X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2Fweek1_advanced_notes.mdwn;h=9bac7eb64fbec8625f85a055d59b1bac6d52067a;hp=d843ee72790c1be59b1b59235ed2e7dca3ed44ff;hb=222fceeec976f4e512b5d24969b54ae71ff473a3;hpb=7a8d016ba68d0c03c37ab5ce52e1b12b7c97c568

diff --git a/topics/week1_advanced_notes.mdwn b/topics/week1_advanced_notes.mdwn
index d843ee72..9bac7eb6 100644
--- a/topics/week1_advanced_notes.mdwn
+++ b/topics/week1_advanced_notes.mdwn
@@ -51,7 +51,7 @@ I agree it's annoying that these conventions are so diverse. There are plenty ot
 
 A function value doesn't have any structure---at least none that's visible to the pattern-matching system. You can only match against simple patterns like `_` or the variable `f`.
 
-When matching a variable against a λ-generated function value in a `let`- or `letrec`-construction, there's an alternative syntax that you may find more convenient. This:
+When matching a λ-generated function value against a variable in a `let`- or `letrec`-construction, there's an alternative syntax that you may find more convenient. This:
 
 `let`  
   `f match` λ`x.` φ`;`  
@@ -99,9 +99,9 @@ If we get to the `y & ys` line in the pattern list, and the pattern-match succee
 
 ### As-patterns ###
 
-Sometimes it's useful to bind variables against overlapping parts of a structure. For instance, suppose I'm writing a pattern that is to be matched against multivalues like `([10, 20], 'true)`. And suppose I want to end up with `ys` bound to `[10, 20]`, `x` bound to `10`, and `xs` bound to `[20]`. Using the techniques introduced so far, I have two options. First, I could bind `ys` against `[10, 20]`, and then initiate a second pattern-match to break that up into `10` and [20]`. Like this:
+Sometimes it's useful to bind variables against overlapping parts of a structure. For instance, suppose I'm writing a pattern that is to be matched against multivalues like `([10, 20], 'true)`. And suppose I want to end up with `ys` bound to `[10, 20]`, `x` bound to `10`, and `xs` bound to `[20]`. Using the techniques introduced so far, I have two options. First, I could bind `ys` against `[10, 20]`, and then initiate a second pattern-match to break that up into `10` and `[20]`. Like this:
 
-    case [10, 20] of
+    case ([10, 20], 'true) of
       [ys, _] then case ys of
                      x & xs then ...;
                      ...
@@ -111,7 +111,7 @@ Sometimes it's useful to bind variables against overlapping parts of a structure
 
 Alternatively, I could directly bind `x` against `10` and `xs` against `[20]`. But then I would have to re-cons them together again to get `ys`. Like this:
 
-    case [10, 20] of
+    case ([10, 20], 'true) of
       [x & xs, _] then let
                          ys match x & xs
                        in ...;
@@ -120,7 +120,7 @@ Alternatively, I could directly bind `x` against `10` and `xs` against `[20]`. B
 
 Both of these strategies work. But they are a bit inefficient. I said you didn't really need to worry about efficiency in this seminar. But these are also a bit cumbersome to write. There's a special syntax that enables us to bind all three of `ys`, `x`, and `xs` in the desired way, despite the fact that they will be matching against overlapping, rather than discrete, parts of the value `[10, 20]`. The special syntax looks like this:
 
-    case [10, 20] of
+    case ([10, 20], 'true) of
       [(x & xs) as ys, _] then ...
       ...
     end
@@ -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)