Examples of expressions:
- x
- (y x)
- (x x)
- (\x y)
- (\x x)
- (\x (\y x))
- (x (\x x))
- ((\x (x x)) (\x (x x)))
+<blockquote><code>
+x<p>
+(y x)<p>
+(x x)<p>
+(\x y)<p>
+(\x x)<p>
+(\x (\y x))<p>
+(x (\x x))<p>
+((\x (x x)) (\x (x x)))<p>
+</code></blockquote>
-<p>
The lambda calculus has an associated proof theory. For now, we can regard the
proof theory as having just one rule, called the rule of **beta-reduction** or
"beta-contraction". Suppose you have some expression of the form: