mercury/library/bt_array.m

%-----------------------------------------------------------------------------%
% Copyright (C) 1997, 1999-2000, 2002-2003 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: bt_array.m
% Main author: bromage.
% Stability: medium-low

% This file contains a set of predicates for generating an manipulating
% a bt_array data structure.  This implementation allows O(log n) access
% and update time, and does not require the bt_array to be unique.  If you
% need O(1) access/update time, use the array datatype instead.
% (`bt_array' is supposed to stand for either "binary tree array"
% or "backtrackable array".)

% Implementation obscurity: This implementation is biased towards larger
% indices.  The access/update time for a bt_array of size N with index I
% is actually O(log(N-I)).  The reason for this is so that the resize
% operations can be optimised for a (possibly very) common case, and to
% exploit accumulator recursion in some operations.  See the documentation
% of bt_array__resize and bt_array__shrink for more details.

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

:- module bt_array.
:- interface.
:- import_module int, list.

:- type bt_array(T).

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

	% bt_array__make_empty_array(Low, Array) is true iff Array is a
	% bt_array of size zero starting at index Low.
:- pred bt_array__make_empty_array(int, bt_array(T)).
:- mode bt_array__make_empty_array(in, out) is det.

:- func bt_array__make_empty_array(int) = bt_array(T).

	% bt_array__init(Low, High, Init, Array) is true iff Array is a
	% bt_array with bounds from Low to High whose elements each equal Init.
:- pred bt_array__init(int, int, T, bt_array(T)).
:- mode bt_array__init(in, in, in, out) is det. % want a bt_array_skeleton?

:- func bt_array__init(int, int, T) = bt_array(T).

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

	% array__min returns the lower bound of the array
:- pred bt_array__min(bt_array(_T), int).
:- mode bt_array__min(in, out) is det.

:- func bt_array__min(bt_array(_T)) = int.

	% array__max returns the upper bound of the array
:- pred bt_array__max(bt_array(_T), int).
:- mode bt_array__max(in, out) is det.

:- func bt_array__max(bt_array(_T)) = int.

	% array__size returns the length of the array,
	% i.e. upper bound - lower bound + 1.
:- pred bt_array__size(bt_array(_T), int).
:- mode bt_array__size(in, out) is det.

:- func bt_array__size(bt_array(_T)) = int.

	% bt_array__bounds returns the upper and lower bounds of a bt_array.
:- pred bt_array__bounds(bt_array(_T), int, int).
:- mode bt_array__bounds(in, out, out) is det.

	% bt_array__in_bounds checks whether an index is in the bounds
	% of a bt_array
:- pred bt_array__in_bounds(bt_array(_T), int).
:- mode bt_array__in_bounds(in, in) is semidet.

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

	% bt_array__lookup returns the Nth element of a bt_array.
	% It is an error if the index is out of bounds.
:- pred bt_array__lookup(bt_array(T), int, T).
:- mode bt_array__lookup(in, in, out) is det.

:- func bt_array__lookup(bt_array(T), int) = T.

	% bt_array__semidet_lookup is like bt_array__lookup except that
	% it fails if the index is out of bounds.
:- pred bt_array__semidet_lookup(bt_array(T), int, T).
:- mode bt_array__semidet_lookup(in, in, out) is semidet.

	% bt_array__set sets the nth element of a bt_array, and returns the
	% resulting bt_array.
	% It is an error if the index is out of bounds.
:- pred bt_array__set(bt_array(T), int, T, bt_array(T)).
:- mode bt_array__set(in, in, in, out) is det.

:- func bt_array__set(bt_array(T), int, T) = bt_array(T).

	% bt_array__set sets the nth element of a bt_array, and returns the
	% resulting bt_array (good opportunity for destructive update ;-).  
	% It fails if the index is out of bounds.
:- pred bt_array__semidet_set(bt_array(T), int, T, bt_array(T)).
:- mode bt_array__semidet_set(in, in, in, out) is semidet.

	% `bt_array__resize(BtArray0, Lo, Hi, Item, BtArray)' is true
	% if BtArray is a bt_array created by expanding or shrinking
	% BtArray0 to fit the bounds (Lo,Hi).  If the new bounds are
	% not wholly contained within the bounds of BtArray0, Item is
	% used to fill out the other places.
	%
	% Note: This operation is optimised for the case where the
	% lower bound of the new bt_array is the same as that of
	% the old bt_array.  In that case, the operation takes time
	% proportional to the absolute difference in size between
	% the two bt_arrays.  If this is not the case, it may take
	% time proportional to the larger of the two bt_arrays.
:- pred bt_array__resize(bt_array(T), int, int, T, bt_array(T)).
:- mode bt_array__resize(in, in, in, in, out) is det.

:- func bt_array__resize(bt_array(T), int, int, T) = bt_array(T).

	% `bt_array__shrink(BtArray0, Lo, Hi, Item, BtArray)' is true
	% if BtArray is a bt_array created by shrinking BtArray0 to
	% fit the bounds (Lo,Hi).  It is an error if the new bounds
	% are not wholly within the bounds of BtArray0.
	%
	% Note: This operation is optimised for the case where the
	% lower bound of the new bt_array is the same as that of
	% the old bt_array.  In that case, the operation takes time
	% proportional to the absolute difference in size between
	% the two bt_arrays.  If this is not the case, it may take
	% time proportional to the larger of the two bt_arrays.
:- pred bt_array__shrink(bt_array(T), int, int, bt_array(T)).
:- mode bt_array__shrink(in, in, in, out) is det.

:- func bt_array__shrink(bt_array(T), int, int) = bt_array(T).

	% `bt_array__from_list(Low, List, BtArray)' takes a list (of
	% possibly zero length), and returns a bt_array containing
	% those elements in the same order that they occurred in the
	% list.  The lower bound of the new array is `Low'.
:- pred bt_array__from_list(int, list(T), bt_array(T)).
:- mode bt_array__from_list(in, in, out) is det.

:- func bt_array__from_list(int, list(T)) = bt_array(T).

	% bt_array__to_list takes a bt_array and returns a list containing
	% the elements of the bt_array in the same order that they
	% occurred in the bt_array.
:- pred bt_array__to_list(bt_array(T), list(T)).
:- mode bt_array__to_list(in, out) is det.

:- func bt_array__to_list(bt_array(T)) = list(T).

	% bt_array__fetch_items takes a bt_array and a lower and upper
	% index, and places those items in the bt_array between these
	% indices into a list.  It is an error if either index is
	% out of bounds.
:- pred bt_array__fetch_items(bt_array(T), int, int, list(T)).
:- mode bt_array__fetch_items(in, in, in, out) is det.

:- func bt_array__fetch_items(bt_array(T), int, int) = list(T).

	% bt_array__bsearch takes a bt_array, an element to be matched
	% and a comparison predicate and returns the position of
	% the first occurrence in the bt_array of an element which is
	% equivalent to the given one in the ordering provided.
	% Assumes the bt_array is sorted according to this ordering.
	% Fails if the element is not present.
:- pred bt_array__bsearch(bt_array(T), T, comparison_pred(T), int).
:- mode bt_array__bsearch(in, in, in(comparison_pred), out) is semidet.

	% Field selection for arrays.
	% Array ^ elem(Index) = bt_array__lookup(Array, Index).
:- func bt_array__elem(int, bt_array(T)) = T.

	% Field update for arrays.
	% (Array ^ elem(Index) := Value) = bt_array__set(Array, Index, Value).
:- func 'bt_array__elem :='(int, bt_array(T), T) = bt_array(T).

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

:- implementation.

:- import_module require.

:- type bt_array(T)	--->	bt_array(int, int, ra_list(T)).

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

bt_array__make_empty_array(Low, bt_array(Low, High, ListOut)) :-
	High = Low - 1,
	ra_list_nil(ListOut).

bt_array__init(Low, High, Item, bt_array(Low, High, ListOut)) :-
	ra_list_nil(ListIn),
	ElemsToAdd = High - Low + 1,
	bt_array__add_elements(ElemsToAdd, Item, ListIn, ListOut).

:- pred bt_array__add_elements(int, T, ra_list(T), ra_list(T)).
:- mode bt_array__add_elements(in, in, in, out) is det.

bt_array__add_elements(ElemsToAdd, Item, RaList0, RaList) :-
	( ElemsToAdd =< 0 ->
		RaList0 = RaList
	;
		ra_list_cons(Item, RaList0, RaList1),
		ElemsToAdd1 = ElemsToAdd - 1,
		bt_array__add_elements(ElemsToAdd1, Item, RaList1, RaList)
	).

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

bt_array__min(bt_array(Low, _, _), Low).

bt_array__max(bt_array(_, High, _), High).

bt_array__size(bt_array(Low, High, _), Size) :-
	Size = High - Low + 1.

bt_array__bounds(bt_array(Low, High, _), Low, High).

bt_array__in_bounds(bt_array(Low, High, _), Index) :-
	Low =< Index, Index =< High.

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

:- pragma inline(actual_position/4).
:- pred actual_position(int, int, int, int).
:- mode actual_position(in, in, in, out) is det.

actual_position(Low, High, Index, Pos) :-
	Pos = High - Low - Index.

bt_array__lookup(bt_array(Low, High, RaList), Index, Item) :-
	actual_position(Low, High, Index, Pos),
	( ra_list_lookup(Pos, RaList, Item0) ->
		Item = Item0
	;
		error("bt_array__lookup: Array subscript out of bounds")
	).

bt_array__semidet_lookup(bt_array(Low, High, RaList), Index, Item) :-
	actual_position(Low, High, Index, Pos),
	ra_list_lookup(Pos, RaList, Item).

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

bt_array__set(BtArray0, Index, Item, BtArray) :-
	( bt_array__semidet_set(BtArray0, Index, Item, BtArray1) ->
		BtArray = BtArray1
	;
		error("bt_array__set: index out of bounds")
	).

bt_array__semidet_set(bt_array(Low, High, RaListIn), Index, Item,
		bt_array(Low, High, RaListOut)) :-
	actual_position(Low, High, Index, Pos),
	ra_list_update(RaListIn, Pos, Item, RaListOut).

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

bt_array__resize(Array0, L, H, Item, Array) :-
	Array0 = bt_array(L0, H0, RaList0),
	( L = L0 ->
		% Optimise the common case where the lower bounds are
		% the same.

		( H < H0 ->
			SizeDiff = H0 - H,
			( ra_list_drop(SizeDiff, RaList0, RaList1) ->
				RaList = RaList1
			;
				error("bt_array__resize: Can't resize to a less-than-empty array")
			),
			Array = bt_array(L, H, RaList)
		; H > H0 ->
			SizeDiff = H - H0,
			bt_array__add_elements(SizeDiff, Item, RaList0, RaList),
			Array = bt_array(L, H, RaList)
		;
			Array = Array0
		)
	;
		int__max(L, L0, L1),
		int__min(H, H0, H1),
		bt_array__fetch_items(Array0, L1, H1, Items),
		bt_array__init(L, H, Item, Array1),
		bt_array__insert_items(Array1, L1, Items, Array)
	).

bt_array__shrink(Array0, L, H, Array) :-
	Array0 = bt_array(L0, H0, RaList0),
	( ( L < L0 ; H > H0 ) ->
		error("bt_array__shrink: New bounds are larger than old ones")
	; L = L0 ->
		% Optimise the common case where the lower bounds are
		% the same.

		SizeDiff = H0 - H,
		( ra_list_drop(SizeDiff, RaList0, RaList1) ->
			RaList = RaList1
		;
			error("bt_array__shrink: Can't resize to a less-than-empty array")
		),
		Array = bt_array(L, H, RaList)
	;
		( ra_list_head(RaList0, Item0) ->
			Item = Item0
		;
			error("bt_array__shrink: Can't shrink an empty array")
		),
		int__max(L, L0, L1),
		int__min(H, H0, H1),
		bt_array__fetch_items(Array0, L1, H1, Items),
		bt_array__init(L, H, Item, Array1),
		bt_array__insert_items(Array1, L1, Items, Array)
	).

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

bt_array__from_list(Low, List, bt_array(Low, High, RaList)) :-
	list__length(List, Len),
	High = Low + Len - 1,
	ra_list_nil(RaList0),
	bt_array__reverse_into_ra_list(List, RaList0, RaList).

:- pred bt_array__reverse_into_ra_list(list(T), ra_list(T), ra_list(T)).
:- mode bt_array__reverse_into_ra_list(in, in, out) is det.

bt_array__reverse_into_ra_list([], RaList, RaList).
bt_array__reverse_into_ra_list([X | Xs], RaList0, RaList) :-
	ra_list_cons(X, RaList0, RaList1),
	bt_array__reverse_into_ra_list(Xs, RaList1, RaList).

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

:- pred bt_array__insert_items(bt_array(T), int, list(T), bt_array(T)).
:- mode bt_array__insert_items(in, in, in, out) is det.

bt_array__insert_items(Array, _N, [], Array).
bt_array__insert_items(Array0, N, [Head|Tail], Array) :-
	bt_array__set(Array0, N, Head, Array1),
	N1 = N + 1,
	bt_array__insert_items(Array1, N1, Tail, Array).

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

bt_array__to_list(bt_array(_, _, RaList), List) :-
	bt_array__reverse_from_ra_list(RaList, [], List).

:- pred bt_array__reverse_from_ra_list(ra_list(T), list(T), list(T)).
:- mode bt_array__reverse_from_ra_list(in, in, out) is det.

bt_array__reverse_from_ra_list(RaList0, Xs0, Xs) :-
	( ra_list_head_tail(RaList0, X, RaList1) ->
		bt_array__reverse_from_ra_list(RaList1, [X | Xs0], Xs)
	;
		Xs0 = Xs
	).

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

bt_array__fetch_items(bt_array(ALow, AHigh, RaList0), Low, High, List) :-
	(
		Low > High
	->
		List = []
	;
		actual_position(ALow, AHigh, High, Drop),
		ra_list_drop(Drop, RaList0, RaList),
		Take = High - Low + 1,
		bt_array__reverse_from_ra_list_count(Take, RaList, [], List0)
	->
		List = List0
	;
		List = []
	).

:- pred bt_array__reverse_from_ra_list_count(int, ra_list(T), list(T), list(T)).
:- mode bt_array__reverse_from_ra_list_count(in, in, in, out) is det.

bt_array__reverse_from_ra_list_count(I, RaList0, Xs0, Xs) :-
	(
		ra_list_head_tail(RaList0, X, RaList1),
		I >= 0
	->
		I1 = I - 1,
		bt_array__reverse_from_ra_list_count(I1, RaList1, [X | Xs0], Xs)
	;
		Xs0 = Xs
	).

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

bt_array__bsearch(A, El, Compare, I) :-
	bt_array__bounds(A, Lo, Hi),
	Lo =< Hi,
	bt_array__bsearch_2(A, Lo, Hi, El, Compare, I).

	% XXX Would we gain anything by traversing the ra_list instead
	%     of doing a vanilla binary chop?
:- pred bt_array__bsearch_2(bt_array(T), int, int, T,
			pred(T, T, comparison_result), int).
:- mode bt_array__bsearch_2(in, in, in, in, pred(in, in, out) is det,
				out) is semidet.
bt_array__bsearch_2(A, Lo, Hi, El, Compare, I) :-
	Width = Hi - Lo,

	% If Width < 0, there is no range left.
	Width >= 0,

	% If Width == 0, we may just have found our element.
	% Do a Compare to check.
	( Width = 0 ->
		bt_array__lookup(A, Lo, X),
		call(Compare, El, X, (=)),
		I = Lo
	;
		% Otherwise find the middle element of the range
		% and check against that.  NOTE: We can't use
		% "// 2" because division always rounds towards
		% zero whereas we want the result to be rounded
		% down.  (Indices can be negative.)  We could use
		% "div 2", but that's a little more expensive, and
		% we know that we're always dividing by a power of
		% 2.  Until such time as we implement strength
		% reduction, the >> 1 stays.

		Mid = (Lo + Hi) >> 1,
		bt_array__lookup(A, Mid, XMid),
		call(Compare, XMid, El, Comp),
		( Comp = (<),
			Mid1 = Mid + 1,
			bt_array__bsearch_2(A, Mid1, Hi, El, Compare, I)
		; Comp = (=),
			bt_array__bsearch_2(A, Lo, Mid, El, Compare, I)
		; Comp = (>),
			Mid1 = Mid - 1,
			bt_array__bsearch_2(A, Lo, Mid1, El, Compare, I)
		)
	).

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

% This is a perfect application for submodules, but Mercury doesn't have
% them. :-(

% The heart of the implementation of bt_array is a `random access list'
% or ra_list for short.  It is very similar to a list data type, and
% it supports O(1) head/tail/cons operations, but O(log n) lookup and
% update.  The representation is a list of perfectly balanced binary
% trees.
%
% For more details on the implementation:
%
%	Chris Okasaki, "Purely Functional Random-Access Lists"
%	Functional Programming Languages and Computer Architecture,
%	June 1995, pp 86-95.

% :- module ra_list.
% :- interface.

% :- type ra_list(T).

:- pred ra_list_nil(ra_list(T)).
:- mode ra_list_nil(uo) is det.

:- pred ra_list_cons(T, ra_list(T), ra_list(T)).
:- mode ra_list_cons(in, in, out) is det.

:- pred ra_list_head(ra_list(T), T).
:- mode ra_list_head(in, out) is semidet.

:- pred ra_list_tail(ra_list(T), ra_list(T)).
:- mode ra_list_tail(in, out) is semidet.

:- pred ra_list_head_tail(ra_list(T), T, ra_list(T)).
:- mode ra_list_head_tail(in, out, out) is semidet.

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

:- pred ra_list_lookup(int, ra_list(T), T).
:- mode ra_list_lookup(in, in, out) is semidet.

:- pred ra_list_update(ra_list(T), int, T, ra_list(T)).
:- mode ra_list_update(in, in, in, out) is semidet.

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

:- pred ra_list_drop(int, ra_list(T), ra_list(T)).
:- mode ra_list_drop(in, in, out) is semidet.

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

% :- implementation.

:- type ra_list(T) --->
		nil
	;	cons(int, ra_list_bintree(T), ra_list(T)).

:- type ra_list_bintree(T) --->
		leaf(T)
	;	node(T, ra_list_bintree(T), ra_list_bintree(T)).


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

:- pragma inline(ra_list_nil/1).

ra_list_nil(nil).

:- pragma inline(ra_list_cons/3).

ra_list_cons(X, List0, List) :-
	(
		List0 = cons(Size1, T1, cons(Size2, T2, Rest)),
		Size1 = Size2
	->
		NewSize = 1 + Size1 + Size2,
		List = cons(NewSize, node(X, T1, T2), Rest)
	;
		List = cons(1, leaf(X), List0)
	).

:- pragma inline(ra_list_head/2).

ra_list_head(cons(_, leaf(X), _), X).
ra_list_head(cons(_, node(X, _, _), _), X).

:- pragma inline(ra_list_tail/2).

ra_list_tail(cons(_, leaf(_), Tail), Tail).
ra_list_tail(cons(Size, node(_, T1, T2), Rest), Tail) :-
	Size2 = Size // 2,
	Tail = cons(Size2, T1, cons(Size2, T2, Rest)).

:- pragma inline(ra_list_head_tail/3).

ra_list_head_tail(cons(_, leaf(X), Tail), X, Tail).
ra_list_head_tail(cons(Size, node(X, T1, T2), Rest), X, Tail) :-
	Size2 = Size // 2,
	Tail = cons(Size2, T1, cons(Size2, T2, Rest)).

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

:- pragma inline(ra_list_lookup/3).

ra_list_lookup(I, List, X) :-
	I >= 0,
	ra_list_lookup_2(I, List, X).

:- pred ra_list_lookup_2(int, ra_list(T), T).
:- mode ra_list_lookup_2(in, in, out) is semidet.

ra_list_lookup_2(I, cons(Size, T, Rest), X) :-
	( I < Size ->
		ra_list_bintree_lookup(Size, T, I, X)
	;
		NewI = I - Size,
		ra_list_lookup_2(NewI, Rest, X)
	).

:- pred ra_list_bintree_lookup(int, ra_list_bintree(T), int, T).
:- mode ra_list_bintree_lookup(in, in, in, out) is semidet.

ra_list_bintree_lookup(_, leaf(X), 0, X).
ra_list_bintree_lookup(Size, node(X0, T1, T2), I, X) :-
	( I = 0 ->
		X0 = X
	;
		Size2 = Size // 2,
		( I =< Size2 ->
			NewI = I - 1,
			ra_list_bintree_lookup(Size2, T1, NewI, X)
		;
			NewI = I - 1 - Size2,
			ra_list_bintree_lookup(Size2, T2, NewI, X)
		)
	).

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

:- pragma inline(ra_list_update/4).

ra_list_update(List0, I, X, List) :-
	I >= 0,
	ra_list_update_2(List0, I, X, List).

:- pred ra_list_update_2(ra_list(T), int, T, ra_list(T)).
:- mode ra_list_update_2(in, in, in, out) is semidet.

ra_list_update_2(cons(Size, T0, Rest), I, X, List) :-
	( I < Size ->
		ra_list_bintree_update(Size, T0, I, X, T),
		List = cons(Size, T, Rest)
	;
		NewI = I - Size,
		ra_list_update_2(Rest, NewI, X, List0),
		List = cons(Size, T0, List0)
	).

:- pred ra_list_bintree_update(int, ra_list_bintree(T), int, T,
		ra_list_bintree(T)).
:- mode ra_list_bintree_update(in, in, in, in, out) is semidet.

ra_list_bintree_update(_, leaf(_), 0, X, leaf(X)).
ra_list_bintree_update(Size, node(X0, T1, T2), I, X, T) :-
	( I = 0 ->
		T = node(X, T1, T2)
	;
		Size2 = Size // 2,
		( I =< Size2 ->
			NewI = I - 1,
			ra_list_bintree_update(Size2, T1, NewI, X, T0),
			T = node(X0, T0, T2)
		;
			NewI = I - 1 - Size2,
			ra_list_bintree_update(Size2, T2, NewI, X, T0),
			T = node(X0, T1, T0)
		)
	).

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

ra_list_drop(N, As, Bs) :-
	(
		N > 0
	->
		As = cons(Size, _, Cs),
		( Size < N ->
			N1 = N - Size,
			ra_list_drop(N1, Cs, Bs)
		;
			ra_list_slow_drop(N, As, Bs)
		)
	;
		As = Bs
	).

:- pred ra_list_slow_drop(int, ra_list(T), ra_list(T)).
:- mode ra_list_slow_drop(in, in, out) is semidet.

ra_list_slow_drop(N, As, Bs) :-
	(
		N > 0
	->
		N1 = N - 1,
		ra_list_tail(As, Cs),
		ra_list_slow_drop(N1, Cs, Bs)
	;
		As = Bs
	).

%-----------------------------------------------------------------------------%
%-----------------------------------------------------------------------------%
% Ralph Becket <rwab1@cl.cam.ac.uk> 29/04/99
% 	Function forms added.

bt_array__make_empty_array(N) = BTA :-
	bt_array__make_empty_array(N, BTA).

bt_array__init(N1, N2, T) = BTA :-
	bt_array__init(N1, N2, T, BTA).

bt_array__min(BTA) = N :-
	bt_array__min(BTA, N).

bt_array__max(BTA) = N :-
	bt_array__max(BTA, N).

bt_array__size(BTA) = N :-
	bt_array__size(BTA, N).

bt_array__lookup(BTA, N) = T :-
	bt_array__lookup(BTA, N, T).

bt_array__set(BT1A, N, T) = BTA2 :-
	bt_array__set(BT1A, N, T, BTA2).

bt_array__resize(BT1A, N1, N2, T) = BTA2 :-
	bt_array__resize(BT1A, N1, N2, T, BTA2).

bt_array__shrink(BT1A, N1, N2) = BTA2 :-
	bt_array__shrink(BT1A, N1, N2, BTA2).

bt_array__from_list(N, Xs) = BTA :-
	bt_array__from_list(N, Xs, BTA).

bt_array__to_list(BTA) = Xs :-
	bt_array__to_list(BTA, Xs).

bt_array__fetch_items(BTA, N1, N2) = Xs :-
	bt_array__fetch_items(BTA, N1, N2, Xs).

bt_array__elem(Index, Array) = bt_array__lookup(Array, Index).

'bt_array__elem :='(Index, Array, Value) = bt_array__set(Array, Index, Value).