4. using structures: example programs

4. Using Structures: 4. Using Structures: Example ProgramsExample Programs

Contents

Retrieving structured information from a database

Doing data abstraction Simulating a non-deterministic

automaton Travel planning The eight queens problem

Retrieving Structured Information from a DBRetrieving 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.


A database about families:

We can refer to all Armstrong families by:family(person(_,armstrong,_,_),_,_)

Refer to all families with three children:family(_,_,[_,_,_])

family( person(tom,fox,date(7,may,1950),works(bbc,15200)), person(ann,fox,date(9,may,1951),unemployed), [person(pat,fox,date(5,may,1973),unemployed), person(jim,fox,date(5,may,1973),unemployed)]).


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

[_,_,_|_]).


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).

Retrieving Structured Information from a DBRetrieving Structured Information from a DBFind the names of all the people in the DB:?-exists(person(Name,Surname,_,_)).Find all children born in 1981:?-child(X),dateofbirth(X,date(_,_,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),unemployed)), Y<1963.Find people born before 1950 whose salary is less than 8000:?-exists(P),dateofbirth(P,date(_,_,Year)), Year<1950,salary(P,S),S<8000.


Total income of a family:

total([],0).total([Person|List],Sum):- salary(Person,S0, total(List,Rest), Sum is S+Rest.

Simulating an NDASimulating an NDA

s1 s2

s4 s3

b

a

a

b

b

null

null

final(s3).trans(s1,a,a1).trans(s1,a,s2).trans(s1,b,s1).trans(s2,b,s3).trans(s3,b,s4).silent(s2,s4).silent(s3,s1).

Simulating an NDASimulating an NDA

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

?-accepts(s1,[a,a,a,b]).yes?-accepts(S,[a,b]).S=s1;S=s3.?-accepts(s1,[X1,X2,X3]).X1=aX2=aX3=b;X1=bX2=aX3=b;no?-String=[_,_,_], accepts(s1,String).String=[a,a,b];String=[b,a,b];no

Travel PlanningTravel 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 L

ondon to Ljubljana?– How can I get from Ljubljana to Edinburgh on Thurs

day?– I have to visit Milan, Ljubljana and Zurich, starting fr

om 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?


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, [9:40/10:50/ba4733/alldays, 17:40/20:50/ba4833/[mo,tu,we,th,fr,su]]).


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.


The route is represented as a list of structured objects of the form:

From-to:Flight_Number:departure_time Some auxiliary predicates:

– flight(Place1,Place2,Day,Flight_num,Dep_time,Arr_time)– deptime(Route,Time)– transfer(time1,Time2)

There is at least 40 minutes between Time1 and Time2.


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.


Defining the route relation:– Direct flight

route(Place1,Place2,Day,[Place1-Place2:Fnum:Dep]):- flight(Place,Place2,Day,Fnum,Dep,Arr).– Indirect flight

route(P1,P2,Day,[P1-P3:Fnum1:Dep1|Route]):- 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.

Travel PlanningTravel Planning Some example questions:

– What days of the week is tehre a direct flight from London to Ljubljana??-flight(london,ljubljana,Day,_,_,_).

Day=fr; day=su; no– How can I get from Ljubljana to Edinburgh on Thursday?

?-route(ljubljana,edinburgh,th,R). R=[ljubljana-zurich:yu322:11:30, zurich-london:sr806:16:10, london-edinburgh:ba4822:18:40]

The Eight Queens The Eight Queens Problem:Program 1Problem:Program 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

43

2

11 2 3 4 5 6 7 8

The Eight Queens Problem: Program The Eight Queens Problem: Program 11

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]


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/Y|Others]. 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.


solution([]).solution([X/Y|Others]):- solution(Others), member(Y,[1,2,3,4,5,6,7,8]), noattack(X/Y,Others).noattack(_,[]).noattack(X/Y,[X1/Y1|Others]):- Y=\=Y1,Y1-Y=\=X1-X,Y1-Y=\=X-X1, noattack(X/Y,Others).template([1/Y1,2/Y2,3/Y3,4/Y4,5/Y5, 6/Y6,7/Y7,8/Y8]).

?-template(S),solution(S).


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.


solution(S):- permutation([1,2,3,4,5,6,7,8],S), safe(S).safe([]).safe([Queen|Others]):- sate(Others), noattack(Queen,Others,1).noattack(_,[],_).noattack(Y,[Y1|Ylist],Xdist):- Y1-Y=\=Xdist,Y-Y1=\=Xdist, Dist1 is Xdist+1, noattack(Y,Ylist,Disy1).


QueenOthers

Xdist=1

Xdist=3

4. using structures: example programs

Documents

flight information

s rest

structured data objects

sequence of flight

family persontom

names of unemployed

direct flight

given day