Introduction to Prolog

INTRODUCTION TO PROLOG
- Brian Hutchinson
Present by -
W.J.A.I.U. Jayaweera- 100227D
G.K.M.C Sajeewa- 100470N
M.M.D.T.K Wijewardane- 100612E

OUTLINE
 Introduction
 Language Features
 More Features
 Behind the scenes
 Language Classifications
 Examples

INTRODUCTION
 Prolog is the most popular language of the logic
programing languages.
 It is goal based language, it has automatic
backtracking and uses recursion.
 Prolog stands for programmation en logique", or
programming in logic."

INTRODUCTION [CTD...]
 Invented by Alain Colmerauer and Philippe Roussel
of the Groupe d'Intelligence Articielle (GIA) in early
1970s.
 The earliest Prolog interpreter was written in Algol
in1972 by Roussel.
 The official ISO standard for Prolog was published
in 1996.

CURRENT IMPLEMENTATIONS
 There are several popular Prolog interpreters
available. They include:
 GNU Prolog (http://pauillac.inria.fr/vdiaz/gnu-
prolog/)
 SWI-Prolog (http://www.swi-prolog.org/)
 Visual Prolog (http://www.visual-
prolog.com/vip6/Download/Default.htm)
 BProlog
(http://www.cad.mse.kyutech.ac.jp/people/zhou/bpr
olog.html)

LANGUAGE FEATURES
Prolog Program
Facts
Rules
(Relationships)
Questions
(Goals)
Clauses

LANGUAGE FEATURES[CTD...]
 Facts-Something that is declared to always be true.
Ex-father(bob,george)
mother(alice,jeffrey)
 Rules- Something which is true only if all conditions
(sub goals) on the right are true
Ex-
parent(X,Y) :- father(X,Y).
parent(X,Y) :- mother(X,Y).
grandparent(X,Z) :- parent(X,Y), parent(Y,Z).

 Questions- Something which asks from the system
Ex- ?-ancestor(X,cindy),sibling(X,jeffrey)
 Clauses- Something which has a head and a body.
 Fact = head
 Rules = head + body
 Question=body

LANGUAGE FEATURES [CTD...]
Ex-
 uncle(X,Y) :- sibling(X,Z), parent(Z,Y).
(head) (body)
 ?- ancestor(X,cindy),sibling(X,jeffrey)
(body)
 father(john,mary)
(head)

 Terms - term can be number, constant (Albert) or
variable(X).
 Compound Terms- data structure, convenient way
of grouping relevant data together
Ex- fullname( joe,brown )
student( fullname( joe,brown ), 25 )
Full name , Student are called as functors.

MORE FEATURES
 Order- order matters in prolog, order is top to
bottom.
Ex- dog(rover).
dog(duke).
We enter the following question:
?- dog(X).
Answer : X = rover
 Order is important for the efficiency and correctness
of the program.

MORE FEATURES[CTD...]
 Backtracking-
 prolog stores data in tree.
 It uses depth first search to find answers.
 In its attempt to prove a goal, Prolog sometimes
goes down a dead-end, at which point it needs to
backtrack.ck

Ex- Sample Code
Facts- green(poisonivy).
green(broccoli).
edible(icecream).
edible(broccoli).
Question- ?- green(X),edible(X).
Answer- X = broccoli

Execution trace-
?- green(X),edible(X).
1 1 Call: green(poisoniyy) ?
1 1 Exit: green(poisonivy) ?
2 1 Call: edible(poisonivy) ?
2 1 Fail: edible(poisonivy) ?
1 1 Redo:green(poisonivy)1
1 1 Call: green(broccoli) ?
1 1 Exit: green(broccoli) ?
2 1 Call: edible(broccoli) ?
2 1 Exit: edible(broccoli) ?
Green(p)
Edible(p)
Green(b)
Root
Edible(b)
Answer

 Cuts- The cut is denoted by exclamation mark “!” and
disallows prolog from backtracking past that point.
 Ex-
With Out Cut
grade(G,a) :- G > 90.
grade(G,b) :- G > 80.
grade(G,c) :- G > 70.
grade(G,d) :- G > 60.
grade(_,f).
With Cut
grade2(G,a) :- G > 90, !.
grade2(G,b) :- G > 80, !.
grade2(G,c) :- G > 70, !.
grade2(G,d) :- G > 60, !.
grade2(_,f).

Forced Backtrack With Grade
?- grade(83,X)
X = b;
X = c;
X = d;
X = f
yes
Forced Backtrack With Grade2
?- grade2(83,X)
X = b;
yes
Forced back tracking with semi
colon.
Types of Cuts
Red Cuts
Green Cuts

Recursion- like functional languages prolog uses
recursion.
Ex-
ancestor(X,Z) :- parent(X,Z).
(Base Case)
ancestor(X,Z) :- parent(X,Y),ancestor(Y,Z).
(Recursive Rule)

MORE FEATURES [CTD...]
 Lists- important data structure in prolog and are
processed recursively.
Ex-
[a, b, a, a, c, d]
[]
[the, dog]
List= Head + Tail
List= [Head | Tail ]
Ex-
List- [a,b,a] can be represented as
[a | [b,a] ] or
[a, b | [a]] or
[a, b, a | []]

MORE FEATURES [CTD...]
There are several other features in prolog
 Negation
 Assertion and Retract

RESOLUTION AND UNIFICATION
 Resolution
 The resolution principle,
 If C1 and C2 are Horn clauses and the head of C1 matches
one of the terms in the body of C2 then we can replace the
term in C2 with the body of C1.
 Example :
 takes(Saman, cs123).
 classmates(X, Y) :- takes(X, Z), takes(Y, Z).
 classmates(Saman, Y) :- takes(Y, cs123).

RESOLUTION AND UNIFICATION [CTD…]
 Unification
 Prolog associates variables and values using a process
known as unification
 Variables that receive a value are said to be instantiated
 Example :
 The pattern-matching process used to associate variable X
with Saman and Z with cs123 is known as unification.

RESOLUTION AND UNIFICATION [CTD…]
The unification rules for Prolog :
 A constant unifies only with itself.
 Two structures unify if and only if they have the same
functor and the same number of arguments, and the
corresponding arguments unify recursively.
 Example :
 ?- f(a, b) = f(a, b, c).
No
 A variable unifies with anything.

DEPTH FIRST SEARCH
Prolog uses a depth-first search strategy when
traversing the tree.
 Advantage :
 Less memory usage
 Disadvantage :
 Prolog may descend down an endless branch (Black
holes)

TOP DOWN VERSUS BOTTOM UP
 Top Down Control
 we start from the goal and attempt to reach the
hypotheses
 Bottom Up Control
 we start with the hypotheses and attempt to reach the
goal

BOTTOM UP CONTROL
 Example :
 Method for calculating a fibonacci number,
 Starting with the bases cases and accumulating until it
reaches the goal.
fib(0,1). fib(1,1).
fib(N,F) :- N=M+1, M=K+1, fib(M,G),
fib(K,H), F=G+H, N>1.
:-fib(3,F).
N=3, M=2, K=1,
F = G + H
:-fib(2,F).
N=2, M=1, K=0,
F = G + H
:-fib(1,F).
F = 1
:-fib(1,1).
:-fib(0,F).
F = 1
:-fib(0,1).
:-fib(1,F).
F = 1
:-fib(1,1).

COMPILING PROLOG CODE
 A program exists called wamcc, based on the
Warren Abstract Machine.
 C code may then be compiled to produce stand
alone executable.
GNU Prolog logo

STRENGTHS OF PROLOG [CTD…]
 Simplicity of Prolog
 Ability to model certain problems very concisely and
elegantly
 Capability of solving problems that it wasn't
originally designed to solve
 Ability to manipulate symbolic data

STRENGTHS OF PROLOG [CTD…]
Prolog’s strength to manipulate symbolic data:
“There are well-known examples of symbolic
computation whose implementation in other standard
languages took tens of pages of indigestible code.
When the same algorithms were implemented in
Prolog, the result was a crystal-clear program easily
fitting on one page.”
‒ Bratko

WEAKNESSES OF PROLOG
 Lack of structure
 Issues with readability of Prolog code
 serious implications for the readability and
declarativeness of code due to cut predicate (!).
 Inefficiency of Prolog code
 Logical imperfectness

HIERARCHY OF LANGUAGES
According to Programming Language Pragmatics by Michael L.
Scott,
 Declarative
 functional
 Lisp/Scheme
 ML
 Haskell
 dataflow
 Id
 Val
 logic
 Prolog
 VisiCalc

HIERARCHY OF LANGUAGES [CTD…]
 Imperative
 von Neumann
 Fortran
 Pascal
 Basic
 C
 Object-Oriented
 Smalltalk
 Eiel
 C++
 Java

SCOPE
 Scope of a variable
 in scope within a clause
 Scope of the head of each clause
 in global scope
 Scope of constants
 in global scope
• Example
1. hates(X,Y) :- friends(X,Z),hates(Z,Y).
2. loves(X,Y) :- hates(X,Z),hates(Y,Z).

TYPE SYSTEMS
 Prolog is dynamically typed.
 At runtime, if a built-in predicate is given the wrong type
of argument an error will occur.
 For example:
1. ?- X is 1+1.
X = 2
Yes
2. ?- X is 1+dog.
uncaught exception: error(type_error(evaluable,dog/0),(is)/2)

TYPE SYSTEMS [CTD…]
 A term can be quarried to find out its type with
Prolog in the following way:
 ?- number(5).
yes
 ?- number(dog).
no
 ?- var(X).
yes
 ?- var(5).
no

BINDINGS
 Variable Cells
 A variable is stored in a single heap cell.
 This cell contains a tag and a store address of the that
which it is bound to.
 Unbound variables,
 by convention, point at their own cell.
3 REF 5
2 REF 2

BINDINGS [CTD…]
 Structure Cells
 A non-variable term is stored in a structure cell.
 For a structure f(t1:::tn), there will be n + 2 cells in the
heap.
0 STR 1
1 f/n
2 REF 2
…… ……
…… ……
n + 1 REF n + 1

EXAMPLES
1. Implementing the Towers of Hanoi problem
2. Implementing a non-deterministic finite state
automaton

TOWERS OF HANOI
 In this puzzle, we have three pegs and several
disks, initially stacked from largest to smallest on
the left peg

 Our goal is to move the entire tower to the
middle peg
 We can only move one disk at a time
 We can use right peg to temporally hold the
disks
 We can never place a larger disk on a smaller
disk in any peg

Recursive solution
- Move N - 1 discs from stack 1 to 3 with the help of stack
2.
- Move the Nth disc from 1 to 2
- Move N - 1 discs from stack 3 to 2 with the help of stack
1

Implementation in Prolog
hanoi(N) :- dohanoi(N, 1, 2, 3).
dohanoi(0, _ , _ , _ ) :- !.
dohanoi(N, A, B, C) :- N_1 is N-1,
dohanoi(N_1, A, C, B),
moveit(A, B),
dohanoi(N_1, C, B, A).
moveit(F, T) :- write([move, F, -->, T]), nl.

Output when n=3
?- hanoi(3).
[move,1,-->,2]
[move,1,-->,3]
[move,2,-->,3]
[move,1,-->,2]
[move,3,-->,1]
[move,3,-->,2]
[move,1,-->,2]
yes

Output when n=4
?- hanoi(4).
[move,1,-->,3]
[move,1,-->,2]
[move,3,-->,2]
[move,1,-->,3]
[move,2,-->,1]
[move,2,-->,3]
[move,1,-->,3]
[move,1,-->,2]
[move,3,-->,2]
[move,3,-->,1]
[move,2,-->,1]
[move,3,-->,2]
[move,1,-->,3]
[move,1,-->,2]
[move,3,-->,2]
yes

NON-DETERMINISTIC FINITE STATE
AUTOMATON

final(s3).
trans(s1,a,s1).
trans(s1,a,s2).
trans(s1,b,s1).
trans(s2,b,s3).
trans(s3,b,s4).
silent(s2,s4).
silent(s3,s1).

accepts(State,[]) :- final(State).
accepts(State, [X|Rest]) :- trans(State,X,State1),
accepts(State1,Rest).
accepts(State, String) :- silent(State,State1),
accepts(State1,String).

Questions we can ask
1) Whether a given string is accepted by the automaton
?- accepts(s1,[a,a,a,b]).
yes

Questions we can ask (cont.)
2) What states can we start in if we accept a certain
string?
?- accepts(S,[a,b]).
S = s1;
S = s3

Questions we can ask (cont.)
3) What are all strings of length 3 that can be accepted by
the automaton?
?- accepts(s1,[X1,X2,X3]).
X1 = a
X2 = a
X3 = a;
X1 = b
X2 = a
X3 = b
yes

CONCLUSION
 Prolog is the most popular language of the logic
programing languages.
 It is a declarative logic programming language
 It is goal based language, it has automatic
backtracking and uses recursion.

Introduction to Prolog

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