%% break_nth( ?Nth, +List, -Left, -Right ).
%
% List is split on Nth Position, into Left, and Right Parts
% First element position  is number 1. Nth element is last element in Left.
%
% ==
%
%  ?- break_nth( 0, [a,b,c], L, R ).  L=[], R=[a,b,c]
%  ?- break_nth( 1, [a,b,c], L, R ).  L=[a], R=[b,c]
%  ?- break_nth( 3, [a,b,c], L, R ).  L=[a,b,c], R=[].
%  ?- break_nth( 4, [a,b,c], L, R ).  error
%
%  ?- break_nth( N, [a,b,c], L, R ).
%    N = 1,
%    L = [a],
%    R = [b, c] ;
%    N = 2,
%    L = [a, b],
%    R = [c] ;
%    N = 3,
%    L = [a, b, c],
%    R = [] ;
%    false.
% ==
% 
break_nth( N, List, Left, Right ) :-
	G = break_nth/4,
     ( var(N) ->
          break_nth_gen( N, List, Left, Right )
          ;
	( N < 0 ->
        % fixme: use must_be or pack_error
     	write( user_error, expected_a_natural_number(N,G) ),
		nl( user_error ),
		abort
		;
		( N =:= 0 ->
			Left = [],
			Right = List
			;
     		length( List, Length ),
			( Length =:= N ->
				Left = List, Right = []
				;
				( Length < N ->
					write( user_error, list_of_insufficient_length(legth(Length),limit(N),G) ), nl( user_error ), abort
					;
     				break_nth_1( N, List, Left, Right )
				)
			)
		)
	)
     ).

break_nth_1( 1, [H|T], [H], T ) :- !.
% break_nth_for_list_1( 1, [X|Xs], [X], Xs ) :- !.
break_nth_1( N, [X|Xs], [X|Ls], Right ) :-
     N1 is N - 1,
     break_nth_1( N1, Xs, Ls, Right ).

break_nth_gen( 1, [H|T], [H], T ).
% break_nth_for_list_1( 1, [X|Xs], [X], Xs ) :- !.
break_nth_gen( N, [X|Xs], [X|Ls], Right ) :-
     break_nth_gen( N1, Xs, Ls, Right ),
     N is N1 + 1.