Advanced Functional Programming

A coworker pointed out that the Advanced Functional Programming class at Harvard has a public Wiki. The semester has only just started, but there's already some interesting comments coming from the daily discussions. For example, on the first day, they had a puzzle of trying to figure out a way of writing postscript in haskell. They came up with something that could handle expressions like "psbegin push 2 push 3 add psend". I'm currently trying to one-up them by making something like "rpn [2, 3, add]" work.

On the second day, they read Why Functional Programming Matters, and then everybody in the class had to post a question. Reading a paper all by itself has a much different feel than reading the paper and then a bunch of comments by other people. For example, some people pointed out that the paper ignores issues like space leaks and over abstraction. Responding to the space leak question, the teacher posted a reference to this paper which describes a profiler for haskell that measures both time as well as space. I'm glad to have found this because space leaks have been a source of serious unease for me when trying to use haskell.

I've added their Wiki's RecentChanges to my list of links to check periodically. If you're interested in this kind of thing you might want to check it out as well.

Followups to Advanced Functional Programming:

Programming Languages Textbook

Posted on September 26, 2003 05:28 PM
More languages articles

Comments

Is there a problem description somewhere, beyond "do Postscript in Haskell?" The page you linked to just talks about some of the solutions, and I looked around to no avail.

Posted by: Ralph Richard Cook at September 26, 2003 09:33 PM

I didn't see a problem description. It's not like MIT's online courseware initiative -- their wiki is just a place for people who take the class to collaborate. Presumably the problem was given orally in class.

Posted by: kim at September 26, 2003 10:37 PM

After spending a couple hours on the problem, I've decided that it's not possible to one-up the solution that the class came up with. I did, however, learn a couple things about haskell in the attempt.

I had originally hoped to use a type class to allow me to create a list of "operation" objects that could then be applied sequentially. The main idea was going to be based on something like this:

    class Op a where
        op2func :: a -> [Int] -> [Int]

    instance Op Int where

        op2func val stack = val:stack

    rpn :: (Op a) => [a] -> Int

    rpn ops = ...

I was hoping that haskell's type checker would unify on the argument type of the "rpn" function to decide that it should automatically coerce the elements of the list to instances of the type class. But alas, haskell merely told me that I couldn't create a list of heterogenous types (in this case a list of Ints and functions). Apparently it didn't care that all the elements were members of the type class. I should have noticed that I wasn't even able to express this idea in the type of the "rpn" function -- the best I could do was to state that it took a list of a bunch of Ops that are actually all the same type. What bothers me is that I know how type classes are implemented, and so I know that something like this could work. I'm just not sure how to express it.

Anyway, after my first attempt failed, I tried to build on the technique used by the example that the class developed. When I started down this dead end, I thought that "psbegin push 1 push 2 add psend" would be parsed as

(psbegin (push 1 (push 2 (add (psend)))))

In other words, I thought that the operations took a kind of continuation that represented the rest of the computation. But it turns out that it's parsed like this:

(((((psbegin push) 1) push) 2) add) psend)

And the only reason it works is because of currying. To me, this feels like it's merely taking advantage of a quirk of the haskell parser, as opposed to being a real semantic technique. It does, however, take spectacular advantage of haskell's polymorphism features -- it almost feels like dependant types (the return type of psbegin depends on the return type of its argument, which almost feels like it depends on the actual value of its argument).

Even after realizing how haskell parsed the expression, I still hadn't given up. I decided to see if I could still make my type class idea work, by making psbegin return a function that promoted its argument to a function before calling it. This way you could write "psbegin 1" directly, without having to insert a "push" function. It would convert the integer to a function, and then apply that function. But the problem with this idea is that, while it works just fine, there's no way to ever get at the result. After you evaluate the entire expression, you are still left with a function that will convert any argument it receives into a stack operator function, and then call it. Sounds fine, except that the stack operator function is required to have exactly the same static type -- it also has to convert any arguments it receives into a stack function, and then call it. So you're stuck in the land of stack operator functions and you can't get out.

This design is very similar to the design of monads in that I'm lifting values into a special type that I then perform operations on, and that frustrated me for a long time because I knew that you could "un-lift" a monad to turn it back into a regular value. But eventually I realized that monads are values that you apply functions to, while what I had created were functions that you apply values to. And at that point I realized that there really, truly was no way to get out of the stack operator black hole.

At this point, I finally gave up and did a search to see if anybody else had a solution I hadn't considered. I came across this paper which was very interesting, but which basically confirmed my conclusion that it couldn't be done.

You simply have to have an explicit "push" operator in haskell. This, by the way, is a good example of static typing preventing me from solving a problem that would be trivial in a dynamic language (as long as the dynamic language had currying).

Posted by: kim at September 26, 2003 10:46 PM

Someone wrote a paper on how to do something like printf in Haskell, which strikes me as a similar problem. IIRC they had an infix operator to stitch together the parts of the format, and then did the typeclass thing. But I suppose that would also be covered in the linked paper on embedding postfix, which I can't access the text of.

Stack sublanguages can also be a nice example of macros -- I wrote some macros you use like

(define swap (stack-op (y z) (z y)))
(define under+ (stack-op (x y z) ((+ x z) y)))

Posted by: Darius at October 20, 2003 12:20 AM

The paper with printf in ML-Family languages is Functional Unparsing.

Posted by: Matt at October 20, 2003 05:04 AM

I like the stack-op macro :)

As for the printf example, given that the point is the syntax, I think relying on an infix operator is cheating.

Posted by: kim at October 20, 2003 11:29 AM

Posted by: Matt at October 20, 2003 01:31 PM

Ack, I mangled my comment. What I meant was, it's cheating to use infix operators in order to create a postfix syntax. Please ignore the bit about printf.

Posted by: kim at October 20, 2003 04:26 PM

Yup, it's cheating. :) But not greatly more than [2, 3, add] is cheating, IMHO, compared to just "2 3 add".

Posted by: Darius at October 21, 2003 11:21 PM

Very useful files search engine. http://myrapida.com is a search engine designed to search files in various file sharing and uploading sites.

Posted by: Facepalm at March 15, 2009 02:08 AM

ugg boot australia
bailey button ugg sale
ugg classic cardy cheap
classic cardy ugg sale online
ugg unique bailey button

ugg bailey button unique

Posted by: ugg boots on sale and free shipping at October 11, 2009 12:06 AM

i am trying to understand how this works. What do i need to do here.

Car Hifi

Posted by: james lee at October 21, 2009 01:10 PM

Thanks for your useful info, I think it’s a good topic. So would you like the info about the
jordan shoes
Air jordan shoes
cardy ugg boots
Tiffany Jewelry
ugg bailey button boots
cheap jordan shoes
ugg boots uk
Michael jordan shoes
ugg london
ugg nightfall boots
ugg boots sale
classic ugg boots
sundance ugg boots
air jordan fusion 6
air jordan 6 rings
jordan shoes for sale

Posted by: xinxi at October 23, 2009 10:50 PM

Great post dude, keep it up.

Posted by: free online games at October 25, 2009 04:11 PM

I wouldn't call that cheating. I would call that a shortcut. Haha.

Posted by: Bed Bugs at October 26, 2009 08:58 PM

These Women's Classsic Tall 5815 Boots in pink flower print can either be worn at their normal height if you want Ugg boots, but in order for you to create a more casual look to what you are wearing they can be pushed down Women's UGG Classic Tall 5815 Boots in Baked Clay

Posted by: ugg boots on sale at October 27, 2009 02:34 PM

Good ! I like it ! Welcome to read following news: ugg boots,Nike dunk sb,discount ugg boots, uggs ,nike dunk low,ugg boots sale,UGG Bailey Button boots,new nike sb,UGG Classic short boots,UGG Nightfall boots,cheap nike dunks,UGG Classic tall boots.

Posted by: ugg boots at October 27, 2009 10:35 PM

Posted by: tiffany jewelry at October 28, 2009 05:35 AM

I don't understand how it's cheating. I mean, I have to put all those %foo's for various foo's in regular printf. It's just the dual to C's weak dependent typing (not even really typing - but what else should I call it?). hotels austria imst hotel imst Imst hotels fiss hotels Fiss hotels fiss Ehrwald Ehrwald hotels Ehrwald hotel austria

Posted by: hotel austria at October 28, 2009 09:04 AM

Posted by: hotel austria at October 28, 2009 09:05 AM

Posted by: hotel austria at October 28, 2009 09:10 AM

Love this man. Great stuff, great prices, free shipping. Email him if you cant find what you are looking for and he will look for you. Good customer service.louis vuittonSomeone who is knowledgeable in louis vuitton.Another guy from hong Kong (Largest louis vuitton second hand city, I believe) he has great stuff at fair prices but his shipping is insane

Posted by: louis vuitton at October 29, 2009 08:25 AM

Posted by: louis vuitton at October 29, 2009 08:28 AM

Ugg
Ugg Boots
Cheap Ugg
New Ugg Boots
Ugg Boot
Ugg Classic Boots
Cheap Ugg Boots
Uggs on sale
Uggs
Ugg Boots
Cheap Ugg Boots
Ugg Classic Boots
Ugg Boots Sale

Posted by: cheap ugg at October 30, 2009 09:05 AM

Supra Shoes
Mens Supra Cruizer Shoes ---Special
Men's Supra Cruizer Red Shoes
Mens Supra Cruizer Cool Shoes
Mens Supra Cruizer Shoes --Charming
Mens Supra Cruizer Pure black Shoes
Mens Supra Cruizer Shoes --Leisure
Man's Supra Cruizer Shoes
Men's Supra Muska Skytop Shoes
Men's Supra Skateboarding Shoes
Men's Supra Strapped Shoes
Men's Supra Suprano High Shoes
Women's Supra Muska Skytop Shoes
cheap ugg boots sale
uggs classic mini sale
UGG Ultra Tall Boots
Cheap Ugg Boots
UGG Classic Tall Boots
UGG Classic Cardy
UGG Classic Short Boots

Posted by: supra shoes at November 1, 2009 12:01 PM

Eliminating the need for the extra trouble to wear ugg boots uk 、
ugg boots sale、 uggs, in the extreme sports, look for happiness in life, with UGG Classic boots and nike sb showed off your tall body, do not worry about being laughed at, dancing new style ugg australia and nike sb dunk . The flavor of life that is colorful, there are Christian Louboutin 、cheap nike dunks、UGG cardy boots、and nike sb for sale also used fear to creep away money from your pocket Mody ? Love beauty, you might even love UGG Classic tall boots 、UGG Nightfall boots、UGG Classic short boots、new nike sb。There are an infinite high power drivers of popular front ugg boots sale、ugg sale、uggs、nike dunk、discount ugg boots、nike dunk sb, our website also have UGG Nightfall boots、button ugg boots、bailey button ugg、ugg button boots、bailey button boots、nike dunk mid、nike dunk high、Christian Louboutin Boots, pick your favorite, do not hesitate!

Posted by: ugg boots sale at November 12, 2009 03:58 AM

People all over the world know the abercrombie and fitch,but not everyone really knows how fashion the abercrombie is,hollister is the Legend maker. Everybody wears the hollister clothing would be the abercrombie mensand the abercrombie womens, if you want know you can search the Ruehl No.925 or abercrombie outlet in the www.google.com .

Posted by: fitch at November 14, 2009 01:41 AM

replica handbags
replica designer handbags
gucci Handbags
fendi Handbags
Louis Vuitton handbags
LV Handbags
Prada Handbags
Bottega Veneta Handbags
Burberry Handbags
Hermes Handbags
Jimmy Choo Handbags
Miu Miu Handbags

Play with the Most Expensive Handbags-Chanel Classic and Chanel 2.55
Louis Vuitton Released Two Monogram Watch Cases
Juicy Couture Leather Crossbody Hobo Bag
Nico Shearling Satchel by Tory Burch
Hello Kitty 35th Birthday Collection: Bags, Pendant Set and Music Player
Tag Heuer Aquaracer 500m Caliber 5 Leonardo DiCaprio Limited Edition-WAJ2116.FT6022
Horological Machine 2.2 by MB&F and Alain Silberstein
Coach Poppy Signature Zip Around Wallet
Haute Joaillerie Timepieces from Piaget 2009 Limelight Collection
Audemars Piguet Millenary Carbon One Tourbillon Chronograph
Patek Philippe Ladies First Chronograph Ref. 7071R and CH 29-535 PS caliber
Raymond Weil Freelancer Rose Gold Date Chronograph
Girard Perregaux 1966 Chronograph Review

Posted by: Valentino Handbags at November 16, 2009 02:42 AM

Uggs on sale now.UGG Classic Cardy Boot makes me different form the other

girls. The UGG Bailey Button Boot is a good choice for female.

Posted by: ugg classic cardy boots at November 16, 2009 11:37 PM

Louis Vuitton , commonly referred to as LV Comes First In 2009 World's Top Ten Brands and Mother Shopping With LV Bag!, or sometimes shortened to Journey On LV has become one of the most Sofia Coppola Design Louis Vuitton Bags Agendas luxurybrands Louis Vuitton Flagship Store Opened In California.

Posted by: 1 at November 17, 2009 01:22 AM

UGG Bailey Button bootsis a new style in 2009.The classic cardy uggs boots is another hot boots that worth of buying.And the classic tall ugg boots will make your winter amusing.And now uggs on sale,if you are looking for such a boot,the ugg boots is good choice this year.

Posted by: UGG Bailey Button Boots at November 17, 2009 02:09 AM

I love Women's UGG Classic Cardy Boot 5819 very much. And the new style UGG Mayfaire Boots is aslo a good choice this year.

Posted by: UGG Bailey Button Fancy Boots at November 17, 2009 02:57 AM

I like this post, thank you. and i Just got my ugg boots! They are absolutely beautiful, and the quality is just amazing. No wearing them in, no blisters just absolutely snug strait out of the box. Lol. Uggs boots on sale! So pretty! I will pair them with my new jeans.

Posted by: uggs at November 17, 2009 08:37 PM

Good day! Thx for your great post and Im thinking about how to introduce my ugg boots to you cos Im not sure if u like this. Many people who live in the cold area like the ugg boots, especially the north-europe. Our uggshare.co.uk supply the cheapest classic cardy ugg boots, class tall ugg boots, classic short ugg boots and other series of uggs, hope my words didn’t trouble u, cy!

Posted by: ugg boots at November 17, 2009 09:18 PM

www.enjoywholesale.com

china wholesale clothing,china wholesale shoes,china wholesale electronics,china wholesale suppliers,china manufacturers

china wholesale products,light in the box,wholesale lots,wholesale ipod
china direct,china dropship,china trade,made in china

electronics wholesaler,ebay wholesaler,financial wholesaler
fashion wholesaler,clothing wholesaler,wholesaler magazine

computer wholesaler,external wholesaler,dvd wholesaler,wholesaler definition,china wholesaler,mutual fund wholesaler,define wholesaler,insurance wholesaler

discount ugg boots
forture
ugg boots
Discount store

Posted by: wholesaler business website, net shopping site, external wholesaler,dvd wholesaler,wholesaler definition,china wholesaler,mutual fund wholesaler,define wholesaler,insurance wholesaler at November 18, 2009 03:03 AM

lxjuan08ed hardyis a famous ed hardy store which sell directly ed hardy clothing, shoes, boots, swim suit and other cheap ed hardy.

Browse through our catalogue of hundreds of ed hardy clothing,Ed hardy Shirt,Ed hardy ... Buy Ed Hardy today for a gift, for a friend, or for yourself.

Posted by: ed hardy at November 18, 2009 03:51 AM

movado watches
omega watches
oris watches
Panerai watches
Patek Philippe watches

Posted by: rolex replica at November 18, 2009 10:04 PM

Supra Shoes
Supra Skytop Shoes
Supra Society
Supra Thunder
Supra Suprano Hi
Supra Strapped
Supra Trinity
Supra Skylow 1.5
Supra Dixon
Diablo 1.5
Supra Cruizer
Supra Vaider Shoes
Supra Cuban

Posted by: Supra Shoes at November 19, 2009 02:51 AM

What is good for winter in 2009? I think the new UGG Mayfaire Boots
5116 is a good choice for lady.And the UGG Classic Cardy Boots makes you special.If you want to be warm in the cold days,the UGG Classic Tall Boots makes your dream come true.And aslo the UGG Women's Bailey Button Boot is as fashion as comfortable.There is a special ugg boots for you.

Posted by: uggs on sale at November 19, 2009 03:58 AM

Very good transaction.

mayfaire-boots-c-99.html">ugg mayfaire

boots

are exactly what my daughter wears. Wonderful!!

Posted by: 4wtw4tw at November 19, 2009 08:29 PM

We are the best online sales for the china wholesale . Here you can have a large of choices of kinds Ugg Boots,Converse Shoes,Timberland Boots,puma shoes,Nike Shox Shoes ,Nike Dunk SB Shoes,Nike Air Max，Links Of London,Tiffany Jewelry,Dior Handbags?,jimmy choo handbags ,Cartier Watches, 8GB Mp4 Players,Bluetooth Car DVDs. All our cheap online cheap goods are high quality and original packages, and best service. We offer our customers the best service, 7 days arrive at your door.Enjoy your easy and happy shopping with us.

Posted by: cheap goods sale. at November 19, 2009 09:53 PM

Do you like sports? If you like it,the NIke Air Max TN and Nike Air Max 360 is a good choice for you.And now the there is a good news,CheapNike Air Max running Shoes is waiting for you.I think The New Nike Air MAX 2009 Running Shoes makes you great comfortable.

Posted by: Nike Air Max shoes at November 20, 2009 03:23 AM

Nike Men's AF1 Light-up Shoes
light up air force
light up mens shoes
air force lights-up
light up shoes mens
light up air force ones
light up air force
air force lights-up
light up shoes af1

Posted by: nike af1 light up mens shoes at November 21, 2009 02:52 AM

xiaorong Auction house Antiquorum auctioned off a very rare vintage chronograph Patek Philippe that
replica watches
replica watches
replica Jaeger LeCoultre watches

replica watches
replica watches
replica A.Lange&Sohne watches

replica watches
replica watches
replica Breitling watches

Posted by: replica Piaget watches at November 21, 2009 05:41 AM

Your article is write very well, I like it very much ~
ghd Hair Straightener
ghd Hair Straighteners
ghd straighteners
GHD
hair straighteners
bose in ear headphones
bose on ear headphones
bose headphones
nike sb dunks
nike dunks
I wish you have a wonderful day!Thank you.

Posted by: ghd straighteners at November 22, 2009 08:48 PM

Timeberland boots on sale now! Do you want moreTimeberland boots information?Just move your mouse and press it to our Timberland shoes online store.

Posted by: Timberland uk at November 22, 2009 11:12 PM

discount nike air yeezy
china wholesale online
discount ugg boots
nike free shoes
furture
ugg boots
Discount store

Posted by: nike-airyeezy at November 24, 2009 04:34 AM

Laptop Battery Laptop Battery Laptop Batteries
Laptop Batteries discount laptop battery
discount laptop battery
notebook battery notebook battery
computer battery computer battery
replacement laptop battery replacement laptop battery
notebook batteries notebook batteries

Posted by: Laptop Battery at November 24, 2009 09:47 PM

rongTiffany Jewelry Online - Discount Tiffany & Co Jewelry On Sale

Hot Sell Tiffany Jewelry - Tiffany Jewelry Online

Return To Tiffany Double Heart Detachable Pendant Necklace - Tiffany Jewelry Online

Tiffany&Co 1837 Titanium I.D. Bracelet - Tiffany Jewelry Online
Tiffany & Co Bead Bracelet - Tiffany Jewelry Online

Tiffany&Co Atlas Round Pendant Necklace - Tiffany Jewelry Online
Tiffany&Co Bar Pendant Necklace - Tiffany Jewelry Online
Tiffany&Co Bead Necklace(N242) - Tiffany Jewelry Online
Tiffany&Co Bean Pendant Necklace(N157) - Tiffany Jewelry Online

Posted by: at November 24, 2009 11:08 PM

Ugg Classic Cardy

Boots

Ugg Classic Tall

Boots

Ugg Classic Short

Boots

Posted by: topuggshoes at November 26, 2009 03:20 AM

$75 Replica Rolex Watches sale, Our site provides Rolex replica, replica Rolex Watches, replica breitling, replica Cartier, replica Omega, Tag Heuer Watches. . .more than 100 famous rolex brands"
rolex air king
rolex datejust
rolex day date
rolex daytona
rolex gmt
rolex submariner
rolex yachtmaster
a lange sohne watches
alain silberstein watches
bell&ross watches
breguet watches
breitling watches
bvlgari watches
cartier watches
omega watches
patek philippe watches

Posted by: replica rolex at November 27, 2009 02:21 AM

chaoying nfl jerseys
Giants Jerseys
Patriots Jerseys

Posted by: jerseysleague at November 29, 2009 04:12 AM

China Electronics Wholesale China

Phone Cheap Cell Phones

href="http://www.thechinaphone.com/index.php?main_page=advanced_search_result&keyword=China%20Wholesale">China

Wholesale

replica handbags
Louis Vuitton Replica
Louis Vuitton handbags
fake Louis Vuitton bags
fake Louis Vuitton
replica rolex
replica rolex
fake rolex
buy cheap fake rolex
rolex Submariner

Posted by: lovebo at November 29, 2009 10:54 AM

Paul Smith has been collaborating with a few different organizations recently and his latest venture sees him teaming up with Japanese bicycle saddle, Paul Smith bag, on a limited edition leather saddle. The release features Smith’s signature stripes where only 20 will be available at Paul Smith Clothing store in Japan and 8 at the Floral Street store in London. Get on it quick

Posted by: dasf at November 29, 2009 11:41 AM

Just wanted to say great job with the blog, today is my first visit here and I’ve enjoyed reading your posts so far
ugg bailey button
Wow, my ugg classic mini will not be coming off now! I’ve had them on for 12hrs strait and I do not want to take them off. Thanks for everything, well worth the wait.

Posted by: ugg bailey button boots at November 30, 2009 06:06 AM

replica watch
replica Rolex Datejust
replica croum
Cartier replica
Rolex Submariner replica
handbag sale

Posted by: replica Rolex Datejust at November 30, 2009 02:11 PM

Spring is near,every girl wants to be the bride in the special season.They are eager to put on beautiful Wedding Dresses or the Bridal gowns.During the day the Wedding gowns is the good choose,and the night,if you want radiant,you need the Evening gowns.
About the bridesmaid,they have to wear Bridesmaid Dresses in order to avoid grab limelight with the bride.And the Flower Girl has the Flower Girl Dresses,too.In the wedding,the Cocktail Dresses and the Evening Dresses is necessary,too!And remember,the Wedding Dress of the Bridal Dress must be the most glaring!

Posted by: weddingdressclub at December 1, 2009 01:25 AM

When a girl has Eugenie Wallet experience the poor day, she may have many kinds of imaginations. And the Louis Vuitton Eugenie Wallet desire of shopping may become stronger Louis Vuitton Eugenie Wallet Replica than the desire when she has gucci a good economical situation. Nowadays, it is very common for many young female graduates to go to matrimonial agency to find a good husband but not go to the talent
Neverfull MM

Posted by: fanqin at December 1, 2009 01:49 AM

Posted by: Jimmy Choo Handbags at December 1, 2009 04:31 AM

replica watch
replica Breguet
Bell & Ross watch for sale
replica Bell & Ross
Omega replica
Christian Louboutin Fashion Boots

Posted by: nike sports at December 1, 2009 01:02 PM

Christian Louboutin
cheap Alexander McQueen shoes
Manolo Blahnik shoes
Manolo Blahnik on sale
Alexander McQueen on sale
Tiffany&Co

Posted by: replica Audemars Piguet at December 1, 2009 08:42 PM

UGG Bailey Button
UGG Classic Argyle Knit
UGG Mayfaire
UGG Stripe Cable Knit
Ugg Tall New Arrival
UGG Classic Cardy
UGG Classic Crochet
UGG Classic Mini
UGG Classic Short
UGG Classic Tall
Women's Coquette

UGG Ascot
UGG Nightfall
UGG Sundance
UGG Ultra Short
UGG Ultra Tall
UGG Tasmina
buy cheap ugg bailey button
ugg bailey button sale
ugg short boots
ugg cardy boots
buy cheap women's classic argyle knit
ugg tall boots
wholesale uggs
australian wholesalers ugg boots
Ugg Boots Wholesale
ugg classic authentic sale

Posted by: ugg wholesale at December 2, 2009 07:49 AM

ugg boots sale at a time when large heat has set off a winter 08/09 to Ewha.Outlines the

warm wool winter fashion degree to wool crocheted wool ugg boots uk to join after the

body does not stimulate your skin soft, soft comfort UP. Fashion can not without
ugg boots presence in Winter.and ugg boots have many series.such as:
ugg classic
UGG Bailey Button boots
ugg nightfall
ugg kids

Posted by: uggboots at December 2, 2009 08:41 PM

Merry Christmas ! Go to puma store buy a pair of puma sneakers that have a nice holiday, cat puma,Ferrari puma and Women's Puma Speed Cat etc cheap puma shoes are the best gift for christmas,go on!

Posted by: buy cheap puma shoes on puma store at December 3, 2009 06:57 AM

Merry Christmas ! Go to puma store buy a pair of puma sneakers that have a nice holiday, cat puma,Ferrari puma and Women's Puma Speed Cat etc cheap puma shoes are the best gift for christmas,go on!

Posted by: buy cheap puma shoes on puma store at December 3, 2009 06:58 AM

Search UGG Classic Cardy for long, buy uggs boots on ugg boots online you will get high quality and first-class service, Bailey boots, UGG Classic Tall,UGG Classic Mini etc cheap ugg boots at www.mimiugg.com you could get.

Posted by: cheap ugg boots at December 3, 2009 06:59 AM