January 31, 2008

Sick of Blogger

And yes! I'm sick of Blogger... going to change that really soon...

More on Python 2.5's generators

The implementation I proposed is actually flawed. No sooner than I wrote it, I noticed that the value returned after a send call doesn't depend on the value passed to send itself.

Why? Let me explain the situation. First, let's call the "sender" the function calling send, and "recipient" the function calling the yield.

The recipient's yield call is:

y <- yield x

Conversely, the sender's call is:

x <- send y

Can you see the point? x depends only on what happened in the receiver's past, so it can't depend on y, which is actually in the receiver's future. The same happens to the sender. So:

bar = do x <- yield 1
yield $ x+5

foo = do y1 <- send 1999
y2 <- send 100
return [y1,y2]

returns [1,2004]. That's not the way a Python 2.5's iterator works. Actually, such an iterator can't work at all!

If you can't believe this, try and run the equivalent piece of code in a Python 2.5 interpreter:

def bar():
x = (yield 1)
yield x+5

def foo():
it = bar()

y1 = it.send(1999)
y2 = it.send(100)

return [y1,y2]

You'll get the following error:

TypeError: can't send non-None value to a just-started generator

That simply means that you can't call send() if haven't previously called next(). That's exactly the same reason why my implementation was wrong: the semantics of send() says that the value returned by it must depend on the value passed to it. But, in the first yield() this semantics can't be fulfilled because the value passed to the yield depends only on the past in which, for the first call, can't include the value passed to send().

On subsequent calls, how can Python assure the semantics of send()? The answer is both easy and surprising: the value returned by send() depends on the next yield(), for which that value is actually in its past!

The solution I come up with is rewriting the send function and writing a next in this way:

next = do (RP (y,_)) <- get
return y

send x = do (RP (_,f)) <- get
let rp@(RP (y',f')) = f x
put rp
return y'

Now it works as expected. Notice that, surprisingly, the semantics of send/next depends only on send and next implementation: the yield function is completely apart from it.

Python 2.5's iterators in Haskell (sort of)

DISCLAIMER! The code I present here is likely to be far from perfect and in fact I ask for comments from the community, specifically on how to get rid of the "RecPair" user data type.

Is it possible to mimic Python 2.5's iterators in Haskell? If you don't
know what iterators are (or you're used to 2.4's ones), have a look to PEP343.
By and large, iterators are Python's way to surrogate continuations, which
represent a more general concept usually found in FP languages.

Basically, I want to be able to write something like:

bar = do y <- yield 1
yield (y+2)

and have bar return immediately the argument in a yield call to the caller. Yet, the caller should look like:

foo k = do x <- send undefined -- this will be ignored
y <- send k
return $ [x,y]

First two considerations:

  • It natural to use the Cont monad when implementing the yield function.

  • As two successive calls to send may have different outcomes, some sort of state must be involved. For the basic implementation we resort to State monad.

When trying to solve the puzzle, I stumbled upon a beautiful and straightforward implementation of Python 2.4's iterators by David Menendez. The problem of extending his approach to 2.5 iterators turned out to be a bit more difficult. First, I'll show you the code:

module Main where

import Control.Monad.Cont
import Control.Monad.State

data RecPair a b = Nil RP (b,a -> RecPair a b)

yield x = Cont $ \k -> RP (x,k)

send x = do (RP (y,f)) <- get
put $ f x
return y

runYield it cl = evalState cl $ runCont it $ \_ -> Nil

Let's discuss the yield funtion's implementation. First, as we're working
in the Cont monad, we must return a Cont value which is basically a
function taking a continuation (what to do next) and build a pair (x,k).

x is the value passed to the yield function and then returned to the

What about k? In my mind, k is a function taking an argument (the
receiving variable of a '<-' statement in a do-block) and returning another pair (x',k'), which is the result of the next small step of the Cont computation, till the next yield call. In this way, a computation can't go on after a yield statement until you feed it with a value through a send call, which is the semantics of iterators. Naively, at start I wrote: yield x = Cont $ \k -> (x,k)

But ghc promptly issued the following error:

Occurs check: cannot construct the infinite type t = a -> (t1,t)

What's going on? Let's try and do some type analysis:

  1. The type of "\k -> (x,k)" is "t -> (b,t)" which is perfectly right, as long as "x" is in the scope of that definition and is of type "b".

  2. But, the argument of "Cont" must have type "(a -> r) -> r".

  3. Let's do the bindings: "t = a -> r" and "r = (b,t)".

  4. Substituting the latter in the former we obtain "t = a -> (b,t)".

This equation is clearly impossible to solve (no types exist to make the
equation true) and the Haskell's type system did his job.

How to escape the problem? The real point here is that the above type
equation can be expanded infinitely. There must be a way to stop the
expansion. What if "r" would be masked by an opaque type?

Enter RecPair. We turn the above equation into:

t = a -> RecPair a b

which is perfectly solvable provided there are instances of the type
"RecPair a b". In the above snippet you can find a convenient definition of
RecPair which is suitable to our goal. There are other, like:

data RecPair a b = Nil RP (a -> (b,RecPair a b))

which turns out to be less elegant when you modify yield and send

The other part of the code is just plain Haskell code. Notice that solution
I proposed doesn't mimic completely Python 2.5's iterators: for example,
send can't deal with more than one iterator at the time due to the use of the State monad.

But these are only technicalities which can be easily overcome, for instance,
using the IO Monad and a couple of IORef here and there.

January 29, 2008

syb-with-class 0.4 for HAppS

While I was trying to compile HAppS, I needed version 0.4 the syb-with-class package, which is not in the HackageDB (yet, I hope). I had to grab it from:

darcs get http://happs.org/HAppS/syb-with-class

Hope this will help anyone trying to compile HAppS.

January 21, 2008

Xmonad side bye side KDE

As you may know, I recently switched to ArchLinux... those guys are doing an excellent work and, after some months, I got completely addicted to that kdemod thing... I missed Xmonad though, which jumped from 0.2 to 0.5 in the meanwhile and I badly wanted to give it a try and test out the new features...

What to do? Well, it's indeed possible to run xmonad and kde side-by-side on the same PC. You could fire up a new Xserver on a different display but switching between them may not be fast enough.

Instead, my solution relies on Xnest, an X server running in a window of another X server.

Here's the command line I use:

kstart --desktop 2 --fullscreen -- xinit ~/.xinitrc.xmonad -- /usr/bin/Xnest :10 -geometry 1600x1200 -ac

where .xinit.xmond simply contains:


The command will open a new full-screen Xnest window, with no window decoration, on virtual desktop number 2. Now, you can use the usual shortcuts to switch between virtual desktops to go back and forth KDE and Xmonad.

Best of the two worlds!

UPDATE! Too bad, cut&paste doesn't work between Xnset and the real X server beneath. Any hints?