Logic Programming
Prof. Xin Yuan

Topics


More on Prolob
Prolog by examples
4/12/2020 COP4020 Spring 2013
2

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
4/12/2020 COP4020 Spring 2014
3

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
G
1
-> G
2
; G
3 forms an if-then-else: if G true is a true goal and acts like a no-op
1 failed then G
2 else G
3
 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, !.
4/12/2020 COP4020 Spring 2014
4

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
4/12/2020 COP4020 Spring 2014
5

Example 1 fact(n) = 1*2*…*n

 fact(1, 1).
fact(N, X) :- M is N-1, fact(M, Y), X is Y*N.
4/12/2020 COP4020 Spring 2014
6

Example 2


Sum the elements of a list sum([1,2,3], X).
X=6
4/12/2020 COP4020 Spring 2014
7

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.
4/12/2020 COP4020 Spring 2014
8

Example 4



Generate a list of n copies of x
Fill(3, x, Y)
Y=[x,x,x]
4/12/2020 COP4020 Spring 2014
9

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).
4/12/2020 COP4020 Spring 2014
10

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]
4/12/2020 COP4020 Spring 2014
11

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).
4/12/2020 COP4020 Spring 2014
12

Example 6
 Search on binary search tree, where [] are leaves and [ val, left, right ] is a node bsearch[4, [3, [], [4, [],[]]], X).
X=1
4/12/2020 COP4020 Spring 2014
13

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).
14
4/12/2020 COP4020 Spring 2014

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).
4/12/2020 COP4020 Spring 2014
15

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).
16
4/12/2020 COP4020 Spring 2014

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).
4/12/2020 COP4020 Spring 2014
17

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).
4/12/2020 COP4020 Spring 2014
18

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).
4/12/2020 COP4020 Spring 2014
19

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).
20
4/12/2020 COP4020 Spring 2014

Example 12
 Insertion sort isort([], []).
isort([X|T], Y):- isort(T, T1), insertsorted(X, T1, Y).
4/12/2020 COP4020 Spring 2014
21