X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=8484b17f975b74344e233ed94868b6e2a65c3b6e;hp=8d1ad0dd3a0ec34188415d1b6d76dc817c1956f2;hb=6885a008cfcbb9fed72b19db62a6046665860c44;hpb=75b0a95a29b968c3a6c42c04bdb4a908f586cd15 diff --git a/week1.mdwn b/week1.mdwn index 8d1ad0dd..8484b17f 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -62,21 +62,21 @@ Some authors reserve the term "term" for just variables and abstracts. We won't 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)
+ ((lambda 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**.