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I just learned about GHC's RebindableSyntax extension from chrisdoner's thread on reddit and wanted to play around with scratching a couple itches I've had. In this post I'll illustrate using RebindableSyntax to allow us to use haskell's do notation in a State-monad-like construction, in which our state type is allowed to change (I've played with this idea previously).

The dynamic state construction looks like the traditional State, but with separate types for input and output state:

{-# LANGUAGE DeriveFunctor, MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-} newtype DynState s1 s2 a = DynState { runState :: s1 -> (a,s2) } deriving Functor get :: DynState s s s get = DynState $ \s-> (s,s) put :: s -> DynState x s () put = DynState . const . (,) () modify :: (s1 -> s2) -> DynState s1 s2 () modify = DynState . fmap ((,) ())

We can compose these by defining a (for the moment, very verbose) function dynStateBind. Interestingly, this is actually easier to understand IMHO than the State monad because the type signature makes explicit the fact that our lambda-bound state s1 is the initial state value that we run the construction on:

infixl 1 `dynStateBind` dynStateBind :: DynState s1 s2 a -> (a -> DynState s2 s3 b) -> DynState s1 s3 b dynStateBind x f = DynState $ \s1-> let ~(a,s2) = runState x s1 in runState (f a) s2

We also need stand-ins for (>>) and return:

-- It would be nice if >> inherited default instances in terms of bind, as in -- an instance declaration infixl 1 `dynThen` dynThen :: DynState s1 s2 a -> DynState s2 s3 b -> DynState s1 s3 b dynThen x y = x `dynStateBind` \_ -> y dynReturn :: a -> DynState s s a dynReturn a = DynState $ \s-> (a,s)

So then we can use all the nonsense above as follows:

{-# LANGUAGE RebindableSyntax #-} module Main where import Prelude -- since RebindableSyntax implies NoImplicitPrelude import DynState -- avoid lame "Not in scope: `ifThenElse'" ifThenElse b x y | b = x | otherwise = y -- oops, infinite loop fail! --ifThenElse b x y = if b then x else y test :: DynState Int Int String test = let (>>=) = dynStateBind (>>) = dynThen return = dynReturn in do i <- get -- state :: Int put (even i, show i) -- state :: (Bool, String) (b,i_str) <- get put (i+1) -- state :: Int if b then return "uh oh, even!" else return $ "pre-incremented: "++i_str

If we want to we can even enrich our bind and add some machinery to support composing traditional StateT computations with our dynamic state:

-- | a silly class to support comosing regular State monad computations with -- dynamic state computations. class Stateful n s1 s2 | n -> s1 s2 where expand :: n a -> DynState s1 s2 a instance Stateful (DynState s1 s2) s1 s2 where expand = id instance Stateful (M.StateT s Identity) s s where expand = DynState . M.runState -- category with bind sort of situation... polyDynStateBind :: (Stateful x s1 s2, Stateful y s2 s3)=> x a -> (a -> y b) -> DynState s1 s3 b polyDynStateBind x f = expand x `dynStateBind` fmap expand f -- | convert a dynamic stateful computation into the usual State monad, so we -- can compose it with normal state computations flatten :: DynState s s a -> M.State s a flatten = M.state . runState Zippers

At some point while working on zippo (you
should check out this instead) I made up detailed notes on a DSL for zipper operations that I wished I could shoe-horn into do or Arrow notation, but never quite could.

Lost the notes, but the idea would be to have bind expose the "focus" of the zipper and allow motions down and up to be sequenced nicely with minimal boilerplate, as in the state monad. Maybe I'll find those and fill in this section properly.

Trying to install Ed Kmett's category-extras package and ran into this:

$ cabal-dev install category-extras Resolving dependencies... cabal: Could not resolve dependencies: trying: category-extras-1.0.2 trying: representable-functors-3.0.1 trying: mtl-2.1.1/installed-801... trying: pointed-3.0.2 rejecting: indexed-extras-0.1.1 (conflict: pointed==3.0.2, indexed-extras => pointed<2.2) rejecting: indexed-extras-0.1 (conflict: mtl==2.1.1/installed-801..., indexed-extras => mtl<2.1)

submitted by peterjoel
[link] [8 comments]

Is there a page somewhere that aggregates all of Haskell's community output into one place? As a consumer of Haskell content I neither have the time nor inclination to follow haskell-cafe and other various mailing lists, the reddits, the google+ community, planet haskell, hackage releases, twitter, youtube and whatever other submission places I haven't heard of. I made this page for the Lojban community some years ago: http://jbotcan.org/hub/ Lojban doesn't have much community activity (tho this doesn't include mailing list posts), but Haskell's community is much larger and more active, it would be far more useful. I may write such a page for Haskell content, if not for the community then at least for myself, as I keep missing out on cool things because I didn't happen to check out that particular medium of exchange. For example, even this message will be lost on a thousand people who doesn't follow the mailing list but maybe follows G+ or reddit. Kind of like a Haskell Weekly news, except more like "Ha

submitted by timthelion
[link] [45 comments]

Hi, Linuxmint Nadia, ghc-7.6.1 was built and running OK. Just downloaded ghc-7.6.2, without changing anything and environment, and boot and configure returned OK, I got these. What happened? 20130210Sun183147magicloud< at >ctu-9986008283~/s/ghc-7.6.2 $ make + test -f mk/config.mk.old + cp -p mk/config.mk mk/config.mk.old touch -r mk/config.mk.old mk/config.mk + test -f mk/project.mk.old + cp -p mk/project.mk mk/project.mk.old touch -r mk/project.mk.old mk/project.mk + test -f compiler/ghc.cabal.old + cp -p compiler/ghc.cabal compiler/ghc.cabal.old touch -r compiler/ghc.cabal.old compiler/ghc.cabal ===--- building phase 0 make -r --no-print-directory -f ghc.mk phase=0 phase_0_builds libraries/hpc/ghc.mk:3: libraries/hpc/dist-boot/package-data.mk: No such file or directory libraries/Cabal/Cabal/ghc.mk:3: libraries/Cabal/Cabal/dist-boot/ package-data.mk: No such file or directory libraries/binary/ghc.mk:3: libraries/binary/dist-boot/package-data.mk: No such file or directory libraries/bin-package-db/ghc.mk:3: l

Path Dependency

Now we are able to price options using parallelism, let us consider a more exotic financial option.

Let us suppose that we wish to price an Asian call option. The payoff at time is

Thus the payoff depends not just on the value of the underlying at time but also on the path taken. We do not need to know the entire path, just the average at discrete points in time. Thus the payoff is a function of time, the value of the underlying and the average of the underlying sampled at discrete points in time .

We can rewrite this equation as a recursive relation:

If is the -th sampling time then for small let:

Now we can write the equation for the value of the average just before and after the sampling time as:

Since there is no arbitrage, the value of the option cannot change as it crosses the sampling date:

Substituting in:

But we have a problem, we do not know the value of . Away from the sampling times there is no dependence on as its value cannot change. We already know how to step back in time in this case: we use the pricer we have already developed.

So let us assume a value for . Then we can diffuse backwards from the final payoff but when we reach a sampling date, we reset the values on the grid using the interfacing formula above.

In summary, we assume a set of values for and then diffuse backwards for each pricer with that ; at each sampling time, we reset the values of the pricers and continue until we reach the last sampling time. At this point, so we diffuse one pricer back to the start time which gives us the price of the option for any given on our grid.

Our usual imports and options.

> {-# LANGUAGE FlexibleContexts #-} > {-# LANGUAGE TypeOperators #-} > {-# LANGUAGE NoMonomorphismRestriction #-} > > {-# OPTIONS_GHC -Wall #-} > {-# OPTIONS_GHC -fno-warn-name-shadowing #-} > {-# OPTIONS_GHC -fno-warn-type-defaults #-} > > import Data.Array.Repa as Repa hiding ((++), map) > import Control.Monad > import AsianDiagram > import Diagrams.Prelude((===)) > import Diagrams.Backend.Cairo.CmdLine > import Text.Printf > import Data.List

First some constants for the payoff and the pricer. We make the space grid deliberately coarse so we can draw diagrams showing the grid before and after interfacing.

> r, sigma, k, t, xMax, aMax, deltaX, deltaT, deltaA:: Double > m, n, p :: Int > r = 0.05 > sigma = 0.2 > k = 50.0 > t = 3.0 > m = 10 > p = 10 > xMax = 150 > deltaX = xMax / (fromIntegral m) > aMax = 150 > deltaA = aMax / (fromIntegral p) > n = 100 > deltaT = t / (fromIntegral n)

We take the times at which do our Asian observations and calculate the number of steps between each observation including the initial and terminal times.

> asianTimes :: [Int] > asianTimes = map (\x -> floor $ x*(fromIntegral n)/t) [1.5,2.0,2.5] > > numSteps :: [Int] > numSteps = snd $ mapAccumL (\s x -> (x, x - s)) 0 times > where times = asianTimes ++ [n]

As before we can define a single pricer that updates the grid over one time step and at multiple points in space using the Explicit Euler method. We parameterize the upper and lower boundaries and as we will want to use our pricer not just for a vanilla call option.

> type BoundaryCondition = Array D DIM1 Double -> Double > > singleUpdater :: BoundaryCondition -> > BoundaryCondition -> > Array D DIM1 Double -> > Array D DIM1 Double > singleUpdater lb ub arr = traverse arr id f > where > Z :. m = extent arr > f _get (Z :. ix) | ix == 0 = lb arr > f _get (Z :. ix) | ix == m-1 = ub arr > f get (Z :. ix) = a * get (Z :. ix-1) + > b * get (Z :. ix) + > c * get (Z :. ix+1) > where > a = deltaT * (sigma^2 * x^2 - r * x) / 2 > b = 1 - deltaT * (r + sigma^2 * x^2) > c = deltaT * (sigma^2 * x^2 + r * x) / 2 > x = fromIntegral ix

Again we can extend this to update many pricers on one time step and multiple points in space.

> multiUpdater :: Source r Double => > BoundaryCondition -> > BoundaryCondition -> > Array r DIM2 Double -> > Array D DIM2 Double > multiUpdater lb ub arr = fromFunction (extent arr) f > where > f :: DIM2 -> Double > f (Z :. ix :. jx) = (singleUpdater lb ub x)!(Z :. ix) > where > x :: Array D DIM1 Double > x = slice arr (Any :. jx)

We define the boundary condition at the maturity date of our Asian option. Notice for each pricer the boundary condition is constant, this being determined by the value of the Asian payoff.

> priceAtTAsian :: Array U DIM2 Double > priceAtTAsian = fromListUnboxed (Z :. m+1 :. p+1) > [ max 0 (deltaA * (fromIntegral l) - k) > | _j <- [0..m], > l <- [0..p] > ]

With this we can step backwards in time for any number of timesteps.

> stepMulti :: Monad m => > Int -> > BoundaryCondition -> > BoundaryCondition -> > Array U DIM2 Double -> > m (Array U DIM2 Double) > stepMulti n lb ub = updaterM > where > updaterM :: Monad m => Array U DIM2 Double -> > m (Array U DIM2 Double) > updaterM = foldr (>=>) return updaters > where > updaters = replicate n (computeP . multiUpdater lb ub) Boundary Conditions

But now we are stuck. What are the boundary conditions for each of the pricers after we have done our interfacing? We follow many practioners and assume that the underlying is linear in this area. Thus in the Black-Scholes equation

we set the second derivative to . Thus we can use a forward method at the boundary to solve the equation below.

When , we have a simpler situation.

The corresponding difference equation for the lower boundary is:

Which is easily represented in Haskell (rembering we are stepping backwards in time).

> lBoundaryUpdater :: BoundaryCondition > lBoundaryUpdater arr = x - deltaT * r * x > where > x = arr!(Z :. (0 :: Int))

The corresponding difference equation for the upper boundary is:

Re-arranging

We can write this in Haskell as follows (again remembering we are stepping backwards in time).

> uBoundaryUpdater :: BoundaryCondition > uBoundaryUpdater arr = x - deltaT * r * (a - b) > where > Z :. m = extent arr > x = arr!(Z :. m - 1) > y = arr!(Z :. m - 2) > a = x * fromIntegral (m - 1) > b = y * fromIntegral m Interfacing

We interface by linear interpolation if value we require lies between 2 points on our grid otherwise we use linear extrapolation.

> interface :: Int -> Array U DIM2 Double -> > Array D DIM2 Double > interface n grid = traverse grid id (\_ sh -> f sh) > where > (Z :. _iMax :. jMax) = extent grid > f (Z :. i :. j) = inter > where > x = deltaX * (fromIntegral i) > aPlus = deltaA * (fromIntegral j) > aMinus = aPlus + (x - aPlus) / (fromIntegral n) > jLower = if k > jMax - 1 then jMax - 1 else k > where k = floor $ aMinus / deltaA > jUpper = if (jLower == jMax - 1) > then jMax - 1 > else jLower + 1 > aLower = deltaA * (fromIntegral jLower) > prptn = (aMinus - aLower) / deltaA > vLower = grid!(Z :. i :. jLower) > vUpper = grid!(Z :. i :. jUpper) > inter = vLower + prptn * (vUpper - vLower) Example

Now we are in a position to give an example of pricing our option with a few helper functions

> showD :: Double -> String > showD = printf "%.2f" > > showArrD1 :: Array U DIM1 Double -> String > showArrD1 = intercalate ", " . map showD . toList > > showSlices :: String -> Array U DIM2 Double -> IO () > showSlices message prices = do > putStrLn ('\n' : message) > > let (Z :. _i :. j) = extent prices > slicesD = map (\m -> slice prices (Any :. m)) [0..j-1] > > slices <- mapM computeP slicesD > mapM_ (putStrLn . showArrD1) slices > > diagonal :: Source a Double => > Array a DIM2 Double -> > Array D DIM2 Double > diagonal arr = traverse arr g f > where > f :: (DIM2 -> Double) -> DIM2 -> Double > f get (Z :. ix :. _) = get (Z :. ix :. ix) > > g :: DIM2 -> DIM2 > g (Z :. ix :. iy) = Z :. (min ix iy) :. (1 :: Int) > > main :: IO () > main = do putStrLn "\nAsianing times" > putStrLn $ show asianTimes > > let lb = lBoundaryUpdater > ub = uBoundaryUpdater > > showSlices "Initial pricers" priceAtTAsian

Now instead of stepping all the way back to the initial time of the option, we only step back to just before the last observation.

> grid3b <- stepMulti (numSteps!!3) lb ub priceAtTAsian > showSlices ("Just before 3") grid3b

The diagram below shows our grid just before we make the last observation. The -axis is the value of the underlying and the -axis is the value of the Asian value. Both have been normalised to 1.0. That is the value 1.0 represents 150.0 (our maximum value on the grid for both the underlying and the Asian / auxiliary variable).

> grid3a <- computeP $ interface 3 grid3b > showSlices ("Just after 3") grid3a

The diagram below shows our grid after before we make the last observation i.e., after interfacing. Again, the -axis is the value of the underlying and the -axis is the value of the Asian value. Both have been normalised to 1.0. That is the value 1.0 represents 150.0 (our maximum value on the grid for both the underlying and the Asian / auxiliary variable).

And then step backwards with the new final boundary condition.

> grid2b <- stepMulti (numSteps!!2) lb ub grid3a > showSlices ("Just before 2") grid2b > > grid2a <- computeP $ interface 2 grid2b > showSlices ("Just after 2") grid2a

Again we step backwards in time with a new final boundary condition.

> grid1b <- stepMulti (numSteps!!1) lb ub grid2a > showSlices ("Just before 1") grid1b

Finally we step all the way back to the time at which we wish to know the price. Here the interface condition is just so we can take the diagonal of our grid and diffuse backwards using a single pricer.

> grid1a <- computeP $ diagonal grid1b > showSlices ("Just after 1") grid1a > grid1b <- stepMulti (numSteps!!0) lb ub grid1a > showSlices "Final pricer" grid1b

submitted by crntaylor
[link] [23 comments]

I’m busy revising the “How Idris works” paper, and you can find the latest draft here. Any further comments on how to improve it would be most welcome! Abstract:

Many components of a dependently typed programming language are by now well understood, for example the underlying type theory, type checking, unification and evaluation. How to combine these components into a realistic and usable high level language is, however, folklore, discovered anew by successive language implementations. In this paper, I describe the implementation of a new dependently typed functional programming language, IDRIS. IDRIS is intended to be a general purpose programming language and as such provides high level concepts such as implicit syntax, type classes and do notation. I describe the high level language and the underlying type theory, and present a method for elaborating concrete high level syntax with implicit arguments and type classes into a fully explicit type theory. Furthermore, I show how this method, based on a domain specific language embedded in Haskell, facilitates the implementation of new high level language constructs.

I discovered an Haskell channel on Vimeo but last update was 3 years ago. It's a shame, because that, combined with the fact there are a lot of false positives when searching for "Haskell", I sometimes struggle to find something relevant, so a lot of cool Haskell videos posted here simply get forgot (at least, I tend to forget about them, simply because I'm on my iPad and I'm too lazy to login on Vimeo and add the video to my favourite one / watch later). Put this with the fact that not everyone has a Vimeo account, for this last time of users there's almost no way to find the videos later (well, you can use the old school Bookmarks/Read it Later but I tend to forget about stuff I put in there :D )

In a nutshell, I've created this channel here:

https://vimeo.com/channels/472404

It's a shame to have such a duplication though, so if someone has the contact of the original channel moderator I will be more than happy than do a bit of housekeeping and to add a bit of more recent content. I've also decided to give the channel a different name, to make it more explicit during searches. For now I've added just a bunch of cool videos from the NYC Haskell meetup, but if you send me as PM your video links I'll add them for you.

At the end of the day I'm sorry for the duplication on Vimeo, and I hope we can have an updated, modern channel to collect stuff, but I've created this channel primary for me as container of useful stuff and I though it could have been useful also for someone else :)

submitted by CharlesStain
[link] [7 comments]

submitted by Thirsteh
[link] [7 comments]

[Resending; looks like libraries< at > does not like my < at >debian.org address] Hi, the readline package (used by lambdabot) lists libraries< at >haskell.org as the maintainer. Is that accurat: Does anyone on this list feel responsible for the package? If so, would you care to make it GHC-7.6-compatible: System/Console/Readline.hsc:587:1: Unacceptable result type in foreign declaration: IO CInt When checking declaration: foreign import ccall unsafe "static rl_unbind_key" rl_unbind_key :: CInt -> IO CInt (and many more of that kind) Greetings, Joachim

[sorry for the possible double-post, apparently posting through the google groups interface is futile] Hi, In case someone is around Budapest on the 14th of Feb (Thursday), there is going to be a Haskell meetup in the heart of the city. Hamish Mackenzie will talk about yet-to-be-released Leksah features and David Terei will explain how his memcache client works. Details and sign up at http://www.meetup.com/fp-bud/events/102245252/ Hope to see you there :) Zsolt _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe< at >haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

[Apologies if you receive multiple copies of this CFP] ======================================================= CALL FOR PAPERS 17th BRAZILIAN SYMPOSIUM ON PROGRAMMING LANGUAGES Brasília, Distrito Federal, Brazil September 29th to October 4th, 2013 http://cbsoft2013.cic.unb.br/sblp ======================================================== IMPORTANT DATES Paper abstract submission (15 lines): April 19th Full paper submission: April 26th, 2013 Notification of acceptance: May 31st, 2013 Final papers due: June 28th, 2013 INTRODUCTION The 17th Brazilian Symposium on Programming Languages, SBLP 2013, will be held in Brasília, Brazil, on September 29th to October 4th, 2013. SBLP provides a venue for researchers and practitioners interested in the fundamental principles and innovations in the design and implementation of programming languages and systems. The symposium will be part of the 4th Brazilian Conference on Software: Theory and Practice, CBSoft 2013, http://cbsoft2013.cic.unb.br/, which will host f

I talked about some of Haskell’s type system features. You can find a write-up of my talk on my personal blog.