Question

LISP lambda calculate， expression

3) Consider reducing the following λ-expression to its normal form. Show the sequence of normal order reductions the sequence of applicative order reductions. · · 4) Consider the following function: Fx) ifx-0) then return 0 else return x+1 a) Express F as a lambda calculus expression b) Evaluate F(0) as a lambda expressiorn c) Evaluate F(1) as a lambda expression HINT: Use the representations introduces in Section 10. 5) Describe a function to compute the sum of the cubes of the first n positive numbers, using the abstract programming language introduced in section 11

Answer 1

5) SUM OF CUBES OF FIRST N POSITIVE NNUMBERS

Fist of all know that java , c++ and other where you hide the details of operation from user is the absttract proggramming language.

so heres the program for cube addition in jva as a function

import java.util.*;

import java.lang.*;

public class CubeSum {

/* Returns the sum of series */

public static int cubeSum(int n)

{

int x;

if (n % 2 == 0)

x = (n/2) * (n+1);

else

x = ((n + 1) / 2) * n;

return x * x;

}

// Main function for calling of cubeSum()

public static void main(String[] args)

{

int n;

Scanner reader = new Scanner(System.in); // Reading from System.in

System.out.println("Enter a number: ");

n = reader.nextInt(); // Scans the next token of the input as an int.

//once finished

reader.close();

  

int sum=cubeSum(n);

System.out.println("Sum of cubeis of first "+n+" numbers is "+sum);

}

}