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 Which of the following are syntactically correct lists? If the representation is correct, how many elements does the list have?

1. [1|[2,3,4]]
2. [1,2,3|[]]
3. [1|2,3,4]
4. [1|[2|[3|[4]]]]
5. [1,2,3,4|[]]
6. [[]|[]]
7. [[1,2]|4]
8. [[1,2],[3,4]|[5,6,7]]

Exercise  4.3 Write a predicate second(X,List) which checks whether X is the second element of List .

Exercise  4.4 Write a predicate swap12(List1,List2) which checks whether List1 is identical to List2 , except that the first two elements are exchanged.

Exercise  4.5 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  4.6 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  4.7 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]).

(Search trees were introduced in Chapter   2 .)