Prolog

1
Prolog

• Developed in the early 1970s
• Algol interpreter in 1972
• Fortran interpreter in 1973
• Pascal interpreter in 1976

2
Parts of a program

• series of clauses that define the problem domain
• clauses stating a number of particular facts
• a question

3
Example - define the problem domain

• parent (X, Y) - father(X,Y).
• parent (X, Y) - mother (X, Y).
• grandparent (X, Z) - parent (X, Y), parent (Y,
  Z).
• ancestor (X, Z) - parent (X, Z).
• ancestor (X, Z) - parent (X, Y), ancestor (Y,
  Z).
• sibling(X,Y) - mother(M,X), mother(M,Y),
  father(F,X), father(F,Y), X \ Y.
• cousin(X,Y) - parent(U,X), parent(V,Y),
  sibling(U,V).

4
Example - stating facts

• father(albert, jeffrey).
• mother(alice, jeffrey).
• father(albert, george).
• mother(alice, george).
• father(john, mary).
• mother(sue, mary).
• father(george, cindy).
• mother(mary, cindy).
• father(george, victor).
• mother(mary, victor).

5
Example - question

• Goal of program
• - ancestor(X, cindy), sibling (X, jeffrey).
• Program response
• X george
• is a fact is provable
• - grandparent(albert, victor).
• yes
• - cousin(alice, john).
• no

6
Multiple answers

• - sibling(A,B).
• Response
• A jeffrey, B george
• A jeffrey, B george
• A george, B jeffrey
• A cindy, B victor
• A victor, B cindy
• no

7
Proving the Theorem

• - ancestor (X, cindy), sibling(X, jeffrey).
• answer X George
• find an X such that ancestor (X, cindy) and
  sibling (X, jeffrey)
• sibling (X, jeffrey) is true if there are M and F
  such that mother (M, jeffrey),father (F,
  jeffrey),mother (M, X), and father (F, X)
• if M alice and F albert, then mother (M,
  jeffrey) and father (F, jeffrey)
• find X such that mother (alice, X) and father
  (albert, X)
• X is george

8
Clauses Are Constructed from Relationships

• Hypotheses (or facts)
• mother(mary, cindy).
• Goals
• - ancestor(john,X).
• Conditions (or rules)
• grandparent (X, Z) - parent (X, Y), parent (Y,
  Z).
• General form of a clause
• - .
• Goal if omitted

9
Relationships and Terms

• Terms in the relationships may be
• atoms, such as john or 25
• variables, such as X or
• compound terms

10
Terms Can Be Compound

• d (X, plus (U, V), plus (DU,DV)) - d(X,U,DU),
  d(X,V,DV).
• name plus is called a functor because it acts
  like a function
• d (X, U V, DU DV) - d (X, U, DU), d (X, V,
  DV).
• d (X, W, Z) - sum (U, V, W), d (X, U, DU), d (X,
  V, DV), sum (DU, DV, Z).

11
Few Primitives and No Constructors

• natural number arithmetic
• sum(succ(X), Y, succ(Z)) - sum(X, Y, Z).
• sum(0, X, X). dif(X, Y, Z) - sum (Z, Y, X).
• dif(X, Y, Z) - sum(Z, Y, Z).
• Goal
• - sum(succ(succ(0)), succ(succ(succ(0))), A).
• 23A
• Response
• A succ(succ(succ(succ(succ(0)))))
• 5