Question

Se the prolog language for sorting:
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. Write a faster sorting algorithm, such as insertion sort or quicksort, in prolog.

Answer 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. Runsort 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.

Step-by-step solution:

Step 1 of 3

Prolog is a logical programming language, which is laid using the basics from First-order logic. Prolog parses the natural language and its clauses are generally used as Context-free grammar rules.

A Prolog clause that defines the sorted(L) predicate is as follows:

sorted([])

sorted([A])

sorted([A,B|L]) :- A < B, sorted([B|L]).

The clause initially declares a sorted() function with an empty list. The list A is the first element, which is passed to the function. The element B represents the next first element of the list and L represents elements until the end of the list. The clause is true only when A < B. The list L is sorted in ascending order.

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