Using Prolog as a CAS

Transcription

1 Using Prolog as a CAS Kharkiv Pedagogical University A. Stolyarevska July 2002

2 References 1) Robinson J.A. A machine-oriented logic based on the resolution principle. J. ACM, 12, ) Colmerauer A. Prolog-based theoriques et development actuals. TSI, 2, 4, ) Clocksin W.F., Mellish C.S. Programming in Prolog. Springer-Verlag, New York, 1985.

3 What is Prolog? Prolog stands for PROgramming in LOGic. Prolog programs are interpreted by an Prolog interpreter, Turbo-Prolog is such an interpreter. A Prolog program consists of facts and rules. A Prolog program describes the problem instead of the solution for the problem.

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5 An example of a small program (1) %This is a fact which states that john is a parent of bart parent(john,bart). %This is a fact which states that barbara is a parent of bart parent(barbara,bart). %This is a fact which states that john is a male male(john). %This is a fact which states that bart is a male male(bart). %This is a fact which states that barbara is a female female(barbara). To be continued

6 An example of a small program (2) %This is a rule which states that X is a father of Y if %X is a male and X is the parent of Y father(x,y) :- male(x),parent(x,y). %This is a rule which states that X is a mother of Y if %X is a female and X is the parent of Y mother(x,y) :- female(x),parent(x,y).

7 An example of a small program (3) In the example shown above you see several facts and rules. With these facts and rules in a Prolog database you can ask the Prolog interpreter several questions. In the table below you can see some questions translated to prolog predicates. If a question has multiple solutions then 'no' indicates that there are no other solutions

8 An example of a small program (4)

9 The Prolog system recognizes the type of a term object by its syntax. A variable always starts with an uppercase character and all other data types start with a lowercase character. There is a picture showing the hierarchy of types in Prolog:

10 Principal elements Terms - for representing data objects Facts & rules - for specifying relationships between terms Queries - for asking questions about how terms are related with respect to a collection of facts and rules

11 Glossary Variable - a name beginning with a capital letter that can be used to interpret the value of a certain object Relation - a name describing the manner in which a collection of objects belong together Atom - a relation, possibly involving objects or variables Domains specify the types of values objects may take in relation Fact - a relation between objects Sub-goal - a relation, possibly involving objects or variables, which Prolog must attempt to satisfy Rule - a relationship between a fact and a list of sub-goals which must be for that fact to be true

12 Structure of program A program consists of such sections domains predicates goal clauses Predicates and clauses sections are necessary Let s consider the simple program - welcome.pro

13 This the example of the famous "hello world" program %Welcome.pro predicates hello goal hello. clauses hello:-write("hello, World!"), nl.

14 Building the program Run the file Prolog.exe The main Prolog window includes system menu, four sub-windows: Editor Dialog Message Trace

15 predicates Our first example Ch03ex01.pro likes(symbol,symbol) clauses likes(ellen, tennis). likes(john, football). likes(tom, baseball). likes(eric, swimming). likes(mark, tennis). likes(bill, Activity):- likes(tom, Activity).

16 Examples of dialogue

17 Example: Dif.pro program Run! How to write the program similar to this? First of all, it is necessary to learn to work with numbers and lists. It is necessary to understand idea of recursion.

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19 Numbers Numbers are the most important group of symbols in computing. Prolog includes facilities for unifyng a variable or number with a numeric expression. Examples: factorial function power function Individual task: function e x

20 Iteration and recursion Let's consider definition given by Malpas for recursive procedure. Every recursive procedure should include: 1. Non-recursive phrase determines an initial kind of procedure, i.e. procedure at the moment of termination of recursion, 2. Recursive rule. First sub-aim, settling down in a body of this rule, develops new values of arguments. Further recursive sub-aim is placed, in which the new values of arguments are used.

21 Factorial function (Pascal language)

22 Factorial function (Prolog language)

23 /* Numbers likely to exceed are declared as reals! */ /* Recursive program to compute factorials. Ordinary recursion, not tail recursion. */ predicates factorial (integer, real) clauses factorial (1, 1):-!. factorial (X, FactX):- Y = X-1, factorial (Y, FactY), FactX = X*FactY. predicates factorial (integer, real) factorial_aux (integer, real, integer, real) clauses factorial (N, FactN):- factorial_aux (N, FactN, 1, 1). factorial_aux (N, FactN, I, P):- I < = N,!, NewP = P * I, NewI = I + 1, factorial_aux (N, FactN, NewI, NewP). factorial_aux (N, FactN, I, FactN):- I > N.

24 Between.pro /* iteration */ predicates between(integer,integer, clauses integer) between(i,j,i):-i<=j. between(i,j,k):- I<J,I1=I+1, between(i1,j,k). Compare them! Predicates %Recursion! count ( real ) Clauses count(number) :- write(number), nl, Goal New_number = Number + 1, count(new_number), write("this added call makes this clause non-tail recursive!"). count(1).

25 Function x n predicates power(real,integer,real) clauses power(_,0,1). power(x,n,xn):- N>0, M=N-1, power(x,m,xm), Xn=X*Xm. predicates power(real,integer,real) odd(integer) even(integer) clauses power(_,0,1). power(x,n,xn):-n>0, odd(n),m=n-1, power(x,m,xm), Xn=X*Xm. power(x,n,xn):-n>0, even(n),x2=x*x, M=N/2, power(x2,m,xn). even(x):-0=x mod 2. odd(x):-1=x mod 2.

26 Individual task: function e x e x = 1+ x + x 2 2! + x 3 3! +... In this program You can use relations power and factorial.

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28 Glossary List- a special sort of object consisting of a collection of elements enclosed in square brackets and separated by commas Head of a list - the first element of a list Tail of a list - the list that remains the first element of a given list (and its separating comma) are removed

29 Simple programs 1) This program determines the length of the list: length_of([], 0). length_of([_ T], L) :- length_of(t, TailLength), L = TailLength ) Finding a sum of the list of integers. sumlist ([I Is], Sum):- sumlist (Is, IsSum), Sum=I+IsSum. sumlist ([], 0). 3) Integer element X belongs to the list member(x, [X _]). member(x, [_ T]) :- member(x,t).

30 Exercises Define the next operations under lists: 1)conc - concatenation of two lists conc([],l,l). conc([x L1],L2,[X L3]):-conc(L1,L2,L3). 2) append - insert an element to the head of the list: append(x,l,[x L]). 3) delete - delete an element from the list domains ilist=integer* predicates delete(integer,ilist,ilist) clauses delete(x,[x Tail],Tail). delete(x,[y Tail],[Y Tail1]):- delete(x,tail,tail1).

31 Exercises 4) inner product domains ilist=integer* predicates inner_product(ilist,ilist,integer) inner_product(ilist,ilist,integer,integer) clauses inner_product(xs,ys,ip):- inner_product(xs,ys,0,ip). inner_product([x Xs],[Y Ys],Temp,IP):- Temp1=X*Y+Temp,inner_product(Xs,Ys,Temp1,IP). inner_product([],[],ip,ip).

32 Examples of questions for exercises 1-4 1) L1=[1,2],L2=[6,12],conc(L1,L2,L3) L3=[1,2,6,12] 2)append(1,[2,3,4],K) K=[1,2,3,4] 3) delete(3,[2,3,4,6],l) L=[2,4,6] 4) inner_product([1,2,3],[2,3,4],p) P=20

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34 Tools & Features inbuilding predicates unification backtracking declarative and procedural semantics Application fields artificial intelligence interfaces databases expert systems

35 Examples Graphics AI Interface

36 AI - FWGC.pro PROBLEM: A farmer with his goat, wolf and cabbage come to a river that they wish to cross. There is a boat, but it only has room for two, and the farmer is the only one that can row. If the goat and cabbage get in the boat at the same time, the cabbage gets eaten. Similarly, if the wolf and goat are together without the farmer, the goat is eaten. Devise a series of crossings of the river so that all concerned make it across safely.

37 FWGC.pro The state of the system is indicated by stating where the farmer, the goat the wolf and the cabbage are located. state( Farmer, Wolf, Goat, Cabbage ) The problem is that a state must only be visited once, and some states are illegal. This is checked by 'unsafe' and 'member'. The Predicate "go" can be called with a start state and a final state go( state(east,east,east,east), state(west,west,west,west) ).

38 References (in Ukraine language) Stolyarevska A.L. About experience of teaching of Prolog language in the course of informatics in pedagogical high school // Pedagogics and psychology. The collection of scientific works. Is. 14. Kharkov, Pp Stolyarevska A.L. Prolog Language and Programming of Expert Systems. The manual. - Kiev. 1997, 86 p.

39 Training Course: a course of informatics (computer science) at Kharkiv State Pedagogical University Students: of mathematics and physics faculty Topics: numbers, realization of recurrent and iterative algorithms (calculation of sums, fast degree, Fibonacci numbers), operation with polynomials, other tasks

40 Conclusion PROLOG is a method of declarative programming (PROgramming in LOGic) Students use Prolog programming language while processing knowledge and data represented as symbolical structures stolyare@yahoo.com Thank You!