%--------------------------------------------------%
% vim: ft=mercury ts=4 sw=4 et
%--------------------------------------------------%
% Copyright (C) 1996-1997,1999-2002, 2004-2006, 2008-2012 The University of Melbourne.
% Copyright (C) 2014-2015, 2018-2022, 2024-2025 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
%--------------------------------------------------%
%
% File: set_ordlist.m.
% Main authors: conway, fjh.
% Stability: medium.
%
% This file contains a `set' ADT.
% Sets are implemented here as sorted lists without duplicates.
%
%--------------------------------------------------%
%--------------------------------------------------%

:- module set_ordlist.
:- interface.

:- import_module bool.
:- import_module list.

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

:- type set_ordlist(_T).

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

    % init(Set) is true if-and-only-if Set is an empty set.
    %
:- func init = set_ordlist(T).
:- pred init(set_ordlist(_T)::uo) is det.

    % singleton_set(Elem, Set) is true if-and-only-if
    % Set is the set containing just the single element Elem.
    %
:- pred singleton_set(T, set_ordlist(T)).
:- mode singleton_set(in, out) is det.
:- mode singleton_set(out, in) is semidet.

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

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

    % is_empty(Set) is true if-and-only-if Set is an empty set.
    %
:- pred is_empty(set_ordlist(T)::in) is semidet.

    % is_non_empty(Set) is true if-and-only-if Set is not an empty set.
    %
:- pred is_non_empty(set_ordlist(T)::in) is semidet.

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

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

    % member(X, Set) is true if-and-only-if X is a member of Set.
    %
:- pred member(T, set_ordlist(T)).
:- mode member(in, in) is semidet.
:- mode member(out, in) is nondet.

    % is_member(X, Set, Result) returns `Result = yes' if-and-only-if
    % X is a member of Set.
    %
:- pred is_member(T::in, set_ordlist(T)::in, bool::out) is det.

    % contains(Set, X) is true if-and-only-if X is a member of Set.
    %
:- pred contains(set_ordlist(T)::in, T::in) is semidet.

    % nondet_member(Set, X):
    %
    % Nondeterministically produce each element in Set.
    % Each time this call succeeds, X will be bound to an element in Set.
    %
:- pred nondet_member(set_ordlist(T)::in, T::out) is nondet.

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

    % insert(X, Set0, Set) is true if-and-only-if Set is the union
    % of Set0 and the set containing only X.
    %
:- func insert(set_ordlist(T), T) = set_ordlist(T).
:- pred insert(T::in, set_ordlist(T)::in, set_ordlist(T)::out) is det.

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

    % insert_list(Xs, Set0, Set) is true if-and-only-if
    % Set is the union of Set0 and the set containing only the members of Xs.
    %
:- func insert_list(set_ordlist(T), list(T)) = set_ordlist(T).
:- pred insert_list(list(T)::in, set_ordlist(T)::in, set_ordlist(T)::out)
    is det.

    % delete(X, Set0, Set) is true if-and-only-if 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_ordlist(T), T) = set_ordlist(T).
:- pred delete(T::in, set_ordlist(T)::in, set_ordlist(T)::out) is det.

    % delete_list(Xs, Set0, Set) is true if-and-only-if
    % Set is the relative complement of Set0 and the set containing
    % only the members of Xs.
    %
:- func delete_list(set_ordlist(T), list(T)) = set_ordlist(T).
:- pred delete_list(list(T)::in, set_ordlist(T)::in, set_ordlist(T)::out)
    is det.

    % remove(X, Set0, Set) is true if-and-only-if 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_ordlist(T)::in, set_ordlist(T)::out) is semidet.
:- pred det_remove(T::in, set_ordlist(T)::in, set_ordlist(T)::out) is det.

    % remove_list(Xs, Set0, Set) is true if-and-only-if
    % 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_ordlist(T)::in, set_ordlist(T)::out)
    is semidet.
:- pred det_remove_list(list(T)::in, set_ordlist(T)::in, set_ordlist(T)::out)
    is det.

    % remove_least(X, Set0, Set) is true if-and-only-if
    % X is the least element in Set0, and Set is the set which contains
    % all the elements of Set0 except X.
    %
:- pred remove_least(T::out, set_ordlist(T)::in, set_ordlist(T)::out)
    is semidet.

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

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

    % subset(SetA, SetB) is true if-and-only-if SetA is a subset of SetB.
    %
:- pred subset(set_ordlist(T)::in, set_ordlist(T)::in) is semidet.

    % superset(SetA, SetB) is true if-and-only-if SetA is a superset of SetB.
    %
:- pred superset(set_ordlist(T)::in, set_ordlist(T)::in) is semidet.

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

    % union(SetA, SetB, Set) is true if-and-only-if
    % Set is the union of SetA and SetB. The efficiency of the union operation
    % is O(card(SetA)+card(SetB)), and is not sensitive to the argument
    % ordering.
    %
:- func union(set_ordlist(T), set_ordlist(T)) = set_ordlist(T).
:- pred union(set_ordlist(T)::in, set_ordlist(T)::in, set_ordlist(T)::out)
    is det.

    % union_list(A, B) is true if-and-only-if
    % B is the union of all the sets in A.
    %
:- func union_list(list(set_ordlist(T))) = set_ordlist(T).
:- pred union_list(list(set_ordlist(T))::in, set_ordlist(T)::out) is det.

    % power_union(A, B) is true if-and-only-if
    % B is the union of all the sets in A,
    %
:- func power_union(set_ordlist(set_ordlist(T))) = set_ordlist(T).
:- pred power_union(set_ordlist(set_ordlist(T))::in,
    set_ordlist(T)::out) is det.

    % intersect(SetA, SetB, Set) is true if-and-only-if
    % Set is the intersection of SetA and SetB. The efficiency
    % of the intersection operation is not influenced by the argument order.
    %
:- func intersect(set_ordlist(T), set_ordlist(T)) = set_ordlist(T).
:- pred intersect(set_ordlist(T), set_ordlist(T), set_ordlist(T)).
:- mode intersect(in, in, out) is det.
:- mode intersect(in, in, in) is semidet.

    % intersect_list(A) = B' is true if-and-only-if
    % B is the intersection of all the sets in A.
    %
:- func intersect_list(list(set_ordlist(T))) = set_ordlist(T).
:- pred intersect_list(list(set_ordlist(T))::in, set_ordlist(T)::out) is det.

    % power_intersect(A, B) is true if-and-only-if
    % B is the intersection of all the sets in A.
    %
:- func power_intersect(set_ordlist(set_ordlist(T)))
    = set_ordlist(T).
:- pred power_intersect(set_ordlist(set_ordlist(T))::in,
    set_ordlist(T)::out) is det.

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

    % intersection_and_differences(SetA, SetB, InAandB, OnlyInA, OnlyInB):
    % Given SetA and SetB, return the elements that occur in both sets,
    % and those that occur only in one or the other.
    %
:- pred intersection_and_differences(set_ordlist(T)::in, set_ordlist(T)::in,
    set_ordlist(T)::out, set_ordlist(T)::out, set_ordlist(T)::out) is det.

%--------------------------------------------------%
%
% Operations that divide a set into two parts.
%

    % 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.
    %
:- pred divide(pred(T)::in(pred(in) is semidet),
    set_ordlist(T)::in, set_ordlist(T)::out, set_ordlist(T)::out) is det.

    % 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 Set which are not in DivideBySet.
    %
:- pred divide_by_set(set_ordlist(T)::in, set_ordlist(T)::in,
    set_ordlist(T)::out, set_ordlist(T)::out) is det.

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

    % list_to_set(List, Set) is true if-and-only-if Set is the set
    % containing only the members of List.
    %
:- func list_to_set(list(T)) = set_ordlist(T).
:- pred list_to_set(list(T)::in, set_ordlist(T)::out) is det.

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

    % sorted_list_to_set(List, Set) is true if-and-only-if Set is the set
    % containing only the members of List. List must be sorted
    % in ascending order.
    %
:- func sorted_list_to_set(list(T)) = set_ordlist(T).
:- pred sorted_list_to_set(list(T)::in, set_ordlist(T)::out) is det.

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

    % rev_sorted_list_to_set(List, Set) is true if-and-only-if Set is the set
    % containing only the members of List. List must be sorted
    % in descending order and must not contain any duplicates.
    %
:- func rev_sorted_list_to_set(list(T)) = set_ordlist(T).
:- pred rev_sorted_list_to_set(list(T)::in, set_ordlist(T)::out) is det.

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

    % to_sorted_list(Set, List) is true if-and-only-if
    % List is the list of all the members of Set, in sorted order.
    %
:- func to_sorted_list(set_ordlist(T)) = list(T).
:- pred to_sorted_list(set_ordlist(T)::in, list(T)::out) is det.

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

    % count(Set, Count) is true if-and-only-if Set has Count elements.
    %
:- func count(set_ordlist(T)) = int.
:- pred count(set_ordlist(T)::in, int::out) is det.

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

    % all_true(Pred, Set) succeeds if-and-only-if
    % Pred(Element) succeeds for all the elements of Set.
    %
:- pred all_true(pred(T)::in(pred(in) is semidet), set_ordlist(T)::in)
    is semidet.

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

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

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

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

:- func fold(func(T, A) = A, set_ordlist(T), A) = A.
:- pred fold(pred(T, A, A), set_ordlist(T), A, A).
:- 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.

:- func foldl(func(T, A) = A, set_ordlist(T), A) = A.
:- pred foldl(pred(T, A, A), set_ordlist(T), A, A).
:- mode foldl(in(pred(in, in, out) is det), in, in, out) is det.
:- mode foldl(in(pred(in, mdi, muo) is det), in, mdi, muo) is det.
:- mode foldl(in(pred(in, di, uo) is det), in, di, uo) is det.
:- mode foldl(in(pred(in, in, out) is semidet), in, in, out) is semidet.
:- mode foldl(in(pred(in, mdi, muo) is semidet), in, mdi, muo) is semidet.
:- mode foldl(in(pred(in, di, uo) is semidet), in, di, uo) is semidet.

:- pred fold2(pred(T, A, A, B, B), set_ordlist(T),
    A, A, B, B).
:- 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 foldl2(pred(T, A, A, B, B), set_ordlist(T),
    A, A, B, B).
:- mode foldl2(in(pred(in, in, out, in, out) is det), in,
    in, out, in, out) is det.
:- mode foldl2(in(pred(in, in, out, mdi, muo) is det), in,
    in, out, mdi, muo) is det.
:- mode foldl2(in(pred(in, in, out, di, uo) is det), in,
    in, out, di, uo) is det.
:- mode foldl2(in(pred(in, in, out, in, out) is semidet), in,
    in, out, in, out) is semidet.
:- mode foldl2(in(pred(in, in, out, mdi, muo) is semidet), in,
    in, out, mdi, muo) is semidet.
:- mode foldl2(in(pred(in, in, out, di, uo) is semidet), in,
    in, out, di, uo) is semidet.

:- pred fold3(pred(T, A, A, B, B, C, C),
    set_ordlist(T), A, A, B, B, C, C).
:- 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 foldl3(pred(T, A, A, B, B, C, C),
    set_ordlist(T), A, A, B, B, C, C).
:- mode foldl3(in(pred(in, in, out, in, out, in, out) is det), in,
    in, out, in, out, in, out) is det.
:- mode foldl3(in(pred(in, in, out, in, out, mdi, muo) is det), in,
    in, out, in, out, mdi, muo) is det.
:- mode foldl3(in(pred(in, in, out, in, out, di, uo) is det), in,
    in, out, in, out, di, uo) is det.
:- mode foldl3(in(pred(in, in, out, in, out, in, out) is semidet), in,
    in, out, in, out, in, out) is semidet.
:- mode foldl3(in(pred(in, in, out, in, out, mdi, muo) is semidet), in,
    in, out, in, out, mdi, muo) is semidet.
:- mode foldl3(in(pred(in, in, out, in, out, di, uo) is semidet), in,
    in, out, in, out, di, uo) is semidet.

:- pred fold4(pred(T, A, A, B, B, C, C, D, D),
    set_ordlist(T), A, A, B, B, C, C, D, D).
:- 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 foldl4(pred(T, A, A, B, B, C, C, D, D),
    set_ordlist(T), A, A, B, B, C, C, D, D).
:- mode foldl4(
    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 foldl4(
    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 foldl4(
    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 foldl4(
    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 foldl4(
    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 foldl4(
    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(T, A, A, B, B, C, C, D, D, E, E),
    set_ordlist(T), A, A, B, B, C, C, D, D, E, E).
:- 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 foldl5(
    pred(T, A, A, B, B, C, C, D, D, E, E),
    set_ordlist(T), A, A, B, B, C, C, D, D, E, E).
:- mode foldl5(
    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 foldl5(
    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 foldl5(
    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 foldl5(
    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 foldl5(
    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 foldl5(
    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(T, A, A, B, B, C, C, D, D, E, E, F, F),
    set_ordlist(T), A, A, B, B, C, C, D, D, E, E, F, F).
:- 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.

:- pred foldl6(pred(T, A, A, B, B, C, C, D, D, E, E, F, F),
    set_ordlist(T), A, A, B, B, C, C, D, D, E, E, F, F).
:- mode foldl6(
    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 foldl6(
    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 foldl6(
    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 foldl6(
    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 foldl6(
    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 foldl6(
    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.

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