Accessing to an input in higher order procedures in scheme

Question

I need to understand how can I access to an input of a function which is given to another function as an input.

For example; I have a function called f which simply does (define f (lambda (x) (if (null? x) #t (car x)))) this. I need to write a function which takes this f as an input and returns another function such that,

-Define a function (twoback f) which takes a function f as its input.

-As its output, it should return a new function g which has the following behaviour:

g(x) = #t if x is the empty list or a list of length 1.

 = f(y) where y=(cdr x) otherwise.

And the function will called like this : ((twoback f3) (list #t #f #t #f))

So actually my question is : How can I access the list given with the function call in the function that I'm going to write(the twoback function) ? Because i need to check whether it is empty or not.

Answer 1

Short answer, by currying the x parameter. Something like this:

(define twoback
  (lambda (f)
    (lambda (x)
      ...)))     ; fill-in with the logic requested

The above will define a procedure called twoback which receives f as parameter, and in turn it will return a new procedure which receives x as parameter. This second procedure being returned is the one called g in the question, from it you can access both f and x as you would normally do.

Now just complete the ... part with the expected output.

Answer 2

I think this is what you mean:

(define (twoback f)
 (lambda (x)
  (if
   (or (null? x) (null? (cdr x)))
   #t
   (f (cdr x)))))
(define f (lambda (x) (if (null? x) #t (car x))))