+[[!toc]]
+
Building Lists
==============
Adding *m* to *n* is a matter of applying the successor function to *n* *m* times. And we know how to apply an arbitrary function s to *n* *m* times: we just give that function s, and the base-value *n*, to *m* as arguments. Because that's what the function we're using to implement *m* *does*. Hence **add** can be defined to be, simply:
- \m \n. m succ n
+ \m n. m succ n
Isn't that nice?
+Alternatively, one could do:
+
+ \m n. \s z. m s (n s z)
+
How would we tell whether a number was 0? Well, look again at the implementations of the first few numbers:
<pre><code>zero ≡ \s z. s<sup>0</sup> z ≡ \s z. z