X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=5ae3e65f5c154f36a84432585178ed81bdb179ba;hp=2c686583929b8e65d537b04ada523f7909c45813;hb=9452f39dcc5b7babde45142e2b24e3617813d6a6;hpb=74149f64a2c684075745513abc97730f034a65d4
diff --git a/week1.mdwn b/week1.mdwn
index 2c686583..5ae3e65f 100644
--- 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:
-
-
-Variables: x, y, z...
-
-
-Each variable is an expression. For any expressions M and N and variable a, the following are also expressions:
-
-
-Abstract: (λa M)
-
-
-We'll tend to write (λa M) as just `(\a M)`, so we don't have to write out the markup code for the λ. You can yourself write (λa M) or `(\a M)` or `(lambda a M)`.
-
-
-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:
@@ -74,7 +56,7 @@ 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**.