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Midterm II Solutions

• Problem 1

  abstype ezVector
  with newV :: posint -> real -> ezVector
       elem :: ezVector -> posint -> real
       add :: ezVector -> ezVector -> ezVector
       mul :: real -> ezVector -> ezVector

  ezVector == [real]

  newV 1 r = [r]
  newV (n+1) r = 0:(newV n r)

  elem [] n = 0
  elem (h:t) 1 = h
  elem (h:t) i = elem t (i-1)

  add [] v = v
  add v [] = v
  add (r1:v1) (r2:v2) = (r1+r2):(add v1 v2)

  mul k [] = []
  mul k (r:v) = (k*r):(mul k v)

• Problem 2
  1. A=2, Z=3
  2. no (the constant x does not unify with the constant 1)
  3. X = jim, Y=ben
  4. no (the two lists have different lengths)
  5. Y=a, X=b
  6. no (Y cannot unify with both a and b)
  7. no (== succeeds iff both of its sides evaluate to the same term)
  8. no (the terms 3+2 and 1+3 do not unify)
  9. X = 7
  10. no (in the first subgoal, X is bound to the term 7, which does not unify with the term 3+4)
  11. X=1, T1=[3|T2]
  12. A = 1+2, B=2, X=1, Y=2
• Problem 3

  

• Problem 4

  evaluate([], _).
  evaluate([G|Gs], KB) :- list(G), evaluate(G, KB), evaluate(Gs, KB).
  evaluate([G|Gs], KB) :- goal(G), expand(G, KB, SubGs), add(SubGs, Gs, NewGs),
                          evaluate(NewGs, KB).