4' Using Structures: Example Programs

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4. Using Structures Example Programs
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Contents

• Retrieving structured information from a database
• Doing data abstraction
• Simulating a non-deterministic automaton
• Travel planning
• The eight queens problem

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Retrieving Structured Information from a DB

• This exercise develops the skill of representing
  and manipulating structured data objects.
• It also illustrates Prolog as a natural database
  query language.
• A database can be represented in Prolog as a set
  of facts.

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Retrieving Structured Information from a DB

• A database about families

family( person(tom,fox,date(7,may,1950),works(bb
c,15200)), person(ann,fox,date(9,may,1951),unemp
loyed), person(pat,fox,date(5,may,1973),unemplo
yed), person(jim,fox,date(5,may,1973),unemploye
d)).

• We can refer to all Armstrong families by
• family(person(_,armstrong,_,_),_,_)
• Refer to all families with three children
• family(_,_,_,_,_)

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Retrieving Structured Information from a DB

• To find all married women that have at least
  three children
• ?-family(_,person(Name,Surname,_,_),
• _,_,__).

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Retrieving Structured Information from a DB

• Provide a set of procedures that can serve as a
  utility to make the intersection with the
  database more comfortable.

husband(X)- family(X,_,_). wife(X)-
family(_,X,_). child(X)- family(_,_,Children),
member(X,Children). exist(X)-
husband(X) wife(X) child(X).
dateofbirth( person(_,_,Date,_),Date)). salary(
person(_,_,_Works(_,S),S)). salary(
person(_,_,_,unemployed),0).
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Retrieving Structured Information from a DB
Find the names of all the people in the
DB ?-exists(person(Name,Surname,_,_)). Find all
children born in 1981 ?-child(X),dateofbirth(X,da
te(_,_,1981)). Find all employed
wives ?-wife(person(Name,Surname,_,works(_,_))).
Find the names of unemployed people who were born
before 1963 ?-exists(person,N,S,date(_,_,Y),unem
ployed)), Ylt1963. Find people born before 1950
whose salary is less than 8000 ?-exists(P),dateo
fbirth(P,date(_,_,Year)), Yearlt1950,salary(P,S),
Slt8000.
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Retrieving Structured Information from a DB

• Total income of a family

total(,0). total(PersonList,Sum)-
salary(Person,S0, total(List,Rest), Sum is
SRest.
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Simulating an NDA
b
final(s3). trans(s1,a,a1). trans(s1,a,s2). trans(s
1,b,s1). trans(s2,b,s3). trans(s3,b,s4). silent(s2
,s4). silent(s3,s1).
a
s1
s2
null
a
b
null
s4
s3
b
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Simulating an NDA
?-accepts(s1,a,a,a,b). yes ?-accepts(S,a,b). S
s1 Ss3. ?-accepts(s1,X1,X2,X3). X1a X2a X3
b X1b X2a X3b no ?-String_,_,_,
accepts(s1,String). Stringa,a,b Stringb,a,b
no
accepts(State,)- final(State). accepts(State
,XRest)- trans(State,X,State1),
accepts(State1,Rest). accepts(State,String)-
silent(State,State1), accepts(State1,String).
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Travel Planning

• Develop an advisor program that will be able to
  answer useful questions, such as
• What days of the week is there a direct flight
  from London to Ljubljana?
• How can I get from Ljubljana to Edinburgh on
  Thursday?
• I have to visit Milan, Ljubljana and Zurich,
  starting from London on Tuesday and returning to
  London on Friday. In what sequence should I visit
  these cities so that I have no more than one
  flight each day of the tour?

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Travel Planning

• The program will be centered around a DB holding
  the flight information.
• timetable(Place1,Place2,List_of_flight)
• where List_of_flight is of the form

Departure_time/Arrival_time/Flight_number/List_of_
days
timetable(london,edinburgh,
940/1050/ba4733/alldays,
1740/2050/ba4833/mo,tu,we,th,fr,su).
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Travel Planning

• To find exact routes between two given cities on
  a given day of the week.
• route(Place1,Place2,Day,Route)
• Here Route is a sequence of flight satisfying
  the following criteria
• the start point of the route is Place1
• the end of the route is Place2
• all the flights are one the same day of the week
  Day
• all the flight in Route are in the timetable
  relation
• there is enough time for transfer between flights.

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Travel Planning

• The route is represented as a list of structured
  objects of the form
• From-toFlight_Numberdeparture_time
• Some auxiliary predicates
• flight(Place1,Place2,Day,Flight_num,Dep_time,Arr_t
  ime)
• deptime(Route,Time)
• transfer(time1,Time2)
• There is at least 40 minutes between Time1 and
  Time2.

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Travel Planning

• The problem of finding a route is similar to the
  simulation of the NDA
• States of NDA ? cities
• Transition between two states ? a flight between
  two cities
• transition ? timetable
• Finding a path ? finding a route.

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Travel Planning

• Defining the route relation
• Direct flight
• route(Place1,Place2,Day,Place1-Place2FnumDep)
  -
• flight(Place,Place2,Day,Fnum,Dep,Arr).
• Indirect flight
• route(P1,P2,Day,P1-P3Fnum1Dep1Route)-
• route(P3,P2,Day,Route),
• flight(P1,P3,Fnum1,Dep1,Arr1),
• deptime(Route,Dep2),
• transfer(Arr1,Dep2).

See Fig. 4.5, pp 111-112 for the complete program.
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Travel Planning

• Some example questions
• What days of the week is tehre a direct flight
  from London to Ljubljana?
• ?-flight(london,ljubljana,Day,_,_,_).
• Dayfr
• daysu
• no
• How can I get from Ljubljana to Edinburgh on
  Thursday?
• ?-route(ljubljana,edinburgh,th,R).
• Rljubljana-zurichyu3221130,
• zurich-londonsr8061610,
• london-edinburghba48221840

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The Eight Queens ProblemProgram 1

• The problem here is to place eight queens on the
  empty chessboard in such a way that no queen
  attacks any other queen.

8
7
6
5
4
3
2
1
1
8
2
3
4
5
6
7
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The Eight Queens Problem Program 1

• The problem is to find such as list
• X1/Y1,X2/Y2,X3/Y3,X4/Y4,X5/Y5,X6/Y6,X7/Y7,X8/Y8
  
• To make the search task easier, we fix the
  X-coordinates
• 1/Y1,2/Y2,3/Y3,4/Y4,5/Y5,6/Y6,7/Y7,8/Y8

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The Eight Queens Problem Program 1

• Case 1 The list of the queen is empty the empty
  list id certainly a solution because there is no
  attack.
• Case 2 The list of queen is non-empty it looks
  like X/YOthers. Then
• There must be no attack between the queens in the
  list Others i.e., Others must be a solution.
• X and Y must be integers between 1 and 8.
• A queen at square X/Y must not attack any of the
  queens in the list Others.

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The Eight Queens Problem Program 1
solution(). solution(X/YOthers)-
solution(Others), member(Y,1,2,3,4,5,6,7,8),
noattack(X/Y,Others). noattack(_,). noattack(
X/Y,X1/Y1Others)- Y\Y1,Y1-Y\X1-X,Y1-Y\
X-X1, noattack(X/Y,Others). template(1/Y1,2/Y
2,3/Y3,4/Y4,5/Y5, 6/Y6,7/Y7,8/Y8). ?-t
emplate(S),solution(S).
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The Eight Queens Problem Program 2

• X-coordinates can be omitted, retaining only
  Y-coordinates Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8.
• To prevent the horizontal attack, no two queens
  can be in the same row.
• Each solution is therefore represented by a
  permutation of the list 1,2,3,4,5,6,7,8.
• Such a permutation, S, is a solution if all
  queens are safe.

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The Eight Queens Problem Program 2
solution(S)- permutation(1,2,3,4,5,6,7,8,S),
safe(S). safe(). safe(QueenOthers)-
sate(Others), noattack(Queen,Others,1). noattac
k(_,,_). noattack(Y,Y1Ylist,Xdist)-
Y1-Y\Xdist,Y-Y1\Xdist, Dist1 is Xdist1,
noattack(Y,Ylist,Disy1).
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The Eight Queens Problem Program 2
Others
Queen
Xdist1
Xdist3