From: Jim Pryor <profjim@jimpryor.net>
Date: Thu, 9 Dec 2010 01:53:41 +0000 (-0500)
Subject: prettier associative law in week7
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=fec57bcf43af67bac0f25f0a0b0a797015139d96

prettier associative law in week7

Signed-off-by: Jim Pryor <profjim@jimpryor.net>
---

diff --git a/week7.mdwn b/week7.mdwn
index 35deeb29..7544425c 100644
--- a/week7.mdwn
+++ b/week7.mdwn
@@ -402,11 +402,16 @@ them from hurting the people that use them or themselves.
 
 *	**Associativity: bind obeys a kind of associativity**. Like this:
 
-		(u >>= f) >>= g == u >>= (fun x -> f x >>= g)
+		(u >>= f) >>= g  ==  u >>= (fun x -> f x >>= g)
 
 	If you don't understand why the lambda form is necessary (the
 	"fun x -> ..." part), you need to look again at the type of `bind`.
 
+	Wadler and others try to make this look nicer by phrasing it like this,
+	where U, V, and W are schematic for any expressions with the relevant monadic type:
+
+		(U >>= fun x -> V) >>= fun y -> W  ==  U >>= fun x -> (V >>= fun y -> W)
+
 	Some examples of associativity in the Option monad (bear in
 	mind that in the Ocaml implementation of integer division, 2/3
 	evaluates to zero, throwing away the remainder):
@@ -426,15 +431,15 @@ them from hurting the people that use them or themselves.
 		# Some 3 >>= (fun x -> divide 2 x >>= divide 6);;
 		- : int option = None
 
-Of course, associativity must hold for *arbitrary* functions of
-type `'a -> 'b m`, where `m` is the monad type.  It's easy to
-convince yourself that the `bind` operation for the Option monad
-obeys associativity by dividing the inputs into cases: if `u`
-matches `None`, both computations will result in `None`; if
-`u` matches `Some x`, and `f x` evalutes to `None`, then both
-computations will again result in `None`; and if the value of
-`f x` matches `Some y`, then both computations will evaluate
-to `g y`.
+	Of course, associativity must hold for *arbitrary* functions of
+	type `'a -> 'b m`, where `m` is the monad type.  It's easy to
+	convince yourself that the `bind` operation for the Option monad
+	obeys associativity by dividing the inputs into cases: if `u`
+	matches `None`, both computations will result in `None`; if
+	`u` matches `Some x`, and `f x` evalutes to `None`, then both
+	computations will again result in `None`; and if the value of
+	`f x` matches `Some y`, then both computations will evaluate
+	to `g y`.
 
 *	**Right identity: unit is a right identity for bind.**  That is, 
 	`u >>= unit == u` for all monad objects `u`.  For instance,