Description
Problem 1 [B] [1 mark, submit to PS2P01]
Write a Prolog predicate definition that counts the number of occurrences of an operator
inside an expression. For instance, the query:
?- count(a+b*c-(2+3*4)/(5*(2+a)+(b+c)^f((d-e)*(x-y))), *, C).
would count the number of occurrences of operator * in the expression given as the first
argument. The return value should be bound to the variable passed as the third argument. For
the query given above, the answer should be C=4.
Problem 2 [C] [2 marks, submit to PS2P02]
Write a Prolog program called primes, with two arguments N and L, that computes the list
of the first N prime numbers and binds L to it. The following is an example of correct
interaction with your predicate:
?- primes(5,L).
L = [2,3,5,7,11]
Problem 3 [C] [2 marks, submit to PS2P03]
Consider the language of arithmetic expressions with the operators +, -, *, and /, where
the operands are either numeric constants, or Prolog atoms denoting mathematical variables.
Thus, the Prolog term:
Submission: In IVLE, in the cs2104 workbin, you will find a folder called “Homework
submissions”. In that folder, there are currently 3 subfolders: PS2P01,…,PS2P03. The
last two digits of the folder name indicate the solution that is to be submitted into that folder: the
solution to Question 1 into PS2P01, and so on (that is, you need to submit 3 separate solutions to
3 questions). A solution should consist of a single text file that can be compiled, or loaded into the
interpreter of interest and executed. You should provide as much supplementary information about
your solution as you can, in the form of program comments.
9 marks
(x+2)*(a-x)
stands for the mathematical function f(x)=(x+2)(a-x), where a would be symbolic constant.
Write a Prolog program that computes the derivative of such an expression. For instance, the
query:
?- derive((x+2)*(a-x),x,D).
should derive the expression given as the first argument with respect to the variable given as
the second argument. The result should be placed in the variable given as the third argument.
For the query above, the answer should be
D = (1+0)*(a-x)+(x+2)*(0-1)
Do not perform any arithmetic simplification in your solution to this problem. Simplification
is the topic of the next problem.
Problem 4 [A] [4 marks, submit to PS2P04]
Write a Prolog program that performs the following arithmetic expression simplifications.
• Replaces Expr+0, Expr-0, 0+Expr with Expr.
• Replaces Expr*1, Expr/1, 1*Expr with Expr.
• Replaces -1*Expr, Expr*(-1), Expr/(-1) , 0-Expr with –Expr.
• Replaces Expr1+(-Expr2) with Expr –Expr2.
In the rules given above, Expr, Expr1, and Expr2 are generic expressions, of arbitrary
complexity.
For instance, the expression
(1+0)*(a-x)+(x+2)*(0-1)
should be simplified into:
a-x-(x+2)