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 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 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_diff(L) that is
true if all elements of L are all different.
Write a predicate ordered(L) that is
true if the integers in L are in non-decreasing order.
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.
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 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.
Write a predicate subset(L, M) that
is true if M is a subset of the elements in L, with elements in the
same order as they appear in L.
Write a predicate permutation(L, M)
that is true if the list L is a permutation of M.
Write a predicate combination(L, N, M)
that is true if M is a combination
of N elements of L, i.e. a subset of size N that has its elements in
the same order as in L. Elements
in M should appear in the same order as in L.
Write a predicate insertion_sort(L, S) that sorts a list L of integers. Use an insertion sort.
Suppose that we'd like to fill in a 3 x 3 grid with letters so that every row and column contains one of these words:
AGE, AGO, CAN, CAR, NEW, RAN, ROW, WON
Write a Prolog program that can find all possible solutions.
Consider the following tiny Minesweeper board of dimensions 5 x 2:
A number N means that there are N mines in adjacent squares (which may be adjacent horizontally or diagonally).
Write a Prolog program that can find all possible positions for the mines.
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.