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Prolog

Prolog. The language of logic. 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. Warren: mid 70’s First version of Prolog that was efficient. Characteristics.

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Prolog

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  1. Prolog The language of logic

  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. • 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. Strawberry Prolog

  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):- female(X), likes(X,john). • Some Facts: • likes(bill,wine). female(mary). female(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).

  8. Finding max in a list max(X, [X|T]):- geq(X,T). max(X, [Y|T]):- Y =< X, max(X, T). geq(X, [Y]):- Y =< X. geq(X, [H|T]):- H =< X, geq(X, T). ?-geq(11, [8, 9, 11, 12]). no ?-max(24, [23, 8, 24, 21, 14]). Yes ?-max(24, [23, 8, 24, 21, 14]). Yes.

  9. A different program for max

  10. Merge sorting in Prolog merge(X,[],X). merge([], X, X). merge([X|Y],[P|Q],[X|Z]):- X =< P, merge(Y,[P|Q],Z). merge([X|Y],[P|Q],[P|Z]):- P =< X, merge([X|Y],Q,Z). % ?-merge([3, 17], [11, 12, 20, 26], X), write(X), nl.

  11. Merge sorting in Prolog split([X,Y], [X], [Y]). split([X],[],[X]). split([X,Y|Z],[X|X1], [Y|X2]):-split(Z, X1, X2). %?-split([12, 6, 7, 11, 9], X, Y), write(X), nl, write(Y), nl.

  12. Merge sorting in Prolog msort([],[]). msort([X], [X]). msort(X,Y):- split(X, X1, X2), msort(X1,Y1), msort(X2, Y2), merge(Y1, Y2, Y). ?-msort([6, 12, 20, 7, 3, 21, 36, 14, -3], X), write(X), nl.

  13. Example involving an arithmetic operation Write a Prolog program to compute the prefix sums of elements in an array. Example: ?-prefix_sum([1, 3, -4, 8, 2], X), write(X), nl. Output: Compiling the file: F:\fall09\cs480fa09\programs\prefix_sum 0 errors, 0 warnings. [1,4,0,8,10] Yes.

  14. Prolog function to implement prefix sum First we create a function add that adds X to each member of a list: add(X,[Y],[Z]):- Z is X + Y. add(X, [H|T], [P|Q]):- P is X + H, add(X,T,Q). % some test cases ?-add(3, [-2, 12, 8, 3], X), write(X), nl. ?-add(3, [-2], X), write(X), nl.

  15. Prolog function to implement prefix sum We can use add to write prefix_sum: prefix_sum([X],[X]). prefix_sum([H|T], [H|T1]):- prefix_sum(T, T2), add(H, T2, T1), nl. %?-prefix_sum([2, 1], X), write(X), nl. ?-prefix_sum([1, 3, -4, 8, 2], X), write(X), nl.

  16. Permutation & Insert Write a program to generate all the permutations of a given sequence. insert(X,L, [X|L]). insert(X,[H|T],[H|T1]):- insert(X,T,T1). ?-insert(1, [3, 2, 4], X), write(X), nl, fail. perm([],[]). perm([H|T],P):-perm(T,T1),insert(H,T1,P). ?-perm([1, 2, 3, 4], X), write(X), nl, fail.

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