X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=1bc2309e1e9c79eea7118b9f6e72045a90b3317d;hp=2c686583929b8e65d537b04ada523f7909c45813;hb=c86596d41ed6ca32fff882b468eade84bc13fb07;hpb=74149f64a2c684075745513abc97730f034a65d4

diff --git a/week1.mdwn b/week1.mdwn
index 2c686583..1bc2309e 100644
--- a/week1.mdwn
+++ b/week1.mdwn
@@ -57,7 +57,7 @@ We'll tend to write <code>(&lambda;a M)</code> as just `(\a M)`, so we don't hav
 <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:
 
@@ -74,7 +74,7 @@ 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**.
 
@@ -285,18 +285,16 @@ It's possible to enhance the lambda calculus so that functions do get identified
 
 It's often said that dynamic systems are distinguished because they are the ones in which **order matters**. However, there are many ways in which order can matter. If we have a trivalent boolean system, for example---easily had in a purely functional calculus---we might choose to give a truth-table like this for "and":
 
-<pre><code>
-true and true   = true
-true and true   = true
-true and *      = *
-true and false  = false
-* and true      = *
-* and *         = *
-* and false     = *
-false and true  = false
-false and *     = false
-false and false = false
-</code></pre>
+	true and true   = true
+	true and true   = true
+	true and *      = *
+	true and false  = false
+	* and true      = *
+	* and *         = *
+	* and false     = *
+	false and true  = false
+	false and *     = false
+	false and false = false
 
 And then we'd notice that `* and false` has a different intepretation than `false and *`. (The same phenomenon is already present with the material conditional in bivalent logics; but seeing that a non-symmetric semantics for `and` is available even for functional languages is instructive.)
 
@@ -603,7 +601,6 @@ Here's how it looks to say the same thing in various of these languages.
 
 	It's easy to be lulled into thinking this is a kind of imperative construction. *But it's not!* It's really just a shorthand for the compound "let"-expressions we've already been looking at, taking the maximum syntactically permissible scope. (Compare the "dot" convention in the lambda calculus, discussed above.)
 
-
 9.	Some shorthand
 
 	OCaml permits you to abbreviate:
@@ -674,9 +671,8 @@ Here's how it looks to say the same thing in various of these languages.
 
 	and there's no more mutation going on there than there is in:
 
-	<pre>
-	<code>&forall;x. (F x or &forall;x (not (F x)))</code>
-	</pre>
+	<pre><code>&forall;x. (F x or &forall;x (not (F x)))
+	</code></pre>
 
 	When a previously-bound variable is rebound in the way we see here, that's called **shadowing**: the outer binding is shadowed during the scope of the inner binding.