Tacit programming in Lisp

Question

Is it possible to use/implement tacit programming (also known as point-free programming) in Lisp? And in case the answer is yes, has it been done?

Answer 1

This style of programming is possible in CL in principle, but, being a Lisp-2, one has to add several #'s and funcalls. Also, in contrast to Haskell for example, functions are not curried in CL, and there is no implicit partial application. In general, I think that such a style would not be very idiomatic CL.

For example, you could define partial application and composition like this:

(defun partial (function &rest args)
  (lambda (&rest args2) (apply function (append args args2))))

(defun comp (&rest functions)
  (flet ((step (f g) (lambda (x) (funcall f (funcall g x)))))
    (reduce #'step functions :initial-value #'identity)))

(Those are just quick examples I whipped up – they are not really tested or well thought-through for different use-cases.)

With those, something like map ((*2) . (+1)) xs in Haskell becomes:

CL-USER> (mapcar (comp (partial #'* 2) #'1+) '(1 2 3))
(4 6 8)

The sum example:

CL-USER> (defparameter *sum* (partial #'reduce #'+))
*SUM*
CL-USER> (funcall *sum* '(1 2 3))
6

(In this example, you could also set the function cell of a symbol instead of storing the function in the value cell, in order to get around the funcall.)

In Emacs Lisp, by the way, partial application is built-in as apply-partially.

In Qi/Shen, functions are curried, and implicit partial application (when functions are called with one argument) is supported:

(41-) (define comp F G -> (/. X (F (G X))))
comp

(42-) ((comp (* 2) (+ 1)) 1)
4

(43-) (map (comp (* 2) (+ 1)) [1 2 3])
[4 6 8]

There is also syntactic threading sugar in Clojure that gives a similar feeling of "pipelining":

user=> (-> 0 inc (* 2))
2