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60 set_ctree234

%--------------------------------------------------%
% vim: ts=4 sw=4 et ft=mercury
%--------------------------------------------------%
% Copyright (C) 2005-2006, 2010-2012 The University of Melbourne.
% This file may only be copied under the terms of the GNU Library General
% Public License - see the file COPYING.LIB in the Mercury distribution.
%--------------------------------------------------%
% 
% File: set_ctree234.m.
% Author: zs.
% Stability: high.
% 
% This module implements sets using 2-3-4 trees extended with element counts.
% This representation has higher constant factors for most operations than
% ordered lists, but it has much better worst-case complexity, and is likely
% to be faster for large sets. Specifically,
%
% - the cost of lookups is only logarithmic in the size of the set, not linear;
%
% - for operations that are intrinsically linear in the size of one input
%   operand or the other, the counts allow us to choose to be linear in the
%   size of the smaller set.
% 
%--------------------------------------------------%
%--------------------------------------------------%

:- module set_ctree234.
:- interface.

:- import_module bool.
:- import_module list.

%--------------------------------------------------%

:- type set_ctree234(_T).

    % `set_ctree234.init = Set' is true iff `Set' is an empty set.
    %
:- func set_ctree234.init = set_ctree234(T).

    % `set_ctree234.singleton_set(Elem, Set)' is true iff `Set' is the set
    % containing just the single element `Elem'.
    %
:- pred set_ctree234.singleton_set(T, set_ctree234(T)).
:- mode set_ctree234.singleton_set(in, out) is det.
:- mode set_ctree234.singleton_set(out, in) is semidet.

:- func set_ctree234.make_singleton_set(T) = set_ctree234(T).

:- pred set_ctree234.is_singleton(set_ctree234(T)::in, T::out) is semidet.

    % `set_ctree234.empty(Set)' is true iff `Set' is an empty set.
    %
:- pred set_ctree234.empty(set_ctree234(_T)::in) is semidet.

:- pred set_ctree234.is_empty(set_ctree234(_T)::in) is semidet.

:- pred set_ctree234.non_empty(set_ctree234(T)::in) is semidet.

    % `set_ctree234.member(X, Set)' is true iff `X' is a member of `Set'.
    %
:- pred set_ctree234.member(T, set_ctree234(T)).
:- mode set_ctree234.member(in, in) is semidet.
:- mode set_ctree234.member(out, in) is nondet.

    % `set_ctree234.one_member(Set, X)' is true iff `X' is a member of `Set'.
    %
:- pred set_ctree234.one_member(set_ctree234(T)::in, T::out) is nondet.

    % `set_ctree234.is_member(Set, X, Result)' returns
    % `Result = yes' iff `X' is a member of `Set'.
    %
:- func set_ctree234.is_member(set_ctree234(T), T) = bool.
:- pred set_ctree234.is_member(set_ctree234(T)::in, T::in, bool::out) is det.

    % `set_ctree234.contains(Set, X)' is true iff `X' is a member of `Set'.
    %
:- pred set_ctree234.contains(set_ctree234(T)::in, T::in) is semidet.

    % `set_ctree234.list_to_set(List) = Set' is true iff `Set' is the set
    % containing only the members of `List'.
    %
:- func set_ctree234.list_to_set(list(T)) = set_ctree234(T).

:- func set_ctree234.from_list(list(T)) = set_ctree234(T).

    % `set_ctree234.sorted_list_to_set(List) = Set' is true iff `Set' is
    % the set containing only the members of `List'. `List' must be sorted.
    %
:- func set_ctree234.sorted_list_to_set(list(T)) = set_ctree234(T).

    % `set_ctree234.to_sorted_list(Set) = List' is true iff `List' is the
    % list of all the members of `Set', in sorted order.
    %
:- func set_ctree234.to_sorted_list(set_ctree234(T)) = list(T).

    % `set_ctree234.equal(SetA, SetB)' is true iff
    % `SetA' and `SetB' contain the same elements.
    %
:- pred set_ctree234.equal(set_ctree234(T)::in, set_ctree234(T)::in)
    is semidet.

    % `set_ctree234.subset(SetA, SetB)' is true iff `SetA' is a subset of
    % `SetB'.
    %
:- pred set_ctree234.subset(set_ctree234(T)::in, set_ctree234(T)::in)
    is semidet.

    % `set_ctree234.superset(SetA, SetB)' is true iff `SetA' is a
    % superset of `SetB'.
    %
:- pred set_ctree234.superset(set_ctree234(T)::in, set_ctree234(T)::in)
    is semidet.

    % `set_ctree234.insert(X, Set0, Set)' is true iff `Set' is the union
    % of `Set0' and the set containing only `X'.
    %
:- func set_ctree234.insert(T, set_ctree234(T)) = set_ctree234(T).
:- pred set_ctree234.insert(T::in, set_ctree234(T)::in, set_ctree234(T)::out)
    is det.

    % `set_ctree234.insert_new(X, Set0, Set)' is true iff `Set0' does
    % not contain `X', and `Set' is the union of `Set0' and the set containing
    % only `X'.
    %
:- pred set_ctree234.insert_new(T::in,
    set_ctree234(T)::in, set_ctree234(T)::out) is semidet.

    % `set_ctree234.insert_list(Xs, Set0, Set)' is true iff `Set' is the
    % union of `Set0' and the set containing only the members of `Xs'.
    %
:- func set_ctree234.insert_list(list(T), set_ctree234(T)) = set_ctree234(T).
:- pred set_ctree234.insert_list(list(T)::in,
    set_ctree234(T)::in, set_ctree234(T)::out) is det.

    % `set_ctree234.delete(X, Set0, Set)' is true iff `Set' is the
    % relative complement of `Set0' and the set containing only `X', i.e.
    % if `Set' is the set which contains all the elements of `Set0'
    % except `X'.
    %
:- func set_ctree234.delete(T, set_ctree234(T)) = set_ctree234(T).
:- pred set_ctree234.delete(T::in, set_ctree234(T)::in, set_ctree234(T)::out)
    is det.

    % `set_ctree234.delete_list(Xs, Set0, Set)' is true iff `Set' is the
    % relative complement of `Set0' and the set containing only the members
    % of `Xs'.
    %
:- func set_ctree234.delete_list(list(T), set_ctree234(T)) = set_ctree234(T).
:- pred set_ctree234.delete_list(list(T)::in,
    set_ctree234(T)::in, set_ctree234(T)::out) is det.

    % `set_ctree234.remove(X, Set0, Set)' is true iff `Set0' contains `X',
    % and `Set' is the relative complement of `Set0' and the set
    % containing only `X', i.e.  if `Set' is the set which contains
    % all the elements of `Set0' except `X'.
    %
:- pred set_ctree234.remove(T::in, set_ctree234(T)::in, set_ctree234(T)::out)
    is semidet.

    % `set_ctree234.remove_list(Xs, Set0, Set)' is true iff Xs does not
    % contain any duplicates, `Set0' contains every member of `Xs',
    % and `Set' is the relative complement of `Set0' and the set
    % containing only the members of `Xs'.
    %
:- pred set_ctree234.remove_list(list(T)::in,
    set_ctree234(T)::in, set_ctree234(T)::out) is semidet.

    % `set_ctree234.remove_least(X, Set0, Set)' is true iff `X' is the
    % least element in `Set0', and `Set' is the set which contains all the
    % elements of `Set0' except `X'.
    %
:- pred set_ctree234.remove_least(T::out,
    set_ctree234(T)::in, set_ctree234(T)::out) is semidet.

    % `set_ctree234.union(SetA, SetB) = Set' is true iff `Set' is the union
    % of `SetA' and `SetB'.
    %
:- func set_ctree234.union(set_ctree234(T), set_ctree234(T)) = set_ctree234(T).
:- pred set_ctree234.union(set_ctree234(T)::in, set_ctree234(T)::in,
    set_ctree234(T)::out) is det.

    % `set_ctree234.union_list(A, B)' is true iff `B' is the union of
    % all the sets in `A'
    %
:- func set_ctree234.union_list(list(set_ctree234(T))) = set_ctree234(T).
:- pred set_ctree234.union_list(list(set_ctree234(T))::in,
    set_ctree234(T)::out) is det.

    % `set_ctree234.power_union(A) = B' is true iff `B' is the union of
    % all the sets in `A'
    %
:- func set_ctree234.power_union(set_ctree234(set_ctree234(T)))
    = set_ctree234(T).
:- pred set_ctree234.power_union(set_ctree234(set_ctree234(T))::in,
    set_ctree234(T)::out) is det.

    % `set_ctree234.intersect(SetA, SetB) = Set' is true iff `Set' is the
    % intersection of `SetA' and `SetB'.
    %
:- func set_ctree234.intersect(set_ctree234(T), set_ctree234(T))
    = set_ctree234(T).
:- pred set_ctree234.intersect(set_ctree234(T)::in, set_ctree234(T)::in,
    set_ctree234(T)::out) is det.

    % `set_ctree234.power_intersect(A, B)' is true iff `B' is the
    % intersection of all the sets in `A'.
    %
:- func set_ctree234.power_intersect(set_ctree234(set_ctree234(T)))
    = set_ctree234(T).

    % `set_ctree234.intersect_list(A) = B' is true iff `B' is the
    % intersection of all the sets in `A'.
    %
:- func set_ctree234.intersect_list(list(set_ctree234(T))) = set_ctree234(T).

    % `set_ctree234.difference(SetA, SetB, Set)' is true iff `Set' is the
    % set containing all the elements of `SetA' except those that
    % occur in `SetB'.
    %
:- func set_ctree234.difference(set_ctree234(T), set_ctree234(T))
    = set_ctree234(T).
:- pred set_ctree234.difference(set_ctree234(T)::in, set_ctree234(T)::in,
    set_ctree234(T)::out) is det.

    % `set_ctree234.count(Set, Count)' is true iff `Set' has
    % `Count' elements.
    %
:- func set_ctree234.count(set_ctree234(T)) = int.

:- func set_ctree234.map(func(T1) = T2, set_ctree234(T1)) = set_ctree234(T2).
:- pred set_ctree234.map(pred(T1, T2)::in(pred(in, out) is det),
    set_ctree234(T1)::in, set_ctree234(T2)::out) is det.

:- pred set_ctree234.filter_map(pred(T1, T2)::in(pred(in, out) is semidet),
    set_ctree234(T1)::in, set_ctree234(T2)::out) is det.

:- func set_ctree234.filter_map(func(T1) = T2, set_ctree234(T1))
    = set_ctree234(T2).
:- mode set_ctree234.filter_map(func(in) = out is semidet, in) = out is det.

:- func set_ctree234.fold(func(T1, T2) = T2, set_ctree234(T1), T2) = T2.
:- pred set_ctree234.fold(pred(T1, T2, T2), set_ctree234(T1), T2, T2).
:- mode set_ctree234.fold(pred(in, in, out) is det, in, in, out) is det.
:- mode set_ctree234.fold(pred(in, mdi, muo) is det, in, mdi, muo) is det.
:- mode set_ctree234.fold(pred(in, di, uo) is det, in, di, uo) is det.
:- mode set_ctree234.fold(pred(in, in, out) is semidet, in, in, out)
    is semidet.
:- mode set_ctree234.fold(pred(in, mdi, muo) is semidet, in, mdi, muo)
    is semidet.
:- mode set_ctree234.fold(pred(in, di, uo) is semidet, in, di, uo)
    is semidet.

:- pred set_ctree234.fold2(pred(T1, T2, T2, T3, T3), set_ctree234(T1),
    T2, T2, T3, T3) is det.
:- mode set_ctree234.fold2(pred(in, in, out, in, out) is det,
    in, in, out, in, out) is det.
:- mode set_ctree234.fold2(pred(in, in, out, mdi, muo) is det,
    in, in, out, mdi, muo) is det.
:- mode set_ctree234.fold2(pred(in, in, out, di, uo) is det,
    in, in, out, di, uo) is det.
:- mode set_ctree234.fold2(pred(in, in, out, in, out) is semidet,
    in, in, out, in, out) is semidet.
:- mode set_ctree234.fold2(pred(in, in, out, mdi, muo) is semidet,
    in, in, out, mdi, muo) is semidet.
:- mode set_ctree234.fold2(pred(in, in, out, di, uo) is semidet,
    in, in, out, di, uo) is semidet.

:- pred set_ctree234.fold3(
    pred(T1, T2, T2, T3, T3, T4, T4), set_ctree234(T1),
    T2, T2, T3, T3, T4, T4).
:- mode set_ctree234.fold3(pred(in, in, out, in, out, in, out) is det, in,
    in, out, in, out, in, out) is det.
:- mode set_ctree234.fold3(pred(in, in, out, in, out, mdi, muo) is det, in,
    in, out, in, out, mdi, muo) is det.
:- mode set_ctree234.fold3(pred(in, in, out, in, out, di, uo) is det, in,
    in, out, in, out, di, uo) is det.
:- mode set_ctree234.fold3(pred(in, in, out, in, out, in, out) is semidet, in,
    in, out, in, out, in, out) is semidet.
:- mode set_ctree234.fold3(pred(in, in, out, in, out, mdi, muo) is semidet, in,
    in, out, in, out, mdi, muo) is semidet.
:- mode set_ctree234.fold3(pred(in, in, out, in, out, di, uo) is semidet, in,
    in, out, in, out, di, uo) is semidet.

:- pred set_ctree234.fold4(
    pred(T1, T2, T2, T3, T3, T4, T4, T5, T5), set_ctree234(T1),
    T2, T2, T3, T3, T4, T4, T5, T5).
:- mode set_ctree234.fold4(pred(in, in, out, in, out, in, out, in, out) is det,
    in, in, out, in, out, in, out, in, out) is det.
:- mode set_ctree234.fold4(pred(in, in, out, in, out, in, out, mdi, muo) is det,
    in, in, out, in, out, in, out, mdi, muo) is det.
:- mode set_ctree234.fold4(pred(in, in, out, in, out, in, out, di, uo) is det,
    in, in, out, in, out, in, out, di, uo) is det.
:- mode set_ctree234.fold4(
    pred(in, in, out, in, out, in, out, in, out) is semidet,
    in, in, out, in, out, in, out, in, out) is semidet.
:- mode set_ctree234.fold4(
    pred(in, in, out, in, out, in, out, mdi, muo) is semidet,
    in, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode set_ctree234.fold4(
    pred(in, in, out, in, out, in, out, di, uo) is semidet,
    in, in, out, in, out, in, out, di, uo) is semidet.

:- pred set_ctree234.fold5(
    pred(T1, T2, T2, T3, T3, T4, T4, T5, T5, T6, T6),
    set_ctree234(T1), T2, T2, T3, T3, T4, T4, T5, T5, T6, T6).
:- mode set_ctree234.fold5(
    pred(in, in, out, in, out, in, out, in, out, in, out) is det,
    in, in, out, in, out, in, out, in, out, in, out) is det.
:- mode set_ctree234.fold5(
    pred(in, in, out, in, out, in, out, in, out, mdi, muo) is det,
    in, in, out, in, out, in, out, in, out, mdi, muo) is det.
:- mode set_ctree234.fold5(
    pred(in, in, out, in, out, in, out, in, out, di, uo) is det,
    in, in, out, in, out, in, out, in, out, di, uo) is det.
:- mode set_ctree234.fold5(
    pred(in, in, out, in, out, in, out, in, out, in, out) is semidet,
    in, in, out, in, out, in, out, in, out, in, out) is semidet.
:- mode set_ctree234.fold5(
    pred(in, in, out, in, out, in, out, in, out, mdi, muo) is semidet,
    in, in, out, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode set_ctree234.fold5(
    pred(in, in, out, in, out, in, out, in, out, di, uo) is semidet,
    in, in, out, in, out, in, out, in, out, di, uo) is semidet.

:- pred set_ctree234.fold6(
    pred(T1, T2, T2, T3, T3, T4, T4, T5, T5, T6, T6, T7, T7),
    set_ctree234(T1), T2, T2, T3, T3, T4, T4, T5, T5, T6, T6, T7, T7).
:- mode set_ctree234.fold6(
    pred(in, in, out, in, out, in, out, in, out, in, out, in, out) is det,
    in, in, out, in, out, in, out, in, out, in, out, in, out) is det.
:- mode set_ctree234.fold6(
    pred(in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is det,
    in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is det.
:- mode set_ctree234.fold6(
    pred(in, in, out, in, out, in, out, in, out, in, out, di, uo) is det,
    in, in, out, in, out, in, out, in, out, in, out, di, uo) is det.
:- mode set_ctree234.fold6(
    pred(in, in, out, in, out, in, out, in, out, in, out, in, out) is semidet,
    in, in, out, in, out, in, out, in, out, in, out, in, out) is semidet.
:- mode set_ctree234.fold6(
    pred(in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is semidet,
    in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode set_ctree234.fold6(
    pred(in, in, out, in, out, in, out, in, out, in, out, di, uo) is semidet,
    in, in, out, in, out, in, out, in, out, in, out, di, uo) is semidet.

    % all_true(Pred, Set) succeeds iff Pred(Element) succeeds
    % for all the elements of Set.
    %
:- pred set_ctree234.all_true(pred(T)::in(pred(in) is semidet),
    set_ctree234(T)::in) is semidet.

    % Return the set of items for which the predicate succeeds.
    %
:- pred set_ctree234.filter(pred(T)::in(pred(in) is semidet),
    set_ctree234(T)::in, set_ctree234(T)::out) is det.

    % Return the set of items for which the predicate succeeds,
    % and the set for which it fails.
    %
:- pred set_ctree234.filter(pred(T)::in(pred(in) is semidet),
    set_ctree234(T)::in, set_ctree234(T)::out, set_ctree234(T)::out) is det.

    % set_ctree234.divide(Pred, Set, TruePart, FalsePart):
    % TruePart consists of those elements of Set for which Pred succeeds;
    % FalsePart consists of those elements of Set for which Pred fails.
    % NOTE: This is the same as filter/4.
    %
:- pred set_ctree234.divide(pred(T)::in(pred(in) is semidet),
    set_ctree234(T)::in, set_ctree234(T)::out, set_ctree234(T)::out) is det.

    % set_ctree234.divide_by_set(DivideBySet, Set, InPart, OutPart):
    % InPart consists of those elements of Set which are also in
    % DivideBySet; OutPart consists of those elements of which are
    % not in DivideBySet.
    %
:- pred set_ctree234.divide_by_set(set_ctree234(T)::in, set_ctree234(T)::in,
    set_ctree234(T)::out, set_ctree234(T)::out) is det.

:- pred verify_depths(set_ctree234(T)::in, list(int)::out) is det.

%--------------------------------------------------%
%--------------------------------------------------%


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