval Tree Interface.

Interval tree is a mapping from intervals to arbitrary values. The intervals are allowed to intersect. Thus a single point may belong to more than one interval. Unlike a regular map, when an association is extract by using a key value, the interval tree uses notions of domination and intersection to extract values associated with all intervals that either dominate (i.e., are super sets) or intersects with the provided key. In that sense an interval tree is a multimap.

type 'a t

interval tree abstract representation

val sexp_of_t : ('a -> Sexplib0.Sexp.t) -> 'a t -> Sexplib0.Sexp.t
type key

the interval

type point

an element of the interval

val empty : 'a t

empty x an empty interval tree

val singleton : key -> 'a -> 'a t

singleton k x creates an interval tree that has only one mapping - from the key k to data x

val least : 'a t -> point option

least t returns the least bound of the tree t.

Returns None if t is empty.

val greatest : 'a t -> point option

greatest t returns the greatest bound of the tree t.

Returns None if t is empty.

val min_binding : 'a t -> (key * 'a) option

min_bining t returns the least binding in the tree

val max_binding : 'a t -> (key * 'a) option

max_binding t returns the greatest binding in the tree

val add : 'a t -> key -> 'a -> 'a t

add t k x adds a new binding (k,x) to the mapping.

val dominators : 'a t -> key -> (key * 'a) Core_kernel.Sequence.t

dominators t k returns all intervals and their associated values that include k.

val intersections : 'a t -> key -> (key * 'a) Core_kernel.Sequence.t

intersections t k returns all intervals and their associated values that intersects with k

val intersects : 'a t -> key -> bool

intersects t k is true iff t contains an interval that intersects with k

val dominates : 'a t -> key -> bool

dominates t k is true iff all intervals in t are included in k.

val contains : 'a t -> point -> bool

contains t p is true if p belongs to at least one interval in t

val lookup : 'a t -> point -> (key * 'a) Core_kernel.Sequence.t

lookup t p returns bindings of all intervals that contain the given point

val map : 'a t -> f:('a -> 'b) -> 'b t

map k ~f maps all data values with the function f

val mapi : 'a t -> f:(key -> 'a -> 'b) -> 'b t

mapi k ~f maps all bindings with the function f

val filter : 'a t -> f:('a -> bool) -> 'a t

filter t ~f returns a tree where all elements for which f returned false are removed.

val filter_map : 'a t -> f:('a -> 'b option) -> 'b t

filter t ~f returns a tree where all elements for which f returned None are removed and all others are mapped.

val filter_mapi : 'a t -> f:(key -> 'a -> 'b option) -> 'b t

filter t ~f returns a tree where all elements for which f returned None are removed and all others are mapped.

val remove : 'a t -> key -> 'a t

remove t k removes all bindings to the key k

val remove_intersections : 'a t -> key -> 'a t

remove_intersections t k removes all bindings that intersect with the key k.

val remove_dominators : 'a t -> key -> 'a t

remove_dominators t k removes all bindings that are included (dominated by) in the interval k

val to_sequence : 'a t -> (key * 'a) Core_kernel.Sequence.t

to_sequence t returns all bindings in t

Interval Trees implement common container interface

include Core_kernel.Container.S1 with type 'a t := 'a t
val mem : 'a t -> 'a -> equal:('a -> 'a -> bool) -> bool

Checks whether the provided element is there, using equal.

val length : 'a t -> int
val is_empty : 'a t -> bool
val iter : 'a t -> f:('a -> unit) -> unit
val fold : 'a t -> init:'accum -> f:('accum -> 'a -> 'accum) -> 'accum

fold t ~init ~f returns f (... f (f (f init e1) e2) e3 ...) en, where e1..en are the elements of t

val fold_result : 'a t -> init:'accum -> f:('accum -> 'a -> ('accum, 'e) Base.Result.t) -> ('accum, 'e) Base.Result.t

fold_result t ~init ~f is a short-circuiting version of fold that runs in the Result monad. If f returns an Error _, that value is returned without any additional invocations of f.

val fold_until : 'a t -> init:'accum -> f:('accum -> 'a -> ('accum, 'final) Base.Container.Continue_or_stop.t) -> finish:('accum -> 'final) -> 'final

fold_until t ~init ~f ~finish is a short-circuiting version of fold. If f returns Stop _ the computation ceases and results in that value. If f returns Continue _, the fold will proceed. If f never returns Stop _, the final result is computed by finish.

Example:

type maybe_negative =
  | Found_negative of int
  | All_nonnegative of { sum : int }

(** [first_neg_or_sum list] returns the first negative number in [list], if any,
    otherwise returns the sum of the list. *)
let first_neg_or_sum =
  List.fold_until ~init:0
    ~f:(fun sum x ->
      if x < 0
      then Stop (Found_negative x)
      else Continue (sum + x))
    ~finish:(fun sum -> All_nonnegative { sum })
;;

let x = first_neg_or_sum [1; 2; 3; 4; 5]
val x : maybe_negative = All_nonnegative {sum = 15}

let y = first_neg_or_sum [1; 2; -3; 4; 5]
val y : maybe_negative = Found_negative -3
val exists : 'a t -> f:('a -> bool) -> bool

Returns true if and only if there exists an element for which the provided function evaluates to true. This is a short-circuiting operation.

val for_all : 'a t -> f:('a -> bool) -> bool

Returns true if and only if the provided function evaluates to true for all elements. This is a short-circuiting operation.

val count : 'a t -> f:('a -> bool) -> int

Returns the number of elements for which the provided function evaluates to true.

val sum : (module Base.Container.Summable with type t = 'sum) -> 'a t -> f:('a -> 'sum) -> 'sum

Returns the sum of f i for all i in the container.

val find : 'a t -> f:('a -> bool) -> 'a option

Returns as an option the first element for which f evaluates to true.

val find_map : 'a t -> f:('a -> 'b option) -> 'b option

Returns the first evaluation of f that returns Some, and returns None if there is no such element.

val to_list : 'a t -> 'a list
val to_array : 'a t -> 'a array
val min_elt : 'a t -> compare:('a -> 'a -> int) -> 'a option

Returns a minimum (resp maximum) element from the collection using the provided compare function, or None if the collection is empty. In case of a tie, the first element encountered while traversing the collection is returned. The implementation uses fold so it has the same complexity as fold.

val max_elt : 'a t -> compare:('a -> 'a -> int) -> 'a option