1. COP4020 Programming Languages Logic Programming Prof. Xin Yuan

2. COP4020 Spring 2013 2 3/13/2016 Topics More on Prolob Prolog by examples

3. COP4020 Spring 2014 3 3/13/2016 Control Features Prolog offers built-in constructs to support a form of control-flow  \+ G negates a (sub-)goal G  ! (cut) terminates backtracking for a predicate  fail always fails (so to trigger backtracking) Examples  ?- \+ member(b, [a,b,c]). no  ?- \+ member(b, []). yes  We can (re)define: if(Cond, Then, Else) :- Cond, !, Then. if(Cond, Then, Else) :- Else.  ?- if(true, X=a, X=b). X = a ; % type ';' to try to find more solutions no  ?- if(fail, X=a, X=b). X = b ; % type ';' to try to find more solutions no

4. COP4020 Spring 2014 4 3/13/2016 Control Features Prolog offers built-in constructs to support a form of control-flow  G 1 ; G 2 forms an “or”: try G 1 then G 2 if G 1 failed  G 1 -> G 2 ; G 3 forms an if-then-else: if G 1 then G 2 else G 3  true is a true goal and acts like a no-op  repeat always succeeds (for looping) Examples:  We can use an “or” instead of two clauses: rainy(C) :- ( C = rochester ; C = seattle ).  Using an if-then-else: guess(X) :- ( X = heads -> format(“~s~n”, [“Guessed it!”]) ; format(“~s~n”, [“Sorry, no luck”]) ).  Repeat drawing a random X until X=1 (and then cuts backtracking): do_until_one :- repeat, X is random(10), X = 1, !.

5. Meta-Logical Meta-logical predicates perform operations that require reasoning about terms  X == Y true if X is identical to Y (vice versa X \= Y )  var(X) true if X is uninstantiated (vice versa nonvar(Y) )  ground(X) true if X is a ground term, has no variables  atom(X) true if X is an atom  functor(X, F, N) true if X is a functor F with N arguments  X =.. [F,A1,A2,…,An] true if X a functor F with arguments Impact:  Pure logic has no ordering constraints, e.g. X “or” Y = Y “or” X X=3, var(X).  var(X), X=3.  Meta-logical predicates are order sensitive and influence control  Theoretically, cannot be expressed using predicate definitions with a finite number of clauses COP4020 Spring 2014 5 3/13/2016

6. COP4020 Spring 2014 6 3/13/2016 Example 1 fact(n) = 1*2*…*n fact(1, 1). fact(N, X) :- M is N-1, fact(M, Y), X is Y*N.

7. COP4020 Spring 2014 7 3/13/2016 Example 2 Sum the elements of a list sum([1,2,3], X). X=6

8. COP4020 Spring 2014 8 3/13/2016 Example 3 Sum the elements of a list sum([1,2,3], X). X=6 sum([], 0). sum([X|T], Y) :- sum(T, Y1), Y is X + Y1.

9. COP4020 Spring 2014 9 3/13/2016 Example 4 Generate a list of n copies of x Fill(3, x, Y) Y=[x,x,x]

10. COP4020 Spring 2014 10 3/13/2016 Example 4 Generate a list of n copies of x Fill(3, x, Y) Y=[x,x,x] fill(0, _, []). fill(N, X, [X|T]):- M is N-1, fill(M, X, T).

11. COP4020 Spring 2014 11 3/13/2016 Example 5 Replace x with y in list xs subst(3, 0, [8,2,3,4,3,5], X). X=[8,2,0,4,0,5]

12. COP4020 Spring 2014 12 3/13/2016 Example 5 Replace x with y in list xs subst(3, 0, [8,2,3,4,3,5], X). X=[8,2,0,4,0,5] replace1(_, _, [], []). replace1(X, Y, [X|T], [Y|T1]) :- replace1(X, Y, T, T1). replace1(X, Y, [Z|T], [Z|T1]) :- replace1(X, Y, T, T1).

13. COP4020 Spring 2014 13 3/13/2016 Example 6 Search on binary search tree, where [] are leaves and [val, left, right] is a node bsearch[4, [3, [], [4, [],[]]], X). X=1

14. COP4020 Spring 2014 14 3/13/2016 Example 6 Search on binary search tree, where [] are leaves and [val, left, right] is a node bsearch[4, [3, [], [4, [],[]]], X). X=1 bsearch(_, [], 0). bsearch(X, [X | _], 1). bsearch(X, [Y, L, _], Z) :- X < Y, bsearch(X, L, Z). bsearch(X, [Y, _, R], Z) :- X > Y, bsearch(X, R, Z).

15. COP4020 Spring 2014 15 3/13/2016 Example 7 Binary tree insertion, where [] are leaves and [val, left, right] is a node binsert(X, [], [X, [], []]). binsert(X, [X | T], [X | T]). binsert(X, [Y, L, R], [Y, L1, R]) :- X < Y, binsert(X, L, L1). binsert(X, [Y, L, R], [Y, L, R1]) :- X > Y, bsearch(X, R, R1).

16. Example 8 Scheme: (genlist ‘(1 2 3 4)) => (() (1) (1 2) (1 2 3) (1 2 3 4)) Prolog removelast([_], []). removelast([X|T], [X|T1]) :- removelast(T, T1). append(X, [], [X]). append(X, [Y|T], [Y|T1]):- append(X, T, T1). genlist([], [[]]). genlist(X, Y) :- removelast(X, T), genlist(T, Y1), append(X, Y1, Y). COP4020 Spring 2014 16 3/13/2016

17. Example 9 Search an item in list, if found, return original list; otherwise, insert at the beginning of the list. Search: search(_, [], 0). search(X, [X|_], 1). search(X, [_|T], C) :- search(X, T, C). COP4020 Spring 2014 17 3/13/2016

18. Example 9 Search an item in list, if found, return original list; otherwise, insert at the beginning of the list. Searchinsert searchinsert(X, Y, Y):- search(X, Y, 1). searchinsert(X, Y, [X|Y]) :- search(X, Y, 0). COP4020 Spring 2014 18 3/13/2016

19. Example 10 Remove all items in a list equal to x  (remove 1 ‘(1 2 3 4 1 2)) => (2 3 4 2) remove(_, [], []). remove(X, [X|T], T1):- remove(X, T, T1). remove(X, [Y|T], [Y|T1]) :- remove(X, T, T1). COP4020 Spring 2014 19 3/13/2016

20. Example 11 Insert into a sorted list (insertsort 14 ‘(0 10 20 30 40)) => (0 10 14 20 30 40) insertsorted(X, [], [X]). insertsorted(X, [Y|T], [X, Y|T]) :- X =< Y. insertsorted(X, [Y|T], [Y|T1]) :- X > Y, insertsorted(X, T, T1). COP4020 Spring 2014 20 3/13/2016

21. Example 12 Insertion sort isort([], []). isort([X|T], Y):- isort(T, T1), insertsorted(X, T1, Y). COP4020 Spring 2014 21 3/13/2016