Question

Write a Racket function "combine" that takes two functions, f and g, as parameters and evaluates to a new function. Both f and g will be functions that take one parameter and evaluate to some result. The returned function should be the composition of the two functions with f applied first and g applied to f's result.

For example (combine add1 sub1) should evaluate to a function equivalent to (define (h x) (sub1 (add1 x))). You will need to use a lambda function to achieve your result. Essentially you want (combine f g) to evealuate to a lambda function with f and g embedded inside.

You can test your combine with invications such as ((combine add1 add1) 1), which should evaluate to 3 since the anonymous function returned by combine is being applied to 1.

Note: This is an example of a "function closure". f and g are defined in the scope of combine, but the lambda embeds a copy of them in the lambda function that can be used outside of combine's scope. When creating a lambda function in Racket, anything in the enclosing scope can be captured in this way so that the lambda is functional outside of its defining scope.

Answer 1

racket code:

; combibe function that returns a function
; which is composition of two input functions
(define (combine f g)
; returning lambda function which is f applied first and g applied to f's result
(lambda (x) (g (f x)))
)

; Testing combine function for different functions

(define (square x) (* x x))

(writeln ((combine add1 add1) 1))
(writeln ((combine sub1 add1) 1))
; takes square first and then add1
(writeln ((combine square add1) 2))

Testing output: