1. Prolog rules
Module 14.3 COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez

2. Topics Some Useful Predicates Examples: member, select, nth length
Backtracking,
Depth-first search

3. Some Useful Predicates
The predicate append(X,Y,Z) is true iff appending Y onto the end of X yields Z.
append can be used with any pattern of instantiation (i.e.with variables in any position). Examples:
?- append(X,Y,[1,2,3]). X = [] Y = [1, 2, 3] ; X = [1] Y = [2, 3] ; X = [1, 2] Y = [3] ; X = [1, 2, 3] Y = [] ; No.
?- append([1,2],[3,4],X). X = [1, 2, 3, 4] Yes.
?- append(X,[3,4],[1,2,3,4]). X = [1, 2] Yes.

4. Other Predefined List Predicates
Queries using these predicates can contain variables anywhere.
Predicate
Description
member(X,Y)
Provable if list Y contains element X.
select(X,Y,Z)
Provable if list Y contains element X, and removing X from Y yields Z.
nth0(X,Y,Z)
Provable if Z is the Xth element of list Y, counting from 0.
length(X,Y)
Provable if X is a list of length Y.

5. Sample Use of select
select(X,Y,Z): provable if list Y contains element X, and removing X from Y yields Z.
?- select(2,[1,2,3],Z). Z = [1, 3] ; No. ?- select(2,Y,[1,3]). Y = [2, 1, 3] ; Y = [1, 2, 3] ; Y = [1, 3, 2] ; No.

6. example More complex rules:
FatherOf(john,ted).
FatherOf(fred,carol).
FatherOf(ted,ken).
FatherOf(ted,lloyd).
FatherOf(lloyd,jim).
FatherOf(lloyd,joan).
MotherOf(connie,ted).
MotherOf(connie,carol).
MotherOf(jane,ken).
MotherOf(alice,lloyd)
MotherOf(carol,jim).
MotherOf(carol,joan).
More complex rules:
ParentOf(X,Y) :- FatherOf(X,Y).
ParentOf(X,Y) :- MotherOf(X,Y).
Alternatives are attempted in the order specified:
?- ParentOf(connie,ted).
First, match FatherOf(connie,ted). Fails.
Then, match MotherOf(connie,ted). Succeed.
Note: There is no gender.

7. example Using variables, we can get answers: ?- ParentOf(ted,C)
FatherOf(john,ted).
FatherOf(fred,carol).
FatherOf(ted,ken).
FatherOf(ted,lloyd).
FatherOf(lloyd,jim).
FatherOf(lloyd,joan).
MotherOf(connie,ted).
MotherOf(connie,carol).
MotherOf(jane,ken).
MotherOf(alice,lloyd)
MotherOf(carol,jim).
MotherOf(carol,joan).
Using variables, we can get answers:
?- ParentOf(ted,C)
C = ken;
C = lloyd;
No.
?- ParentOf(P,carol)
P = fred;
P = connie;

8. example Using more than one condition:
FatherOf(john,ted).
FatherOf(fred,carol).
FatherOf(ted,ken).
FatherOf(ted,lloyd).
FatherOf(lloyd,jim).
FatherOf(lloyd,joan).
MotherOf(connie,ted).
MotherOf(connie,carol).
MotherOf(jane,ken).
MotherOf(alice,lloyd)
MotherOf(carol,jim).
MotherOf(carol,joan).
Using more than one condition:
GrandParent(X,Y) :ParentOf(X,Z),ParentOf(Z,Y).
?- GrandParent(G, jim)
Prolog performs a backtracking, depth-first,
left-to-right search for values to satisfy the predicate(s) sought.

9. example GP(G=X,Y=jim) PO(G=X,Z) PO(Z,Y=jim)
GrandParent(X,Y) :ParentOf(X,Z),ParentOf(Z,Y).
?- GrandParent(G, jim)
FatherOf(john,ted).
FatherOf(fred,carol).
FatherOf(ted,ken).
FatherOf(ted,lloyd).
FatherOf(lloyd,jim).
FatherOf(lloyd,joan).
MotherOf(connie,ted).
MotherOf(connie,carol).
MotherOf(jane,ken).
MotherOf(alice,lloyd)
MotherOf(carol,jim).
MotherOf(carol,joan).
GP(G=X,Y=jim)
PO(G=X,Z)
PO(Z,Y=jim)
fff FO
(G=X= ,
Z= ) MO
Z= )
(Z= ,
Y=jim)
G = fred, ted, connie, alice
AND OR

10. Another example To choose a reviewer, we’d like an author who:
- has written books on the same subject:
Reviewer(Book,Person) :- SubjectOf(Book,Sub),
SubjectOf(AnotherBook,Sub),
AuthorOf(AnotherBook,Person),
not AuthorOf(Book,Person).
If not available (by subject), then find someone who has written for the same audience.
Reviewer(Book,Person) :- AudienceOf(Book,Aud), AudienceOf(AnotherBook,Aud), AuthorOf(AnotherBook,Person), not AuthorOf(Book,Person).
AuthorOf("Life on a Donkey","Swartz").
AuthorOf("Big and Little","Jones").
AuthorOf("Where are We","White").
AuthorOf("In a Pig’s Eye","Brown").
AuthorOf("High Flight","Smith").
SubjectOf("Life on a Donkey",travel).
SubjectOf("Big and Little",life).
SubjectOf("Where are We",life).
SubjectOf("In a Pig’s Eye",travel).
SubjectOf("High Flight",bio).
AudienceOf("Life on a Donkey",adult).
AudienceOf("Big and Little",child).
AudienceOf("Where are We",teen).
AudienceOf("In a Pig’s Eye",adult).
AudienceOf("High Flight",adult).

11. summary Some Useful Predicates Examples: member, select, nth length
Backtracking,
Depth-first search