use SCHEME program, use R5RS

1. Function composition f g is an operation that takes two functions f and g and returns a function h such that h(x) = f(g(x)). [2 marks] Define a function (compose f g) that returns a composed function f g, such that the following usage works as shown. (define square (lambda(x)(* x x)))

    (define double (lambda(x)(+ x x))) ((compose square double) 3) -> 6^2 = 36 

2. [1 mark] Define a function (divisibleBy x) that takes an integer argument and returns a predicate function. The returned predicate should accept an integer y and return true if y is evenly divisible by x, false otherwise. E.g.:

    (define mod3 (divisibleBy 3)) (mod3 7) -> #f (mod3 9) -> #t 

3. [3 marks] Define a function called (newmap f) that takes a function f as argument and returns a function. The returned function should take a list as argument and map the function f over each element of the list. You should not use the built-in map function in your solution. E.g.

    (define double-mapper (newmap (lambda(x)(* x 2)))) (double-mapper '(1 2 3 4)) --> (2 4 6 8) (double-mapper '(10 20 30)) --> (20 40 60) 

4. [3 marks] Define a function called (newfilter f) that takes a function f as argument and returns a function. That returned function should take a list as argument and filter the list using f. You should not use the built-in filter function in your solution. E.g.

    (define evens-filter (newfilter (divisibleBy 2))) 

5. [2 marks] Using the functions you created above (and given the range function from lecture), fill in the blank () on the statement below so that the definition of the function myfunc produces the expected results as shown.

    (define myfunc ) (myfunc (range 1 20))  (16 64 144 256 400)