X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=week1.mdwn;h=36ebdfcc6a48bf72288e2023a0186b9c6665de2d;hp=5ae3e65f5c154f36a84432585178ed81bdb179ba;hb=e8385d4bbe1cc7549cb8f7724f489370b5dcd426;hpb=9452f39dcc5b7babde45142e2b24e3617813d6a6 diff --git a/week1.mdwn b/week1.mdwn index 5ae3e65f..36ebdfcc 100644 --- a/week1.mdwn +++ b/week1.mdwn @@ -39,6 +39,24 @@ Basics of Lambda Calculus The lambda calculus we'll be focusing on for the first part of the course has no types. (Some prefer to say it instead has a single type---but if you say that, you have to say that functions from this type to this type also belong to this type. Which is weird.) +Here is its syntax: + +
+Variables:+ +Each variable is an expression. For any expressions M and N and variable a, the following are also expressions: + +x
,y
,z
... +
+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)`.
+
+
+Application: (M N)
+
+
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: