A Third Look At Prolog
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 1
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Understanding Prolog: Instantiation, Equalities, and Search, Slides of Advanced Computer Programming
An excerpt from 'modern programming languages' 2nd edition, focusing on prolog. It covers topics such as instantiation, real values and integers, comparisons, equalities, and the use of predicates like is, abs, sqrt, gcd, and findall. The text also includes examples of prolog code for sum, fact, and subseq, as well as an explanation of how prolog handles search and problem space solutions.
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A Third Look At Prolog
Chapter Twenty-Two Modern Programming Languages, 2nd ed. (^) Docsity.com 1
Outline
ļ® Numeric computation in Prolog
ļ® Problem space search
ā Knapsack
ā 8-queens
ļ® Farewell to Prolog
Chapter Twenty-Two Modern Programming Languages, 2nd ed. (^) Docsity.com 2
Evaluating Expressions
ļ® The predefined predicate is can be used to
evaluate a term that is a numeric expression
ļ® is(X,Y) evaluates the term Y and unifies
X with the resulting atom
ļ® It is usually used as an operator
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 4
?- X is 1+2*3.
X = 7.
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Instantiation Is Required
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 5
?- Y=X+2, X=1.
Y = 1+2,
X = 1.
?- Y is X+2, X=1. ERROR: is/2: Arguments are not sufficiently instantiated ?- X=1, Y is X+2. X = 1, Y = 3.
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Real Values And Integers
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 7
?- X is 1/2. X = 0.5.
?- X is 1.0/2.0. X = 0.5.
?- X is 2/1. X = 2.
?- X is 2.0/1.0. X = 2.0.
There are two numeric types:
integer and real.
Most of the evaluable
predicates are overloaded for
all combinations.
Prolog is dynamically typed;
the types are used at runtime
to resolve the overloading.
But note that the goal 2=2.
would fail.
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Comparisons
ļ® Numeric comparison operators:
<, >, =<, >=, =:=, ==
ļ® To solve a numeric comparison goal, Prolog
evaluates both sides and compares the
results numerically
ļ® So both sides must be fully instantiated
Chapter Twenty-Two Modern Programming Languages, 2nd ed. (^) Docsity.com 8
Equalities In Prolog
ļ® We have used three different but related
equality operators:
ā X is Y evaluates Y and unifies the result with X:
3 is 1+2 succeeds, but 1+2 is 3 fails
ā X = Y unifies X and Y, with no evaluation: both
3 = 1+2 and 1+2 = 3 fail
ā X =:= Y evaluates both and compares: both
3 =:= 1+2 and 1+2 =:= 3 succeed
(and so does 1 =:= 1.0)
ļ® Any evaluated term must be fully instantiated
Chapter Twenty-Two Modern Programming Languages, 2nd ed. (^) Docsity.com 10
Example: mylength
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 11
mylength([],0). mylength([_|Tail], Len) :- mylength(Tail, TailLen), Len is TailLen + 1.
?- mylength([a,b,c],X). X = 3.
?- mylength(X,3). X = [_G266, _G269, _G272].
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Example: sum
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 13
sum([],0). sum([Head|Tail],X) :- sum(Tail,TailSum), X is Head + TailSum.
?- sum([1,2,3],X). X = 6.
?- sum([1,2.5,3],X). X = 6.5.
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Example: gcd
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 14
gcd(X,Y,Z) :- X =:= Y, Z is X. gcd(X,Y,Denom) :- X < Y, NewY is Y - X, gcd(X,NewY,Denom). gcd(X,Y,Denom) :- X > Y, NewX is X - Y, gcd(NewX,Y,Denom).
Note: not just
gcd(X,X,X)
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Cutting Wasted Backtracking
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 16
gcd(X,Y,Z) :- X =:= Y, Z is X, !. gcd(X,Y,Denom) :- X < Y, NewY is Y - X, gcd(X,NewY,Denom), !. gcd(X,Y,Denom) :- X > Y, NewX is X - Y, gcd(NewX,Y,Denom).
If this rule succeeds, thereās
no point in trying the others
Same here.
With those cuts, this test is
unnecessary (but weāll leave
it there).
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Example: fact
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 17
fact(X,1) :- X =:= 1, !. fact(X,Fact) :- X > 1, NewX is X - 1, fact(NewX,NF), Fact is X * NF.
?- fact(5,X). X = 120.
?- fact(20,X). X = 2432902008176640000.
?- fact(-2,X). false.
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Problem Space Search
ļ® Prologās strength is (obviously) not numeric
computation
ļ® The kinds of problems it does best on are
those that involve problem space search
ā You give a logical definition of the solution
ā Then let Prolog find it
Chapter Twenty-Two Modern Programming Languages, 2nd ed. (^) Docsity.com 19
The Knapsack Problem
ļ® You are packing for a camping trip
ļ® Your pantry contains these items:
ļ® Your knapsack holds 4 kg.
ļ® What choice <= 4 kg. maximizes calories?
Chapter Twenty-Two Modern Programming Languages, 2nd ed. 20
Item Weight in kilograms Calories bread 4 9200 pasta 2 4600 peanut butter 1 6700 baby food 3 6900
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