CIS505/705  Sample solution

1. For these clauses:

(1) expensive(house).                  
(2) expensive(car).              
(3) likes(john, X) :- expensive(X).
(4) likes(X, mary).
(5) likes(ed, Z).
(6) likes(mary, Y) :- likes(Y, john).

There are two answers to this query:

?- likes(A, house).

Draw, as best you can, the search trees for the two answers:



{} ?-  likes(A, house)
                      doesn't match Lines 1-2. Matches Line 3:

{ A == john, house == X} ?-  expensive(X)
                                         matches Line 1.  SUCCESS



{} ?-  likes(A, house)
                      doesn't match Line 4.  Matches Line 5:

{ A == ed, house == Z } ?-  .
                             Nothing more to prove.  SUCCESS


Try the example with SWI Prolog:

?- trace(expensive).
?- trace(likes).
?- likes(A, house).




2. Code the following facts into Prolog definitions.  You are welcome to use Prolog pattern-matching style:

"eggs are fresh"
"lettice is fresh"                            (define  fresh(.)  )

  fresh(eggs).
  fresh(lettuce).       (OR,  fresh(X) :- X = eggs ; X = lettuce.) 


"everything that is fresh is tasty"           (define  tasty(.)  )
     ("if X is fresh, then X is tasty")

  tasty(X) :- fresh(X).


"john likes everything that is tasty"        (define  likes(.,.)  )
     ("if X is tasty, then john likes X")

  likes(john, X) :- tasty(X).



"everyone who likes eggs likes everything that is fresh"

Step 1: untangle into if-then format:

  "if X likes eggs, then  if Y is fresh then X likes Y"

Step 2: write as a predicate-calculus assertion:

  Forall X (likes(X, eggs) ->  (Forall Y (fresh(Y) -> likes(X,Y))))

Step 3: use logical laws to reformat as a Horn clause:

  Forall X Forall Y ( (likes(X, eggs) ^ fresh(Y)) -> likes(X,Y) )

Step 4: code in Prolog (drop leading quantifiers, reverse the -> ):

  likes(X,Y) :- likes(X, eggs), fresh(Y).