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Chapter 2 Syntax and meaning of prolog programs

Chapter 2 Syntax and meaning of prolog programs. Part 1. Outline. Data objects Matching Meaning of prolog programming. Quick review . Objects Relationship Facts Rules Questions . Data objects. Data objects. Constants : start with a lower-case letter

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Chapter 2 Syntax and meaning of prolog programs

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  1. Chapter 2Syntax and meaning of prolog programs Part 1

  2. Outline • Data objects • Matching • Meaning of prolog programming.

  3. Quick review • Objects • Relationship • Facts • Rules • Questions

  4. Data objects

  5. Data objects • Constants : start with a lower-case letter • Variable: start with an upper-case letter.

  6. Data objects - constants • Atoms • String of letters, digits and the underscore character ‘_’ starting with a lower-case letter anna x25 x_34a x___y3 miss_Jones • String of special characters <----> ===> … ::= But be careful ! Somestrings already havea predefined meaning (e.g. :- ) • String of characters enclosed in single quotes ‘Tom’ ‘tom’

  7. Data objects - constants • Numbers • Integer and real numbers. • Real number are not heavily used in prolog program. (Prolog is for symbolic, non-numeric computation). • Example of integer and real numbers: • Integer numbers e.g. 1 133 0 -97 • Real numbers e.g. 3.14 -0.0035 100.2

  8. Data objects - variables • Variables Variables are strings of letters, digits and underscores characters, starting with upper-case letter or an underscore E.g. X , Result , Object2 • Anonymous variables When a variable appear in a clause just once. haschlid(X) : - parent(X ,_). somebody_has_child :- parent(_,_).

  9. Lexical scope. • The lexical scope of atom names is the whole program. • The lexical scope of variable names is one clauseexcept the anonymous variable; it signifies new variable each time it occurs even in the same clause

  10. Data objects - structures • Structures are objects that have several components which can be structured themselves. date (1, may, 2001) • To represent any day in may; day is variable date (Day, may, 2001) functor arguments

  11. Data objects - structures • All structured objects can be presented as tree: date 1 may 2001

  12. Example (1) • How to structures the following expression? (a + b) * (c - 5) • Using symbols : * , + , and – as functors: • *(,) • *( +(a,b) ,). • *(+(a,b), -(c,5) ) * - + c 5 a b

  13. Class exercise (1) • Structure the following geometric shapes: • 2d point. • Line segment • Triangle.

  14. Matching • The most important operation on terms is Matching. • Given two terms, we say that they match when: • They are identical, or • The variables in both terms can be instantiated to objects such a way that after the substitution of variables by these objects the terms become identical.

  15. Matching - example • date(D, M, 2001) and date(D1, may, Y1) D= D1 M= may. Y1=2001 • date(D, M, 2001) and date(D1, M1, 1444) Not matched • date(X, Y, Z) and point(X, Y, Z) Not matched.

  16. Matching • Matching is a process that takes as inputs two terms and check whether they match. If the terms do not match, we say this process fails. If they match, the process succeeds. • To request Prolog matching operation, we use ‘=‘ : ?- date(D, M, 2001)=date(D1, may, Y1). D=D1 M=may Y1=2001 • Matchingin Prolog always results in the most general instantiation.

  17. Example (2) • ?- date(D, M, 2001)=date(D1, may, Y1), date(D, M, 2001)=date(15, M, Y). To satisfy the first goal : date(D, M, 2001)=date(D1, may, Y1). , prolog instantiation will be: D=D1 M = may Y1= 2001 After specifying the second goal, the instantiation become more specific as follow: D= 15 D1 = 13 M = may Y1= 2001

  18. Example (2) triangle triangle point point X point A point 1 1 2 3 4 2 Z Y The result instantiation is: X = point(1,1) A = point(4,Y) Z =3.

  19. Example (3) • Declare vertical and horizontal relations vertical (seg(point(X,_), point(X,_))). horizontal (seg(point(_,Y), point(_,Y))). Formulate the following questions and find Prolog answers: • Is the segment (1,1), (1,4) is vertical? • Is the segment (1,1), (2,Y) vertical? • Is the segment (1,1), (2,Y) horizontal? • Are there any vertical segment that start at point(2,3)? • Is there a segment that is both vertical and horizontal?

  20. Example (3) (cont.) • Is the segment (1,1), (1,4) is vertical? ?- vertical (seg(point(1,1), point(1,4))). Yes • Are there any vertical segment that start at point(2,3)? -? Vertical(seg(point(2,3),P). P= point(2,Y) • Is there a segment that is both vertical and horizontal? -?vertical (S), horizontal (S) S= segment(point(X,Y),point(X,Y).

  21. Class exercise (1) • Is the segment (1,1), (2,Y) vertical? • Is the segment (1,1), (2,Y) horizontal

  22. Class exercise (1) (cont.) • Is the segment (1,1), (2,Y) vertical? ?- vertical (seg(point(1,1), point(2,Y))). No • Is the segment (1,1), (2,Y) horizontal -?horizontal (seg(point(1,1), point(2,Y))). Y=1

  23. Meaning of Prolog programs

  24. Meaning of Prolog programs • Consider the clause: P :- Q, R. • Declarative readings: • P is true if Q and R is true • From Q and R follows P • Procedural readings: • To solve problem P, first solve the subproblem Q, and then the subproblem R. • To satisfy P, first satisfy Q and then R.

  25. Meaning of Prolog programs • Consider the clause: P :- Q; R. • ; means OR • Same as the following two clauses together: P :- Q.P :- R. • The comma binds stronger than the semicolon. • P :- Q,R;S,T,U. is understood as: • P:- (Q,R);(S,T,U). and means the same as the clauses: • P :- Q,R. • P :- S,T,U.

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