X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=5ae3e65f5c154f36a84432585178ed81bdb179ba;hp=8d1ad0dd3a0ec34188415d1b6d76dc817c1956f2;hb=9452f39dcc5b7babde45142e2b24e3617813d6a6;hpb=75b0a95a29b968c3a6c42c04bdb4a908f586cd15

diff --git a/week1.mdwn b/week1.mdwn
index 8d1ad0dd..5ae3e65f 100644
--- a/week1.mdwn
+++ b/week1.mdwn
@@ -39,44 +39,24 @@ 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 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'll probably just say "term" and "expression" indiscriminately for expressions of any of these three forms.
 
 Examples of expressions:
 
-<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>
+	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
 "beta-contraction". Suppose you have some expression of the form:
 
-	((\a M) N)
+	((\ 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**.