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+---
+
+title: Three-way conditional for number signs
+
+date: 2021-04-24
+
+layout: post
+
+lang: en
+
+ref: three-way-conditional-for-number-signs
+
+---
+
+A useful macro from Paul Graham's [On Lisp][on-lisp] book:
+
+```lisp
+(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 anyonelse using it.
+
+The latest example I can think of is section 1.3.3 of [Structure and Interpretation of Computer Programs][sicp], which I was reading recently:
+
+```scheme
+(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 a `nif` macro, which could even remove the need for the intermediate `test-value` variable:
+
+```scheme
+(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.
+
+[on-lisp]: http://www.paulgraham.com/onlisptext.html
+[sicp]: https://mitpress.mit.edu/sites/default/files/sicp/index.html