week1: fix markup processing?

[lambda.git] / week1.mdwn

diff --git a/week1.mdwn b/week1.mdwn
index e8154e3..5ae3e65 100644 (file)
--- a/week1.mdwn
+++ b/week1.mdwn
@@ -39,25 +39,7 @@ 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:
 
@@ -70,9 +52,11 @@ Examples of expressions:
        (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)
+       ((\ 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**.