X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=8124ffe62832fd961146810859fb0b12e49dcd93;hp=27a79796fe92b77ea02ec76a7ada37625962f641;hb=dc4a37d3f21dae7e6aceb29c6291fc2e7daa2f5e;hpb=f38560c70588aa58d7db41afb7904c2bd4638287
diff --git a/week1.mdwn b/week1.mdwn
index 27a79796..8124ffe6 100644
--- 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
Abstract: (λa M)
-We'll tend to write (λa M)
as just `( \a 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)
@@ -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`.