X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;f=week1.mdwn;h=0207f0ceae92b3e0eafc4513fa279d8007de294e;hb=6ca041c08f7d5eccc1550af16de405c66fb23139;hp=e65919563b4ac23de3d1140d07172f6e9f141f14;hpb=7b5614a9122ebf1671f0bf5c7dd5fb35d4c81286;p=lambda.git diff --git a/week1.mdwn b/week1.mdwn index e6591956..0207f0ce 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -57,8 +57,9 @@ 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 @@ -70,12 +71,13 @@ 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: - ((\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**.