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module Core_set

: sig

This module defines the Set module for Core.Std. We use "core_set" as the file name rather than "set" to avoid conflicts with OCaml's standard set module.

This module uses the same organizational approach as Core_map. See the documentation in core_map.mli for a description of the approach.

Functions that construct a set take as an argument the comparator for the element type.

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type ('elt, 'cmp) t

The type of a set. The first type parameter identifies the type of the element, and the second identifies the comparator, which determines the comparison function that is used for ordering elements in this set. Many operations (e.g., union), require that they be passed sets with the same element type and the same comparator type.

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module Tree : sig
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type ('a, 'cmp) t

A Tree.t contains just the tree data structure that a set is based on, without including the comparator. Accordingly, any operation on a Tree.t must also take as an argument the corresponding comparator.

include Core_set_intf.Creators_and_accessors2_with_comparator with type ('a, 'b) set := ('a, 'b) t and type ('a, 'b) t := ('a, 'b) t and type ('a, 'b) tree := ('a, 'b) t
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val sexp_of_t : ('a -> Sexplib.Sexp.t) -> ('cmp -> Sexplib.Sexp.t) -> ('a, 'cmp) t -> Sexplib.Sexp.t
end
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val invariants : (_, _) t -> bool

Tests internal invariants of the set data structure. Returns true on success.

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val comparator : ('a, 'cmp) t -> ('a, 'cmp) Comparator.t
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val empty : comparator:('a, 'cmp) Comparator.t -> ('a, 'cmp) t

Creates an empty set based on the provided comparator.

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val singleton : comparator:('a, 'cmp) Comparator.t -> 'a -> ('a, 'cmp) t

Creates a set based on the provided comparator that contains only the provided element.

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val length : (_, _) t -> int

Returns the number of elements in the set. O(1).

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val is_empty : (_, _) t -> bool

is_empty t is true iff t is empty. O(1).

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val mem : ('a, _) t -> 'a -> bool

mem t a returns true iff a is in t. O(log n).

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val add : ('a, 'cmp) t -> 'a -> ('a, 'cmp) t

add t a returns a new set with a added to t, or returns t if mem t a. O(log n).

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val remove : ('a, 'cmp) t -> 'a -> ('a, 'cmp) t

remove t a returns a new set with a removed from t if mem t a, or returns t otherwise. O(log n).

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val union : ('a, 'cmp) t -> ('a, 'cmp) t -> ('a, 'cmp) t

union t1 t2 returns the union of the two sets. O(length t1 + length t2).

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val union_list : comparator:('a, 'cmp) Comparator.t -> ('a, 'cmp) t list -> ('a, 'cmp) t

union ~comparator list returns the union of all the sets in list. The comparator argument is required for the case where list is empty. O(max(List.length list, n log n)), where n is the sum of sizes of the input sets.

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val inter : ('a, 'cmp) t -> ('a, 'cmp) t -> ('a, 'cmp) t

inter t1 t2 computes the intersection of sets t1 and t2. O(log(length t1) + log(length t2)).

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val diff : ('a, 'cmp) t -> ('a, 'cmp) t -> ('a, 'cmp) t

diff t1 t2 computes the set difference t1 - t2, i.e., the set containing all elements in t1 that are not in t2. O(log(length t1) + log(length t2)).

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val compare_direct : ('a, 'cmp) t -> ('a, 'cmp) t -> int

compare_direct t1 t2 compares the sets t1 and t2. It returns the same result as compare, but unlike compare, doesn't require arguments to be passed in for the type parameters of the set. O(length t1 + length t2).

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val equal : ('a, 'cmp) t -> ('a, 'cmp) t -> bool

equal t1 t2 returns true iff the two sets have the same elements. O(length t1 + length t2)

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val exists : ('a, _) t -> f:('a -> bool) -> bool

exists t ~f returns true iff there exists an a in t for which f a. O(n), but returns as soon as it finds an a for which f a.

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

for_all t ~f returns true iff for all a in t, f a. O(n), but returns as soon as it finds an a for which not (f a).

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

count t returns the number of elements of t for which f returns true. O(n).

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val sum : (module Commutative_group.S with type t = 'sum) -> ('a, _) t -> f:('a -> 'sum) -> 'sum

sum t returns the sum of f t for each t in the set. O(n).

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

find t f returns an element of t for which f returns true, with no guarantee as to which element is returned. O(n), but returns as soon as a suitable element is found.

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

find_map t f returns b for some a in t for which f a = Some b. If no such a exists, then find returns None. O(n), but returns as soon as a suitable element is found.

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val find_exn : ('a, _) t -> f:('a -> bool) -> 'a

Like find, but throws an exception on failure.

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val find_index : ('a, _) t -> int -> 'a option

find_index t i returns the ith smallest element of t, in O(log n) time. The smallest element has i = 0. Returns None if i < 0 or i >= length t.

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val remove_index : ('a, 'cmp) t -> int -> ('a, 'cmp) t

remove_index t i returns a version of t with the ith smallest element removed, in O(log n) time. The smallest element has i = 0. Returns t if i < 0 or i >= length t.

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val subset : ('a, 'cmp) t -> ('a, 'cmp) t -> bool

subset t1 t2 returns true iff t1 is a subset of t2.

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val of_list : comparator:('a, 'cmp) Comparator.t -> 'a list -> ('a, 'cmp) t

The list or array given to of_list and of_array need not be sorted.

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val of_array : comparator:('a, 'cmp) Comparator.t -> 'a array -> ('a, 'cmp) t
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val to_list : ('a, _) t -> 'a list

to_list and to_array produce sequences sorted in ascending order according to the comparator.

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val to_array : ('a, _) t -> 'a array
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val to_tree : ('a, 'cmp) t -> ('a, 'cmp) Tree.t
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val of_tree : comparator:('a, 'cmp) Comparator.t -> ('a, 'cmp) Tree.t -> ('a, 'cmp) t
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val of_sorted_array : comparator:('a, 'cmp) Comparator.t -> 'a array -> ('a, 'cmp) t Or_error.t

Create set from sorted array. The input must be sorted (either in ascending or descending order as given by the comparator) and contain no duplicates, otherwise the result is an error. The complexity of this function is O(n).

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val of_sorted_array_unchecked : comparator:('a, 'cmp) Comparator.t -> 'a array -> ('a, 'cmp) t

Similar to of_sorted_array, but without checking the input array.

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val stable_dedup_list : comparator:('a, _) Comparator.t -> 'a list -> 'a list

stable_dedup_list is here rather than in the List module because the implementation relies crucially on sets, and because doing so allows one to avoid uses of polymorphic comparison by instantiating the functor at a different implementation of Comparator and using the resulting stable_dedup_list.

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val map : comparator:('b, 'cmp) Comparator.t -> ('a, _) t -> f:('a -> 'b) -> ('b, 'cmp) t

map ~comparator t ~f returns a new set created by applying f to every element in t. The returned set is based on the provided comparator. O(n log n).

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val filter_map : comparator:('b, 'cmp) Comparator.t -> ('a, _) t -> f:('a -> 'b option) -> ('b, 'cmp) t

Like map, except elements for which f returns None will be dropped.

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

filter t ~f returns the subset of t for which f evaluates to true. O(n log n).

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val fold : ('a, _) t -> init:'accum -> f:('accum -> 'a -> 'accum) -> 'accum

fold t ~init ~f folds over the elements of the set from smallest to largest.

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val fold_until : ('a, _) t -> init:'accum -> f:('accum -> 'a -> [
| `Continue of 'accum
| `Stop of 'accum
]) -> 'accum

Like fold, except that it will terminate early, if f returns `Stop.

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val fold_right : ('a, _) t -> init:'accum -> f:('a -> 'accum -> 'accum) -> 'accum

Like fold, except that it goes from the largest to the smallest element.

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val iter : ('a, _) t -> f:('a -> unit) -> unit

iter t ~f calls f on every element of t, going in order from the smallest to largest.

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val iter2 : ('a, 'cmp) t -> ('a, 'cmp) t -> f:([
| `Left of 'a
| `Right of 'a
| `Both of 'a * 'a
] -> unit) -> unit

Iterate two sets side by side. Complexity is O(m+n) where m and n are the sizes of the two input sets. As an example, with the inputs 0; 1 and 1; 2, f will be called with `Left 0; `Both (1, 1); and `Right 2.

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val partition_tf : ('a, 'cmp) t -> f:('a -> bool) -> ('a, 'cmp) t * ('a, 'cmp) t

if a, b = partition_tf set ~f then a is the elements on which f produced true, and b is the elements on which f produces false.

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val elements : ('a, _) t -> 'a list

Same as to_list.

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val min_elt : ('a, _) t -> 'a option

Returns the smallest element of the set. O(log n).

Like min_elt, but throws an exception when given an empty set.

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val min_elt_exn : ('a, _) t -> 'a
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val max_elt : ('a, _) t -> 'a option

Returns the largest element of the set. O(log n).

Like max_elt, but throws an exception when given an empty set.

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val max_elt_exn : ('a, _) t -> 'a
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val choose : ('a, _) t -> 'a option

returns an arbitrary element, or None if the set is empty.

Like choose, but throws an exception on an empty set.

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val choose_exn : ('a, _) t -> 'a
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val split : ('a, 'cmp) t -> 'a -> ('a, 'cmp) t * bool * ('a, 'cmp) t

split t x produces a triple (t1, b, t2) where t1 is the set of elements strictly less than x, b = mem set x, and t2 is the set of elements strictly larger than x.

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val group_by : ('a, 'cmp) t -> equiv:('a -> 'a -> bool) -> ('a, 'cmp) t list

if equiv is an equivalence predicate, then group_by set ~equiv produces a list of equivalence classes (i.e., a set-theoretic quotient). E.g.,

      let chars = Set.of_list ['A'; 'a'; 'b'; 'c'] in
      let equiv c c' = Char.equal (Char.uppercase c) (Char.uppercase c') in
      group_by chars ~equiv

produces:

      Set.of_list['A';'a']; Set.singleton 'b'; Set.singleton 'c']

group_by runs in O(n^2) time, so if you have a comparison function, it's usually much faster to use Set.of_list.

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val to_sequence : ?in_:[
| `Increasing_order
| `Decreasing_order
| `Increasing_order_greater_than_or_equal_to of 'a
| `Decreasing_order_less_than_or_equal_to of 'a
] -> ('a, 'cmp) t -> 'a Sequence.t

to_sequence ?in_ t converts the set t to a sequence of the elements in the order indicated by in_.

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val to_map : ('key, 'cmp) t -> f:('key -> 'data) -> ('key, 'data, 'cmp) Core_set_intf.Map.t

Convert a set to or from a map. to_map takes a function to produce data for each key. Both functions run in O(n) time (assuming the function passed to to_map runs in constant time).

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val of_map_keys : ('key, _, 'cmp) Core_set_intf.Map.t -> ('key, 'cmp) t

Polymorphic sets

Module Poly deals with sets that use OCaml's polymorphic comparison to compare elements.

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module Poly : sig
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type ('a, 'b) set
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module Tree : sig
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type 'elt t = ('elt, Comparator.Poly.comparator_witness) Tree.t
include Core_set_intf.Creators_and_accessors1 with type ('a, 'b) set := ('a, 'b) Tree.t and type 'elt t := 'elt t and type 'elt tree := 'elt t and type comparator_witness := Comparator.Poly.comparator_witness
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val t_of_sexp : (Sexplib.Sexp.t -> 'elt) -> Sexplib.Sexp.t -> 'elt t
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val sexp_of_t : ('elt -> Sexplib.Sexp.t) -> 'elt t -> Sexplib.Sexp.t
end
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type 'elt t = ('elt, Comparator.Poly.comparator_witness) set
include Core_set_intf.Creators_and_accessors1 with type ('a, 'b) set := ('a, 'b) set and type 'elt t := 'elt t and type 'elt tree := 'elt Tree.t and type comparator_witness := Comparator.Poly.comparator_witness
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val t_of_sexp : (Sexplib.Sexp.t -> 'elt) -> Sexplib.Sexp.t -> 'elt t
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val sexp_of_t : ('elt -> Sexplib.Sexp.t) -> 'elt t -> Sexplib.Sexp.t
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val compare : ('elt -> 'elt -> int) -> 'elt t -> 'elt t -> int
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val bin_t : 'elt Bin_prot.Type_class.t -> 'elt t Bin_prot.Type_class.t
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val bin_read_t : 'elt Bin_prot.Read.reader -> 'elt t Bin_prot.Read.reader
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val __bin_read_t__ : 'elt Bin_prot.Read.reader -> (int -> 'elt t) Bin_prot.Read.reader
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val bin_reader_t : 'elt Bin_prot.Type_class.reader -> 'elt t Bin_prot.Type_class.reader
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val bin_size_t : 'elt Bin_prot.Size.sizer -> 'elt t Bin_prot.Size.sizer
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val bin_write_t : 'elt Bin_prot.Write.writer -> 'elt t Bin_prot.Write.writer
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val bin_writer_t : 'elt Bin_prot.Type_class.writer -> 'elt t Bin_prot.Type_class.writer
end
with type ('a, 'b) set := ('a, 'b) t

Signatures and functors for building Set modules

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module type Elt = Core_set_intf.Elt

The signature that something needs to match in order to be used as a set element.

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module type Elt_binable = Core_set_intf.Elt_binable

The signature that something needs to match in order to be used as a set element if the resulting set is going to support bin_io.

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module type S = Core_set_intf.S0 with type ('a, 'b) set := ('a, 'b) t and type ('a, 'b) tree := ('a, 'b) Tree.t

Module signature for a Set.

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module type S_binable = Core_set_intf.S0_binable with type ('a, 'b) set := ('a, 'b) t and type ('a, 'b) tree := ('a, 'b) Tree.t

Module signature for a Set that supports bin_io.

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module Make : functor (Elt : Elt) -> S with type Elt.t = Elt.t

Make builds a set from an element type that has a compare function but doesn't have a comparator. This generates a new comparator.

Make_binable is similar, except the element and set types support bin_io.

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module Make_binable : functor (Elt : Elt_binable) -> S_binable with type Elt.t = Elt.t
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module Make_using_comparator : functor (Elt : sig
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type t
include Comparator.S with type t := t
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val t_of_sexp : Sexplib.Sexp.t -> t
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val sexp_of_t : t -> Sexplib.Sexp.t
end
) -> S with type Elt.t = Elt.t and type Elt.comparator_witness = Elt.comparator_witness

Make_using_comparator builds a set from an element type that has a comparator.

Make_binable_using_comparator is similar, except the element and set types support bin_io.

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module Make_binable_using_comparator : functor (Elt : sig
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type t
include Comparator.S with type t := t
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val t_of_sexp : Sexplib.Sexp.t -> t
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val sexp_of_t : t -> Sexplib.Sexp.t
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val bin_t : t Bin_prot.Type_class.t
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val bin_read_t : t Bin_prot.Read.reader
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val __bin_read_t__ : (int -> t) Bin_prot.Read.reader
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val bin_reader_t : t Bin_prot.Type_class.reader
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val bin_size_t : t Bin_prot.Size.sizer
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val bin_write_t : t Bin_prot.Write.writer
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val bin_writer_t : t Bin_prot.Type_class.writer
end
) -> S_binable with type Elt.t = Elt.t and type Elt.comparator_witness = Elt.comparator_witness
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val compare : ('elt -> 'elt -> int) -> ('cmp -> 'cmp -> int) -> ('elt, 'cmp) t -> ('elt, 'cmp) t -> int
end