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--- a/week1.mdwn
+++ b/week1.mdwn
@@ -39,18 +39,29 @@ Basics of Lambda Calculus
 
 The lambda calculus we'll be focusing on for the first part of the course has no types. (Some prefer to say it instead has a single type---but if you say that, you have to say that functions from this type to this type also belong to this type. Which is weird.)
 
+Here is its syntax:
+
+<blockquote>
+<strong>Variables</strong>: <code>x</code>, <code>y</code>, <code>z</code>...
+</blockquote>
+
+Each variable is an expression. For any expressions M and N and variable a, the following are also expressions:
+
+<blockquote>
+<strong>Abstract</strong>: <code>(&lambda;a M)</code>
+</blockquote>
+
+We'll tend to write <code>(&lambda;a M)</code> as just `(\a M)`, so we don't have to write out the markup code for the <code>&lambda;</code>. You can yourself write <code>(&lambda;a M)</code> or `(\a M)` or `(lambda a M)`.
+
+<blockquote>
+<strong>Application</strong>: <code>(M N)</code>
+</blockquote>
+
 Some authors reserve the term "term" for just variables and abstracts. 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)))
 
 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