Write a predicate triple(L) that is
true if L is a list with three elements, all of which are identical.
Write a predicate triple_diff(L) that
is true if L is a list with three elements, all of which are
different.
Write a predicate last_elem(X, L)
that is true if X is the last element of the list L.
Write a predicate second_last(X, L)
that is true if X is the next-to-last element of L.
Write a predicate next_to(X, Y, L)
that is true if elements X and Y appear in L, with Y immediately
after X.
Write a predicate even_length(L) that
is true if the length of L is an even integer.
Write a predicate same_length(L, M)
that is true if L and M have the same length.
Write a predicate longer(L, M) that
is true if L is longer than M.
Write a predicate double_length(L, M)
that is true if L is twice as long as M.
Write a predicate is_list(L) that is
true if L is a list of any length.
Write a predicate len(L, N) that is
true if the length of list L is N.
Write a predicate all_same(L) that is
true if all elements of L are identical.
Write a predicate all_diff(L) that is
true if all elements of L are all different.
Write a predicate sum(L, N) that is
true if N is the sum
of the integers in
the list L.
Write a predicate sum(L, R) that is
true if R is the
floating-point sum of the numbers
in the list L.
Write a predicate ordered(L) that is
true if the floating-point numbers in L are in non-decreasing order.
Write a predicate mem(X, L) that is
true if X is a member of the list L.
Write a predicate nth(N, L, X) that
is true if the nth element of list L is X, where the first element
has index 0.
Write a predicate append(L, M,
N) that is true if the lists L and M can be appended to form
N.
Write a predicate reverse(L, M) that
is true if L and M contain
the same elements in reverse order.
When we rotate a list one element to the right, the last element moves to the first position and all other elements shift rightward.
Write a predicate rotate(L, M) that
is true if M is L rotated one element to the right (or, equivalently,
L is M rotated one element to the left).
Write a predicate select(X, L, M)
that is true if X can be removed from L to make M. Equivalently,
select(X, L, M) is true if X can be inserted anywhere in
M to make L.
Write a predicate select(X, L, Y, M)
that is true if L and M are identical except (possibly) for a single
element, which is X
in L and is Y in M.
Write a predicate num_list(I, J, L)
that is true if L is the list containing integers I through J,
inclusive. If J < I, then L should be the empty list.
Write a predicate slice(L, I, J, M)
that is true if M contains elements I .. J of L, where elements are
indexed starting from
0. For example, slice([r, i, v, e, r], 1,
3, [i, v, e]) is true.
Write a predicate gcd(I, J, K) that
is true if the greatest common divisor of I and J is K.
Write a predicate is_prime(N) that is
true if N is prime.
Write a predicate all_primes(I, J)
that returns a list of all prime numbers between I and J, inclusive.
Write a predicate smallest_factor(N, P)
that is true if P is the smallest prime factor of N.
Someone has stolen Beethoven's wig and has put it in one of four locked boxes. The boxes are numbered 1,2,3,4 in that order. There are four different keys that each have their own color. Also:
The green key goes to the third or fourth box.
The wig is to the left of the fourth box.
The wig is to the right of the first box.
The yellow key is to the left of the wig.
The blue key is to the right of the yellow key and to the left of the green key.
The red key goes to the first box.
Which box contains Beethoven's wig? Write a Prolog program that can find the answer.
Consider this acyclic directed graph:
One way to represent a graph in Prolog is as a list of edges. For example, we can represent the graph above by this term:
G = [ [a, b], [a, e], [b, c], [b, f], [e, d],
[e, f], [f, c], [g, d], [g, h], [h, f] ].Write a predicate path(G, V, W, L) that is true if L is a list of vertices along a path from V to W in the graph G.
Let's modify the graph from the previous exercise by adding an edge from f back to a, so that the graph is now cyclic:
G = [ [a, b], [a, e], [b, c], [b, f], [e, d],
[e, f], [f, c], [g, d], [g, h], [h, f],
[f, a] ].Write a predicate path(G, V, W, L) that is true if L is a list of vertices along a path from V to W in G, such that your predicate can always find all paths between given vertices V and W.