X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=assignment1.mdwn;h=fa02cb83634bd078c64230e2b5b97f244a68e460;hp=615e1832765c4529ce070c5e41cb6d3bf22c0702;hb=dc9298c6718ec9bc63550ec6bc6b5a187f235e50;hpb=1f6748544a73f4bde9fc537750e7da2d13eb3615
diff --git a/assignment1.mdwn b/assignment1.mdwn
index 615e1832..fa02cb83 100644
--- a/assignment1.mdwn
+++ b/assignment1.mdwn
@@ -40,9 +40,7 @@ evaluates to 10.
Define an `and` operator.
-Define an `xor` operator.
-
-If you haven't seen this term before, here's a truth table:
+Define an `xor` operator. If you haven't seen this term before, here's a truth table:
true xor true = false
true xor false = true
@@ -93,13 +91,11 @@ Now we can write:
(p get-first) ; will evaluate to 10
(p get-second) ; will evaluate to 20
-If you're bothered by having the pair to the left and the function that
+If you're puzzled by having the pair to the left and the function that
operates on it come second, think about why it's being done this way: the pair
-is a package that takes a function for operating on its elements as an
-argument, and returns the result of operating on its elemens with that
-function. In other words, the pair is also a function. (Of course, in the
-untyped lambda calculus, absolutely *everything* is a function: functors,
-arguments, abstracts, redexes, values---everything.)
+is a package that takes a function for operating on its elements *as an
+argument*, and returns *the result of* operating on its elements with that
+function. In other words, the pair is a higher-order function. (Consider the similarities between this definition of a pair and a generalized quantifier.)
If you like, you can disguise what's going on like this:
@@ -114,7 +110,7 @@ instead of:
(p get-first)
-However, the latter is still what's going on under the hood.
+However, the latter is still what's going on under the hood. (Remark: `(lifted-f ((make-pair 10) 20))` stands to `(((make-pair 10) 20) f)` as `(((make-pair 10) 20) f)` stands to `((f 10) 20)`.)