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Spring 2006 IA008, Prolog logic program : a finite set of Horn clauses Logic programming inference (interpretation) based on SLD-resolution declarativness: the specification of a program is equal to the program popel@fi.muni.cz 1/18

  1. Spring 2006 IA008, Prolog � logic program : a finite set of Horn clauses Logic programming � inference (interpretation) based on SLD-resolution � declarativness: the specification of a program is equal to the program popel@fi.muni.cz 1/18

  2. Spring 2006 IA008, Prolog � implementation of a logic programming language Prolog � strategy: depth-first search in the SLD-tree � historie: in 70th. – Colmerauer, Kowalski; D.H.D. Warren (WAM) popel@fi.muni.cz 2/18

  3. Spring 2006 IA008, Prolog Syntax of Prolog I � terms (constants, variables, compound terms) � constants: Data structures � variables ( N, – 0, 123, -12, 1.0, 4.5E7, -0.12e+8 , – atoms ( ’Bob Kowalski’, [], s1, ==, ’beaver’, atom ) � compound terms: functor(name, arity), arguments VYSLEDEK, Hodnota, A1, 12 ), anonymous variable ( ) point(X,Y,Z), tree(Value,tree(LV,LL,LR),tree(RV,RL,RR)) popel@fi.muni.cz 3/18

  4. Spring 2006 IA008, Prolog Syntax of Prolog II � an ordered set of program clauses (pravidla, fakta) � variables local in a clause Program � rule: head, body � fact: a rule with an empty body (body = true ) date(D,M,Y):- day(D), month(M), year(R). � a goal: ?- date(29,’January’,2001). date(14,’February’,2001). Explicit unification: = operator Ex.: X=Y, f(g(a,X))=f(Y) popel@fi.muni.cz 4/18

  5. Spring 2006 IA008, Prolog SLD-tree for a Prolog program 1. p(X,Y) :- q(X,Z), r(Z,Y). 5. q(X,a) :- r(a,X). 9. s(X) :- t(X,X). 2. p(X,X) :- s(X). 6. r(b,a). 10. t(a,b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. q(X,b). . . . . . . 7. s(X) :- t(X,a). . . . . . . 11. t(b,a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. q(b,a). . . . 8. s(X) :- t(X,b). . ?- p(X,X). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . 5 7 . . . . . . 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?- p(X,X). . ?- q(X,Z), r(Z,X). . . . ?- s(X). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . . . 11 . . 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 2 [ X = a ℄ [ X = b ℄ [ X = a ℄ ?- r(b,X). ?- r(a,b). ?- r(a,X), r(a,X). ?- t(X,a). ?- t(X,b). ?- t(X,X). fail fail fail popel@fi.muni.cz 5/18

  6. Spring 2006 IA008, Prolog SLD-resolution for a Prolog program : num(s(s(0)) : num(X) num(0). ?- num(0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ex.: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . num(s(X)):- num(X). . . ?- num(s(s(0))). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : num(s(0)) : num(X) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . num(s(X)), . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X/s(0) X/s(0) : num(0) : num(0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . num(s(X)), . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X/0 X/0 2 2 num(0) num(0) popel@fi.muni.cz 6/18

  7. Spring 2006 IA008, Prolog Example: Incompletness equal(X,Y):- equal(Y,X). 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . equal(3+2,5). . . . . . . . . . . . . . . . . 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?- equal(3+2,5). 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?- equal(3+2,5). 1 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?- equal(5,3+2). 2 1 . . . . ?- equal(3+2,5). 1 2 ?- equal(5,3+2). 1 popel@fi.muni.cz 7/18

  8. Spring 2006 IA008, Prolog � recursive data structure, ordered List � functor ./2 ; pr´ � .(Head,Tail) , the notation used: [Head|Tail] , Tail is a list y seznam [] azdn´ .(a,[]) [a] [a|[]] � can be represented as a tree .(a,.(b,.(c,[]))) [a,b,c] [a,b|[c]] [a|[b,c]] [a,b,c|[]] [a|[b,c|[]]] [a|[b|[c|[]]]] popel@fi.muni.cz 8/18

  9. Spring 2006 IA008, Prolog member/2 I 1) unification: member(X,[X|_]). member(X,[_|T]):- member(X,T). ?- member(a,[b,c,a]). yes ?- member(a,[X,b,c]). X=a yes popel@fi.muni.cz 9/18

  10. Spring 2006 IA008, Prolog member/2 II 2) identity: member(X,[Y|_]):- X == Y. member(X,[_|T]):- member(X,T). ?- member(a,[X,b,c]). % No ?- member(a,[a,b,a]),write(ok),nl,fail. ok ok No 3) without a multiple occurence: member(X,[Y|_]):- X == Y. member(X,[Y|T]):- X \== Y, member(X,T). ?- member(a,[a,b,a]),write(ok),nl,fail. ok No popel@fi.muni.cz 10/18

  11. Spring 2006 IA008, Prolog Example: Append two lists append([],L,L). append([H|T1],L2,[H|T]):- append(T1,L2,T). ------------------------------------------ ?- append([a,b],[c,d],L). L = [a, b, c, d] Yes ?- append(X,[c,d],[a,b,c,d]). X = [a, b] Yes ?- append(X,Y,[a,b,c]). X = [] Y = [a, b, c]; X = [a] Y = [b, c]; X = [a, b] Y = [c]; X = [a, b, c] Y = []; No popel@fi.muni.cz 11/18

  12. Spring 2006 IA008, Prolog reverse/2 reverse([],[]). reverse([H|T],L):- reverse(T,L1), append(L1,[H],L). --------------------------------------------------- ?- reverse([a,b,c],L). L = [c, b, a] Yes ?- reverse([a,b,c],[c,b,a]). Yes ?- reverse(L,[a,b,c]). L = [c, b, a] Yes delete, permutation, prefix, postfix, sublist . . . popel@fi.muni.cz 12/18

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