Three-way conditional for number signs

Posted on April 24, 2021

A useful macro from Paul Graham’s On Lisp book:

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(defmacro nif (expr pos zero neg)
  (let ((g (gensym)))
    `(let ((,g ,expr))
       (cond ((plusp ,g) ,pos)
             ((zerop ,g) ,zero)
             (t ,neg)))))

After I looked at this macro, I started seeing opportunities to using it in many places, and yet I didn’t see anyone else using it.

The latest example I can think of is section 1.3.3 of Structure and Interpretation of Computer Programs, which I was reading recently:

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(define (search f neg-point pos-point)
  (let ((midpoint (average neg-point pos-point)))
    (if (close-enough? neg-point post-point)
        midpoint
        (let ((test-value (f midpoint)))
          (cond ((positive? test-value)
                 (search f neg-point midpoint))
                ((negative? test-value)
                 (search f midpoint pos-point))
                (else midpoint))))))

Not that the book should introduce such macro this early, but I couldn’t avoid feeling bothered by not using the nif macro, which could even remove the need for the intermediate test-value variable:

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(define (search f neg-point pos-point)
  (let ((midpoint (average neg-point pos-point)))
    (if (close-enough? neg-point post-point)
        midpoint
        (nif (f midpoint)
             (search f neg-point midpoint)
             (midpoint)
             (search f midpoint pos-point)))))

It also avoids cond’s extra clunky parentheses for grouping, which is unnecessary but built-in.

As a macro, I personally feel it tilts the balance towards expressivenes despite its extra cognitive load toll.