X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=36ebdfcc6a48bf72288e2023a0186b9c6665de2d;hp=388fb9fcbbd47c5fb252c352c5c7e4ec4d5c6362;hb=e23f91437e64baf1fadd0266e1b47ecfa8dd593a;hpb=0df9a0974bf6e02aa9f5f63164f409d8b26da67a
diff --git a/week1.mdwn b/week1.mdwn
index 388fb9fc..36ebdfcc 100644
--- a/week1.mdwn
+++ b/week1.mdwn
@@ -57,26 +57,24 @@ We'll tend to write (λa M)
as just `(\a M)`, so we don't hav
Application: (M N)
-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:
-
-x
-(y x)
-(x x)
-(\x y)
-(\x x)
-(\x (\y x))
-(x (\x x))
-((\x (x x)) (\x (x x)))
-
+ 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**.