1 This exercise looks at sorting in Prolog.

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

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

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

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

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