2' Syntax and Meaning

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2. Syntax and Meaning
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Contents

• Data Objects
• Matching
• Declarative meaning of Prolog
• Procedural meaning
• Example monkey and banana
• Order of clauses and goals
• The relation between Prolog and logic

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Data Objects

• Data objects in Prolog

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Data Objects

• Atoms can be constructed in three ways
• Strings of letters, digits and _, starting with
  a lower-case letter.
• anna nil x25 x_25 x_ x_ _y
• Strings of special characters
• lt---lt gt ... ..
• String of characters enclosed in single quote
• Tom South_America Sarah Jones ??
• Numbers used in Prolog include integer numbers
  and real numbers.

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Data Objects

• Variables are strings of letters, digits and
  underscore characters, starting with an
  upper-case character
• X Result Object2 _x23 _23
• Anonymous variable
• haschild(X)-parent(X,Y).
• haschild(X)-parent(X, _ )
• somebody_has_child-parent(_,_).
• somebody_has_child-parent(X,Y).

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Data Objects

• Structured objects (or simply structure) are
  objects that have several components.
• The components themselves can, in turn, be
  structures.
• The date can be viewed as a structure with three
  components day, month, year.
• date(1,may,1983)

date
may
1983
functor
arguments
1

• Any day in May 1983 can be represented as
• date(Day, may, 1983)

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Data Objects
P1point(1,1) P2point(2,3) Sseg(P1,P2)
seg(point(1,1),point(2,3)) Ttriangle(point(4,2),
point(6,4), point(7,1))
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Data Objects

• We can use the same name, point, for points in
  both 2D and 3D
• point(X,Y) point(X,Y,Z)
• Prolog will recognize the difference because each
  functor is defined by two things
• the name, whose syntax is that of atoms
• the arity - i.e., the number of arguments.

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Data Objects

• All structured objects in Prolog are trees,
  represented in the program by terms.

(ab)(c-5) ((a,b),-(c,5))



c
5
a
b
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Data Objects
seq
par
seq(r1,r2)
par(r1,r2)
r1
r2
r1
r2
par
r1
par
par(r1,par(r2,r3))
r2
r3
par
r1
seq
par(r1,seq(par(r2,r3),r4))
par
r3
r2
r3
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Matching

• The most important operation on terms is
  matching.
• Given two terms, we say that they match if
• they are identical or
• the variables in both terms can be instantiated
  to objects in such a way that after the
  substitution of variables by those objects the
  terms become identical.
• For example, the following instantiation makes
  the terms date(D,M,1983) and date(D1,may,Y1)
  identical
• D is instantiated to D1
• M is instantiated to may
• Y1 is instantiated to 1983.

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Matching

• Matching is a process that takes as input two
  terms and checks whether they match.
• If the terms do not match we say that this
  process fails.
• If they do match then the process succeeds and it
  also instantiates the variables in both terms to
  such value that the terms become identical.

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Matching

• The request for the matching operation can be
  communicated to the Prolog system by using the
  operator .
• ?- date(D,M,1983)date(D1,may,Y1).

DD1 Mmay Y11983
D1 D11 Mmay Y11983
Dthird D1third Mmay Y11983
Matching in Prolog always results in the most
general instantiation.
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Matching
?- date(D,M,1983)date(D1,may,Y1),
date(D,M,1983)date(15,M,Y).
To satisfy the first goal DD1 Mmay Y11983
After having satisfied the second
goal D15 D115 Mmay Y11983 Y1983
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Matching

• The general rules to decide whether two terms, S
  and T, match
• If S and T are constants the S and T match only
  if they are the same object.
• IF S is a variable and T is anything, then they
  match, and S is instantiated to T. Conversely, if
  T is a variable then T is instantiated to S.
• If S and T are structures then they match only if
• S and T have the same principal functor, and
• all their corresponding components match

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Matching
triangle
point
A
2
2
triangle
X
point
point
4
y
2
Z
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Matching
vertical(seg(point(X,Y),point(X,Y1)). horizontal(s
eg(point(X,Y),point(X1,Y)).
?-vertical(seg(point(1,1),point(1,2)). yes ?-verti
cal(seg(point(1,1),point(2,Y)). no ?-horizontal(se
g(point(1,1),point(2,Y)). Y1 ?-vertical(seg(point
(2,3),P)). Ppoint(2,Y) ?-vertical(S),horizontal(S
). Sseg(point(X,Y),point(X,Y))
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Declarative Meaning of Prolog Programs

• Given a program and a goal G, the declarative
  meaning says
• A goal G is true (i.e., satisfiable, or logically
  follows from the program) if and only if
• there is a clause C in the program such that
• there is a clause instance I of C such that
• the head of I is identical to G, and
• all the goals in the body of I are true.

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Declarative Meaning of Prolog Programs

• In general, a question to the Prolog system is a
  list of goals separated by commas.
• A list of goals is true if all the goals in the
  list are true for the same instantiation of
  variables.
• A comma between goals thus denotes the
  conjunction of goals they all have to be true.
• The disjunction of goals any one of the goals in
  a disjunction has to be true.

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Procedural Meaning
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Procedural Meaning
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Procedural Meaning

• The procedural meaning specifies how Prolog
  answers question.

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Example Monkey and Banana

• The problem
• There is a monkey at the door into a room. In the
  middle of the room a banana is hanging from the
  ceiling. The monkey is hungry and and wants to
  get the banana, but he cannot stretch high enough
  from the floor. At the window of the room there
  is a box the monkey may use. The monkey can
  perform the following actions walk on the floor,
  climb the box, push the box around and grasp the
  banana if standing on the box directly under the
  banana. Can the monkey get the banana?

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Example Monkey and Banana

• Finding a representation of the problem
• We can think of the monkey world as always
  being in some state that can change in time.
• The current state is determined by the positions
  of the objects.
• For example, the initial state is determined by
• Monkey is at door.
• Monkey is on the floor.
• Box is at window.
• Monkey does not have banana.

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Example Monkey and Banana

• It is convenient to combine all these four pieces
  of information into one structured object.
• Let us choose the word state as the functor to
  hold the four components together.
• The initial state becomes
• state(atdoor,onflorr,atwindow,hasnot)

Vertical position of monkey
Position of box
Monkey has or has not banana
Horizontal position of monkey
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Example Monkey and Banana

• Formalize the rules of the game
• The goal is a situation in which the monkey has
  the banana.
• state(_, _, _, has)
• What are the allowed moves that change the world
  from one state to another?
• grasp banana, climb box, push box, walk around
• Such rules can be formalized in Prolog as a
  3-place relation named move move(State1, Move,
  State2)

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Example Monkey and Banana
canget(state(_, _, _, has)). canget(State1)-
move(State1,move State2), canget(State2).
move(state(middle,onbox,middle,hasnot),
grasp, state(middle,onbox,middle,has)).

move(state(P,onfloor,P,H), climb,
state(P,onbox,P,H)).
move(state(P1,onfloor,P1,H),
push(P1,P2), state(P2,onfloor,P2,H)).
State1
Statem
State2
move
canget
canget
has
move(state(P1,onfloor,B,H),
walk(P1,P2), state(P2,onfloor,B,H)).
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Example Monkey and Banana
state(atdoor,onfloor,arwindow,hasnot)
walk(atdoor,P2)
state(P2,onfloor,arwindow,hasnot)
push(P2,P2) P2atwindow
climb
backtrack
state(atwindow,onbox,arwindow,hasnot)
state(P2,onfloor,P2,hasnot)
No move possible
climb
state(P2,onbox,P2,hasnot)
grasp P2middle
state(middle,onbox,middle,has)
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Order of Clauses and Goals

• Danger of indefinite looping
• Program variation through reordering of clauses
  and goals