Non-unifiable
Exercise 11.1
Implement predicate nonunifiable/2 that succeeds whenever its arguments cannot be unified. Provide three implementations:
1. First, using = and \+
2. Second, using = without \+
3. Third, using cut-fail combination, without = or \+
?- nonunifiable(test, test). false
Partitioning a list
Exercise 11.2(a)
Implement predicate partition/4 that takes a pivot and a list and produces two lists: one with elements less than the pivot and another one with elements greater than or equal to the pivot.
?- partition(3, [1, 5, 2, 6, 3, 0], L, G).
L = [1, 2, 0]
G = [5, 6, 3]
Partitioning a list efficiently
Exercise 11.2(b)
Improve predicate partition/4, making it more efficient without changing its meaning with green cuts.
?- partition(3, [1, 5, 2, 6, 3, 0], L, G).
L = [1, 2, 0]
G = [5, 6, 3]
Siblings
Exercise 11.3
Implement predicate sibling/2 that succeeds whenever two people are siblings (they share a common parent). Make sure that a person cannot be its own sibling.
?- sibling(jack, jack). false
DFS proper
Exercise 11.4
Implement predicate path/3 that searches for a path between two nodes in an undirected graph.
?- path(1, 3, Path). Path = [1, 4, 3]
connected(1,2). connected(3,4). connected(5,6). connected(7,8). connected(9,10). connected(12,13). connected(13,14). connected(15,16). connected(17,18). connected(19,20). connected(4,1). connected(6,3). connected(4,7). connected(6,11). connected(14,9). connected(11,15). connected(16,12). connected(14,17). connected(16,19).
Filtering unifiable terms
Exercise 11.5
Implement predicate filterUnifiable/3 that takes two lists and a term. The second list is the output argument and should contain terms from the first list that unify with the given term. The variables in the first list should not be instantiated as a result of this predicate:
?- filterUnifiable([X, b, t(Y)], t(a), List). List = [X, t(Y)]
Hint: consider using checks of the form \+ term1 = term2.
Eight queens problem
Exercise 11.6
Solve the eight queens problem.
Use green cuts to make the implementation efficient.
