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Prolog CSE2303 Formal Methods I Lecture 20

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Overview Prolog Database List Arithmetic Implementing NFA Towers of Hanoi SWI-Prolog

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Prolog PROgramming in LOGic Used for solving problems between objects and the relationships between objects. A logic program is a finite set of program clauses. Programs clauses are: –Facts. –Rules.

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Parent Relationship We represent the statement: “bob is a parent of pat” as parent(bob, pat). The compound statement “If X is a parent of Z, then X is a predecessor of Z” is represented as: predecessor(X, Z) :- parent(X,Z).

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database parent(bob, ann). parent(bob, pat). parent(pat, jim). predecessor(X, Z) :- parent(X,Z). predecessor(X, Z) :- parent(X,Y), predecessor(Y, Z). Facts Rules Constants Variables

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Using Prolog To read in the file database. Type: [database]. To ask if bob is the parent of pat. Type: parent(bob, pat). To ask who is the predecessors of jim. Type: predecessor(X, jim). To quit. Type: ctrl-D

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Example Session ?- [database]. ?- parent(bob, pat). yes ?- parent(bob, jim). no ?- predecessor(X, jim). X = pat ; X = bob ; no Nothing matches no prompt Ask for another solution

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Program Clauses Rule –The head and the body are nonempty. –The body is the conditional part. –The head is the conclusion. Fact –The body is empty, and is written as: A.A. A :- B 1, …, B n. Head Body End of clause marker “ if ”

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Interpretations Logic X 1,..X m ((B 1 … B n ) A) Procedural –To execute A, first execute B 1, then execute B 2,... Process –A, B 1, …, B n are considered processes. –Shared variables are communication channels A :- B 1, …, B n.

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Syntax Constants –Names: which always begin with a lowercase letter. likes mary parent predecessor –Numbers: Variables –Always begin with either an capital letter or an underline character. X Answer _ _Input Structures –Compound terms. owns(john, book) parent(X, parent(Y, jim))

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Lists A list t 1,…, t n can be represented as: [t 1,…, t n ] For example: [a,b,c,d] Also represented as: [a | b,c,d] The empty list is [ ] Head of the list Tail of the list

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Membership Problem Write a Prolog program which finds the members of a list.

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Membership Relationships X is always a member of a list whose head is X. member(X, [X | T]). If X is a member of a list T, then X is a member of a list whose tail is T. member(X, [H | T]) :- member(X, T).

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Member member(X, [X | T]). member(X, [H | T]) :- member(X, T). ?- member(john, [paul, john]). yes ?- member(X, [paul, john]). X = paul ; X = john ; no

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Arithmetic Operators –X + Y, -X, X-Y, X*Y, X/Y, … Functions –abs(X), max(X, Y), sin(X), … Relations –X Y, X =< Y, X =:= Y, X =\= Y,.. –is “Evaluates arithmetic expression” ?- X is 2* X = 10 yes

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Factorial Relationships The factorial of 0 is 1. factorial(0,F) :- F is 1. If N > 0, and N1 is N – 1, and the factorial of N1 is F1, and F is N*F1, then the factorial of N is F. factorial(N, F) :- N > 0, N1 is N-1, factorial(N1, F1), F is N*F1.

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Factorial factorial(0, F) :- F is 1. factorial(N, F) :- N > 0, N1 is N-1, factorial(N1, F1), F is N*F1. ?- factorial(3, F). F = 6 yes

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Size Relationships The size of an empty list is 0. size([ ], 0). If the size of the list T is N1 and N is N1+1, then the size of the list with tail T is N. size([H | T], N) :- size(T, N1), N is N1+1.

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Size size([ ], 0). size([H | T], N) :- size(T, N1), N is N1+1. ?- size([a,b,c], N). N = 3 yes Note: There is a predefined funtion in SWI-Prolog called length

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accept(W) :- start(S), path(S, W). path(S, [ ]) :- final(S). path(S, [H | T]) :- arc(S, H, N), path(N, T). start(1). final(3). arc(1, a, 1). arc(1, b, 2). arc(1, b, 3). arc(2, b, 3). arc(3, a, 3). a a b b b ?- [nfa]. ?- accept([a, b, a]). yes NFA

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Towers of Hanoi The object is to move the disks, one at a time, from the left peg to the right peg. You are allowed to use the middle peg. At no stage are you allowed to place a bigger disk on top of a smaller one.

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Solution move(1, X, Y, Z) :- write(’ Move top disk from ’), write(X), write(’ to ’), write(Z), nl. move(N, X, Y, Z) :- N > 1, M is N-1, move(M, X, Z, Y), move(1, X, Y, Z), move(M, Y, X, Z). ?- move(3, left, middle, right).

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More Information Courseware web site. Links to: –Prolog tutorial, SWI-Prolog, etc. Books: –“The Art of Prolog: Advanced Programming Techniques”, by L.Sterling and E. Shapiro. –“Prolog Programming for Artificial Intelligence”, by I. Bratko. –“Programming in Prolog”, by W. Clocksin and D. Mellish

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