Question

Given a predicate that tests a single item, such as positive?, I am trying to create an all-are version of it for testing whether all elements of the list satisfy the predicate

Ex:
((all-are positive?) '(1 2 3 4)) => #t
((all-are even?) '(2 4 5 6 8)) => #f

all-are should take a predicate as an argument and return a new function that can be applied to the list of elements

Answer 1

That’s quite simple to express in terms of an existing procedure: andmap – which returns #t if a given predicate, when applied to all the elements in a list, evaluates to true for all of them:

(define ((all-are predicate) lst)
  (andmap predicate lst))

I’m using a bit of syntactic sugar for returning a curried procedure, because the question states that a function must be returned. It works as expected:

((all-are positive?) '(1 2 3 4))
> #t

((all-are even?) '(2 4 5 6 8))
> #f

I’m guessing that you have to implement the procedure from scratch, and not using existing procedures as in my solution. A good exercise would be to turn the short version above (which demonstrates the general idea of what needs to be done) into something simpler using only basic forms – that’s probably what your teacher expects from you.