%--------------------------------------------------%
% vim: ts=4 sw=4 et ft=mercury
%--------------------------------------------------%
% Copyright (C) 1995-1997, 1999-2006, 2010-2012 The University of Melbourne.
% Copyright (C) 2014-2015, 2018-2019, 2021-2022 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
%--------------------------------------------------%
%
% File: set_bbbtree.m.
% Main authors: benyi.
% Stability: low.
%
% This module implements sets using bounded balanced binary trees.
%
%--------------------------------------------------%
%--------------------------------------------------%

:- module set_bbbtree.
:- interface.

:- import_module bool.
:- import_module list.

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

:- type set_bbbtree(T).

%--------------------------------------------------%
%
% Initial creation of sets.
%

    % init(Set) returns an initialized empty set.
    %
:- func init = set_bbbtree(T).
:- pred init(set_bbbtree(T)::uo) is det.

    % singleton_set(X, Set) is true iff Set is the set
    % containing just the single element X.
    %
:- pred singleton_set(T, set_bbbtree(T)).
:- mode singleton_set(in, out) is det.
:- mode singleton_set(in, in) is semidet.
:- mode singleton_set(out, in) is semidet.

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

%--------------------------------------------------%
%
% Emptiness and singleton-ness tests.
%

    % is_empty(Set) is true iff Set is an empty set.
    %
:- pred is_empty(set_bbbtree(T)::in) is semidet.

    % is_non_empty(Set) is true iff Set is not an empty set.
    %
:- pred is_non_empty(set_bbbtree(T)::in) is semidet.

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

%--------------------------------------------------%
%
% Membership tests.
%

    % member(X, Set) is true iff X is a member of Set.
    % O(lg n) for (in, in) and O(1) for (out, in).
    %
:- pred member(T, set_bbbtree(T)).
:- mode member(in, in) is semidet.
:- mode member(out, in) is nondet.

    % is_member(X, Set, Result) is true iff X is a member of Set.
    %
:- pred is_member(T::in, set_bbbtree(T)::in, bool::out) is det.

    % contains(Set, X) is true iff X is a member of Set.
    % O(lg n).
    %
:- pred contains(set_bbbtree(T)::in, T::in) is semidet.

    % least(Set, X) is true iff X is smaller than all the other members of Set.
    %
:- pred least(set_bbbtree(T), T).
:- mode least(in, out) is semidet.
:- mode least(in, in) is semidet.

    % largest(Set, X) is true iff X is larger than all
    % the other members of Set.
    %
:- pred largest(set_bbbtree(T), T).
:- mode largest(in, out) is semidet.
:- mode largest(in, in) is semidet.

%--------------------------------------------------%
%
% Insertions and deletions.
%

    % insert(X, Set0, Set) is true iff Set is the union of
    % Set0 and the set containing only X.
    %
:- func insert(set_bbbtree(T), T) = set_bbbtree(T).
:- pred insert(T, set_bbbtree(T), set_bbbtree(T)).
:- mode insert(di, di, uo) is det.
:- mode insert(in, in, out) is det.

    % 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 insert_new(T::in,
    set_bbbtree(T)::in, set_bbbtree(T)::out) is semidet.

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

    % `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 delete(set_bbbtree(T), T) = set_bbbtree(T).
:- pred delete(T, set_bbbtree(T), set_bbbtree(T)).
:- mode delete(in, di, uo) is det.
:- mode delete(in, in, out) is det.

    % 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 delete_list(set_bbbtree(T), list(T)) = set_bbbtree(T).
:- pred delete_list(list(T)::in,
    set_bbbtree(T)::in, set_bbbtree(T)::out) is det.

    % 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.
    %
    % The det_remove version throws an exception instead of failing.
    %
:- pred remove(T::in, set_bbbtree(T)::in, set_bbbtree(T)::out) is semidet.
:- pred det_remove(T::in, set_bbbtree(T)::in, set_bbbtree(T)::out) is det.

    % 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.
    %
    % The det_remove_list version throws an exception instead of failing.
    %
:- pred remove_list(list(T)::in,
    set_bbbtree(T)::in, set_bbbtree(T)::out) is semidet.
:- pred det_remove_list(list(T)::in,
    set_bbbtree(T)::in, set_bbbtree(T)::out) is det.

    % remove_least(X, Set0, Set) is true iff the union if
    % X and Set is Set0 and X is smaller than all the elements of Set.
    %
:- pred remove_least(T::out,
    set_bbbtree(T)::in, set_bbbtree(T)::out) is semidet.

    % remove_largest(X, Set0, Set) is true iff the union if
    % X and Set is Set0 and X is larger than all the elements of Set.
    %
:- pred remove_largest(T::out,
    set_bbbtree(T)::in, set_bbbtree(T)::out) is semidet.

%--------------------------------------------------%
%
% Comparisons between sets.
%

    % equal(SetA, SetB) is true iff SetA and SetB contain the same elements.
    %
:- pred equal(set_bbbtree(T)::in, set_bbbtree(T)::in) is semidet.

    % subset(SetA, SetB) is true iff all the elements of
    % SetA are also elements of SetB.
    %
:- pred subset(set_bbbtree(T)::in, set_bbbtree(T)::in) is semidet.

    % superset(SetA, SetB) is true iff all the elements of
    % SetB are also elements of SetA.
    %
:- pred superset(set_bbbtree(T)::in, set_bbbtree(T)::in) is semidet.

%--------------------------------------------------%
%
% Operations on two or more sets.
%

    % union(SetA, SetB, Set) is true iff Set is the union
    % of SetA and SetB.
    %
:- func union(set_bbbtree(T), set_bbbtree(T)) = set_bbbtree(T).
:- pred union(set_bbbtree(T)::in, set_bbbtree(T)::in,
    set_bbbtree(T)::out) is det.

    % union_list(Sets) = Set is true iff Set is the union
    % of all the sets in Sets
    %
:- func union_list(list(set_bbbtree(T))) = set_bbbtree(T).

    % power_union(Sets, Set) is true iff Set is the union
    % of all the sets in Sets
    %
:- func power_union(set_bbbtree(set_bbbtree(T))) = set_bbbtree(T).
:- pred power_union(set_bbbtree(set_bbbtree(T))::in,
    set_bbbtree(T)::out) is det.

    % intersect(SetA, SetB, Set) is true iff Set is the
    % intersection of SetA and SetB.
    %
:- func intersect(set_bbbtree(T), set_bbbtree(T)) = set_bbbtree(T).
:- pred intersect(set_bbbtree(T)::in, set_bbbtree(T)::in,
    set_bbbtree(T)::out) is det.

    % intersect_list(Sets) = Set is true iff Set is the
    % intersection of the sets in Sets.
    %
:- func intersect_list(list(set_bbbtree(T))) = set_bbbtree(T).

    % power_intersect(Sets, Set) is true iff Set is the
    % intersection of the sets in Sets.
    %
:- func power_intersect(set_bbbtree(set_bbbtree(T))) = set_bbbtree(T).
:- pred power_intersect(set_bbbtree(set_bbbtree(T))::in, set_bbbtree(T)::out)
    is det.

    % set_bbtree.difference(SetA, SetB, Set) is true iff Set is the
    %  set containing all the elements of SetA except those that
    % occur in SetB.
    %
:- func difference(set_bbbtree(T), set_bbbtree(T)) = set_bbbtree(T).
:- pred difference(set_bbbtree(T)::in, set_bbbtree(T)::in,
    set_bbbtree(T)::out) is det.

%--------------------------------------------------%
%
% Converting lists to sets.
%

    % list_to_set(List, Set) is true iff Set is the set
    % containing only the members of List. O(n lg n).
    %
:- func list_to_set(list(T)) = set_bbbtree(T).
:- pred list_to_set(list(T)::in, set_bbbtree(T)::out) is det.

    % A synonym for set_bbtree.list_to_set/1.
    %
:- func from_list(list(T)) = set_bbbtree(T).

    % sorted_list_to_set(List, Set) is true iff Set is the
    % set containing only the members of List.
    % List must be sorted in ascending order, and must not contain
    % any duplicates. O(n).
    %
    % The sorted_list_to_set_len version allows the caller to provide
    % the length of List, which avoids the cost of computing it again.
    % This version will throw an exception if the length is incorrect.
    %
:- func sorted_list_to_set(list(T)) = set_bbbtree(T).
:- pred sorted_list_to_set(list(T)::in, set_bbbtree(T)::out) is det.
:- pred sorted_list_to_set_len(list(T)::in, set_bbbtree(T)::out,
    int::in) is det.

    % rev_sorted_list_to_set(List) = Set is true iff Set is the set
    % containing only the members of List. List must be sorted
    % in descending order.
    %
:- func rev_sorted_list_to_set(list(T)) = set_bbbtree(T).
:- pred rev_sorted_list_to_set(list(T)::in, set_bbbtree(T)::out) is det.
:- pred rev_sorted_list_to_set_len(list(T)::in, set_bbbtree(T)::out,
    int::in) is det.

    % A synonym for sorted_list_to_set/1.
    %
:- func from_sorted_list(list(T)) = set_bbbtree(T).

%--------------------------------------------------%
%
% Converting sets to lists.
%

    % to_sorted_list(Set, List) is true iff List is the
    % list of all the members of Set, in sorted order. O(n).
    %
:- func to_sorted_list(set_bbbtree(T)) = list(T).
:- pred to_sorted_list(set_bbbtree(T), list(T)).
:- mode to_sorted_list(di, uo) is det.
:- mode to_sorted_list(in, out) is det.

%--------------------------------------------------%
%
% Counting.
%

    % count(Set, Count) is true iff Set has Count elements.
    % i.e. Count is the cardinality (size) of the set.
    %
:- func count(set_bbbtree(T)) = int.
:- pred count(set_bbbtree(T)::in, int::out) is det.

%--------------------------------------------------%
%
% Standard higher order functions on collections.
%

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

    % filter(Pred, Items, Trues):
    % Return the set of items for which Pred succeeds.
    %
:- pred filter(pred(T)::in(pred(in) is semidet),
    set_bbbtree(T)::in, set_bbbtree(T)::out) is det.

    % filter(Pred, Items, Trues, Falses):
    % Return the set of items for which Pred succeeds,
    % and the set for which it fails.
    %
:- pred filter(pred(T)::in(pred(in) is semidet),
    set_bbbtree(T)::in, set_bbbtree(T)::out, set_bbbtree(T)::out) is det.

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

:- func map(func(T1) = T2, set_bbbtree(T1)) = set_bbbtree(T2).

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

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

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

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

:- pred fold5(
    pred(T1, T2, T2, T3, T3, T4, T4, T5, T5, T6, T6),
    set_bbbtree(T1), T2, T2, T3, T3, T4, T4, T5, T5, T6, T6).
:- mode fold5(
    in(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 fold5(
    in(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 fold5(
    in(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 fold5(
    in(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 fold5(
    in(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 fold5(
    in(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 fold6(
    pred(T1, T2, T2, T3, T3, T4, T4, T5, T5, T6, T6, T7, T7),
    set_bbbtree(T1), T2, T2, T3, T3, T4, T4, T5, T5, T6, T6, T7, T7).
:- mode fold6(
    in(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 fold6(
    in(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 fold6(
    in(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 fold6(
    in(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 fold6(
    in(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 fold6(
    in(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.

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