December 2006 - Haskell

Announcing Djinn, version 2004-12-11, a coding wizard
by Lennart Augustsson 07 Apr '11

07 Apr '11

Howdy, y'all! I've written a small program that takes a (Haskell) type and gives you back a function of that type if one exists. It's kind of fun, so I thought I'd share it. It's probably best explained with a sample session. calvin% djinn Welcome to Djinn version 2005-12-11. Type :h to get help. # Djinn is interactive if not given any arguments. # Let's see if it can find the identity function. Djinn> f ? a->a f :: a -> a f x1 = x1 # Yes, that was easy. Let's try some tuple munging. Djinn> sel ? ((a,b),(c,d)) -> (b,c) sel :: ((a, b), (c, d)) -> (b, c) sel ((_, v5), (v6, _)) = (v5, v6) # We can ask for the impossible, but then we get what we # deserve. Djinn> cast ? a->b -- cast cannot be realized. # OK, let's be bold and try some functions that are tricky to write: # return, bind, and callCC in the continuation monad Djinn> type C a = (a -> r) -> r Djinn> returnC ? a -> C a returnC :: a -> C a returnC x1 x2 = x2 x1 Djinn> bindC ? C a -> (a -> C b) -> C b bindC :: C a -> (a -> C b) -> C b bindC x1 x2 x3 = x1 (\ c15 -> x2 c15 (\ c17 -> x3 c17)) Djinn> callCC ? ((a -> C b) -> C a) -> C a callCC :: ((a -> C b) -> C a) -> C a callCC x1 x2 = x1 (\ c15 _ -> x2 c15) (\ c11 -> x2 c11) # Well, poor Djinn has a sweaty brow after deducing the code # for callCC so we had better quit. Djinn> :q Bye. To play with Djinn do a darcs get http://darcs.augustsson.net/Darcs/Djinn or get http://darcs.augustsson.net/Darcs/Djinn/Djinn.tar.gz Then just type make. (You need a Haskell 98 implementation and some libraries.) And then start djinn. For the curious, Djinn uses a decision procedure for intuitionistic propositional calculus due to Roy Dyckhoff. It's a variation of Gentzen's LJ system. This means that (in theory) Djinn will always find a function if one exists, and if one doesn't exist Djinn will terminate telling you so. This is the very first version, so expect bugs. :) Share and enjoy. -- Lennart

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Haskell-mode 2.0
by Stefan Monnier 02 Feb '09

02 Feb '09

I have recently taken over maintainership of Haskell-mode, and after making a bunch of changes, I figured it would be a good idea to make a new release. You can find this new release at: http://www-perso.iro.umontreal.ca/~monnier/elisp/ If you think it should also be found at http://www.haskell.org/haskell-mode/, then please tell John Peterson to get back to me (my email to him seem to go straight to the bitbucket. John?). This release has several changes that have all been only lightly tested, especially w.r.t compatibility with various Emacsen. See appended the NEWS file that describes some of the notewirthy changes. Stefan Changes since 1.45: * keybindings C-c <char> have been replaced by C-c C-<char> so as not to collide with minor modes. * The following modules are now automatically activated without having to add anything to haskell-mode-hook: haskell-font-lock (just turn on global-font-lock-mode). haskell-decl-scan (just bind `imenu' to some key). * In recent Emacsen, haskell-doc hooks into eldoc-mode. * haskell-hugs and haskell-ghci are superceded by inf-haskell. * Indentation rules have been improved when using layout inside parens/braces. * Symbols like -> and \ can be displayed as actual arrows and lambdas. See haskell-font-lock-symbols. * Tweaks to the font-lock settings. Among other things paren-matching with things like \(x,y) should work correctly now. * New maintainer <monnier(a)gnu.org>.

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state of HaXml?
by nr＠eecs.harvard.edu 11 Jan '07

11 Jan '07

I have some XML things to take care of, and I had hoped to use a nice functional language with combinators. But I'm having trouble getting HaXml to do anything useful. Here is a program that I wrote just to read in the XML and prettyprint it. But it fails with an error message. The 'expat' tool 'xmlwf' claims the XML is well formed, and the XML was generated from gpsbabel, a tool I trust to behave properly. And yet: : nr@curlycoat 10429 ; xmlwf 2006-12-27-backup.gpx : nr@curlycoat 10430 ; $AWD/Main 2006-12-27-backup.gpx Main: Parse error: unexpected EOF Here is Main.hs: module Main where import qualified Text.XML.HaXml as X import qualified Text.XML.HaXml.Parse as XP import qualified Text.XML.HaXml.Pretty as XPP import qualified IO import qualified System load :: String -> IO X.Document load fn = do handle <- IO.openFile fn IO.ReadMode contents <- IO.hGetContents handle IO.hClose handle return $ XP.xmlParse fn contents main = do [xml] <- System.getArgs d <- load xml IO.putStrLn $ show $ XPP.document $ d I'm using HaXml version 1.13.2-5 as distributed by Debian, with GHC 6.6. Does anyone have thoughts or suggestions? Is there software I should prefer to HaXml? (I notice that HaXml does not understand XML Schema, which I seem to be stuck with...) Norman

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ghci readline support on FreeBSD: simple patch
by Brandon S. Allbery KF8NH 31 Dec '06

31 Dec '06

The problem people have been having with ghci on FreeBSD turns out to be a bootstrapping issue: if the bootstrap compiler was not built with readline support, or it doesn't include ghc-pkg (the FreeBSD bootstrap ghc has been stripped down to bare essentials, so guess what's not there?), then ghc won't be built with readline support unless you build the stage2 and stage3 compilers. Since ports only builds stage1, with the crippled bootstrap ghc, the result is no readline in ghc itself. (But the readline package is built, so Haskell programs which themselves use readline work fine.) The attached patch is a simplistic, hacky workaround which stubs out the offending configure test. Since ports ghc declares readline as a dependency, this is safe (or at least safe enough). Drop it into / usr/ports/lang/ghc/files and (re)build ghc (either "cd /usr/ports/ lang/ghc; make install clean -DFORCE_PKG_REGISTER", or "portupgrade - f ghc", or deinstall and reinstall from scratch). You will probably want to do something to keep it from being removed or to copy it back when you update the ports tree with portsnap or cvsup. I'm not going to bother reporting this to the port maintainer because it'll just get stuck in the same queue that's holding the ghc-6.6 upgrade. :) -- brandon s. allbery [linux,solaris,freebsd,perl] allbery(a)kf8nh.com system administrator [openafs,heimdal,too many hats] allbery(a)ece.cmu.edu electrical and computer engineering, carnegie mellon university KF8NH

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Converting a 'streaming' monad into a list
by Ryan Ingram 31 Dec '06

31 Dec '06

Hi everyone... it's my newbie post! I am trying to create a monad which allows computations to output data to a stream. (Probably such a thing already exists, but it's a good problem for my current skill level in Haskell) For example: streamDemo = do output 1 output 2 output 5 makelist streamDemo -- [1,2,5] I modelled my implementation around the state monad, but with a different execution model: class (Monad m) => MonadStream w m | m -> w where output :: w -> m () run :: m a -> s -> (s -> w -> s) -> s -- basically foldl on the stream values makelist m = reverse $ run m [] (flip (:)) -- s is the type of the object to stream, r is the return type type StreamFunc s r = forall b. b -> (b -> s -> b) -> (r,b) newtype Stream s r = Stream { run' :: StreamFunc s r } instance Monad (Stream s) where return r = Stream (\s _ -> (r,s)) Stream m >>= k = Stream (\s f -> let (r,s') = (m s f) in run' (k r) s' f) instance (MonadStream w) (Stream w) where output w = Stream (\s f -> ((),f s w)) run m st f = snd $ run' m st f What I don't like is how makelist comes out. It feels wrong to need to use reverse, and that also means that infinite streams completely fail to work. But I think it's impossible to fix with the "foldl"-style "run". Is there a better implementation of "makelist" possible with my current definition of "run"? If not, what type should "run" have so that it can work correctly? As an example, I want to fix the implementation to make the following code work: fibs :: Stream Integer () fibs = fibs' 0 1 where fibs' x y = output y >> fibs' y (x+y) fiblist :: [Integer] fiblist = makelist fibs take 5 fiblist -- [1,1,2,3,5], but currently goes into an infinite loop Thanks, -- ryan

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ANN: vty 2.0
by Stefan O'Rear 31 Dec '06

31 Dec '06

A new major version of vty exists: http://members.cox.net/stefanor/vty/dist/vty-2.0.tar.gz darcs get --tag=rel-2.0 http://members.cox.net/stefanor/vty Differences from 1.0: * vty now uses a record type for attributes, instead of bitfields in an Int. This is the reason for increasing the major version. * vty now supports setting background colors. * You can now explicitly specify 'default' colors (blending in with the terminal configuration). * vty now supports five ANSI boolean attributes: reverse-video, bold, underline, half-bright, and blinking. (1.0 only supported bold.) * vty now supports Unicode characters on output, automatically setting and resetting UTF-8 mode (beware double width and combining characters!) * vty now disables ISIG and IXOFF, allowing C-q, C-s, C-c, C-z, and C-\ to be received as input. * vty now properly handles cleanup, leaving the cursor at the bottom of the screen and erasing the last line.

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"Limits to implicit parallelism in functional applications"
by John DeTreville 31 Dec '06

31 Dec '06

Hello, True or False? "Many interesting functional applications contain significant amounts of implicit parallelism that we can imagine usefully exploiting." I've recently written a short paper about how much implicit parallelism there might be in ordinary functional applications. Here's an abstract. Today's sequential software is executed more and more often on parallel hardware from which it obtains no incremental performance benefit. We can address this mismatch by rewriting old software, and writing new software, in an explicitly parallel style that is better suited to the hardware, or we might take advantage of any implicit parallelism already present in the sequential software. While it is imagined that there might be useful amounts of implicit parallelism in many common applications, particularly in applications written in non-strict functional languages, finding and exploiting it has proven difficult. We have performed a novel limit study to measure the implicit parallelism in one large realistic application written in a non-strict functional language, and find that the amount of implicit parallelism is relatively small. We have also analyzed the measurements to find bottlenecks in the application that limit its implicit parallelism, and we describe how small rewrites directed by these analyses can increase the amount of implicit parallelism available. We also outline ways in which control speculation might help to exploit further implicit parallelism. The aforementioned limit study measures the execution of the NHC98 compiler using the Hat tracer and a few extra pieces. I'd appreciate comments. A draft of the paper is (should be) available at http://www.detreville.org/papers/Limits.pdf, modulo any embarrassing typos on my part. Cheers, John

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ANNOUNCE: Dimensional -- Statically checked physical dimensions
by Björn Buckwalter 28 Dec '06

28 Dec '06

Dear all, Inspired by Dons' blog post [2] and further spurred by the recent CalDims announcement [3] I have wrapped up version 0.1 of my 'Dimensional' module for statically checked physical dimensions (requires GHC 6.6). The module facilitates calculations with physical quantities while statically preventing e.g. addition of quantities with differing physical dimensions. I have used the module to implement (proprietary) algorithms related to spacecraft propulsion systems and my experience is that it is both usable and substantially improves confidence in the code produced. The 'Dimensional' module and the supporting module 'NumType', both written in literate Haskell, follow at the end of this message. For a tarball and/or a current darcs repository see [1]. The code is released under a BSD3 license. Before a 1.0 release I intend to, among other thing, change the name to something more descriptive (also to avoid confusion with Aaron Denney's very similar library [4]). Feedback on whether/where to fit the modules in the "module name space" would be appreciated. Happy New Year! -Bjorn Buckwalter [1] http://code.google.com/p/dimensional/ [2] http://cgi.cse.unsw.edu.au/~dons/blog/2006/12/11#release-a-library-today [3] http://article.gmane.org/gmane.comp.lang.haskell.general/14671 [4] http://www.haskell.org/haskellwiki/Dimensionalized_numbers ~~~~~~~~~~ BEGIN 'Buckwalter/Dimensional.lhs' ~~~~~~~~~~ Buckwalter.Dimensional -- Statically checked physical dimensions Bjorn Buckwalter, bjorn(a)buckwalter.se 2006-12-28, version 0.1 (unstable) License: BSD3 = Summary = In this module we provide data types for performing arithmetic with physical quantities and units. Information about the physical dimensions of the quantities/units is embedded in their types and the validity of operations is verified by the type checker at compile time. The boxing and unboxing of numerical values as quantities is done by multiplication and division of units, of which an incomplete set is provided. We limit ourselves to "Newtonian" physics. We do not attempt to accommodate relativistic physics in which e.g. addition of length and time would be valid. As far as possible and/or practical the conventions and guidelines of NIST's "Guide for the Use of the International System of Units (SI)" [1] are followed. Occasionally we will reference specific sections from the guide and deviations will be explained. = Disclaimer = Merely an engineer, the author doubtlessly uses a language and notation that makes mathematicians and physicist cringe. He does not mind constructive criticism (or darcs patches). The sets of functions and units defined herein are incomplete and reflect only the author's needs to date. Again, patches are welcome. The author has elected to keep the module detached from the standard(?) Haskell library hierarchy. In part because the module name space layout seems to be an open issue and in part because he is unsure where to fit it in. = Preliminaries = This module requires GHC 6.6 or later. We utilize multi-parameter type classes, phantom types, functional dependencies and undecidable instances (and possibly additional unidentified GHC extensions). Clients of the module are generally not required to use these extensions. > {-# OPTIONS_GHC -fglasgow-exts -fallow-undecidable-instances #-} > module Buckwalter.Dimensional > -- TODO discriminate exports, in particular Variants and Dims. > where > import Prelude hiding > ((*), (/), (+), (-), (^), sqrt, negate, pi, sin, cos, exp) > import qualified Prelude as P > ((*), (/), (+), (-), (^), sqrt, negate, pi, sin, cos, exp) > import Buckwalter.NumType (NumType, PosType, NegType, > Zero, Pos, Neg, > incr, decr, Add, Sub, Halve, > zero, > Pos1, Pos2, Pos3, pos1, pos2, pos3, > Neg1, Neg2, Neg3, neg1, neg2, neg3) We will reuse the operators and function names from the Prelude. To prevent unpleasant surprises we give operators the same fixity as the Prelude. > infixr 8 ^ > infixl 7 *, / > infixl 6 +, - = Dimensional = Our primary objective is to define a data type that can be used to represent (while still differentiating between) units and quantities. There are two reasons for consolidating units and quantities in one data type. The first being to allow code reuse as they are largely subject to the same operations. The second being that it allows reuse of operators (and functions) between the two without resorting to occasionally cumbersome type classes. We call this data type 'Dimensional' to capture the notion that the units and quantities it represents have physical dimensions. > newtype (Variant v, Dims d) > => Dimensional v d a = Dimensional a deriving (Show, Eq, Ord) The type variable 'a' is the only non-phantom type variable and represents the numerical value of a quantity or the scale (w.r.t. SI units) of a unit. For SI units the scale will always be 1. For non-SI units the scale is the ratio of the unit to the SI unit with the same physical dimension. Since 'a' is the only non-phantom type we were able to define 'Dimensional' as a newtype, avoiding boxing at runtime. = The variant 'v' of 'Dimensional' = The phantom type variable v is used to distinguish between units and quantities. It should be one of the following: > data DUnit > data DQuantity We enforce this using the (non-exported) type class 'Variant' of which 'DUnit' and 'DQuantity' are the only instances. > class Variant v > instance Variant DUnit > instance Variant DQuantity For convenience we define type synonyms for units and quantities. > type Unit = Dimensional DUnit > type Quantity = Dimensional DQuantity The relationship between (the value of) a 'Quantity', its numerical value and its 'Unit' is described in 7.1 "Value and numerical value of a quantity" of [1]. In short a 'Quantity' is the product of a number and a 'Unit'. We define the '(*~)' operator as a convenient way to declare quantities as such a product. > (*~) :: Num a => a -> Unit d a -> Quantity d a > x *~ Dimensional y = Dimensional (x P.* y) Conversely, the numerical value of a 'Quantity' is obtained by dividing the 'Quantity' by its 'Unit' (any unit with the same physical dimension). The '(/~)' operator provides a convenient way of obtaining the numerical value of a quantity. > (/~) :: Fractional a => Quantity d a -> Unit d a -> a > Dimensional x /~ Dimensional y = x P./ y We give '*~' and '/~' the same fixity as '*' and '/' defined below. Note that this necessitates the use of parenthesis when composing units using '*' and '/', e.g. "1 *~ (meter / second)". > infixl 7 *~, /~ = The dimension 'd' of 'Dimensional' = The phantom type variable d encompasses the physical dimension of the 'Dimensional'. As detailed in [1] there are seven base dimensions, which can be combined in integer powers to a given physical dimension. We represent physical dimensions as the powers of the seven base dimensions that make up the given dimension. The powers are represented using NumTypes. For convenience we collect all seven base dimensions in a data type 'Dim' which is the sole instance of the 'Dims' type class. > data (NumType l, -- Length. > NumType m, -- Mass. > NumType t, -- Time. > NumType i, -- Electric current. > NumType th, -- Thermodynamic temperature. > NumType n, -- Amount of substance. > NumType j) -- Luminous intensity. > => Dim l m t i th n j > class Dims d > instance Dims (Dim l m t i th n j) We could have chosen to provide type variables for the seven base dimensions in 'Dimensional' instead of creating a new data type 'Dim'. However, that would have made any type signatures involving 'Dimensional' very cumbersome. By encompassing the physical dimension in a single type variable we can "hide" the cumbersome type arithmetic behind convenient type classes as will be seen later. Using our 'Dim' data type we define some type synonyms for convenience and illustrative purposes. We start with the base dimensions. > type DOne = Dim Zero Zero Zero Zero Zero Zero Zero > type DLength = Dim Pos1 Zero Zero Zero Zero Zero Zero > type DMass = Dim Zero Pos1 Zero Zero Zero Zero Zero > type DTime = Dim Zero Zero Pos1 Zero Zero Zero Zero > type DCurrent = Dim Zero Zero Zero Pos1 Zero Zero Zero > type DTemperature = Dim Zero Zero Zero Zero Pos1 Zero Zero > type DAmount = Dim Zero Zero Zero Zero Zero Pos1 Zero > type DIntensity = Dim Zero Zero Zero Zero Zero Zero Pos1 We add some derived physical dimensions. > type DArea = Dim Pos2 Zero Zero Zero Zero Zero Zero > type DVolume = Dim Pos3 Zero Zero Zero Zero Zero Zero > type DFrequency = Dim Zero Zero Neg1 Zero Zero Zero Zero > type DVelocity = Dim Pos1 Zero Neg1 Zero Zero Zero Zero > type DAcceleration = Dim Pos1 Zero Neg2 Zero Zero Zero Zero > type DForce = Dim Pos1 Pos1 Neg2 Zero Zero Zero Zero > type DImpulse = Dim Pos1 Pos1 Neg1 Zero Zero Zero Zero > type DMassFlow = Dim Zero Pos1 Neg1 Zero Zero Zero Zero > type DPressure = Dim Neg1 Pos1 Neg2 Zero Zero Zero Zero Using the above type synonyms we can define type synonyms for quantities of particular physical dimensions. Quantities with the base dimensions. > type Dimensionless = Quantity DOne > type Length = Quantity DLength > type Mass = Quantity DMass > type Time = Quantity DTime > type Current = Quantity DCurrent > type Temperature = Quantity DTemperature > type Amount = Quantity DAmount > type Intensity = Quantity DIntensity Some quantities with derived dimensions. > type Frequency = Quantity DFrequency > type Velocity = Quantity DVelocity > type Angle = Dimensionless > type SolidAngle = Dimensionless > type AngularVelocity = Frequency > type Force = Quantity DForce > type Thrust = Force > type Impulse = Quantity DImpulse > type MassFlow = Quantity DMassFlow > type Pressure = Quantity DPressure = Arithmetic on physical dimensions = When performing arithmetic on units and quantities the arithmetics must be applied to both the numerical values of the Dimensionals but also to their physical dimensions. The type level arithmetic on physical dimensions is governed by multi-parameter type classes and functional dependences. Multiplication of dimensions corresponds to adding of the base dimensions' exponents. > class Mul d d' d'' | d d' -> d'' > instance (Add l l' l'', > Add m m' m'', > Add t t' t'', > Add i i' i'', > Add th th' th'', > Add n n' n'', > Add j j' j'') => Mul (Dim l m t i th n j) > (Dim l' m' t' i' th' n' j') > (Dim l'' m'' t'' i'' th'' n'' j'') Division of dimensions corresponds to subtraction of the base dimensions' exponents. > class Div d d' d'' | d d' -> d'' > instance (Sub l l' l'', > Sub m m' m'', > Sub t t' t'', > Sub i i' i'', > Sub th th' th'', > Sub n n' n'', > Sub j j' j'') => Div (Dim l m t i th n j) > (Dim l' m' t' i' th' n' j') > (Dim l'' m'' t'' i'' th'' n'' j'') Taking the square root of a dimension corresponds to halving the base dimensions' exponents. > class Sqrt d d' | d -> d' > instance (Halve l l', > Halve m m', > Halve t t', > Halve i i', > Halve th th', > Halve n n', > Halve j j') => Sqrt (Dim l m t i th n j) > (Dim l' m' t' i' th' n' j') = Arithmetic on units and quantities = Thanks to the arithmetic on physical dimensions having been sorted out separately a lot of the arithmetic on Dimensionals is straight forward. In particular the type signatures are much simplified. Multiplication, division and powers apply to both units and quantities. > (*) :: (Num a, Mul d d' d'') > => Dimensional v d a -> Dimensional v d' a -> Dimensional v d'' a > Dimensional x * Dimensional y = Dimensional (x P.* y) > (/) :: (Fractional a, Div d d' d'') > => Dimensional v d a -> Dimensional v d' a -> Dimensional v d'' a > Dimensional x / Dimensional y = Dimensional (x P./ y) We limit ourselves to integer powers of Dimensionals as fractional powers make little physical sense. Since the value of the exponent affects the type of the result the value of the exponent must be visible to the type system, therefore we will generally represent the exponent with a 'NumType'. We must also use a type class to capture the different behaviors of positive, zero and negative exponents. > class Power a d n d' | d n -> d' > where (^) :: Dimensional v d a -> n -> Dimensional v d' a Anything to the power of zero equals one. > instance (Num a) => Power a d Zero DOne where _ ^ _ = Dimensional 1 Positive exponents. > instance (Num a, PosType n, Power a d n d', Mul d' d d'') > => Power a d (Pos n) d'' where x ^ n = x ^ decr n * x Negative exponents. > instance (Fractional a, NegType n, Power a d n d', Div d' d d'') > => Power a d (Neg n) d'' where x ^ n = x ^ incr n / x A special case is that dimensionless quantities are not restricted to integer powers. Here we utilize the 'a' type variable of 'Power' as well as the fact that the 'n' type variable is not limited to NumTypes to allow a dimensionless quantity to be raised to the power of any other dimensionless quantity. > instance (Floating a) => Power a DOne (Dimensionless a) DOne > where (Dimensional x) ^ (Dimensional y) = Dimensional (x ** y) It is permissible to express powers of length units by prefixing 'square' and 'cubic' (9.6 "Spelling unit names raised to powers" of [1]). > square :: (Num a) => Unit DLength a -> Unit DArea a > square x = x * x > cubic :: (Num a) => Unit DLength a -> Unit DVolume a > cubic x = square x * x Some operations only make sense for quantities. Of these, negation, addition and subtraction are particularly simple as they are done in a single physical dimension. > negate :: (Num a) => Quantity d a -> Quantity d a > negate (Dimensional x) = Dimensional (P.negate x) > (+) :: (Num a) => Quantity d a -> Quantity d a -> Quantity d a > Dimensional x + Dimensional y = Dimensional (x P.+ y) > (-) :: (Num a) => Quantity d a -> Quantity d a -> Quantity d a > x - y = x + negate y = Elementary functions (incomplete set) = It makes little sense to apply elementary functions to units so we limit their use to quantities, and in many cases to quantities with specific physical dimensions. Square root could conceivably be applied to units but valid reasons for doing so elude the author, so their use will be limited to quantities. > sqrt :: (Floating a, Sqrt d d') => Quantity d a -> Quantity d' a > sqrt (Dimensional x) = Dimensional (P.sqrt x) Sine and cosine make sense only for angles (the type synonym 'Angle' is defined later). > sin, cos :: (Floating a) => Angle a -> Dimensionless a > sin (Dimensional x) = Dimensional (P.sin x) > cos (Dimensional x) = Dimensional (P.cos x) The exponential function only makes sense for dimensionless quantities. > exp :: (Floating a) => Dimensionless a -> Dimensionless a > exp (Dimensional x) = Dimensional (P.exp x) = Unit prefixes = Prefixes are used to form decimal multiples and submultiples of SI Units as described in 4.4 of [1]. We will define the SI prefixes in terms of a 'prefix' function which applies a scale factor to a unit. (The 'prefix' function will also be used to define non-SI units.) > prefix :: (Num a) => a -> Unit d a -> Unit d a > prefix x (Dimensional y) = Dimensional (x P.* y) We define all SI prefixes, from Table 5 in [1]. Multiples first. > deca, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta > :: Num a => Unit d a -> Unit d a > deca = prefix 10 > hecto = deca . deca > kilo = deca . hecto > mega = kilo . kilo > giga = kilo . mega > tera = kilo . giga > peta = kilo . tera > exa = kilo . peta > zetta = kilo . exa > yotta = kilo . zetta Then the submultiples. > deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto > :: Fractional a => Unit d a -> Unit d a > deci = prefix 0.1 > centi = deci . deci > milli = deci . centi > micro = milli . milli > nano = milli . micro > pico = milli . nano > femto = milli . pico > atto = milli . femto > zepto = milli . atto > yocto = milli . zepto By defining SI prefixes as functions applied to a 'Unit' we satisfy 6.2.6 "Unacceptability of stand-alone prefixes" of [1]. = SI base and derived units (incomplete) = Finally we define the units. To avoid a myriad of one-letter functions that would doubtlessly cause clashes and frustration in users' code we spell out all unit names in full, as we did for prefixes. We also elect to spell the unit names in singular form, as allowed by 9.7 "Other spelling conventions" of [1]. The first unit we will define is 'one'. The unit one has dimension one and is the base unit of dimensionless values. As detailed in 7.10 "Values of quantities expressed simply as numbers: the unit one, symbol 1" of [1] the unit one generally does not appear in expressions. However, for us it is necessary to use 'one' as we would any other unit to perform the "boxing" of dimensionless values. > one :: Num a => Unit DOne a > one = Dimensional 1 We continue by defining the other SI base units (see 4.1 of [1]). > meter :: Num a => Unit DLength a > meter = Dimensional 1 For mass the SI base unit is kilogram. For sensible prefixes we define gram here (see 6.2.7 "Prefixes and the kilogram" in [1]). The drawback is that we are forced to use 'Fractional'. > gram :: Fractional a => Unit DMass a > gram = Dimensional 1e-3 > second :: Num a => Unit DTime a > second = Dimensional 1 > ampere :: Num a => Unit DCurrent a > ampere = Dimensional 1 > kelvin :: Num a => Unit DTemperature a > kelvin = Dimensional 1 > mole :: Num a => Unit DAmount a > mole = Dimensional 1 > candela :: Num a => Unit DIntensity a > candela = Dimensional 1 Now we go on to define (a limited set of) the SI derived units in terms of the base units (see 4.2 "SI derived units" of [1]). > radian, steradian :: Fractional a => Unit DOne a > radian = meter / meter > steradian = meter ^ pos2 / meter ^ pos2 > hertz :: Fractional a => Unit DFrequency a > hertz = one / second > newton :: Fractional a => Unit DForce a > newton = kilo gram * meter / second ^ pos2 > pascal :: Fractional a => Unit DPressure a > pascal = newton / meter ^ pos2 = Non-SI units = We will define a small subset of the myriad of units that exists outside of the SI. These are generally defined in terms of another unit with a prefix (using the 'prefix' function defined earlier). We start with (a limited set of) the units accepted for use with the SI (see 5.1 of [1]). > degree :: Floating a => Unit DOne a > degree = prefix (P.pi P./ 180) radian > minute, hour, day :: Num a => Unit DTime a > minute = prefix 60 second > hour = prefix 60 minute > day = prefix 24 hour We continue with units not accepted for use in with the SI, in particular the US customary (that is, inch-pound) units. > inch, foot :: Fractional a => Unit DLength a > inch = prefix 2.54 (centi meter) > foot = prefix 12 inch -- 0.3048 m > poundMass :: Fractional a => Unit DMass a > poundMass = prefix 0.45359237 (kilo gram) In order to relate pounds mass to pounds force we define the questionable unit 'gee' (G) as the gravitational acceleration at sea level. > gee :: Fractional a => Unit DAcceleration a > gee = prefix 9.80665 meter / second ^ pos2 > poundForce :: Fractional a => Unit DForce a > poundForce = poundMass * gee -- 4.4482 N Other (non inch-pound) units. > bar :: (Fractional a) => Unit DPressure a > bar = prefix 1.0e5 pascal = Less conformant units = The unit system we have devised and used above will not work well with some non-SI units. In particular units which do not scale linearly with respect to the SI units, for example logarithmic units (see 8.7 "Logarithmic quantities and units: level, neper, bel" of [1]). Another problematic area is units which increase proportionally to the SI units but cross zero at a different point. An example would be degrees Celsius. The author feels that it is appropriate to define a unit for use with relative quantities (taking only into account the proportionality) and complement the unit with functions for converting absolute values. > degreeCelsius :: Num a => Unit DTemperature a > degreeCelsius = kelvin > fromDegreeCelsiusAbsolute :: Fractional a => a -> Temperature a > fromDegreeCelsiusAbsolute x = x *~ degreeCelsius + 273.15 *~ degreeCelsius > toDegreeCelsiusAbsolute :: Fractional a => Temperature a -> a > toDegreeCelsiusAbsolute x = (x - 273.15 *~ degreeCelsius) /~ degreeCelsius = Conclusion and usage = We have defined operators and units that allow us to define and work with physical quantities. A physical quantity is defined by multiplying a number with a unit (the type signature is optional). ] v :: Velocity Prelude.Double ] v = 90 *~ (kilo meter / hour) It follows naturally that the numerical value of a quantity is obtained by division by a unit. ] numval :: Prelude.Double ] numval = v /~ (meter / second) The notion of a quantity as the product of a numerical value and a unit is supported by 7.1 "Value and numerical value of a quantity" of [1]. While the above syntax is fairly natural it is unfortunate that it must violate a number of the guidelines in [1], in particular 9.3 "Spelling unit names with prefixes", 9.4 "Spelling unit names obtained by multiplication", 9.5 "Spelling unit names obtained by division". As a more elaborate example of how to use the module we define a function for calculating the escape velocity of a celestial body [2]. ] escapeVelocity :: (Floating a) => Mass a -> Length a -> Velocity a ] escapeVelocity m r = sqrt (two * g * m / r) ] where ] two = 2 *~ one ] g = 6.6720e-11 *~ (newton * meter ^ pos2 / kilo gram ^ pos2) The following is an example GHC session where the above function is used to calculate the escape velocity of Earth in kilometer per second. *Buckwalter.Dimensional> :set +t *Buckwalter.Dimensional> let me = 5.9742e24 *~ kilo gram -- Mass of Earth. me :: Quantity DMass GHC.Float.Double *Buckwalter.Dimensional> let re = 6372.792 *~ kilo meter -- Mean radius of Earth. re :: Quantity DLength GHC.Float.Double *Buckwalter.Dimensional> let ve = escapeVelocity me re -- Escape velocity of Earth. ve :: Velocity GHC.Float.Double *Buckwalter.Dimensional> ve /~ (kilo meter / second) 11.184537332296259 it :: GHC.Float.Double For completeness we should also show an example of the error messages we will get from GHC when performing invalid arithmetic. In the best case GHC will be able to use the type synonyms we have defined in its error messages. ] x = 1 *~ meter + 1 *~ second Couldn't match expected type `Pos1' against inferred type `Zero' Expected type: Unit DLength t Inferred type: Unit DTime a In the second argument of `(*~)', namely `second' In the second argument of `(+)', namely `1 *~ second' In other cases the error messages aren't very friendly. ] x = 1 *~ meter / (1 *~ second) + 1 *~ kilo gram Couldn't match expected type `Zero' against inferred type `Neg Zero' When using functional dependencies to combine Sub Zero (Pos Zero) (Neg Zero), arising from use of `/' at Buckwalter/Dimensional.lhs:425:9-20 Sub Zero (Pos Zero) Zero, arising from use of `/' at Buckwalter/Dimensional.lhs:532:5-30 It is the author's experience that the usefullness of the compiler error messages is more often than not limited to pinpointing the location of errors. = Future work = While there is an insane amount of units in use around the world it is reasonable to provide at least all SI units. Units outside of SI will most likely be added on an as-needed basis. There are also plenty of elementary functions to add. The 'Floating' class can be used as reference. Another useful addition would be decent 'Show' and 'Read' instances. The 'show' implementation could output the numerical value and the unit expressed in (base?) SI units, along the lines of: ] instance (Fractional a, Show a) => Show (Length a) ] where show x = show (x /~ meter) ++ " m" Additional functions could be provided for "showing" with any unit and prefix. The 'read' implementation should be able to read values with any unit and prefix. It is not clear to the author how to best implement these. Additional physics models could be implemented. See [3] for ideas. = Related work = Henning Thielemann numeric prelude has a physical units library, however, checking of dimensions is dynamic rather than static. Aaron Denney has created a toy example of statically checked physical dimensions covering only length and time. HaskellWiki has pointers [4] to these. Libraries with similar functionality exist for other programming languages and may serve as inspiration. The author has found the Java library JScience [5] and the Fortress programming language [6] particularly noteworthy. = References = [1] http://physics.nist.gov/Pubs/SP811/ [2] http://en.wikipedia.org/wiki/Escape_velocity [3] http://jscience.org/api/org/jscience/physics/models/package-summary.html [4] http://www.haskell.org/haskellwiki/Physical_units [5] http://jscience.org/ [6] http://research.sun.com/projects/plrg/fortress.pdf ~~~~~~~~~~ END 'Buckwalter/Dimensional.lhs' ~~~~~~~~~~ ~~~~~~~~~~ BEGIN 'Buckwalter/NumType.lhs' ~~~~~~~~~~ Buckwalter.NumType -- Type level integers Bjorn Buckwalter, bjorn(a)buckwalter.se 2006-12-19, version 0.1 (unstable) License: Public domain = Summary = This Module provides type level representations, hereafter referred to as "NumTypes", of the (positive and negative) integers and some basic operations (addition, subtraction...) on these. While functions are provided for the operations NumTypes are solely for the type level and their only value is 'undefined'. There are similarities with the HNats of the HList library [1], which was indeed a source of inspiration. Occasionally references are made to the HNats. The main addition in this module is negative numbers. = Preliminaries = This module requires GHC 6.6 or later. We utilize multi-parameter type classes, phantom types, functional dependencies and undecidable instances (and possibly additional unidentified GHC extensions). > {-# OPTIONS_GHC -fglasgow-exts -fallow-undecidable-instances #-} > module Buckwalter.NumType ( > Zero, Pos, Neg, > NumType, PosType, NegType, > Negate, negate, Incr, incr, Decr, decr, > Add, (+), Sub, (-), Halve, halve, > Pos1, Pos2, Pos3, Neg1, Neg2, Neg3, > zero, pos1, pos2, pos3, neg1, neg2, neg3, > ) where > import Prelude (undefined) Use the same fixity for operators as the Prelude. > infixl 6 +, - = NumTypes = We start by defining a class encompassing all integers. > class NumType n Then we define classes encompassing all positive and negative integers respectively. The 'PosType' class corresponds to HList's 'HNat'. > class NumType n => PosType n > class NumType n => NegType n Now we Define the data types used to represent integers. We begin with 'Zero', which we allow to be used as both a positive and a negative number in the sense of the previously defined type classes. 'Zero' corresponds to HList's 'HZero'. > data Zero > instance NumType Zero > instance PosType Zero > instance NegType Zero Next we define the "successor" type, here called 'Pos' (corresponding to HList's 'HSucc'). > data Pos n > instance (PosType n) => NumType (Pos n) > instance (PosType n) => PosType (Pos n) We could be more restrictive using "data (PosType n) => Pos n" but this constraint will not be checked (by GHC) anyway when 'Pos' is used solely at the type level. Finally we define the "predecessor" type used to represent negative numbers. > data Neg n > instance (NegType n) => NumType (Neg n) > instance (NegType n) => NegType (Neg n) = NumType arithmetic = We start off with some basic building blocks. Negation is a simple matter of recursively changing 'Pos' to 'Neg' or vice versa while leaving 'Zero' unchanged. > class (NumType a, NumType b) => Negate a b | a -> b where > negate :: a -> b > negate _ = undefined > instance Negate Zero Zero > instance (PosType a, NegType b, Negate a b) => Negate (Pos a) (Neg b) > instance (NegType a, PosType b, Negate a b) => Negate (Neg a) (Pos b) To increment NumTypes we either prepend 'Pos' to numbers greater than or equal to Zero or remove a 'Neg' from numbers less than Zero. The 'incr' function corresponds roughly to HList's 'hSucc'. > class (NumType a, NumType b) => Incr a b | a -> b where > incr :: a -> b > incr _ = undefined > instance Incr Zero (Pos Zero) > instance (PosType a) => Incr (Pos a) (Pos (Pos a)) > instance (NegType a) => Incr (Neg a) a Decrementing is similar but we either remove a 'Pos' from numbers greater than Zero or prepend a 'Neg' to numbers less than or equal to 'Zero'. The 'decr' function corresponds roughly to HList's 'hPred'. > class (NumType a, NumType b) => Decr a b | a -> b where > decr :: a -> b > decr _ = undefined > instance Decr Zero (Neg Zero) > instance (PosType a) => Decr (Pos a) a > instance (NegType a) => Decr (Neg a) (Neg (Neg a)) We define a class for addition of NumTypes. > class (NumType a, NumType b, NumType c) => Add a b c | a b -> c where > (+) :: a -> b -> c > _ + _ = undefined Adding anything to Zero gives "anything". > instance (NumType a) => Add Zero a a When adding to a non-Zero number our strategy is to "transfer" type constructors from the first type to the second type until the first type is Zero. We use the 'incr' and 'decr' operators to do this. > instance (PosType a, Incr b c, Add a c d) => Add (Pos a) b d > instance (NegType a, Decr b c, Add a c d) => Add (Neg a) b d We define subtraction using negation and addition. > class (NumType a, NumType b, NumType c) => Sub a b c | a b -> c where > (-) :: a -> b -> c > _ - _ = undefined > instance (Negate b b', Add a b' c) => Sub a b c We neglect to provide multiplication and division. However, let us define a halving operator which is useful when using NumTypes to represent powers (taking the square root requires halving the power). > class (NumType a, NumType b) => Halve a b | a -> b where > halve :: a -> b > halve _ = undefined > instance Halve Zero Zero > instance (PosType a, PosType b, Halve a b) => Halve (Pos (Pos a)) (Pos b) > instance (NegType a, NegType b, Halve a b) => Halve (Neg (Neg a)) (Neg b) = Convenince types and values = Finally we define some type synonyms for the convenience of clients of the library. > type Pos1 = Pos Zero > type Pos2 = Pos Pos1 > type Pos3 = Pos Pos2 > type Neg1 = Neg Zero > type Neg2 = Neg Neg1 > type Neg3 = Neg Neg2 Analogously we also define some convenience values (all 'undefined' but with the expected types). > zero :: Zero -- ~ hZero > zero = undefined > pos1 = incr zero > pos2 = incr pos1 > pos3 = incr pos2 > neg1 = decr zero > neg2 = decr neg1 > neg3 = decr neg2 = References = [1] http://homepages.cwi.nl/~ralf/HList/ ~~~~~~~~~~ END 'Buckwalter/NumType.lhs' ~~~~~~~~~~

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GHCi and Hugs ASCII logos
by Nathan Mishra Linger 27 Dec '06

27 Dec '06

Dear Haskellers, I think I remember that some program was used to generate either the Hugs or GHCi ascii logo that appears when you fire up the interpreter. __ __ __ __ ____ ___ || || || || || || ||__ ___ ___ _ ||___|| ||__|| ||__|| __|| / _ \ /\ /\/ __(_) ||---|| ___|| / /_\// /_/ / / | | || || / /_\\/ __ / /___| | || || Version: March 2005 \____/\/ /_/\____/|_| (view with a fixed width font) Where can I find this program? I used to know, but can't remember and can't seem to get Google to tell me. Nathan Mishra Linger

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Re: type hacking hoas
by oleg＠pobox.com 27 Dec '06

27 Dec '06

Jeff wrote: > I'm trying to mix type hackery with HOAS. More specifically, > here is a data type which I would like to use: > > data Exp a where > Lam :: (Exp a -> Exp b) -> Exp (a -> b) > App :: Exp (a -> b) -> Exp a -> Exp b > Rcd :: (IsRecord (HCons (F l (Exp v)) r) => > F l (Exp v) -> Exp r -> Exp (HCons (F l (Exp v)) r) > Proj :: (HasLabel l r v) => l -> Exp r -> Exp v > Thus I would like to be able to successfully infer a type for: > > Lam $ \x -> App (Proj l1 x) (Proj l2 x) > > for some given labels l1 and l2. However, I cannot figure out how to > write HasLabel (or if it's even possible). It seems likely that you have the uses for the inferred type of the above expression other than displaying it. You probably want to statically enforce certain constraints when applying these Lam expressions. That is, you want to apply Lam expressions only to the arguments that satisfy the inferred HasField constraints. Why not to enforce the constraints at that time then? The enclosed is a bit simplified version of the code that demonstrates the idea. It is the typed evaluator statically enforcing the HasField constraints. It does not use GADTs though as they don't add to expressiveness. It would be great if we could delay the more detailed discussion past the first week of Jan. > and TypeEq doesn't work on uninstantiated type vars; correct me if I'm > wrong about these. TypeEq may work on uninstantiated type vars; please see http://pobox.com/~oleg/ftp/Haskell/de-typechecker.lhs and the paragraph containing the phrase ``The ability to operate on and compare *unground* types with *uninstantiated* type variables is often sought but rarely attained. The contribution of this message is the set of primitives for nominal equality comparison and deconstruction of unground types.'' {-# OPTIONS -fglasgow-exts #-} {-# OPTIONS -fallow-undecidable-instances #-} module J where data Lam f = Lam f data App f x = App f x data Proj l e = Proj l e data Rec1 = Rec1 (Int->Int) -- simplified data Rec2 = Rec2 Int -- simplified {- well-formednedd (well-typeness) rules class Exp a t | a -> t instance (Exp ea a, Exp eb b) => Exp (Lam (ea -> eb)) (a->b) instance (Exp f (a->b), Exp x a) => Exp (App f x) b instance (Exp e r, HasField l r v) => Exp (Proj l e) v instance Exp Rec1 Rec1 instance Exp Rec2 Rec2 -} data L1 = L1 data L2 = L2 class HasField l r v | l r -> v where flookup :: l -> r -> v instance HasField L1 Rec1 (Int->Int) where flookup _ (Rec1 x) = x instance HasField L2 Rec2 Int where flookup _ (Rec2 x) = x t1 = Lam $ \x -> App (Proj L1 x) (Proj L2 x) t2 = Lam $ \x -> App (Lam (\x -> x)) (Proj L2 x) class Eval e v | e -> v where eval :: e -> v -- big step, CBN semantics instance (Eval f (Lam (x->e2)), Eval e2 v) => Eval (App f x) v where eval (App f x) = let Lam f' = eval f in eval $ f' x instance (Eval e r, HasField l r v) => Eval (Proj l e) v where eval (Proj _ e) = flookup (undefined::l) $ eval e -- Those are values already instance Eval (Lam e) (Lam e) where eval = id instance Eval Rec1 Rec1 where eval = id instance Eval Rec2 Rec2 where eval = id t3 = eval $ App t2 (Rec2 1) -- The following gives the expected type error: Rec1 has no field L2 -- t4 = eval $ App t2 (Rec1 succ)

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