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diff git a/assignment1.mdwn b/assignment1.mdwn
index 453fa546..fa02cb83 100644
 a/assignment1.mdwn
+++ b/assignment1.mdwn
@@ 17,8 +17,8 @@ Booleans
Recall our definitions of true and false.
> **true** defined to be `\t \f. t`
> **false** defined to be `\t \f. f`
+> **true** is defined to be `\t \f. t`
+> **false** is defined to be `\t \f. f`
In Racket, these can be defined like this:
@@ 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
@@ 75,7 +73,7 @@ Pairs
Recall our definitions of ordered pairs.
> the pair **(**x**,**y**)** is defined as `\f. f x y`
+> the pair **(**x**,**y**)** is defined to be `\f. f x y`
To extract the first element of a pair p, you write:
@@ 93,13 +91,11 @@ Now we can write:
(p getfirst) ; will evaluate to 10
(p getsecond) ; 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, valueseverything.)
+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 higherorder 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:
@@ 114,19 +110,17 @@ instead of:
(p getfirst)
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: `(liftedf ((makepair 10) 20))` stands to `(((makepair 10) 20) f)` as `(((makepair 10) 20) f)` stands to `((f 10) 20)`.)
 Define a `swap` function that reverses the elements of a pair.

Expected behavior:
+
 Define a `swap` function that reverses the elements of a pair. Expected behavior:
(define p ((makepair 10) 20))
((p swap) getfirst) ; evaluates to 20
((p swap) getsecond) ; evaluates to 10
Write out the definition of swap in Racket.
+Write out the definition of `swap` in Racket.
 Define a `dup` function that duplicates its argument to form a pair