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Lecture 9b: Prolog

Lecture 9b: Prolog. The language of logic Concepts Examples. Heshaam Faili hfaili@ece.ut.ac.ir University of Tehran. History. Kowalski: late 60’s Logician who showed logical proof can support computation.

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Lecture 9b: Prolog

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

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

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

  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. More examples • http://www.csupomona.edu/~jrfisher/www/prolog_tutorial/contents.html

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

  22. ?

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