<strong>Application</strong>: <code>(M N)</code>
</blockquote>
-Some authors reserve the term "term" for just variables and abstracts. We won't *participate* in that convention; we'll probably just say "term" and "expression" indiscriminately for expressions of any of these three forms.
+Some authors reserve the term "term" for just variables and abstracts. We won't participate in that convention; we'll probably just say "term" and "expression" indiscriminately for expressions of any of these three forms.
Examples of expressions:
x
(y x)
(x x)
- (_x y)
- (_x x)
- (_x (_y x))
- (x (_x x))
- ((_x (x x)) (_x (x x)))
+ (\x y)
+ (\x x)
+ (\x (\y x))
+ (x (\x x))
+ ((\x (x x)) (\x (x x)))
-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:
+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:
((\a M) N)