Applicative arrows for XML &&& return to pure

Last time I had lots of success using Control.Applicative with Data.Binary parsers. Now I’m onto parsing XML. I’ve done this a few times in Haskell using HXT and its funky Arrows. However, this time I was keen to see if I could factor out Yet More Code in an applicative stylee … and indeed I can.

Let’s start with an example of a round-trip XML parse-then-print. We’ll need all the imports and the arrow language extension eventually, so let’s get them out of the way now.

{-# LANGUAGE Arrows #-}

import Control.Applicative
import Text.XML.HXT.Arrow
import Text.XML.HXT.XPath.Arrows
import Text.Printf

xml = "<menu>\
      \  <course name='starter'>Soup</course>\
      \  <course name='mains'>Pie</course>\
      \  <course name='dessert'>Cake</course>\

testRoundtrip = runX $ readString [(a_remove_whitespace,v_1)] xml >>> writeDocumentToString [] 

Now lets parse the xml properly. Firstly, we’ll have a datatype to represent the menu itself:

data Menu = Menu { starter :: String, mains :: String, dessert :: String } deriving (Show)

The parsing code itself starts off by converting the String into a Tree, skipping down over the root node, and then trying to parse out a menu:

testParse = runX $ readString [(a_remove_whitespace,v_1)] xml >>> getChildren >>> parseMenu

Since we want to do multiple things with the “menu” node, we’ll use the special arrow syntax to name things:

parseMenu :: ArrowXml a => a XmlTree Menu
parseMenu = proc menu -> do
              starter < - parseCourse "starter" -< menu
              mains   <- parseCourse "mains" -< menu
              dessert <- parseCourse "dessert" -< menu
              returnA -< Menu starter mains dessert

parseCourse name = getChildren >>> hasName "course" >>> hasAttrValue "name" (==name) >>> getChildren >>> getText 

BTW, whilst the implementation of parseCourse is very combinatorically worthy, in practise I think I’d probably use the following version instead:

parseCourse name = getXPathTrees (printf "//course[@name='%s']/text()" name) >>> getText

Anyhow, looking back at the implementation of parseMenu, something bugs me. I had to give names to “starter”, “mains” and “dessert” despite only ever intending to use them to construct the final return value.

Sounds like a job for Control.Applicative!

However, sadly typing “:i Arrow” into ghci told me that my Arrow types weren’t Functors and therefore I couldn’t immediately perform the < $> and < *> trick to make a one-liner.


But, a quick glance at Control.Applicative showed that the WrappedArrow type was a Functor. So, all I need to do is use the WrapArrow constructor to package up my arrows and, hey presto, applicative city here I come!

parseCourse name = WrapArrow $ getXPathTrees (printf "//course[@name='%s']/text()" name) >>> getText
parseMenu = unwrapArrow $ Menu < $>
             (parseCourse "starter") < *>
             (parseCourse "mains")   < *>
             (parseCourse "dessert")

Okay, so that’s all nice and concise. But it occurs to me that Control.Applicative is still all about *sequencing* computations. But why does parsing XML require sequencing? Surely it’s pure?

Indeed, this is where some of the flexibility of HXT kicks in. HXT supplies a variety of arrow types to fit your needs. If you want to be able to do some disk IO mid-parse, there’s an ArrowIO for you. If you want to maintain some user state during the parse, ArrowState is your friend. But you have the freedom to choose which one you want to use. If you are NOT performing IO and don’t need state, an ArrowList will do you nicely.

Furthermore, most the HXT combinators are uber-flexible. Their types are minimally constrained, allowing you to choose which arrow you want to work in (ie. an IO arrow, a State arrow or a pure List arrow). For example, the “getChildren” function works with any of those three. The HXT combinators which actually do IO (such as readDocument) understandably have a more specific type.

In the running Menu example, parseCourse is pretty flexible. It works with any arrow in the ArrowXml typeclass, which in turns only requires ArrowList behaviour (and a few others which aren’t relevant here).

Therefore, we can use parseCourse as a pure ArrowList, and do some ArrowList-plumbing to supply the three arguments to the Menu constructor. The end result will be a pure function between XmlTree’s and Menu’s. Furthermore, since we’re not using any effectful arrow combinators, we don’t need to nail down the sequencing.

The arr3 combinator converts a 3-arg function into an arrow whose input is a 3-tuple. Well, actually it’s a tuple that looks like (a,(b,c)). But that’s happily what the ‘plumbing’ combinators which we’ll use to plug in the three input arrows produce. So, without further ado:

parseMenuPure :: LA XmlTree Menu
parseMenuPure =  arr3 Menu <<< (parseCourse "starter") &&& (parseCourse "mains") &&& (parseCourse "dessert")

testParsePure = do 
  [xml] < - runX $ readString [(a_remove_whitespace,v_1)] xml
  return $ runLA (getChildren >>> parseMenuPure) xml

So, I’ve come full circle. Arrow syntax looks like monad syntax, and therefore suggests an ordering (I always make this mistake). Control.Applicative provides a concise way to express some common ordering patterns. But not all arrow types have effects which need ordering. If your arrows are pure, you can plumb them directly.

Update: I later realised where my confusion came from. I still had an early version of “testParse” in my file which did the xml reading and the call to parseMenu in one pipeline. This caused type inference to decide that the type of parseMenu was IOSLA (IO + State + List) just like readString is. I somehow assumed this was due to the explicit ordering demanded by the applicative operators – wrong! Once I noticed and removed my original “testParse”, the type of parseMenu reverted back to its natural type of “ArrowXml a => a XmlTree Entry). And that’s the case whether I use the arr3 version, the applicative version or the arrow syntax version. Hmm, so this tells me that I need to play around with Control.Applicative for some non-Monad types … I have an overly specific notion of “sequencing” which is tricking me.

Parsing binaries, applicative stylee

I’ve been writing a parser for a random file format. As usual, I spent more time playing around with simple functions than anything else. But along the way I learned more about Control.Applicative, and in particular how to write use it to write super-concise Data.Binary parsers.

My file format starts with header containing some “magic” bytes, then an app version (1 byte) and a data version (3 bytes) separated by NULLs. The parsed header will have type Header, as follows:

data Header = Header { dataVersion :: Word8, appVersion :: (Word8,Word8,Word8) } deriving Show

magic = (0x5::Word8, 0x6::Word8,0x7 :: Word8)

I’m using Data.Binary, and the parser is just this …

getHeader :: Get Header
getHeader = do 
  fail "Magic word bad" `unlessM` ((== magic) <$> get )
  Header <$> (skip 1 *> get <* skip 1) <*> (get <* skip 3)

So there’s a lot of cool stuff going on here!

  1. To parse the “magic” bytes, I really wanted perl’s “die unless ok” idiom. I couldn’t find anything in the standard library, so I wrote my own “unlessM”. Used with backticks, we end up with code which looks like “die_action `unlessM` everything_is_fine”. The implementation, pointlessly concise is just:

    unlessM :: Monad m => m () -> m Bool -> m ()
    unlessM m b = b >>= (`unless` m)
  2. The ‘get’ action on the first line yields a triple of Word8’s (thank you type inference). The “(== magic)” section compares it with the expected value. To apply the function to the result of the action, we could use liftM however Control.Applicative provides the nicer <$> – reminiscent of normal function application using ($) but, here, in a monadic setting. By the time we’ve plugged those two together, we get a Bool-yielding action .. exactly what unlessM wants.
  3. After parsing the “magic bytes”, we need to skip a byte, grab the app version byte, skip a byte, grab the three data-version bytes, and skip a final 3 bytes .. and then return a Header value. All of this is done in a single line:

    Header <$> (skip 1 *> get <* skip 1) <*> (get <* skip 3)

    Reading from left to right, this says:

    • We’re going to return a value built using the Header constructor, a function which takes 2 arguments.
    • Header’s first argument comes from a skip-get-skip action. More on this next, but note that <$> is just function-applied-to-result-of-computation which we’ve seen already in line 1.
    • To grok the skip-get-skip action, first imagine that the *-operators mean simply “and then..”, ie. the three actions are sequenced. In practise, they have another trick up their sleeve. What happens to the values yielded by each of the three actions? That’s where the arrows come in. They point to the action whose value is “the chosen one”. So, “a <* b” is a composite action where “a” runs first, followed by “b”, with a’s value being yielded and b’s is ignored. This works quite nicely in this example. Why is this any different to monadic bind? Sure, each sub-parser is independent of it’s mates – the ‘get’ parser has no interest in what the ‘skip’ parser returned – but >> would do that. The important difference is that the values yielded by the parser are only used once – right at the end. In this example, we don’t vary the parsing based on anything we read – although, in general, we might well want to do that. It’s horses for courses; if you want to combine actions but only need to hyperspace one value out, <* and *> are your friends. If you need to combine actions in more complicated ways, >>= is there waiting for you.
    • So far, we’ve glued together the Header function and (the action which produces) its first argument so far. So we need to bake /that/ together with the action for the second argument. That’s what the <*> operator from Control.Applicative gives you. Again, the intuition is that * means sequencing, but this time both the left and right arguments are used to determine the value yielded; specifically via function application.

But now I ask myself: is this readable code, or is it line noise?

Certainly, you have to understand what the four applicative operators do .. and ‘applicative’ sounds scary. However, those operators capture two patterns which occur all the time in parsers. Firstly, a parser yields some final result, based on the data it saw whilst running its component parsers in order (ie. <$> and <*>). Secondly, each part of the returned value corresponds to some subset of the component parsers, although we don’t always use all of the bits we parsed (<* and *>). A parser for a real world file format is going to do these things over and over, so it makes sense to factor the patterns out and give it a (fairly) evocative syntax.

Secondly, type inference is doing a lot of work here. Mostly, I just need to call ‘get’ and the compiler can infer whether I’m expecting to parse a byte or three bytes. It’s all driven off the top level Header type itself. I do worry that this introduces a very strong coupling between the data definitions and the behaviour of the parser. Let’s say I want to elide the third field of the appVersion. If I just change appVersion to be a 2-tuple instead of a 3-tuple, then the parser will still build and run – except it won’t parse the right file format anymore! I need to remember myself to go in and add a “skip 1” into the parser. Sure, type inference is a double edged sword and I can remedy this simply by adding explicit type signatures in appropriate places.

Ho hum, now I need to stop procrastinating and actually parse the files …

Model Checking

Model checking has been on my list of “stuff to understand” for a long time. It’s one of the few ‘formal methods’ which gets noticeable positive press. This month’s Communications of the ACM had a big article about it, of which I understood very little. However, it prompted me to search t’internet and this introduction to model checking which, shockingly, has an actual worked (ableit trivial) example. Now I am enlightened!

Talks @ University

This morning, I did an guest lecture for the Advances in Programming Languages course at Edinburgh University. I’ve talked at the University before, as part of the SPLS seminars. So, when I met Ian Stark again at ICFP and he invited me to talk to his class, I jumped at the chance.

Partly, I just love doing talks. But, specifically, I thought it would be a good opportunity to share some of the stuff I’ve learned over the last 12 years since I left uni. I’ve interviewed lots of graduates over the years, and I’ve seen how they adapt to working in industry. I’ve seen grads grow into world class software developers, and I’ve observed some of the common traits and interests that the best of them have.

And so my talk split into three themes. Firstly, I explained why I think learning languages is a worthwhile use of one’s precious/finite time. Secondly, I explored which languages give you the biggest bang-for-buck in terms of expanding your world view. And, finally, I used erlang as a concrete example to explore both the design pressures that influence a language, and to ‘cherrypick’ the key ideas from the language.

My aim was not to convince anyone to use Erlang day-to-day. My aim was to demonstrate that you can expand your mind by seeking out new ideas. Much like riding a bicycle, once you’ve seen a new way to look at the world you never forget it. And Erlang, operating in the difficult realm of high availability software, was full of good examples.

It’s pretty cool to be asked back to the University you graduated from, and to have the chance to share your thoughts with the next generation of students. Thanks to Ian Stark and David Aspinall for inviting me back to the Uni.

Royal Institution Christmas Lectures, take one

When I visited the Royal Institution in London recently, there was obviously something ‘going on’ in the building. After checking out the official exhibit in the basement, I explored the building by following the staircase up past an interesting succession of portraits. I could hear a professional sounding talk coming from somewhere, and saw several stressed stagehands running from a room packed with scientific props to a door leading to a backstage area.

This, then, would be the world-famous Royal Institution Christmas Lectures! They’re now being shown on TV as I speak. I didn’t want to get in the way of the stagehands and their precious cargo, and so I beat a hasty retreat back downstairs.

However, I noticed today that the RI website says that the christmas lectures are held at 6pm. But I visited there at around 3pm. So how come I managed to overhear a lecture?

Turns out, these slick tv productions don’t “just happen”. I found an article by a previous xmas lecturer which explain the painful reality. Each lecture is preceded by at least a gruelling day and a half of rehearsals and planning. It’s more like a stage show than a simple lecture – the cameras, sound guys, lighting and stagehands all need to figure out what they’ll be doing and when they’ll be doing it. And the lecturer needs to figure out where to look, who to talk to *and* remember their words! Seems like working with children & animals is the least of their troubles.

Having watched the first lecture on TV now, I’m left wondering how they got two donkeys up to the lecture theatre. Did they walk up the stairs? Do they have a lift – and, if so, would you get into a lift with two donkeys?!

And so I leave the Royal Institution, home of Michael Faraday and Humphry Davy, by contemplating the deepest question of science: Donkeys and staircases. Staircases and donkeys.