Exercise 9.20

This exercise looks at sorting in Prolog.

1. Write Prolog clauses that define the predicate sorted(L), which is true if and only if list L is sorted in ascending order.

2. Write a Prolog definition for the predicate perm(L,M), which is true if and only if L is a permutation of M.

3. Define sort(L,M) (M is a sorted version of L) using perm and sorted.

4. Run sort on longer and longer lists until you lose patience. What is the time complexity of your program?

5. Write a faster sorting algorithm, such as insertion sort or quicksort, in Prolog.