1. Introduction to Prolog
© Patrick Blackburn, Johan Bos & Kristina Striegnitz

2. Chapter 1 Facts, Rules, and Queries
© Patrick Blackburn, Johan Bos & Kristina Striegnitz

3. SWI Prolog
A Free Software Prolog environment, licensed under the Lesser GNU public license.
This popular interpreter was developed by Jan Wielemaker.
Freely available Prolog interpreter
Works with
– Linux,
– Windows, or
– Mac OS

4. SWI Prolog
This is the interpreter we used while developing this lecture.
There are many more Prolog interpreters

5. Lecture Theory – Prolog Syntax Exercises – Introduction to Prolog
– Facts, Rules and Queries
– Prolog Syntax
Exercises
– Exercises of LPN chapter 1
– Practical work

6. Aim of this lecture Give some simple examples of Prolog programs
Discuss the three basic constructs in Prolog:
– Facts
– Rules
– Queries

7. Aim of this lecture Introduce other concepts, such as
– the role of logic
– unification with the help of variables
Begin the systematic study of Prolog by defining
– terms
– atoms, and
– variables

8. Prolog "Programming with Logic"
Very different from other programming languages
– Declarative (not procedural)
– Recursion (no “for” or “while” loops)
– Relations (no functions)
– Unification

9. Basic idea of Prolog Describe the situation of interest Ask a question
– logically deduces new facts about the situation we described
– gives us its deductions back as answers

10. Consequences Think declaratively, not procedurally High-level language
– Challenging
– Requires a different mindset
High-level language
– Not as efficient as, say, C
– Good for rapid prototyping
– Useful in many AI applications (knowledge representation, inference)

11. Facts The syntax of facts is the same as in the predicate calculus.
Examples:
fish(ray). % Ray is a fish.
fish(salmon) % Salmon is a fish.
red(car). % Car is red.
likes(mary , john). % Mary likes John.
factorial(3 , 6). % the factorial of 3 is 6

12. Prolog is conversational
Here is an illustrative conversation with a Prolog system:
?- fish(ray).
yes
?- fish(dog). no
?- fish(sardine).
A sardine is a fish, but prolog doesn’t know that unless it is specified as a fact in the source file.

13. Multiple possible answers
?- fish(X).
X = ray
X = salmon
Both ray and salmon are fish.

14. Inference Given the statement: Prove that “Fido will die.” ?
“Fido is a dog”
“All dogs are animals.” and
“All animals will die.”
Prove that “Fido will die.” ?

15. Inference
“Fido is a dog” “All dogs are animals.” and “All animals will die.” dog(fido). animal(X):-dog(X). die(X):-animal(X).
?- die(fido).
yes

16. Knowledge Base 1
woman(mia). woman(jody). woman(yolanda). playsAirGuitar(jody). party.
?- woman(mia). ?-
yes ?-
?- playsAirGuitar(jody).
yes ?-
?- playsAirGuitar(mia). no

17. Knowledge Base 1
woman(mia). woman(jody). woman(yolanda). playsAirGuitar(jody). party.
?- tattoed(jody).
ERROR: predicate tattoed/1 not defined. ?-

18. Knowledge Base 1
woman(mia). woman(jody). woman(yolanda). playsAirGuitar(jody). party.
?- party.
yes ?-

19. Knowledge Base 1
woman(mia). woman(jody). woman(yolanda). playsAirGuitar(jody). party.
?- rockConcert. no ?-

20. Knowledge Base 2
fact
happy(yolanda). listens2music(mia). listens2music(yolanda):- happy(yolanda). playsAirGuitar(mia):- listens2music(mia). playsAirGuitar(yolanda):- listens2music(yolanda).
fact
rule
rule
rule
head
body

21. Knowledge Base 2
happy(yolanda). listens2music(mia). listens2music(yolanda):- happy(yolanda). playsAirGuitar(mia):- listens2music(mia). playsAirGuitar(yolanda):- listens2music(yolanda).
?- playsAirGuitar(mia).
yes ?- ?-
?- playsAirGuitar(yolanda).
yes

22. Clauses
happy(yolanda). listens2music(mia). listens2music(yolanda):- happy(yolanda). playsAirGuitar(mia):- listens2music(mia). playsAirGuitar(yolanda):- listens2music(yolanda).
There are five clauses in this knowledge base:
two facts, and three rules.
The end of a clause is marked with a full stop.

23. Predicates
happy(yolanda). listens2music(mia). listens2music(yolanda):- happy(yolanda). playsAirGuitar(mia):- listens2music(mia). playsAirGuitar(yolanda):- listens2music(yolanda).
There are three predicates in this knowledge base:
happy, listens2music, and playsAirGuitar

24. Knowledge Base 3
happy(vincent). listens2music(butch). playsAirGuitar(vincent):- listens2music(vincent), happy(vincent). playsAirGuitar(butch):- happy(butch). playsAirGuitar(butch):- listens2music(butch).

25. Expressing Conjunction
happy(vincent). listens2music(butch). playsAirGuitar(vincent):- listens2music(vincent), happy(vincent). playsAirGuitar(butch):- happy(butch). playsAirGuitar(butch):- listens2music(butch).
The comma “," expresses conjunction in Prolog

26. Knowledge Base 3
happy(vincent). listens2music(butch). playsAirGuitar(vincent):- listens2music(vincent), happy(vincent). playsAirGuitar(butch):- happy(butch). playsAirGuitar(butch):- listens2music(butch).
?- playsAirGuitar(vincent). no ?-

27. Knowledge Base 3
happy(vincent). listens2music(butch). playsAirGuitar(vincent):- listens2music(vincent), happy(vincent). playsAirGuitar(butch):- happy(butch). playsAirGuitar(butch):- listens2music(butch).
?- playsAirGuitar(butch).
yes ?-

28. Expressing Disjunction
happy(vincent). listens2music(butch). playsAirGuitar(vincent):- listens2music(vincent), happy(vincent). playsAirGuitar(butch):- happy(butch). playsAirGuitar(butch):- listens2music(butch).
happy(vincent).
listens2music(butch).
playsAirGuitar(vincent):- listens2music(vincent), happy(vincent).
playsAirGuitar(butch):- happy(butch); listens2music(butch).

29. Prolog and Logic Clearly Prolog has something to do with logic
Operators

30. Knowledge Base 4
woman(mia). woman(jody). woman(yolanda). loves(vincent, mia). loves(marsellus, mia). loves(pumpkin, honey_bunny). loves(honey_bunny, pumpkin).

31. Prolog Variables
woman(mia). woman(jody). woman(yolanda). loves(vincent, mia). loves(marsellus, mia). loves(pumpkin, honey_bunny). loves(honey_bunny, pumpkin).
?- woman(X).

32. Variable Instantiation
woman(mia). woman(jody). woman(yolanda). loves(vincent, mia). loves(marsellus, mia). loves(pumpkin, honey_bunny). loves(honey_bunny, pumpkin).
?- woman(X).
X=mia

33. Asking Alternatives
woman(mia). woman(jody). woman(yolanda). loves(vincent, mia). loves(marsellus, mia). loves(pumpkin, honey_bunny). loves(honey_bunny, pumpkin).
?- woman(X).
X=mia;
X=jody
X=jody;
X=yolanda
X=yolanda; no

34. Knowledge Base 4
woman(mia). woman(jody). woman(yolanda). loves(vincent, mia). loves(marsellus, mia). loves(pumpkin, honey_bunny). loves(honey_bunny, pumpkin).
?- loves(marsellus,X), woman(X).
X=mia ?-

35. Knowledge Base 4
woman(mia). woman(jody). woman(yolanda). loves(vincent, mia). loves(marsellus, mia). loves(pumpkin, honey_bunny). loves(honey_bunny, pumpkin).
?- loves(pumpkin,X), woman(X). no ?-

36. Knowledge Base 5
loves(vincent,mia). loves(marsellus,mia). loves(pumpkin, honey_bunny). loves(honey_bunny, pumpkin). jealous(X,Y):- loves(X,Z), loves(Y,Z).
?- jealous(marsellus,W).
W=vincent;
W=marsellus; no ?-

37. Prolog Syntax What exactly are facts, rules and queries built out of?
Terms
Terms
Simple Terms
Simple Terms
Complex Terms
Complex Terms
Constants
Constants
Variables
Variables
Atoms
Atoms
Numbers
Numbers

38. Atoms
A sequence of characters of upper-case letters, lower-case letters, digits, or underscore, starting with a lowercase letter
Examples: butch, big_kahuna_burger, playGuitar
An arbitrary sequence of characters enclosed in single quotes
Examples: 'Vincent', 'Five dollar shake',
A sequence of special characters
Examples: : , ; :-

39. Numbers
Integers:
12, -34, 22342
Floats: ,

40. Variables
A sequence of characters of upper-case letters, lower-case letters, digits, or underscore, starting with either an uppercase letter or an underscore
Examples: X, Y, Variable, Vincent, _tag

41. Complex Terms
Atoms, numbers and variables are building blocks for complex terms
Complex terms are built out of a functor directly followed by a sequence of arguments
Arguments are put in round brackets, separated by commas
The functor must be an atom

42. Examples of complex terms
Examples we have seen before:
playsAirGuitar(jody)
loves(vincent, mia)
jealous(marsellus, W)
Complex terms inside complex terms:
hide(X,father(father(father(butch))))

43. Arity The number of arguments a complex term has is called its arity
Examples: woman(mia) is a term with arity 1 loves(vincent,mia) has arity 2 father(father(butch)) arity 1

44. Arity is important
In Prolog you can define two predicates with the same functor but with different arity
Prolog would treat this as two different predicates
In Prolog documentation arity of a predicate is usually indicated with the suffix "/" followed by a number to indicate the arity

45. Example of Arity This knowledge base defines happy/1 listens2music/1
happy(yolanda).
listens2music(mia).
listens2music(yolanda):- happy(yolanda).
playsAirGuitar(mia):- listens2music(mia).
playsAirGuitar(yolanda):- listens2music(yolanda).
This knowledge base defines
happy/1
listens2music/1
playsAirGuitar/1

46. Summary of this lecture
Simple examples of Prolog programs
Introduced three basic constructs in Prolog:
Facts
Rules
Queries
Discussed other concepts, such as
the role of logic
unification with the help of variables
Definition of Prolog constructs: terms, atoms, and variables

47. Exercises
Exercise 1.1 Which of the following sequences of characters are atoms, which are variables, and which are neither?
vINCENT
Footmassage
Variable23
Variable2000
big_kahuna_burger
’big  kahuna  burger’
big  kahuna  burger
‘Jules’
_Jules
’_Jules’

48. Exercises
Exercise 1.2 Which of the following sequences of characters are atoms, which are variables, which are complex terms, and which are not terms at all? Give the functor and arity of each complex term.
loves(Vincent,mia)
’loves(Vincent,mia)’
Butch(boxer)
boxer(Butch)
and(big(burger),kahuna(burger))
and(big(X),kahuna(X))
_and(big(X),kahuna(X))
(Butch  kills  Vincent)
kills(Butch  Vincent)
kills(Butch,Vincent

49. Exercises
Exercise 1.3 How many facts, rules, clauses, and predicates are there in the following knowledge base? What are the heads of the rules, and what are the goals they contain?
woman(vincent).     woman(mia).     man(jules).     person(X):-  man(X);  woman(X).     loves(X,Y):-  father(X,Y).     father(Y,Z):-  man(Y),  son(Z,Y).     father(Y,Z):-  man(Y),  daughter(Z,Y).

50. Exercises Exercise 1.4 Represent the following in Prolog:
Butch is a killer.
Mia and Marsellus are married.
Zed is dead.
Marsellus kills everyone who gives Mia a footmassage.
Mia loves everyone who is a good dancer.
Jules eats anything that is nutritious or tasty.

51. Exercises
Exercise 1.5 Suppose we are working with the following knowledge base:
wizard(ron).      hasWand(harry).      quidditchPlayer(harry).      wizard(X):-  hasBroom(X),  hasWand(X).      hasBroom(X):-  quidditchPlayer(X).

52. Exercises
Exercise 1.5 How does Prolog respond to the following queries?
wizard(ron).
witch(ron).
wizard(hermione).
witch(hermione).
wizard(harry).
wizard(Y).
witch(Y).

53. Chapter 2  Unification
© Patrick Blackburn, Johan Bos & Kristina Striegnitz

54. Unification
Recall previous example, where we said that Prolog unifies woman(X) with woman(mia) thereby instantiating the variable X with the atom mia.

55. Unification Working definition:
Two terms unify if they are the same term or if they contain variables that can be uniformly instantiated with terms in such a way that the resulting terms are equal

56. Unification This means that: This also means that: mia and mia unify
42 and 42 unify
woman(mia) and woman(mia) unify
This also means that:
vincent and mia do not unify
woman(mia) and woman(jody) do not unify

57. Unification What about the terms: mia and X woman(Z) and woman(mia)
loves(mia,X) and loves(X,vincent)

58. Instantiations
When Prolog unifies two terms it performs all the necessary instantiations, so that the terms are equal afterwards
This makes unification a powerful programming mechanism

59. Revised Definition
If T1 and T2 are constants, then T1 and T2 unify if they are the same atom, or the same number.
If T1 is a variable and T2 is any type of term, then T1 and T2 unify, and T1 is instantiated to T2. (and vice versa)
If T1 and T2 are complex terms then they unify if:
They have the same functor and arity, and
all their corresponding arguments unify, and
the variable instantiations are compatible.

60. Prolog unification
?- mia = mia.
yes
?- mia = vincent. no ?-

61. Prolog unification
?- mia = X.
X=mia
yes ?-

62. How will Prolog respond?
?- X=mia, X=vincent. no ?-
Why? After working through the first goal, Prolog has instantiated X with mia, so that it cannot unify it with vincent anymore. Hence the second goal fails.

63. Example with complex terms
?- k(s(g),Y) = k(X,t(k)).
X=s(g)
Y=t(k)
yes ?-

64. Example with complex terms
?- k(s(g),t(k)) = k(X,t(Y)).
X=s(g)
Y=k
yes ?-

65. One last example
?- loves(X,X) = loves(marsellus,mia).

66. Programming with Unification
vertical( line(point(X,Y),
point(X,Z))).
horizontal( line(point(X,Y),
point(Z,Y))).
?- vertical(line(point(1,1),point(1,3))).
yes ?- ?-
?- vertical(line(point(1,1),point(3,2))). no ?-

67. Programming with Unification
vertical( line(point(X,Y),
point(X,Z))).
horizontal( line(point(X,Y),
point(Z,Y))).
?- horizontal(line(point(1,1),point(1,Y))).
Y = 1; no ?-

68. Programming with Unification
vertical( line(point(X,Y),
point(X,Z))).
horizontal( line(point(X,Y),
point(Z,Y))).
?- horizontal(line(point(2,3),Point)).
Point = point(_554,3); no ?-

69. Proof Search
Now that we know about unification, we are in a position to learn how Prolog searches a knowledge base to see if a query is satisfied.
In other words: we are ready to learn about proof search

70. Example f(a). f(b). g(a). g(b). h(b). k(X):- f(X), g(X), h(X).
?- k(Y).

71. Example: search tree f(a). f(b). ?- k(Y). g(a). g(b). h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
?- k(Y).

72. Example: search tree f(a). f(b). ?- k(Y). g(a). g(b). Y=X h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
?- k(Y).

73. Example: search tree f(a). f(b). ?- k(Y). g(a). g(b). Y=X h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
X=a
?- g(a), h(a).
?- k(Y).

74. Example: search tree f(a). f(b). ?- k(Y). g(a). g(b). Y=X h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
X=a
?- g(a), h(a).
?- k(Y).
?- h(a).

75. Example: search tree † f(a). f(b). ?- k(Y). g(a). g(b). Y=X h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
X=a
?- g(a), h(a).
?- k(Y).
?- h(a). †

76. Example: search tree † f(a). f(b). g(a). g(b). h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
X=a
X=b
?- g(a), h(a).
?- g(b), h(b).
?- k(Y).
?- h(a). †

77. Example: search tree † f(a). f(b). g(a). g(b). h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
X=a
X=b
?- g(a), h(a).
?- g(b), h(b).
?- k(Y).
?- h(a).
?- h(b). †

78. Example: search tree † f(a). f(b). g(a). g(b). h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
X=a
X=b
?- g(a), h(a).
?- g(b), h(b).
?- k(Y).
Y=b
?- h(a).
?- h(b). †

79. Example: search tree † f(a). f(b). g(a). g(b). h(b).
k(X):- f(X), g(X), h(X).
?- k(Y).
Y=X
?- f(X), g(X), h(X).
X=a
X=b
?- g(a), h(a).
?- g(b), h(b).
?- k(Y).
Y=b; no ?-
?- h(a).
?- h(b). †

80. Exercise
Exercise 2.1 Which of the following pairs of terms unify? Where relevant, give the variable instantiations that lead to successful unification.
bread  =  bread
’Bread’  =  bread
’bread’  =  bread
Bread  =  bread
bread  =  sausage
food(bread)  =  bread
food(bread)  =  X
food(X)  =  food(bread)
food(bread,X)  =  food(Y,sausage)
food(bread,X,beer)  =  food(Y,sausage,X)
food(bread,X,beer)  =  food(Y,kahuna_burger)
food(X)  =  X
meal(food(bread),drink(beer))  =  meal(X,Y)
meal(food(bread),X)  =  meal(X,drink(beer))

81. Exercise
Exercise 2.2 We are working with the following knowledge base:
house_elf(dobby). witch(hermione). witch(’McGonagall’). witch(rita_skeeter). magic(X):- house_elf(X). magic(X):- wizard(X). magic(X):- witch(X).

82. Exercise
Which of the following queries are satisfied? Where relevant, give all the variable instantiations that lead to success.
?-  magic(house_elf).
?-  wizard(harry).
?-  magic(wizard).
?-  magic(’McGonagall’).
?-  magic(Hermione).