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Lecture 9b: Prolog Heshaam Faili [email protected] University of Tehran The language of logic...
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Lecture 9b: Prolog Heshaam Faili [email protected]. ac.ir University of Tehran The language of logic Concepts Examples
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Transcript of Lecture 9b: Prolog Heshaam Faili [email protected] University of Tehran The language of logic...
Lecture 9b: Prolog
Heshaam [email protected]
rUniversity of
Tehran
The language of logic
Concepts
Examples
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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))).
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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.
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Member Tests
?- member(3,X). X = [3| _G109].
% _G.., system generated variable X= [_G11,3| _]. % etc.
?- member(X,Y). X = _G131, Y= [_G131|, _G321].
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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).
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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] ;
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Cut !
P :- a, b. P :- c.
P :- a, !, b.P :- c.
P (ab)c
P (ab)(a c)
Use to ignore backtracking: performance issue
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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).
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Factorial
factorial(0,1). factorial(N,F) :-
N>0, N1 is N-1, factorial(N1,F1), F is N * F1.
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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
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More examples
http://www.csupomona.edu/~jrfisher/www/prolog_tutorial/contents.html
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Limitations
2nd order: Can’t ask what is relationship between heart and lungs?
Probabilities: What is likelihood of fire destroying Julian?
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