X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=f09f393d653bc0f8cdc0dbc677a6bbfd04b4e775;hp=8484b17f975b74344e233ed94868b6e2a65c3b6e;hb=5739a5066020a0e9dd46e0299165faadb59fc438;hpb=6885a008cfcbb9fed72b19db62a6046665860c44 diff --git a/week1.mdwn b/week1.mdwn index 8484b17f..f09f393d 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -61,22 +61,20 @@ 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: - ((lambda 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**.