64 lines
2.6 KiB
OCaml
64 lines
2.6 KiB
OCaml
(** This module offers the abstract data type of a partition of
|
|
classes of equivalent items (Union & Find). *)
|
|
|
|
(** The items are of type 't, they have to obey a total order,
|
|
but also they must be printable to ease debugging. *)
|
|
|
|
type 'item partition
|
|
type 'item t = 'item partition
|
|
|
|
(** {1 Creation} *)
|
|
|
|
(** The value [empty] is an empty partition. *)
|
|
val empty : ('a -> string) -> ('a -> 'a -> int) -> 'a partition
|
|
|
|
(** The value of [equiv i j p] is the partition [p] extended with
|
|
the equivalence of items [i] and [j]. If both [i] and [j] are
|
|
already known to be equivalent, then [equiv i j p == p]. *)
|
|
val equiv : 'item -> 'item -> 'item t -> 'item partition
|
|
|
|
(** The value of [alias i j p] is the partition [p] extended with
|
|
the fact that item [i] is an alias of item [j]. This is the
|
|
same as [equiv i j p], except that it is guaranteed that the
|
|
item [i] is not the representative of its equivalence class in
|
|
[alias i j p]. *)
|
|
val alias : 'item -> 'item -> 'item partition -> 'item partition
|
|
|
|
(** {1 Projection} *)
|
|
|
|
(** The value of the call [repr i p] is [j] if the item [i] is in
|
|
the partition [p] and its representative is [j]. If [i] is not
|
|
in [p], then the value is [i]. *)
|
|
val repr : 'item -> 'item partition -> 'item
|
|
|
|
(** The value of the call [get_or_set i p] is [j, p] if the item [i] is
|
|
in the partition [p] and its representative is [j]. If [i] is not
|
|
in [p], then the value is [i, p'], where p' is the partition [p]
|
|
extended with the fact that item [i] is a singleton partition. *)
|
|
|
|
val get_or_set : 'item -> 'item t -> 'item * 'item t
|
|
|
|
(** The value of the call [mem i p] is [Some j] if the item [i] is
|
|
in the partition [p] and its representative is [j]. If [i] is
|
|
not in [p], then the value is [None]. *)
|
|
val mem : 'item -> 'item partition -> 'item option
|
|
|
|
(** The value of the call [elements p] is a list of the elements of p,
|
|
ordered in ascending order *)
|
|
val elements : 'item partition -> 'item list
|
|
|
|
(** The call [print p] is a value of type [Buffer.t] containing
|
|
strings denoting the partition [p], based on
|
|
[Ord.to_string]. *)
|
|
val print : Format.formatter -> 'item partition -> unit
|
|
|
|
(** {1 Predicates} *)
|
|
|
|
(** The value of [is_equiv i j p] is [true] if, and only if, the
|
|
items [i] and [j] belong to the same equivalence class in the
|
|
partition [p], that is, [i] and [j] have the same
|
|
representative. In particular, if either [i] or [j] do not
|
|
belong to [p], the value of [is_equiv i j p] is [false]. See
|
|
[mem] above. *)
|
|
val is_equiv : 'item -> 'item -> 'item partition -> bool
|