add dup

diff --git a/topics/week1_advanced_notes.mdwn b/topics/week1_advanced_notes.mdwn
index 2742a7f..9bac7eb 100644 (file)
--- a/topics/week1_advanced_notes.mdwn
+++ b/topics/week1_advanced_notes.mdwn
@@ -165,12 +165,14 @@ Function composition, which mathematicians write as `f` ○ `g`, is defined as
 
 We've already come across the `id` function, namely λ `x. x`.
 
-Other common functions are `fst`, which takes two arguments and returns the first of them; `snd`, which takes two arguments and returns the second of them; and `swap`, which takes two arguments and returns them both but with their positions swapped. These functions can be defined like this:
+Other common functions are `fst`, which takes two arguments and returns the first of them; `snd`, which takes two arguments and returns the second of them; and `swap`, which takes two arguments and returns them both but with their positions swapped. A fourth function is `dup`, which takes one argument and returns it twice.
+These functions can be defined like this:
 
     let
       fst (x, y) = x;
       snd (x, y) = y;
-      swap (x, y) = (y, x)
-    in (fst, snd, swap)
+      swap (x, y) = (y, x);
+      dup x = (x, x)
+    in (fst, snd, swap, dup)