Solutions to practice quiz

1. Write a clearly legible T to the left of each of the following that is true, and a clearly legible F to the left of each that is false.
   1. T In Prolog, all computation is performed by predicates, with none performed by functions.
   2. T In Prolog, an unbound variable can be part of a data structure.
   3. F In Prolog, an unbound variable is uninitialized, and using it without initializing it usually leads to serious errors in programs.
   4. F Prolog allows axioms to be any formula of first order logic. Only atomic formulas and Horn clauses are allowed.
   5. T Variables in Prolog axioms are implicitly universally quantified.
   6. T Cuts are used to reduce memory requirements and to speed up computation. Nothing on cuts will be on the quiz.
   7. F It does not matter in what order axioms in a Prolog program are written. Axioms are tried in the order in which they are written.

2. Unification is a form of pattern matching. Which of the following is not a characteristic of unification?

   Unification never changes the binding of a bound variable.

3. A cut in a Prolog program

   Removes backtrack control frames from the control stack.

4. Which of the following is not a characteristic of the Prolog append predicate?

   It should only be used in one mode because its definition includes a cut.

5. Backtracking

   is a control structure that involves trying more than one answer to an expression or statement.

6. In a Prolog goal (or query), unbound variables

   are implicitly existentially quantified, with the system asked to find their values.

7. Suppose that you know a list Y and a value A. Using only the append predicate and the [|] notation, write a goal that is satisfied just when Y is nonempty and the last member of list Y is A.

   append(X,[A],Y).

8. Write a definition in Prolog of a predicate called allare so that allare(X,A) is true just when X is a list all of whose members are A. For example, allare([3,3,3,3],3) is true, and allare([a,a],a) is true. Note that allare([],2) is true. Do not use any other basic predicates, such as append or member, for this definition.

        allare([],X).
        allare([H|T],H) :- allare(T,H).
     

9. Show the Prolog search tree for goal (member(X,[3,4,5]), member(X,[4])), up to the point where a success is found. The definition of the member predicate is as follows.

         member(M, [M|X]).
         member(M, [X|T]) :- member(M, T).
     

                   member(X,[3,4,5]), member(X,[4])
                  /                                \
                 / X = 3                            \
                /                                    \
        member(3,[4])                 member(X,[4,5]), member(X,[4])
             |                       /                             \
        member(3,[])                / X = 4
             |                     /
             x                member(4,[4])
                                  |
                               success