X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=a5e697a5026751b9fb6b261f657cd2f91f69c99a;hp=9a83861abe305f5d4485d7dc7a7c8e9be24fad8b;hb=aa82fa84a083b7b90862f5f4c368f07dd62ae717;hpb=2a3a4803ddfca1692327ab4577fb886139bfc1e7 diff --git a/week1.mdwn b/week1.mdwn index 9a83861a..a5e697a5 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -57,22 +57,20 @@ 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 won't *participate* in that convention; 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))) - ->   + (_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: +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)