Exercise 4.1

How does Prolog respond to the following queries?

1. [a,b,c,d] = [a,[b,c,d]].

2. [a,b,c,d] = [a|[b,c,d]].

3. [a,b,c,d] = [a,b,[c,d]].

4. [a,b,c,d] = [a,b|[c,d]].

5. [a,b,c,d] = [a,b,c,[d]].

6. [a,b,c,d] = [a,b,c|[d]].

7. [a,b,c,d] = [a,b,c,d,[]].

8. [a,b,c,d] = [a,b,c,d|[]].

9. [] = _.

10. [] = [_].

11. [] = [_|[]].

Exercise 4.2

Suppose we are given a knowledge base with the following facts:

tran(eins,one).
tran(zwei,two).
tran(drei,three).
tran(vier,four).
tran(fuenf,five).
tran(sechs,six).
tran(sieben,seven).
tran(acht,eight).
tran(neun,nine).

Write a predicate listtran(G,E) which translates a list of German number words to the corresponding list of English number words. For example:

listtran([eins,neun,zwei],X).

should give:

X = [one,nine,two].

Your program should also work in the other direction. For example, if you give it the query

listtran(X,[one,seven,six,two]).

it should return:

X = [eins,sieben,sechs,zwei].

Hint: to answer this question, first ask yourself `How do I translate the empty list of number words?'. That's the base case. For non-empty lists, first translate the head of the list, then use recursion to translate the tail.

Exercise 4.3

Write a predicate twice(In,Out) whose left argument is a list, and whose right argument is a list consisting of every element in the left list written twice. For example, the query

twice([a,4,buggle],X).

should return

X = [a,a,4,4,buggle,buggle]).

And the query

twice([1,2,1,1],X).

should return

X = [1,1,2,2,1,1,1,1].

Hint: to answer this question, first ask yourself `What should happen when the first argument is the empty list?'. That's the base case. For non-empty lists, think about what you should do with the head, and use recursion to handle the tail.

Exercise 4.4

Draw the search trees for the following three queries:

?- member(a,[c,b,a,y]).
 
?- member(x,[a,b,c]).
 
?- member(X,[a,b,c]).