week1 tweaks

[lambda.git] / week1.mdwn

diff --git a/week1.mdwn b/week1.mdwn
index 27a7979..8124ffe 100644 (file)
--- a/week1.mdwn
+++ b/week1.mdwn
@@ -123,7 +123,7 @@ Each variable is an expression. For any expressions M and N and variable a, the
 <strong>Abstract</strong>: <code>(&lambda;a M)</code>
 </blockquote>
 
-We'll tend to write <code>(&lambda;a M)</code> as just `( \a M )`.
+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>
@@ -142,7 +142,7 @@ 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)
 
@@ -150,7 +150,7 @@ that is, an application of an abstract to some other expression. This compound f
 
 The rule of beta-reduction permits a transition from that expression to the following:
 
-       M {a:=N}
+       M [a:=N]
 
 What this means is just `M`, with any *free occurrences* inside `M` of the variable `a` replaced with the term `N`.