X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=801ae6984609be27b76abc8ca7f378fc93020dc6;hp=2c686583929b8e65d537b04ada523f7909c45813;hb=787216b36925c3757985a48ced39d6eee1ee5392;hpb=74149f64a2c684075745513abc97730f034a65d4 diff --git a/week1.mdwn b/week1.mdwn index 2c686583..801ae698 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 @@ -69,12 +70,13 @@ Examples of expressions: (\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**.