1. Dr. Muhammed Al-Mulhem ICS535-101 1 An Introduction to Prolog

2. Dr. Muhammed Al-Mulhem ICS535-101 2 Prolog statements Like other programming languages, Prolog consists of collection of statements. Prolog has two basic statement forms: –Headless Horn clause – called facts –Headed Horn clause – called rules

3. Dr. Muhammed Al-Mulhem ICS535-101 3 Facts Represent statements that are always true. The parameters are usually (but not always) constants Examples: –female(mary). –male(bill) –male(jake) –father( bill, jake). –mother( mary, jake). These simple structure state certain facts about jake, bill and mary. Note that these Prolog facts have no intrinsic semantics. They mean whatever the programmer wants them to mean. For example father( bill, jake). Could mean: –Bill and jake have the same father –Jake is the father of bill The most common meaning is that bill is the fatehr of jake.

4. Dr. Muhammed Al-Mulhem ICS535-101 4 Facts (contd.) fortran algol60 cpl bcpl c simula67 cplusplus smalltalk80 Example Facts: link(fortran,algol60). link(c,cplusplus). link(algol60,cpl). link(algol60,simula67). link(cpl,bcpl). link(simula67,cplusplus). link(bcpl,c). link(simula67,smalltalk8).

5. Dr. Muhammed Al-Mulhem ICS535-101 5 Rules This is the other basic form of Prolog statement. Used to construct the database corresponds of facts. It is a headed Horn clause Use :- instead of  and a comma instead of a  Right side: antecedent (if part) –May be single term or conjunction Left side: consequent (then part) –Must be single term

6. Dr. Muhammed Al-Mulhem ICS535-101 6 Rules parent(kim,kathy):- mother(kim,kathy). Can use variables (universal objects) to generalize meaning: parent(X,Y):- mother(X,Y). sibling(X,Y):- mother(M,X), mother(M,Y), mother(M,Y), father(F,X), father(F,X), father(F,Y). father(F,Y).

7. Dr. Muhammed Al-Mulhem ICS535-101 7 Rules (contd.) Example Rules: path(X,Y) :- link(X,Z), link(Z,Y). fortran algol60 cpl bcpl c simula67 cplusplus smalltalk80 Example Facts: link(fortran,algol60). link(c,cplusplus). link(algol60,cpl). link(algol60,simula67). link(cpl,bcpl). link(simula67,cplusplus). link(bcpl,c). link(simula67,smalltalk8).

8. Dr. Muhammed Al-Mulhem ICS535-101 8 Goals Facts and rules are used to describe both known facts and rules that describe logical relationships among facts. These statements are the basis for the theorem proving model. The theorem is in the form of a proposition that we want the system to either prove or disprove. In Prolog, these propositions are called goals. A series of one or more propositions, separated by commas Should be thought of as a query If the parameters of the goal are all constants, then the answer to the query should be “Yes” or “No” If the parameters of the goal contain variable(s), then the answer to the query should be all the values for those variables which satisfy the query, or “No” if no value satisfies it.

9. Dr. Muhammed Al-Mulhem ICS535-101 9 Example: –link(algo60,L), link(L,M). /* “Are there some values for L and M such that algo60 is linked to L and L is linked to M?” */ ============================================= –male(ahmad). /* Answer should be Yes/No */ –father(X,ali). /* Answer should be X = “ ??” or No */ –father(ali,naser). /* Answer should be Yes/No */ –father(bill,X), mother(mary,X). /* Answer should be X = “??? or NO*/ /* Answer should be X = “??? or NO*/ Goals

10. Dr. Muhammed Al-Mulhem ICS535-101 10 Prolog Programs Are a series of facts and/or rules. Can be placed in any order, due to the nonprocedural nature of logic- based languages Are “executed” in a Prolog environment using goal statements.

11. Dr. Muhammed Al-Mulhem ICS535-101 11 Inferencing Process of Prolog If a goal is a compound proposition, each of the facts is a subgoal. To prove a goal is true, the inferencing process must find a chain of inference rules and/or facts in the database that connect the goal to one or more facts in the database. For example, if Q is a goal, then either Q must be found as a fact in the database or the inferencing process must find a fact P1 and a sequence of propositions P2, P3, …Pn such that P2 :- P1. P3 :- P2. … Q :- Pn. Process of proving a subgoal is called matching, satisfying, or resolution

12. Dr. Muhammed Al-Mulhem ICS535-101 12 Example Consider this goal man(bob) This goal is compared with the facts and rules in the database. If the database includes the fact man(bob) The proof is trivial—Yes. If, however, the database contains the following fact and rule. father(bob) man(X) :- father(X) Prolog should find these two statements and use them to infere truth of the goal.

13. Dr. Muhammed Al-Mulhem ICS535-101 13 Trace Example

14. Dr. Muhammed Al-Mulhem ICS535-101 14 Inferencing Process of Prolog Bottom-up resolution, forward chaining –Begin with facts and rules of database and attempt to find sequence that leads to goal –works well with a large set of possibly correct answers Top-down resolution, backward chaining –begin with goal and attempt to find sequence that leads to set of facts in database –works well with a small set of possibly correct answers Prolog implementations use backward chaining

15. Dr. Muhammed Al-Mulhem ICS535-101 15 When goal has more than one subgoal, can use either –Depth-first search: find a complete proof for the first subgoal before working on others –Breadth-first search: work on all subgoals in parallel Prolog uses depth-first search –Can be done with fewer computer resources Inferencing Process of Prolog

16. Dr. Muhammed Al-Mulhem ICS535-101 16 With a goal with multiple subgoals, if fail to show truth of one of subgoals, reconsider previous subgoal to find an alternative solution: backtracking. Begin search where previous search left off. Can take lots of time and space because may find all possible proofs to every subgoal. Inferencing Process of Prolog

17. Dr. Muhammed Al-Mulhem ICS535-101 17 Simple Arithmetic Prolog supports integer variables and integer arithmetic is operator: takes an arithmetic expression as right operand and variable as left operand A is B / 10 + C. Not the same as an assignment statement! Should not be done with parameters Either both sides must have all variables instantiated (in which case is acts as a relational =) or just the lefthand side is not instantiated (which means the lhs receives a value) Therefore, the following is never appropriate: –Sum is Sum + Number.

18. Dr. Muhammed Al-Mulhem ICS535-101 18 Arithmetic Example

19. Dr. Muhammed Al-Mulhem ICS535-101 19 Arithmetic Example

20. Dr. Muhammed Al-Mulhem ICS535-101 20Recursion Is the only way to do iteration in Prolog Is usually accomplished with at least one fact and one rule Example: Consider the following mathematical definition of factorial: –0! = 1 –n! = (n-1)! * n  n > 0 Here is the equivalent Prolog statements: –fact(0,1). –fact(N,NFact) :- N > 0, N1 is N-1, fact(N1,N1Fact), NFact is N1Fact * N.

21. Dr. Muhammed Al-Mulhem ICS535-101 21 List Structures The value of a list consists of zero or more elements, separated by commas and enclosed in square brackets. Example: [apple, prune, grape, kumquat] Each element can be an atom or a list A variable such as L can be used to represent an entire list in a statement. The expression [E] in a statement denotes a one- element list. The expression [ ] in a statement denotes an empty list.

22. Dr. Muhammed Al-Mulhem ICS535-101 22 The expression [X | Y] in a statement denotes a list with one or more elements where the first element is the head X and the rest of the list (which may be empty) is the tail Y. –This is how recursion can be used to traverse each element of a list. –X is called the “car” and Y is called the “cdr”. (These terms are from Lisp.) –For example, in [apple, prune, grape, kumquat], apple is the car, and [prune, grape, kumquat] is the cdr. List Structures

23. Dr. Muhammed Al-Mulhem ICS535-101 23 List Structures A list can be created with simple proposition. new_list ([apple, prune, grape]) This does the kind of thing that the proposition male(ahmad) does. We could have a second proposition like new_list ([ apricot, peach, pear]) In goal mode, the list can be dismantled into head and tail. new_list ([ Head, Tail]) Then Head is instantiated to apricot, and Tail to [peach, pear] The | can specify a list construction or a list dismanteling. Note that the following are equivalent: new_list ([ apricot, peach, pear | [ ]]) new_list ([ apricot, peach | [pear]]) new_list ([ apricot | [peach, pear]])

24. Dr. Muhammed Al-Mulhem ICS535-101 24 Example 1 Appending two lists together –append([ ],List,List). –append([Head|List_1],List_2,[Head|List_3]) :- append(List_1,List_2, List_3). The first one specifies that when the empty list is appended to any other list, that list is the result. The second one specifies several characteristics of the new list. The left-side states that the fist element of the new list is the same as the first element of the first given list, because they are both named Head. The right-side specifies that the tail of the first given list (List_1) has the second given list (List_2) appended to it to form the tail (List_3).

25. Dr. Muhammed Al-Mulhem ICS535-101 25 Example 1

26. Dr. Muhammed Al-Mulhem ICS535-101 26 Reversing a list –reverse([ ], [ ]). –reverse([Head|Tail], List) :- reverse(Tail,Result), append(Result, [Head],List). Example 2

27. Dr. Muhammed Al-Mulhem ICS535-101 27 Example 2

28. Dr. Muhammed Al-Mulhem ICS535-101 28 Seeing if a list has a particular member –member(Element,[Element| _ ]). –member(Element,[ _|List] :- member(Element,List). The _ is an “anonymous” variable; i.e., we don’t care what the value is, although a value does need to be there. Example 3

29. Dr. Muhammed Al-Mulhem ICS535-101 29 Example 3

30. Dr. Muhammed Al-Mulhem ICS535-101 30 Example 4 Definition of sum function: sum([],0). sum([H|T],N):-sum(T,M), N is H+M.

31. Dr. Muhammed Al-Mulhem ICS535-101 31 Example 6 Definition of findOccurrences function: findOccurrences(X,[],0). findOccurrences(X,[X|T],N):- findOccurrences(X,T,Z), N is Z+1. findOccurrences(X,[_|T],N):- findOccurrences(X,T,Z), N is Z.

32. Dr. Muhammed Al-Mulhem ICS535-101 32 Useful Exercises Write a Prolog functor that interleaves two lists. For example given the query: ?- interleave([1,2,3,4,5],[6,7,8,9,10],X). It should return X = [1,6,2,7,3,8,4,9,5,10] Write a Prolog functor that succeeds if its list input consists of palindrome values. For example given the query: ?- palindrome([1,2,3,4,5,4,3,2,1]). It should return Yes. Write functors to compute: – the Fibonacci function – x y for integers x and y.

33. Dr. Muhammed Al-Mulhem ICS535-101 33 Example 5 Definition of diffList function: diffList([], List, []). diffList([H|L1], L2, L3) :- not(member(H,L2)), diffList (L1, L2, L4), append([H],L4,L3). diffList (L1, L2, L4), append([H],L4,L3). diffList([_|L1], L2, L3) :- diffList (L1, L2, L3).

34. Dr. Muhammed Al-Mulhem ICS535-101 34 Deficiencies of Prolog Resolution order control The closed-world assumption The negation problem Intrinsic limitations

35. Dr. Muhammed Al-Mulhem ICS535-101 35 Resolution Order Control Depth-first search method can cause infinite recursion –Example: ancestor(X,X). ancestor(X,Y) :- ancestor(Z,Y), parent(X,Z). –Keeps trying to satisfy the second rule –Can be solved by reversing the two propositions on the right, but that is against the basic nonprocedural philosophy of Prolog Deficiencies of Prolog

36. Dr. Muhammed Al-Mulhem ICS535-101 36 Resolution Order Control (Cont.) The cut operator ! –Can eliminate backtracking –Is useful when a proposition can only be satisfied once –Form is a,b,!,c,d If c is not satisfied, the statement cannot go back and find another possible value for b –Example: member(Element, [Element | _ ]) :- ! member(Element, [ _ | List]) :- member(Element,List). The change in the first statement assumes that the list consists of unique members. –The cut operator also is contrary to the Prolog philosophy of nonprocedural programming Deficiencies of Prolog

37. Dr. Muhammed Al-Mulhem ICS535-101 37 Close World Assumption If Prolog has insufficient data to answer a question, the answer is “no”, just as it would be if it had sufficient data to answer “no”. If Prolog has insufficient data to answer a question, the answer is “no”, just as it would be if it had sufficient data to answer “no”. Deficiencies of Prolog

38. Dr. Muhammed Al-Mulhem ICS535-101 38 The Negation Problem Consider the following statement: sibling(X,Y) :- parent(M,X), parent(M,Y). –Nothing keeps a person from being their own sibling! Can be solved with a not proposition: sibling(X,Y) :- parent(M,X), parent(M,Y),not(X = Y). However, the not proposition is not a not operator (double negation is not allowed), which causes some limitations Deficiencies of Prolog

39. Dr. Muhammed Al-Mulhem ICS535-101 39 Intrinsic Limitations Prolog is often not efficient Prolog is often not efficient Example: Example: sorted([ ]). sorted([x]. sorted([x, y | list]) :- x <= y, sorted([y | list]). –All permutations of list must be tried until the right one is found. Deficiencies of Prolog

40. Dr. Muhammed Al-Mulhem ICS535-101 40 Applications of Logic Programming Relational database management systems Expert systems Natural language processing Education

41. Dr. Muhammed Al-Mulhem ICS535-101 41 Conclusions Advantages: –Prolog programs based on logic, so likely to be more logically organized and written –Processing is naturally parallel, so Prolog interpreters can take advantage of multi- processor machines –Programs are concise, so development time is decreased – good for prototyping

42. Dr. Muhammed Al-Mulhem ICS535-101 42 Summary Predicate calculus provides a formal means for logical expressions (I.e. those that evaluate to true or false) Horn Clauses provide a particular structure which can be used for most logical expressions Declarative semantics allows both for the focus of problem solving to be on “what” rather than “how” and for nonprocedural programming Prolog uses declarative semantics There are some deficiencies in Prolog, some of which are inherent to declarative semantics