Examples of expressions:
<blockquote><code>
-x
-(y x)
-(x x)
-(\x y)
-(\x x)
-(\x (\y x))
-(x (\x x))
+x
+(y x)
+(x x)
+(\x y)
+(\x x)
+(\x (\y x))
+(x (\x x))
((\x (x x)) (\x (x x)))
</code></blockquote>
proof theory as having just one rule, called the rule of **beta-reduction** or
"beta-contraction". Suppose you have some expression of the form:
- ((\a M) N)
+ ((lambda a M) N)
that is, an application of an abstract to some other expression. This compound form is called a **redex**, meaning it's a "beta-reducible expression." `(\a M)` is called the **head** of the redex; `N` is called the **argument**, and `M` is called the **body**.