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Lecture2.md

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Lecture2

LECTURE1 REVISITED

Issue #1

Write the following sentences in prolog syntax:

  1. ahmad likes everything omar likes.
  2. human is mammal.
  3. ahmad hits the ball with his rod.
  4. if somebody studies he will succeed.
  5. X hates everybody who loves dogs or hates cats.
  6. X hates everybody who loves dogs and hates cats.
  7. X loves everybody who has money and is pretty.
  8. Who ate my pizza?

Data types

  1. Atoms: ahmad, true.

  2. Numbers: 1.

  3. Variables: Ahmad.

  4. Predicates: line(point(X1,Y1),point(X2,Z2)).

Unification

Query Unified?
eats(fred, tomatoes) = eats(Whom, What). yes: Whom = fred and What = tomatoes .
eats(fred, Food) = eats(Person, jim). yes: Person = fred and Food = jim .
cd(29, beatles, sgt_pepper) = cd(A, B, help). no: sgt_pepper and help do not unify .
f(X, a) = f(a, X). yes: X = a .
likes(jane, X) = likes(X, jim). no: X can not be bound to both jane and jim .
f(X, Y) = f(P, P). yes: X = P and Y = P.
f(foo, L) = f(A1, A1). yes: A1 = foo and A1 = L . Hence L = foo .
k(s(g), t(k)) = k(X, t(Y)). yes: X = s(g) and Y = k .
k(s(g), Y) = k(X, t(k)). yes: X = s(g) and Y = t(k) .
[a, b, c] = X. yes: X = [a, b, c] .
[a, b, c] = [X, Y, Z]. yes: X = a , Y = b and Z = c .
3 = 3. yes.
3 = 2 + 1. no.
3 =:= 2 + 1. yes, so = is a unification operator whereas =:= is the numeric quality operator.

Assessment

  1. Validate that some line is vertical.
  2. Validate that some line is horizontal.
vertical(line(point(X,Y),point(X,Z))).
horizontal(line(point(X,Y),point(Z,Y))).

/*
?- vertical(line(point(0,0), point(0,10))).
?- vertical(line(point(0,0), point(10,0))).
?- horizontal(line(point(0,0), point(0,10))).
?- horizontal(line(point(0,0), point(10,0))).
?- vertical(line(point(0,0), point(10,10))).
?- horizontal(line(point(0,0), point(10,10))).
*/

Arithmetic

?- 8  is  6+2.
?- 12  is  6*2.
?- 4  is  6-2.
?- -2  is  6-8.
?- 3  is  6/2.
?- 3  is  7/2.
?- 1  is  mod(7,2).
?- X  is  6+2.
?- R  is  mod(7,2).

Keep in mind that you can use the template/rule for either exploration or validation.

  • exploration: R is mod(7,2).

  • validation: 1 is mod(7,2).

Assessment

Write some rule that takes a number, add 3 to it, double it and output the result.

add_3_and_double(X,Y) :-  Y is (X+3) * 2.

% ?- add_3_and_double(2,X).

Comparing Integers

?- 2 < 4.
?- 2 =< 4.
?- 4 =< 4.
?- 4 =:= 4.
?- 4 =\= 5.
?- 4 =\= 4.
?- 4 >= 4.
?- 4 > 2.
?- 2 < 4+1.
?- 2+1 < 4.
?- 2+1 < 3+2.

Remember:

 ?- 4 = 4. % true, not because 4 equals 4, but because string 4 matches with string 4, like a = a.
 ?- 2+2 = 4. % so this will return false.
 ?- 2+2 =:= 4. % this is a valid arithmetic.

Recursion

  1. Stopping Criteria
    rec_rule(0, 1):- true.

  1. Recursive Call (mentioning)

    2.1 Direct

        rec_rule(X,Y):- some_rule(Z,Y), rec_rule(X,Z).

    2.2 Indirect

        rec_rule(X,Y):- some_rule(Z,Y).
    some_rule(X, Y):- some_rule2(X), some_rule3(X), some_rule4(Y), rec_rule(X, Y).

Example:

parent(abo_abo_abo_ahmad, abo_abo_ahmad).
parent(abo_abo_ahmad, abo_ahmad).
parent(abo_ahmad, ahmad).

ancestor(X,Y):- parent(X,Y). % Stopping criteria
ancestor(X,Y):- parent(Z,Y), ancestor(X,Z). % recursive call

% ?- ancestor(abo_abo_abo_ahmad, ahmad).

Exercises

What is the output?

?-  X  =  3,  X  <  4.
?-  X  =  b,  X  <  4.

add/3

add(X,Y, Z):- Z is X + Y.

abs/2

abs(X, Y):- X >= 0, Y is X; Y is -X.

my_print/1, Prints the numbers from 0 to N

my_print(0) :- write(0).
my_print(N) :- N1 is N - 1, my_print(N1), write(N), nl. % this will print the numbers from 0 to N
/*
    but if the recursive call executed after the write instruction, then the numbers will be printed in descending order (from N to 0)
    my_print(N) :- write(N), nl, N1 is N - 1و my_print(N1). % this will print the numbers from N to 0
*/

sum/2

% sum the numbers from 0 to N-1 then add N to the result.
sum(0, 0).
sum(N, Res):-N > 0, N1 is N-1, sum(N1, Res1), Res is Res1 + N.

mult/2, Do X * Y recursivly then put the result in Z

mult(X,0, 0).
mult(0,X, 0).
mult(X,Y, Z):- X > 0, Y > 0,  Y1 is Y-1, mult(X, Y1, Z1), Z is Z1 + X.

factorial/2

factorial(0,1).
factorial(X,Y) :- X>0, X1 is X -1, factorial(X1,Y1), Y is Y1*X.

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