Question

I have this curry function:

(define curry
(lambda (f) (lambda (a) (lambda (b) (f a b)))))

I think it’s like (define curry (f a b)).

my assignment is to write a function consElem2All using curry，which should work like

(((consElem2All cons) 'b) '((1) (2 3) (4)))
>((b 1) (b 2 3) (b 4))

I have wrote this function in a regular way:

(define (consElem2All0 x lst) 
  (map (lambda (elem) (cons x elem)) lst))

but still don’t know how to transform it with curry. Can anyone help me?

thanks in advance

bearzk

Answer 1

You should begin by reading about currying. If you don’t understand what curry is about, it may be really hard to use it… In your case, http://www.engr.uconn.edu/~jeffm/Papers/curry.html may be a good start.

One very common and interesting use of currying is with functions like reduce or map (for themselves or their arguments).

Let’s define two currying operators!

(define curry2 (lambda (f) (lambda (arg1) (lambda (arg2) (f arg1 arg2)))))
(define curry3 (lambda (f) (lambda (arg1) (lambda (arg2) (lambda (arg3) (f arg1 arg2 arg3))))))

Then a few curried mathematical functions:

(define mult (curry2 *))
(define double (mult 2))

(define add (curry2 +))
(define increment (add 1))
(define decrement (add -1))

And then come the curried reduce/map:

(define creduce (curry3 reduce))
(define cmap (curry2 map))

Using them

First reduce use cases:

(define sum ((creduce +) 0))
(sum '(1 2 3 4)) ; => 10

(define product (creduce * 1))
(product '(1 2 3 4)) ; => 24

And then map use cases:

(define doubles (cmap double))
(doubles '(1 2 3 4)) ; => (2 4 6 8)

(define bump (cmap increment))
(bump '(1 2 3 4)) ; => (2 3 4 5)

I hope that helps you grasp the usefulness of currying…