Computer Science 3675
Fall 2001
Solutions to practice questions for quiz 4

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. When a variable occurs in a logic programming goal, the interpreter is being asked whether that goal holds for all values of the variable. F

   2. In logic programming, a variable in an axiom might be used as an input variable sometimes, and as an output variable at other times, when computation uses that axiom. T

   3. Cuts are used to reduce memory requirements and to speed up computation. T

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

   1. Unification never changes the binding of a bound variable.
   2. Unification is symmetric; unifying A with B has exactly the same effect as unifying B with A.
   3. Unification is very slow, and is only used rarely during computations of logic programs.
   4. Unification can bind unbound variables.

3. What is one important motivation for including exception handling in a programming language?

   Some acceptable answers include the following.

   1. Exception handling makes it possible to move error handling code out of the flow of the main program logic.
   2. Exception handling makes recovery from errors easier, thus making programmers more likely to put in the effort to do it.
   3. Exception handling makes it possible to recover from errors in parts of the program that do not perform any error checking, and might be written in an unreliable way.

4. Using backtracking, write an Astarte program fragment that will print all solutions (x,y) to equation xy - 2x² + y = 10, where x and y are both integers in the range 0,...,100. Do not use a loop or recursion. Your program fragment can fail when it is done.

       Let x = each(0 _upto_ 100).
       Let y = each(0 _upto_ 100).
       {x*y - 2*x^2 + y == 10}
       Writeln[$(x,y)].
       {false}
     

5. In a logic programming style, write axioms for computing predicate allsame(X), which is true just when all members of list X are the same. For example, allsame([5,5,5]) is true, as is allsame([a,a]), but allsame([2,4,4]) is false. Note that allsame([]) is true, and allsame([b]) is true.

     allsame([]).
     allsame([X]).
     allsame([X,X|Z]) :- allsame([X|Z])
   

6. Show the logic programming 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, written in Prolog syntax.

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

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