Prolog Shift n times a list function either way - prolog

Question

I have to define a predicate nshift/3 that shift a list N times either way.
Examples:
?- nshift(3,[a,b,c,d,e,f,g,h],Shifted).
Shifted = [d,e,f,g,h,a,b,c]
?-­nshift(1,[1,2,3,4,5],Shifted).
Shifted = [2,3,4,5,1]
?-­nshift(-2,[a,b,c,d,e,f,g,h],Shifted).
Shifted = [g,h,a,b,c,d,e,f]
I created a code that would take care of the first two examples but I'm having problem with the last example where the N time is -2. Can somebody help me.
My code:
my_shift([], []).
my_shift([H|T], L) :-
append(T, [H], L).
nshift(0, L, L) :- !.
nshift(N, L1, L2) :-
N1 is N-1,
my_shift(L1, L),
nshift(N1, L, L2).

Answer 1

I have this old code
rotate(right, L, [T|H]) :- append(H, [T], L).
rotate(left, [H|T], L) :- append(T, [H], L).
Then, I think you could adapt your nshift/3 testing if the first argument is < 0, something like
nshift(0, L, L) :- !.
nshift(N, L1, L2) :-
N < 0, rotate(right, L1, L), N1 is N+1, nshift(N1, L, L2).
nshift(N, L1, L2) :-
N > 0, rotate(left, L1, L), N1 is N-1, nshift(N1, L, L2).

Answer 2

As hinted in another answer, your type of shift is usually called rotate. Rotates with non-negative N can be written in a nicely declarative way as
naive_rotate(N, Xs, Ys) :-
length(Bs, N),
append(As, Bs, Xs),
append(Bs, As, Ys).
While this works, people will be quick to point out that its termination properties are poor: when you backtrack into rotate/3, i.e. ask for more solutions, it will not terminate. This can be addressed by adding redundant conditions on the list lengths, viz.
rotate(N, Xs, Ys) :-
same_length(Xs, Ys),
leq_length(Bs, Xs),
length(Bs, N),
append(As, Bs, Xs),
append(Bs, As, Ys).
same_length([], []).
same_length([_|Xs], [_|Ys]) :- same_length(Xs, Ys).
leq_length([], _).
leq_length([_|Xs], [_|Ys]) :- leq_length(Xs, Ys).
This now works nicely for various query patterns, e.g.
?- rotate(2, [a,b,c,d,e], Ys). % gives Ys = [d,e,a,b,c]
?- rotate(2, Xs, [a,b,c,d,e]). % gives Xs = [c,d,e,a,b]
?- rotate(N, [a,b,c,d,e], Ys). % 5 solutions
?- rotate(N, Xs, [a,b,c,d,e]). % 5 solutions
?- rotate(N, Xs, Ys). % many solutions
You can then write your original nshift/3 as
nshift(N, Xs, Ys) :-
( N>=0 -> rotate(N, Xs, Ys) ; M is -N, rotate(M, Ys, Xs) ).