X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=6773a7714f358bdbc6da564719b018a5000ee271;hp=388fb9fcbbd47c5fb252c352c5c7e4ec4d5c6362;hb=e47611204f506bac2a53a81dd9a0e6e85600575e;hpb=0df9a0974bf6e02aa9f5f63164f409d8b26da67a diff --git a/week1.mdwn b/week1.mdwn index 388fb9fc..6773a771 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -57,26 +57,24 @@ 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))) -
+ 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**. @@ -605,6 +603,7 @@ Here's how it looks to say the same thing in various of these languages. It's easy to be lulled into thinking this is a kind of imperative construction. *But it's not!* It's really just a shorthand for the compound "let"-expressions we've already been looking at, taking the maximum syntactically permissible scope. (Compare the "dot" convention in the lambda calculus, discussed above.) + Some more comparisons between Scheme and OCaml ----------------------------------------------