From: Jim Pryor Date: Wed, 15 Sep 2010 20:47:24 +0000 (-0400) Subject: week1 tweaks X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=dc4a37d3f21dae7e6aceb29c6291fc2e7daa2f5e week1 tweaks Signed-off-by: Jim Pryor --- diff --git a/week1.mdwn b/week1.mdwn index b864d024..8124ffe6 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -123,7 +123,7 @@ Each variable is an expression. For any expressions M and N and variable a, the Abstract: `(λa M)` -We'll tend to write `(λa M)` as just `(\a M)`, so we don't have to write out the markup code for the `λ`. You can yourself write `(λa M)` or `(\a M)` or `lambda a M`. +We'll tend to write `(λa M)` as just `(\a M)`, so we don't have to write out the markup code for the `λ`. You can yourself write `(λa M)` or `(\a M)` or `(lambda a M)`.
Application: `(M N)` @@ -142,7 +142,7 @@ Examples of expressions: (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) @@ -150,7 +150,7 @@ that is, an application of an abstract to some other expression. This compound f The rule of beta-reduction permits a transition from that expression to the following: - M {a:=N} + M [a:=N] What this means is just `M`, with any *free occurrences* inside `M` of the variable `a` replaced with the term `N`.