PROLOG SYNTAX AND MEANING

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PROLOG SYNTAX AND MEANING

• Ivan Bratko
• University of Ljubljana
• Faculty of Computer and Info. Sc.
• Ljubljana, Slovenia

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DATA OBJECTS

• data
  objects
• simple objects
  structures
• constants
  variables
• atoms numbers

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SYNTAX FOR DATA OBJECS

• Type of object always recognisable from its
  syntactic form

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THREE SYNTACIC FORMS FOR ATOMS

• (1) Strings of letters, digits, and _,
  starting with
• lowercase letter
• x x15 x_15
  aBC_CBa7
• alpha_beta_algorithm taxi_35
• peter missJones
  miss_Jones2

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ATOMS, CTD.

• (2) Strings of special characters
• ---gt ltgt ltlt
• . lt gt ! ..
  ..

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ATOMS, CTD.

• (3) Strings in single quotes
• X_35 Peter Britney Spears

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SYNTAX FOR NUMBERS

• Integers
• 1 1313 0 -55
• Real numbers (floating point)
• 3.14 -0.0045 1.34E-21
  1.34e-21

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SYNTAX FOR VARIABLES

• 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.

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ANONYMOUS VARIABLES

• visible_block( B) -
• see( B, _, _).
• Equivalent to
• visible_block( B) -
• see( B, X, Y).

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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

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FUNCTORS

• Functor name chosen by user
• Syntax for functors atoms
• Functor defined by name and arity

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TREE REPRESENTATION OF STRUCTURES

• Often, structures are pictured as trees
• date( 17, june, 2006)
• date
• 17 june 2006

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• Therefore all structured objects in Prolog can be
  viewed as trees
• This is the only way of building structured
  objects in Prolog

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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))

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LINE SEGMENT

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

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ARITHMETIC EXPRESSIONSARE ALSO STRUCTURES

• For example (a b) (c - 5)
• Written as term with functors
• ( ( a, b), -( c, 5))
• -
• a b c 5

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MATCHING

• 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

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EXAMPLE OF MATCHING

• 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 D1D217,
  ...

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MOST GENERAL INSTANTIATION

• 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

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MATCHING

• 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 to T 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

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MATCHING UNIFICATION

• Unification known in predicate logic
• Unification Matching Occurs check
• What happens when we ask Prolog
• ?- X f(X).
• Matching succeeds, unification fails

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COMPUTATION WITH MATCHING

• 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).

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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))

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DECLARATIVE MEANING

• 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 by some term. E.g. an instance of
• p(X,Y) - q(Y,Z)
• is
• p(U,a) - q(a,V).

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DECLARATIVE vs PROCEDURAL MEANING OF PROLOG
PROGRAMS

• 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.

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PROCEDURAL MEANING

• 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

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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
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EXAMPLEQUALITATIVE CIRCUIT ANALYSIS

• Electric circuits made of resistors and diodes
  through sequential and parallel connections
• Circuit par( res, seq( res, diode))
• Current
• Voltage

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RELATION CIRC

• circ( Circuit, Voltage, Current)
• Current Circuit
• 
  -
• Voltage

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• 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).

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• 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).

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• 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

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• 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).

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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).

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• ?- 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?