1. Lecture 9b: Prolog Heshaam Faili hfaili@ece.ut.ac.ir University of Tehran The language of logic Concepts Examples

2. 2 History Kowalski: late 60’s Logician who showed logical proof can support computation. Colmerauer: early 70’s Developed early version of Prolog for natural language processing, mainly multiple parses. Warren: mid 70’s First version of Prolog that was efficient.

3. 3 Characteristics Prolog approximates first-order logic. Every program is a set of Horn clauses. Inference is by resolution. Search is by backtracking with unification. Basic data structure is term or tree. Variables are unknowns not locations. Prolog does not distinguish between inputs and outputs. It solves relations/predicates.

4. 4 SWI-Prolog Notes Free! Down Loadable To load a file: consult( ‘C:\\prolog\\test’). For help: help(predicate-name). “ ; “ will give you next solution. ‘%’ comment listing(member) will give definition.

5. 5 Example Facts: () likes(john,mary). likes(john,X). % Variables begin with capital Queries ?- likes(X,Y). X=john, y=Mary. % hit “;” for more ?- likes(X,X). X=john.

6. 6 Example Rules likes(john,X) :- likes(X,wine). % :- = if likes(john,X):- human(X), likes(X,john). Note: variables are dummy. Standardized apart Some Facts: likes(bill,wine). human(mary). human(sue). Query: ? - likes(john,Y). Y = bill ; no.

7. 7 Family father(a,b). father(e,d). mother(c,b). mother(d,f). parent(X,Y) :- father(X,Y). parent(X,Y) :- mother(X,Y). grandfather(X,Y):- father(X,Z),parent(Z,Y). % Do your own for practice.

8. 8 Informal Summary Program is facts + rules. (horn clauses). Query = conjunct of predicates. First set of bindings for variables that solve query are reported. If none, then Prolog returns no. Use “;” to get other solutions. Can be viewed as constraint satisfaction program.

9. 9 MapColoring color(r). color(g). color(b). colormap(C1,C2,C3):- color(C1),color(C2),color(C3), C1\==C2, C1\==C3, C2\==C3. Query: colormap(X,Y,Z). X = r, Y= g, Z=b.

10. 10 Unification: (matching) terms Two terms UNIFY if there is a common substitution for all variables which makes them identical. f(g(X),Y) = f(Z,Z). % = cheap unification X = _G225, Y=g(_G225). Look at parse tree for each term. variables match variable matches anything (set the binding) function symbols only match identical function symbols.

11. 11 Satisfiability: uses unification sat(true). % base case sat(not(false)). % base case sat(or(X,Y)):- sat(X). sat(or(X,Y)):-sat(Y). sat(and(X,Y)):-sat(X),sat(Y). test1(X,Y):- sat(and(not(X),X)). test2(X,Y):- sat(and(X,not(Y))).

12. 12 List Operator [H |T] [a,b,c] is a list in Prolog. [H|T] = [a,b,c] results in H = a i.e. the head of list T = [b,c] i.e. the tail of the list. membership definition member(H,[H|T]). % base case first. Why? member(H,[_|T]) :- member(H,T). Use it.

13. 13 Member Tests ?- member(3,X). X = [3| _G109]. % _G.., system generated variable X= [_G11,3| _]. % etc. ?- member(X,Y). X = _G131, Y= [_G131|, _G321].

14. 14 Permutation & Insert insert(X,L, [X|L]). insert(X,[H|T],[H|T1]):- insert(X,T,T1). perm([],[]). perm([H|T],P):-perm(T,T1),insert(H,T1,P).

15. 15 DFS % solve(goal, solution Path) % s(state, successor-state) dfs(N,[N]) :- goal(N). dfs(N,[N|Sol1]):- s(N,N1), dfs(N1,Sol1). s(a,b). s(a,c). s(b,d). s(b,e). s(c,f). s(c,g). s(d,h). s(e,i). s(e,j). s(f,k). goal(i). goal(f). ?- dfs(a,N). N = [a, b, e, i] ; N = [a, c, f] ;

16. 16 Cut ! P :- a, b. P :- c. P :- a, !, b. P :- c. P  (a  b)  c P  (a  b)  (  a  c) Use to ignore backtracking: performance issue

17. 17 MAX MAX(X,Y,X) :- X>=Y. MAX(X,Y,Y). ?- MAX(3,2,X). X=3 ; X = 2 !!!!! MAX(X,Y,X) :- X>=Y, !. MAX(X,Y,Y).

18. 18 Factorial factorial(0,1). factorial(N,F) :- N>0, N1 is N-1, factorial(N1,F1), F is N * F1.

19. 19 Hanoi Tower move(1,X,Y,_) :- write('Move top disk from '), write(X), write(' to '), write(Y), nl. move(N,X,Y,Z) :- N>1, M is N-1, move(M,X,Z,Y), move(1,X,Y,_), move(M,Z,Y,X). ?- move(3,left,right,center). Move top disk from left to right Move top disk from left to center Move top disk from right to center Move top disk from left to right Move top disk from center to left Move top disk from center to right Move top disk from left to right yes

20. 20 More examples http://www.csupomona.edu/~jrfisher/w ww/prolog_tutorial/contents.html

21. 21 Limitations 2 nd order: Can’t ask what is relationship between heart and lungs? Probabilities: What is likelihood of fire destroying Julian?

22. 22 ?