diff --git a/Numeric/NumType.lhs b/Numeric/NumType.lhs --- a/Numeric/NumType.lhs +++ b/Numeric/NumType.lhs @@ -34,7 +34,13 @@ type classes, phantom types, functional dependencies and undecidable instances (and possibly additional unidentified GHC extensions). -> {-# LANGUAGE UndecidableInstances, EmptyDataDecls #-} +> {-# LANGUAGE UndecidableInstances +> , ScopedTypeVariables +> , EmptyDataDecls +> , FunctionalDependencies +> , MultiParamTypeClasses +> , FlexibleInstances +> #-} > module Numeric.NumType > -- Basic classes (exported versions). diff --git a/Numeric/Units/Dimensional.lhs b/Numeric/Units/Dimensional.lhs --- a/Numeric/Units/Dimensional.lhs +++ b/Numeric/Units/Dimensional.lhs @@ -46,8 +46,15 @@ Clients of the module are generally not required to use these extensions. -> {-# LANGUAGE UndecidableInstances, ScopedTypeVariables #-} -> -- Does 'ScopedTypeVariables' imply 'EmptyDataDecls'? +> {-# LANGUAGE UndecidableInstances +> , ScopedTypeVariables +> , EmptyDataDecls +> , MultiParamTypeClasses +> , FunctionalDependencies +> , FlexibleInstances +> , TypeSynonymInstances +> , FlexibleContexts +> #-} > module Numeric.Units.Dimensional > -- TODO discriminate exports, in particular Variants and Dims. diff --git a/Numeric/Units/Dimensional/CGS.lhs b/Numeric/Units/Dimensional/CGS.lhs deleted file mode 100644 --- a/Numeric/Units/Dimensional/CGS.lhs +++ /dev/null @@ -1,320 +0,0 @@ -Numeric.Dimensional.CGS -- CGS system of units -Bjorn Buckwalter, bjorn.buckwalter@gmail.com -License: BSD3 - -*** EXPERIMENTAL *** - - -= Introduction = - -This module was prompted by an email from Chuck Blake[1]. He asked if -the Dimensional library could support other systems of units than -SI, in particular systems such as the centimeter-gram-second (CGS) -system where fractional exponents of dimensions occur. He also -wondered whether it was possible to convert quantities between -different systems while statically ensuring that a given conversion -was valid. - -In this module we show that we can in a straight forward manner -support systems with rational exponents, provided that the rationals -that may be encountered are known a priori. As an example we provide -a rudimentary implementation of the CGS system. - -We also show that we can indeed statically prohibit invalid conversions -between different systems. - - -= Caveats = - -I'm ignorantly assuming that when working with the CGS (or MKS) -system you will only (meaningfully?) encounter half-exponents and -only of the length and mass dimensions. Of course, in other systems -other rational exponents may be encountered. - -I am also assuming that the CGS system would not be employed when -working with temperature, amount or luminosity. This is evident in -the below type signatures where I have assumed zero extent in the -temperature, amount and luminosity dimensions. If this is incorrect -I would appreciate pointers to the CGS representation of these -dimensions. - -Please correct and inform me if my assumptions are wrong! - - -= Preliminaries = - -> {-# LANGUAGE UndecidableInstances, ScopedTypeVariables #-} - -> module Numeric.Units.Dimensional.CGS where - -> import Prelude ( undefined, Num, Fractional, Floating, Show, recip, Double ) -> import qualified Prelude -> import Numeric.Units.Dimensional hiding ( DLength, DMass, DTime, DElectricCurrent ) -> import Numeric.Units.Dimensional.Quantities as SIQ -> import qualified Numeric.Units.Dimensional.SIUnits as SI -> import qualified Numeric.NumType as N -> import Numeric.NumType ( Neg2, Neg1, Zero, Pos, Pos1, Pos2, Pos3, NumType ) -> import Numeric.NumType ( neg2, neg1, zero, pos1, pos2, pos3 ) -> import Data.Maybe (catMaybes) - - -= Dimensions = - -Analogously with the SI we collect the base dimensions of the CGS -system in the data type 'CGSDim'. - -> data CGSDim lh mh t - -In the above 'lh' and 'mh' represent the number of half-exponents -of length and mass respectively while 't' represents the number of -whole-exponents. The base dimensions illustrate this. - -> type DLength = CGSDim Pos2 Zero Zero -> type DMass = CGSDim Zero Pos2 Zero -> type DTime = CGSDim Zero Zero Pos1 - -We add a few non-base dimensions for the sake of example. Charge -is particularly interesting as it illustrates the need for -half-exponents as described in [2]. - -> type DElectricCurrent = CGSDim Pos3 Pos1 Neg2 -> type DCharge = CGSDim Pos3 Pos1 Neg1 - - -= 'Mul', 'Div', 'Pow' and 'Root' instances = - -The 'Mul', 'Div', 'Pow' and 'Root' instances are strictly analogous -with the SI. - -> instance ( N.Sum lh lh' lh'' -> , N.Sum mh mh' mh'' -> , N.Sum t t' t'' ) => Mul (CGSDim lh mh t) -> (CGSDim lh' mh' t') -> (CGSDim lh'' mh'' t'') - -> instance ( N.Sum lh lh' lh'' -> , N.Sum mh mh' mh'' -> , N.Sum t t' t'' ) => Div (CGSDim lh'' mh'' t'') -> (CGSDim lh' mh' t') -> (CGSDim lh mh t) - -> instance ( N.Mul lh x lh' -> , N.Mul mh x mh' -> , N.Mul t x t' ) => Pow (CGSDim lh mh t) x -> (CGSDim lh' mh' t') - -> instance ( N.Div lh x lh' -> , N.Div mh x mh' -> , N.Div t x t' ) => Root (CGSDim lh mh t) x -> (CGSDim lh' mh' t') - - -= Units = - -We define the base units of the system. By defining 'meter' with a -"scale" of 100 we get a scale of one for 'centi meter'. - -> meter :: Num a => Unit DLength a -> meter = Dimensional 100 -> gram :: Num a => Unit DMass a -> gram = Dimensional 1 -> second :: Num a => Unit DTime a -> second = Dimensional 1 - -We continue by defining the CGS equivalents of the other base SI -units. Actually we limit ourselves to 'ampere' since I am not sure -if or how the SI base dimensions other than current are expressed -in CGS. - -> ampere :: Floating a => Unit DElectricCurrent a -> ampere = prefix (recip 3.33564e-10) ((SI.centi meter ^ pos3) ^/ pos2 * gram ^/ pos2 * second ^ neg2) - -We also define the preferred CGS unit for charge. - -> franklin :: Floating a => Unit DCharge a -- Also known as "esu". -> franklin = gram ^/ pos2 * (SI.centi meter ^ pos3) ^/ pos2 / second - - -= Conversion from SI = - -At some point we may wish to convert an SI quantity to a CGS quantity -or vice versa. - -In order to convert a 'Quantity' from the SI system to the CGS -system we use the strategy of dividing the quantity by the SI base -unit and multiplying the resulting number (sans dimension) by the -equivalent CGS unit. To realize this strategy we must be able to -obtain the SI base unit and the equivalent CGS unit for a given -quantity. We start with the SI unit since it is trivial. - -> unit_SI :: Num a => Quantity (Dim l m t i th n j) a -> Unit (Dim l m t i th n j) a -> unit_SI _ = Dimensional 1 - -(Perhaps the above function would be better defined in another -module.) - -Obtaining the CGS unit corresponding to the SI base unit of a -Quantity isn't quite as trivial. The function body itself is -straight-forward enough, the hairy part is the type signature. - -> unit_CGS :: forall a l m t i l2 m2 il it l' m' t'. -> ( Floating a -> , N.Mul Zero l Zero, N.Mul Pos2 l l2 -> , N.Mul Zero m Zero, N.Mul Pos2 m m2 -> , N.Mul Zero t Zero, N.Mul Pos1 t t -> , N.Sum l2 Zero l2 -> , N.Sum Zero m2 m2, N.Sum m2 Zero m2 -> , N.Sum Zero t t -> , N.Mul Pos3 i il -> , N.Mul Pos1 i i -> , N.Mul Neg2 i it -> , N.Sum l2 il l' -> , N.Sum m2 i m' -> , N.Sum t it t' -> ) => Quantity (Dim l m t i Zero Zero Zero) a -> Unit (CGSDim l' m' t') a -> unit_CGS _ = meter ^ (undefined :: l) -> * SI.kilo gram ^ (undefined :: m) -> * second ^ (undefined :: t) -> * ampere ^ (undefined :: i) - -Note that since the base dimensions of the CGS are a subset of those -of the SI the mapping of types from SI to CGS is unambiguous. - -Also note that complex as the type signature may be producing it is a -mostly mechanical process. - -With the above two functions we can define the function that converts -a unit from the SI. We omit the type signature since it is hairy -but can be readily inferred. - -> fromSI x = x /~ unit_SI x *~ unit_CGS x - - -= Conversion to SI = - -We use the same strategy to convert from CGS to SI. However, when -converting from CGS to SI there may be several valid SI dimensionalities -for any given CGS dimensionality. We will handle this ambiguity by -requiring the user to specify the desired type (except when it is -inferable) of the resulting quantity. For example: - -] toSI (3.2 *~ centi meter) :: Length Double - -In order to do this we must employ lexically scoped type variables -and provide the hairy type signature for the 'toSI' function. - -> toSI :: forall a l m t i l2 m2 il it l' m' t'. -> ( Floating a -> , N.Mul Zero l Zero, N.Mul Pos2 l l2 -> , N.Mul Zero m Zero, N.Mul Pos2 m m2 -> , N.Mul Zero t Zero, N.Mul Pos1 t t -> , N.Sum l2 Zero l2 -> , N.Sum Zero m2 m2, N.Sum m2 Zero m2 -> , N.Sum Zero t t -> , N.Mul Pos3 i il -> , N.Mul Pos1 i i -> , N.Mul Neg2 i it -> , N.Sum l2 il l' -> , N.Sum m2 i m' -> , N.Sum t it t' -> ) => Quantity (CGSDim l' m' t') a -> Quantity (Dim l m t i Zero Zero Zero) a -> toSI x = x /~ unit_CGS (undefined :: Quantity (Dim l m t i Zero Zero Zero) a) -> *~ unit_SI (undefined :: Quantity (Dim l m t i Zero Zero Zero) a) - -Again, the type signature is complex but deriving it is a mechanical -process. - - -= 'Show' instance = - -We round off by writing 'Show' instance for 'CGSDim' analogous to -that of 'Dim'. - -Out of laziness we use the notation "sqrt(cm)" to represent halves -of integral dimensions. Nothing is technically keeping us from doing -a better job here. - -> instance forall lh mh t. -> ( NumType lh -> , NumType mh -> , NumType t -> ) => Show (CGSDim lh mh t) where -> show _ = (Prelude.unwords Prelude.. catMaybes) -> [ dimUnit "sqrt(cm)" (undefined :: lh) -> , dimUnit "sqrt(g)" (undefined :: mh) -> , dimUnit "s" (undefined :: t) -> ] - - -= Examples = - -Let us try the Coulomb attraction example from [2]. We start by -performing the calculation in the SI. - -> q_si = 1.6021773e-19 *~ SI.coulomb -- Elementary charge in SI. -> r_si = 0.1 *~ SI.nano SI.meter -- Distance in SI -> f_si = q_si ^ pos2 / (_4 * pi * e0 * r_si ^ pos2) -> where -> e0 = 8.8541878e-12 *~ (SI.ampere * SI.second / (SI.volt * SI.meter)) - -The same calculation in the CGS system. - -> q_cgs = fromSI q_si -- Elementary charge in CGS. -> r_cgs = fromSI r_si -- Distance in CGS -> f_cgs = q_cgs ^ pos2 / r_cgs ^ pos2 - -Inspecting the values in GHCi shows us that the results are consistent -(within reasonable accuracy) with [2]. - - *Numeric.Dimensional.CGS> f_si - 2.3070794737101255e-8 m kg s^-2 - *Numeric.Dimensional.CGS> f_cgs - 2.30708078598602e-3 sqrt(cm)^2 sqrt(g)^2 s^-2 - -To convert from CGS to SI we must specify the type of the SI 'Quantity'. - -> f_si' = toSI f_cgs :: SIQ.Force Double - - *Numeric.Dimensional.CGS> f_si' - 2.3070807859860202e-8 m kg s^-2 - -We follow up with another conversion example demonstrating the -ambiguity in the conversion from CGS to SI. - -> c = 1 *~ SI.farad -- A SI capacitance. -> c_cgs = fromSI c -- Capacitance has dimensionality L in CGS. -> c' = toSI c_cgs :: SIQ.Capacitance Double -> c'' = toSI c_cgs :: Length Double - - *Numeric.Dimensional.CGS> c - 1.0 m^-2 kg^-1 s^4 A^2 - *Numeric.Dimensional.CGS> c_cgs - 8.98755691740885e11 sqrt(cm)^2 - *Numeric.Dimensional.CGS> c' - 1.0 m^-2 kg^-1 s^4 A^2 - *Numeric.Dimensional.CGS> c'' - 8.98755691740885e9 m - - -= Future work = - -This is a very rudimentary implementation. To make it more practical -a significant number of quantities and units, in particularly those -commonly used with the CGS, would need to be added. In the mean -time all units defined for the SI can be used with the CGS by -applying 'fromSI' to quantities defined from the SI units. - -If anyone is willing to add quantities/units (or other enhancements) -I will happily to accept patches. Personally I do not expect to use -this module and therefore do not intend to invest much more time -in it. If the module has other users I might reconsider. - -And of course, another direction of future work is to define -additional systems (e.g. natural, relativistic) using this module -as a template. I imagine this should be fairly straight forward. - - -= References = - -[1] http://code.google.com/p/dimensional/wiki/ChuckBlake20070611 -[2] http://www.tf.uni-kiel.de/matwis/amat/mw1_ge/kap_2/basics/b2_1_14.html diff --git a/Numeric/Units/Dimensional/Extensible.lhs b/Numeric/Units/Dimensional/Extensible.lhs --- a/Numeric/Units/Dimensional/Extensible.lhs +++ b/Numeric/Units/Dimensional/Extensible.lhs @@ -26,7 +26,13 @@ Similarly with 'Numeric.Dimensional' this module requires GHC 6.6 or later. -> {-# LANGUAGE UndecidableInstances, ScopedTypeVariables #-} +> {-# LANGUAGE UndecidableInstances +> , ScopedTypeVariables +> , EmptyDataDecls +> , MultiParamTypeClasses +> , FunctionalDependencies +> , FlexibleInstances +> #-} > module Numeric.Units.Dimensional.Extensible ( DExt, showDExt ) where diff --git a/Numeric/Units/Dimensional/NonSI.lhs b/Numeric/Units/Dimensional/NonSI.lhs --- a/Numeric/Units/Dimensional/NonSI.lhs +++ b/Numeric/Units/Dimensional/NonSI.lhs @@ -48,8 +48,9 @@ > 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, ounce :: Fractional a => Unit DMass a > poundMass = prefix 0.45359237 (kilo gram) +> ounce = prefix 28.349523 gram In order to relate pounds mass to pounds force we define the questionable unit 'gee' (G) as the gravitational acceleration at @@ -63,10 +64,12 @@ Other (non inch-pound) units. -> bar :: (Fractional a) => Unit DPressure a -> bar = prefix 1.0e5 pascal > revolution :: (Floating a) => Unit DOne a > revolution = prefix 360 degree +> bar :: (Fractional a) => Unit DPressure a +> bar = prefix 1.0e5 pascal +> teaspoon :: (Fractional a) => Unit DVolume a +> teaspoon = prefix 5 (milli liter) = References = diff --git a/dimensional.cabal b/dimensional.cabal --- a/dimensional.cabal +++ b/dimensional.cabal @@ -1,5 +1,5 @@ Name: dimensional -Version: 0.7 +Version: 0.7.1 License: BSD3 License-File: LICENSE Copyright: Bjorn Buckwalter 2006-2007 @@ -26,7 +26,7 @@ Numeric.Units.Dimensional.Quantities, Numeric.Units.Dimensional.SIUnits, Numeric.Units.Dimensional.NonSI, - Numeric.Units.Dimensional.Extensible, - Numeric.Units.Dimensional.CGS + Numeric.Units.Dimensional.Extensible + --Numeric.Units.Dimensional.CGS ghc-options: -O