X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?a=blobdiff_plain;ds=sidebyside;f=week1.mdwn;h=c9b52d1d52acead984f8a6149cdb62db2a39c111;hb=fceb99fda0c4287f9f3c476a26c6e202cf5e26c5;hp=2c686583929b8e65d537b04ada523f7909c45813;hpb=74149f64a2c684075745513abc97730f034a65d4;p=lambda.git diff --git a/week1.mdwn b/week1.mdwn index 2c686583..c9b52d1d 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -57,24 +57,17 @@ 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 - (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) + ((\ 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**.