PROLOG 1

1
PROLOG 1

• Ahmed M. Zeki

Semester II Nov 2004
2
Low and High Level Languages

• The evolution of computer languages is an
  evolution away form low-level languages toward
  high-level language.
• What is the difference between low-level
  languages and high-level languages?
• In low-level language, the programmer specifies
  how something is to be done.
• In high-level language, the programmer specifies
  simply what is to be done.

3
Goal-Oriented Programming

• is a language in which the satisfaction of goals
  is the basis of program execution.
• or
• is a language in which the set of goals to be
  satisfied is an essential part of a function or
  procedure body.
• Such languages include Prolog and other logic
  programming languages.

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PROLOG

• The best way to learn about goal-oriented
  programming is to read and write goal-oriented
  programs in Prolog, for goal-oriented programming
  is what Prolog is all about.
• Prolog is a language that clearly breaks away
  from the how-type languages, encouraging the
  programmer to describe situations and problems,
  not to the detailed means by which the problems
  are to be solved.

5
Defining Relations by Facts

• Prolog is a programming language for symbolic,
  non-numeric computation.
• It is specially well suited for solving problems
  that involve objects and relations between
  objects.

aishah
ali
khalid
naim
ahmed
zahid
noor
khairul
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Defining Relations by Facts

• The fact that Ali is a parent of Naim can be
  written in Prolog as
• parent(ali, naim).
• parent is the name of the relation ali and naim
  are its arguments.
• Names like ali and naim will be written with
  initial lowercase letters.
• The whole family tree is defined as follows
• parent(ali, naim).
• parent(aishah, naim).
• parent(ali, khalid).
• parent(naim, zahid).
• parent(naim, ahmed).
• parent(ahmed, noor).

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Defining Relations by Facts

• This program consists of 6 clauses. Each clause
  terminates with a full stop.
• Each clause declares 1 fact about the parent
  relation. For example, parent(ali, naim) is a
  particular instance of the parent relation.
• A relation is the set of all its instances.
• The question Is Ali a parent of Naim? can be
  communicated to Prolog by typing
• ?- parent(ali, naim).
• Prolog will answer
• yes
• While
• ?- parent(ali, noor).
• will produce
• no

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Defining Relations by Facts

• More interesting question can also be asked, such
  as Who is Khalids parent?
• ?- parent(X, khalid).
• Prolog will answer
• X ali
• While the question Who are alis children?
  which has more than one answer, can be
  communicated to Prolog as
• ?- parent(ali, X).
• will produce
• X naim
• press to list the other answers
• X khalid
• if you request more solutions, Prolog will
  answer no.

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Defining Relations by Facts

• The question
• ?- parent(X, Y).
• means who is a parent of whom? or Find X
  and Y such that X is a parent of Y. Prolog will
  display all solutions one by one.
• The question who is the grandparent of Noor? is
  also possible but in an indirect way since the
  relationship grandparent is not defined yet.
• ?- parent(Y, noor), parent(X, Y).
• which means Find such X and Y that satisfy
  the two requirements. If we change the order the
  logical meaning remains the same
• ?- parent(X, Y), parent(Y, noor).
• Exercise in the same way ask Who are Aishas
  grandchildren?.

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Defining Relations by Facts

• The question Do Zahid and Ahmed have a common
  parent?
• ?- parent(X, zahid), parent(X, ahmed).
• The arguments of relations can (among other
  things) be
• Concrete objects or constants (known as atoms)
  such as khalid and zahid.
• General objects such as X and Y. (known as
  variables).
• Questions to the system consists of one or more
  goals, such as
• ?- parent(X, zahid), parent(X, ahmed).

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Exercises

• Bratko, page 8
• 1.1
• 1.2

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Defining Relations by Rules

• To add the information about the sex of the
  people that occur in the parent relation
• female(aishah).
• male(ali).
• male(naim).
• male(khalid).
• male(zahid).
• male(ahmed).
• female(noor).
• These relations are unary, hence the output is
  either yes or no.
• Same information can be conveyed using a binary
  relation
• sex(ali, masculine).
• sex(aishah, feminine).

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Defining Relations by Rules

• The following relation is the inverse of the
  parent relation
• Offspring(khalid, ali). ...
• or
• offspring(Y,X) - parent(X, Y).
• Which can be read as For all X and Y, if X is a
  parent of Y then Y is an offspring of X. Such
  Prolog clauses are called rules.
• Facts like offspring(khalid, ali) is always true,
  while rules specify things that are true if some
  condition is satisfied. That is why rules have a
  condition part (body) on the right and a
  conclusion part (head) on the left.

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Defining Relations by Rules

• For all X and Y, X is the mother of Y if X is a
  parent of Y and X is a female.
• mother(X, Y) - parent(X, Y), female(X).
• It can also be written as
• mother(X, Y) - X is Ys mum
• parent(X, Y), / Comments /
• female(X).
• Relations can be illustrated by diagrams
• Nodes correspond to objects.
• Arcs between nodes correspond to binary
• relations.
• The arcs are oriented so as to point from the
• first argument of the relation to the
  second.
• Unary relations are indicated in the diagrams by
• simply marking the corresponding objects
  with the
• name of the relation.

X
parent
offspring
Y
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Defining Relations by Rules

• The relations that are being defined are
  represented by dashed arcs.
• The graph is read as follows
• If the relations shown by solid arcs hold, then
  the relation shown by a dashed are also holds.

female
X
female
X
Z
parent
grandmother
Y
parent
mother
parent
parent
female
parent
Y
X
Y
Z
sister
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• For any X and Y, X is a sister of Y if (1) both X
  and Y have the same parent and (2) X is a female.
• sister(X,Y) - parent(Z,X), parent(Z,Y),
  female(X).
• Prolog will say that Noor is a sister to herself
  ? because Prolog assumes that X and Y can be the
  same. To correct the rule we have to add that X
  and Y must be different (Will be done later).

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Exercise

• Bratko, page 13
• 1.3
• 1.4
• 1.5

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Recursive Rules

• The predecessor relation
• It is defined in terms of parent relation.
• The definition is expressed in two rules
• The direct (immediate) predecessors.
• The indirect predecessor.
• Some X is an indirect predecessor of some Z if
  there is a parent-ship chain of people between X
  and Z.
• The first rule
• For all X and Z
• X is a predecessor of Z if
• X is a parent of Z
• predecessor (X,Z) - parent(X, Z).
• The second rule can be written as a chain
• predecessor (X,Z) - parent(X, Y), parent(Y,
  Z).

X
parent
predecessor
parent
parent
1
Z
19

• But the program is lengthy and works with that a
  certain depth only.
• Predecessor can be defined in terms of itself
• For all X and Z,
• X is a predecessor of Z if
• (1) X is a parent of Y and
• (2) Y is a predecessor of Z.
• predecessor (X, Z) - parent (X, Y), predecessor
  (Y, Z).

2
20

• This is known as recursion, in which we define
  something that is not yet been completely defined
• Recursive programming is one of the fundamental
  principles of programming in Prolog. It is not
  possible to solve tasks of any significant
  complexity in Prolog without the use of
  recursion.
• ?- predecessor (aishah, X).
• There will be 4 answers.
• The two clauses of predecessor are about the
  predecessor relation, such as set of clauses is
  called a procedure.

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Assignment

• Construct the family program by collecting all
  clauses given previously in one program.
• Bratko, exercise 1.6, page 18

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How Prolog Answers Questions?

• Prolog tries to satisfy all the goals.
• Example
• All men are fallible. Socrates is a man.
• We conclude that Socrates is fallible.
• For all X, if X is a man then X is fallible.
• fallible(X) - man(X).
• man(socrates).
• ?- fallible(socrates).
• yes
• ?- predecessor(ali, ahmed). is a derived fact

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Assignment

• Exercise
• Bratko, Exercise 1.7 page 22