60 20 PROLOG Syntax and Meaning DP

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PROLOG

SYNTAX AND MEANING

Ivan Bratko

University of LjubljanaFaculty of Computer and Info. Sc.

Ljubljana, Slovenia



DATA OBJECTS

data objects

simple objects structures

constants variables

atoms numbers



SYNTAX FOR DATA OBJECS

� Type of object always recognisable from its syntactic

form



THREE SYNTACIC FORMS FOR ATOMS

(1) Strings of letters, digits, and ³_´, starting with

lowercase letter:

x x15 x_15 aBC_CBa7

alpha_beta_algorithm taxi_35

peter missJones miss_Jones2



ATOMS, CTD.

(2) Strings of special characters

---> <==> <<

. < > + ++ ! .. .::. ::= []



ATOMS, CTD.

(3) Strings in single quotes

µX _35¶ µPeter¶ µBritney Spears¶



SYNTAX FOR NUMBERS

� Integers

1 1313 0 -55

� Real numbers (floating point)

3.14 -0.0045 1.34E-21 1.34e-21



SYNTAX FOR V ARI ABLES

� Strings of letters, digits, and underscores, starting with

uppercase letter

X Results Object2B Participant_list

_x35 _335

� Lexical scope of variable names is one clause

� Underscore stands for an anonymous variable

� Each appearance of underscore: another anon. var.



ANONYMOUS V ARI ABLES

visible_block( B) :-

see( B, _, _).

Equivalent to:

visible_block( B) :-

see( B, X, Y).



STRUCTURES

� Structures are objects that have several components

� For example: dates are structured objects with three

components

� Date 17 June 2006 can be represented by term:

date( 17, june, 2006)

functor arguments

� An argument can be any object, also a structure



FUNCTORS

� Functor name chosen by user

� Syntax for functors: atoms

� Functor defined by name and arity



TREE REPRESENTATION

OF STRUCTURES

Often, structures are pictured as trees

date( 17, june, 2006)

date

17 june 2006



� Therefore all structured objects in Prolog can be viewed

as trees

� This is the only way of building structured objects inProlog



SOME GEOMETRIC OBJECTS

P2 = (2,3) (6,4)

S T

(4,2)

P1=(1,1) (7,1)

P1 = point( 1, 1) P2 = point( 2, 3)

S = seg( P1, P2) = seg( point(1,1), point(2,3))

T = triangle( point(4,2), point(5,4), point(7,1))



LINE SEGMENT

S = seg( point(1,1), point(2,3))

S = seg

point point

1 1 2 3



ARITHMETIC EXPRESSIONS

ARE ALSO STRUCTURES

� For example: (a + b) * (c - 5)

� Written as term with functors:

*( +( a, b), -( c, 5))

*

+ -

a b c 5



M ATCHING

� Matching is operation on terms (structures)

� Given two terms, they match if:

(1) They are identical, or

(2) They can be made identical by properly

instantiating the variables in both terms



EXAMPLE OF M ATCHING

� Matching two dates:

date( D1, M1, 2006) = date( D2, june, Y2)

� This causes the variables to be instantianted as:D1 = D2

M1 = june

Y2 = 2006

� This is the most general instantiation

� A less general instantiation would be: D1=D2=17, ...



MOST GENER AL INSTANTI ATION

� In Prolog, matching always results in most general

instantiation

� This commits the variables to the least possible extent,leaving flexibility for further instantiation if required

� For example:

?- date( D1, M1, 2006) = date( D2, june, Y2),date( D1, M1, 2006) = date( 17, M3, Y3).

D1 = 17, D2 = 17, M1 = june, M3 = june,

Y2 = 2006, Y3 = 2006



M ATCHING

� Matching succeeds or fails; if succeeds then it results in

the most general instantiation

� To decide whether terms S and T match:(1) If S and T are constants then they match only if they

are identical

(2) If S is a variable then matching succeeds, S is

instantiated toT

; analogously if T

is a variable(3) If S and T are structures then they match only if

(a) they both have the same principal functor, and

(b) all their corresponding arguments match



M ATCHING § UNIFIC ATION

� Unification known in predicate logic

� Unification = Matching + Occurs check

� What happens when we ask Prolog:

?- X = f(X).

Matching succeeds, unification fails



COMPUTATION WITH M ATCHING

% Definition of vertical and horizontal segments

vertical( seg( point( X1,Y1), point( X1, Y2))).

horizontal( seg( point( X1,Y1), point( X2, Y1))).

?- vertical( seg( point( 1,1), point( 1, 3))).

yes

?- vertical( seg( point( 1,1), point( 2, Y))).

no

?- vertical( seg( point( 2,3), P)).

P = point( 2, _173).



AN INTERESTING SEGMENT

� Is there a segment that is both vertical and horizontal?

?- vertical( S), horizontal( S).

S = seg( point( X,Y), point(X,Y))

� Note, Prolog may display this with new variables names

as for example:

S = seg( point( _13,_14), point( _13, _14))



DECL AR ATIVE ME ANING

� Given a program P and a goal G,G is true ( i.e. logically follows from P) if and only if:

(1) There is a clause C in P such that

(2) there is a clause instance I of C such that

(a) the head of I is identical to G, and(b) all the goals in the body of I are true

� An instance of a clause C is obtained by renaming each

variable in C and possibly substituting the variable bysome term. E.g. an instance of

p(X,Y) :- q(Y,Z)

is

p(U,a) :- q(a,V).



DECL AR ATIVE vs PROCEDUR AL

ME ANING OF

PROLOG PROGR AMS� Consider:

P :- Q, R.

� Declarative readings of this:

� P is true if Q and R are true.

� From Q and R follows P.

� Procedural readings:

� To solve problem P, first solve subproblem Q and then R.

� To satisfy P, first satisfy Q and then R.



PROCEDUR AL ME ANING

� Specifies how Prolog answers questions

� Procedural meaning is an algorithm to execute a list of goals

given a Prolog program:

program

success/failure indication

goal list execute

instantiation of variables



procedure execute( Program, GoalList, Success)

� execute = declarative meaning + procedural elements

G is true ( i.e. logically follows from P) if and only if:

(1) there is a clause C in P such that

(2) there is a clause instance I of C such that

(a) the head of I is identical to G, and

(b) all the goals in the body of I are true

Search program from top to bottom to find such clause

Match G and

head of C

Execute goals in order as they

appear in program



EXAMPLE

QU ALITATIVE CIRCUIT AN ALYSIS

� Electric circuits made of resistors and diodes through

sequential and parallel connections

� Circuit = par( res, seq( res, diode))

Current

Voltage



REL ATION CIRC

circ( Circuit, Voltage, Current)

Current Circuit

+ -

Voltage



% Qualitative definition of electric circuits

% Currents and voltages have qualitative values: zero, pos or neg

% All circuits have two terminals

% A circuit may consist of a simple element,

% or it can be composed from two circuits through parallel or sequential

% connection

% circ( Circuit, Voltage, Current)

% The behaviour of resistor: "qualitative" Ohm's law

circ( res, pos, pos). % Both voltage and current positive

circ( res, zero, zero).

circ( res, neg, neg).



% The behaviour of diode

circ( diode, zero, pos). % Open diode: zero voltage, any pos. current

circ( diode, zero, zero).

circ( diode, neg, zero). % Closed diode, zero current, any neg. voltage

% Reversed diode

circ( revdiode, zero, neg). % Open: zero voltage, any neg. current

circ( revdiode, zero, zero).

circ( revdiode, pos, zero).



% Sequential composition of circuits

circ( seq( Circuit1, Circuit2), Volt, Curr) :-

circ( Circuit1, Volt1, Curr),

circ( Circuit2, Volt2, Curr), % The same current

qsum( Volt1, Volt2, Volt). % Add voltages

% Parallel composition of circuits

circ( par( Circuit1, Circuit2), Volt, Curr) :-

circ( Circuit1, Volt, Curr1),circ( Circuit2, Volt, Curr2), % The same voltage

qsum( Curr1, Curr2, Curr). % Add currents



% qsum( Q1, Q2, Q3):

% Q3 = Q1 + Q2, qualitative sum over domain [pos,zero,neg]

qsum( pos, pos, pos).

qsum( pos, zero, pos).

qsum( pos, neg, pos).

qsum( pos, neg, zero).

qsum( pos, neg, neg).

qsum( zero, pos, pos).

qsum( zero, zero, zero).

qsum( zero, neg, neg).

qsum( neg, pos, pos).

qsum( neg, pos, zero).

qsum( neg, pos, neg).

qsum( neg, zero, neg).

qsum( neg, neg, neg).



SOME QUERIES

?- circ( par( seq( res, res), res), V, C).

C = pos,V = pos ? ;

C = zero,V = zero ? ;

C = neg,V = neg ? ;

% Construct a circuit

?- circ( C, pos, pos), circ( C, zero, zero), circ( C, neg, neg).



?- circ( C, pos,pos), circ(C, neg, zero).

C = seq(res,diode) ? ;

C = seq(res,seq(res,diode)) ? ;

C = seq(res,seq(res,seq(res,diode))) ? ;C = seq(res,seq(res,seq(res,seq(res,diode)))) ? ;

% How about some parallel compositions?

60 20 PROLOG Syntax and Meaning DP

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