X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=8d1ad0dd3a0ec34188415d1b6d76dc817c1956f2;hp=2c686583929b8e65d537b04ada523f7909c45813;hb=75b0a95a29b968c3a6c42c04bdb4a908f586cd15;hpb=74149f64a2c684075745513abc97730f034a65d4 diff --git a/week1.mdwn b/week1.mdwn index 2c686583..8d1ad0dd 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -57,18 +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)

+(\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