Is it possible to implement auto-currying to the Lisp-family languages?

Question

That is, when you call a function with >1 arity with only one argument, it should, instead of displaying an error, curry that argument and return the resulting function with

Answer 1

In Scheme it's possible to curry a function using the curry procedure:

(define (add x y)
  (+ x y))

(add 1 2)           ; non-curried procedure call
(curry add)         ; curried procedure, expects two arguments
((curry add) 1)     ; curried procedure, expects one argument
(((curry add) 1) 2) ; curried procedure call

From Racket's documentation:

[curry] returns a procedure that is a curried version of proc. When the resulting procedure is first applied, unless it is given the maximum number of arguments that it can accept, the result is a procedure to accept additional arguments.

You could easily implement a macro which automatically uses curry when defining new procedures, something like this:

(define-syntax define-curried
    (syntax-rules ()
      ((_ (f . a) body ...)
       (define f (curry (lambda a (begin body ...)))))))

Now the following definition of add will be curried:

(define-curried (add a b)
  (+ a b))

add
> #

(add 1)
> #

((add 1) 2)
> 3

(add 1 2)
> 3