(Calculation with Lambda Expressions). For each of the following, write a lambda expression to calculate the function. You can use any of the functions I covered in class or in the slides, but you should not use recursion for any of the functions. For all questions the functions are for numbers represented as Church numerals

Note: There is a typo in the sum-of_squares definition. It should be 1² + 2² + 3² + ... + n². The ... are missing from the definition.

Problem 6 (Calculation with Lambda Expressions). For each of the following, write a lambda expression to calculate the function. You can use any of the functions I covered in class or in the slides, but you should not use recursion for any of the functions. For all questions the functions are for numbers represented as Church numerals. a. NAND-(Xa. 2b..... should calculate a NAND b defined as follows 1. tru NAND tru fls 2. tru NAND fls=tru 3. fis NAND tru-tru 4. fls NAND fls = tru b. sum_squares (n. should calculate 122 32+ n2 c. Fibonacci - (An. ......) should calculate the n'th Fibonacci number defined as follows Fibonacci 0 1 Fibonacci 1-1 Fibonacci (n+2)-(Fibonacci (n+1)) + (Fibonacci n) if n > 1 d. MOD3 = remainder of division by 3. Examples MOD3 52 MOD, 60 MOD,7 = 1 Problem 6 (Calculation with Lambda Expressions). For each of the following, write a lambda expression to calculate the function. You can use any of the functions I covered in class or in the slides, but you should not use recursion for any of the functions. For all questions the functions are for numbers represented as Church numerals. a. NAND-(Xa. 2b..... should calculate a NAND b defined as follows 1. tru NAND tru fls 2. tru NAND fls=tru 3. fis NAND tru-tru 4. fls NAND fls = tru b. sum_squares (n. should calculate 122 32+ n2 c. Fibonacci - (An. ......) should calculate the n'th Fibonacci number defined as follows Fibonacci 0 1 Fibonacci 1-1 Fibonacci (n+2)-(Fibonacci (n+1)) + (Fibonacci n) if n > 1 d. MOD3 = remainder of division by 3. Examples MOD3 52 MOD, 60 MOD,7 = 1