Prolog

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Prolog

• The language of logic

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History

• Kowalski late 60s Logician who showed logical
  proof can support computation.
• Colmerauer early 70s Developed early version of
  Prolog for natural language processing.
• Warren mid 70s First version of Prolog that was
  efficient.

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Characteristics

• Prolog approximates first-order logic.
• Every program is a set of Horn clauses.
• Inference is by resolution.
• Search is by backtracking with unification.
• Basic data structure is term or tree.
• Variables are unknowns not locations.
• Prolog does not distinguish between inputs and
  outputs. It solves relations/predicates.

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Strawberry Prolog

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Example

• Facts ()
• likes(john,mary).
• likes(john,X). Variables begin with capital
• Queries
• ?- likes(X,Y).
• Xjohn, yMary. hit for more
• ?- likes(X,X).
• Xjohn.

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Example

• Rules
• likes(john,X) - likes(X,wine). - if
• likes(john,X)- female(X), likes(X,john).
• Some Facts
• likes(bill,wine). female(mary). female(sue).
• Query ? - likes(john,Y).
• Y bill
• no.

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Family

• father(a,b).
• father(e,d).
• mother(c,b).
• mother(d,f).
• parent(X,Y) - father(X,Y).
• parent(X,Y) - mother(X,Y).
• grandfather(X,Y)-father(X,Z),parent(Z,Y).

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Finding max in a list
max(X, XT)- geq(X,T). max(X, YT)- Y lt X,
max(X, T). geq(X, Y)- Y lt X. geq(X, HT)-
H lt X, geq(X, T). ?-geq(11, 8, 9, 11,
12). no ?-max(24, 23, 8, 24, 21, 14).
Yes ?-max(24, 23, 8, 24, 21, 14). Yes.
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A different program for max
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Merge sorting in Prolog
merge(X,,X). merge(, X, X). merge(XY,PQ,
XZ)- X lt P, merge(Y,PQ,Z). merge(XY,P
Q,PZ)- P lt X, merge(XY,Q,Z).
?-merge(3, 17, 11, 12, 20, 26, X), write(X),
nl.
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Merge sorting in Prolog split(X,Y, X,
Y). split(X,,X). split(X,YZ,XX1,
YX2)-split(Z, X1, X2). ?-split(12, 6, 7,
11, 9, X, Y), write(X), nl, write(Y), nl.

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Merge sorting in Prolog msort(,). msort(X,
X). msort(X,Y)- split(X, X1, X2),
msort(X1,Y1), msort(X2, Y2),
merge(Y1, Y2, Y). ?-msort(6, 12, 20, 7, 3, 21,
36, 14, -3, X), write(X), nl.
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Example involving an arithmetic operation Write
a Prolog program to compute the prefix sums of
elements in an array. Example ?-prefix_sum(1,
3, -4, 8, 2, X), write(X), nl. Output Compilin
g the file F\fall09\cs480fa09\programs\prefix_su
m 0 errors, 0 warnings. 1,4,0,8,10 Yes.
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Prolog function to implement prefix sum First
we create a function add that adds X to each
member of a list add(X,Y,Z)- Z is X
Y. add(X, HT, PQ)- P is X H,
add(X,T,Q). some test cases ?-add(3, -2, 12,
8, 3, X), write(X), nl. ?-add(3, -2, X),
write(X), nl.
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Prolog function to implement prefix sum We can
use add to write prefix_sum prefix_sum(X,X).
prefix_sum(HT, HT1)- prefix_sum(T, T2),
add(H, T2, T1), nl. ?-prefix_sum(2, 1, X),
write(X), nl. ?-prefix_sum(1, 3, -4, 8, 2, X),
write(X), nl.
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Permutation Insert

• Write a program to generate all the permutations
  of a given sequence.
• insert(X,L, XL).
• insert(X,HT,HT1)- insert(X,T,T1).
• ?-insert(1, 3, 2, 4, X), write(X), nl, fail.
• perm(,).
• perm(HT,P)-perm(T,T1),insert(H,T1,P).
• ?-perm(1, 2, 3, 4, X), write(X), nl, fail.