Angles as dimensions

dimensional-dk.cabal

@@ -54,7 +54,11 @@ library
                        Numeric.Units.Dimensional.DK.Dimensions,
                        Numeric.Units.Dimensional.DK.Dimensions.TermLevel,
                        Numeric.Units.Dimensional.DK.Dimensions.TypeLevel,
-                       Numeric.Units.Dimensional.DK.Functor
+                       Numeric.Units.Dimensional.DK.Functor,
+                       Numeric.Units.Dimensional.DK.SI,
+                       Numeric.Units.Dimensional.DK.SI.Prelude,
+                       Numeric.Units.Dimensional.DK.SI.SIUnits,
+                       Numeric.Units.Dimensional.DK.SI.Quantities
 
 test-suite tests
   type:                exitcode-stdio-1.0
@@ -78,4 +82,4 @@ benchmark simple
                        dimensional-dk
   default-language:    Haskell2010
   ghc-options:         -O2
-
+

examples/NewtonianMechanics.hs

@@ -30,8 +30,8 @@ rotationalMomentum i w = i * w
 rotationalPower :: (Num a) => Torque a -> AngularVelocity a -> Power a
 rotationalPower t w = t * w
 
-torque :: (Num a) => Force a -> Length a -> Torque a
-torque r f = r * f
+torque :: (Fractional a) => Force a -> Length a -> Torque a
+torque r f = r * f / (1 *~ radian)
 
 torqueFromChangeInMomentum :: (Fractional a) => AngularMomentum a -> Time a -> Torque a
 torqueFromChangeInMomentum dL dt = dL / dt

src/Numeric/Units/Dimensional/DK.hs

@@ -199,7 +199,7 @@ module Numeric.Units.Dimensional.DK
     Dimension (Dim),
     -- ** Dimension Arithmetic
     -- $dimension-arithmetic
-    type (*), type (/), type (^), Root, Recip,
+    type (*), type (/), type (^), Root, Recip, type SIDim, type ToSIDim,
     -- ** Term Level Representation of Dimensions
     -- $dimension-terms
     Dimension' (Dim'), HasDimension(..), KnownDimension,
@@ -209,20 +209,22 @@ module Numeric.Units.Dimensional.DK
     negate, abs, nroot, sqrt, cbrt,
     -- ** Transcendental Functions
     exp, log, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, atan2,
+    -- ** Dealing with Angles
+    removeAngles, coerceAngles,
     -- ** Operations on Collections
     -- $collections
     (*~~), (/~~), sum, mean, dimensionlessLength, nFromTo,
     -- * Dimension Synonyms
     -- $dimension-synonyms
-    DOne, DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity,
+    DOne, DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity, DPlaneAngle,
     -- * Quantity Synonyms
     -- $quantity-synonyms
-    Dimensionless, Length, Mass, Time, ElectricCurrent, ThermodynamicTemperature, AmountOfSubstance, LuminousIntensity,
+    Dimensionless, Length, Mass, Time, ElectricCurrent, ThermodynamicTemperature, AmountOfSubstance, LuminousIntensity, PlaneAngle,
     -- * Constants
     -- $constants
     _0, _1, _2, _3, _4, _5, _6, _7, _8, _9, pi, tau,
     -- * Constructing Units
-    prefix, siUnit, one,
+    prefix, baseUnit, siUnit, one,
     -- * On 'Functor', and Conversion Between Number Representations
     -- $functor
     dmap, changeRep
@@ -385,6 +387,7 @@ type ElectricCurrent          = Quantity DElectricCurrent
 type ThermodynamicTemperature = Quantity DThermodynamicTemperature
 type AmountOfSubstance        = Quantity DAmountOfSubstance
 type LuminousIntensity        = Quantity DLuminousIntensity
+type PlaneAngle               = Quantity DPlaneAngle
 
 {- $dimension-arithmetic
 When performing arithmetic on units and quantities the arithmetics
@@ -581,39 +584,68 @@ We continue by defining elementary functions on 'Dimensionless'
 that may be obviously useful.
 -}
 
-exp, log, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh
+exp, log, sinh, cosh, tanh, asinh, acosh, atanh
   :: Floating a => Dimensionless a -> Dimensionless a
 exp   = fmap Prelude.exp
 log   = fmap Prelude.log
-sin   = fmap Prelude.sin
-cos   = fmap Prelude.cos
-tan   = fmap Prelude.tan
-asin  = fmap Prelude.asin
-acos  = fmap Prelude.acos
-atan  = fmap Prelude.atan
 sinh  = fmap Prelude.sinh
 cosh  = fmap Prelude.cosh
 tanh  = fmap Prelude.tanh
 asinh = fmap Prelude.asinh
 acosh = fmap Prelude.acosh
 atanh = fmap Prelude.atanh
 
+sin, cos, tan :: Floating a => PlaneAngle a -> Dimensionless a
+sin   = (*~ one) . Prelude.sin . (/~ baseUnit)
+cos   = (*~ one) . Prelude.cos . (/~ baseUnit)
+tan   = (*~ one) . Prelude.tan . (/~ baseUnit)
+
+asin, acos, atan :: Floating a => Dimensionless a -> PlaneAngle a
+asin  = (*~ baseUnit) . Prelude.asin . (/~ one)
+acos  = (*~ baseUnit) . Prelude.acos . (/~ one)
+atan  = (*~ baseUnit) . Prelude.atan . (/~ one)
+
+-- | Removes angular dimensions from a dimensional value by equating radians
+-- with the dimensionless quantity one.
+removeAngles :: Dimensional v ('Dim l m t i th n j pa) a -> Dimensional v (SIDim l m t i th n j) a
+removeAngles = coerceAngles
+
+-- | Equates values whose dimensions differ in plane angles by equating
+-- radians with the dimensionless quantity one.
+--
+-- See `removeAngles`, which offers a more specific result type, if you are only interested
+-- in ignoring angle dimensions.
+coerceAngles :: Dimensional v ('Dim l m t i th n j pa) a -> Dimensional v ('Dim l m t i th n j pa') a
+coerceAngles = coerce
+
 (**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a
 Dimensional x ** Dimensional y = Dimensional (x Prelude.** y)
 
 {-
 For 'atan2' the operands need not be dimensionless but they must be
-of the same type. The result will of course always be dimensionless.
+of the same type. The result will of course always be a plane angle.
 -}
 
-atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a
+atan2 :: RealFloat a => Quantity d a -> Quantity d a -> PlaneAngle a
 atan2 (Dimensional y) (Dimensional x) = Dimensional (Prelude.atan2 y x)
 
+-- | A polymorphic 'Unit' which can be used in place of the coherent
+-- base unit of any dimension. This allows polymorphic quantity
+-- creation and destruction without exposing the 'Dimensional' constructor.
+--
+-- `siUnit` is similar but does not include the radians associated
+-- with plane angles.
+baseUnit :: Num a => Unit d a
+baseUnit = Dimensional 1
+
 -- | A polymorphic 'Unit' which can be used in place of the coherent
 -- SI base unit of any dimension. This allows polymorphic quantity
 -- creation and destruction without exposing the 'Dimensional' constructor.
-siUnit :: Num a => Unit d a
-siUnit = Dimensional 1
+--
+-- `baseUnit` is similar but includes the radians associated
+-- with plane angles.
+siUnit :: Num a => Unit (SIDim l m t i th n j) a
+siUnit = removeAngles baseUnit
 
 {-
 The only unit we will define in this module is 'one'.
@@ -626,7 +658,7 @@ The only unit we will define in this module is 'one'.
 -- 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 = siUnit
+one = baseUnit
 
 {- $constants
 For convenience we define some constants for small integer values
@@ -639,7 +671,7 @@ good measure.
 -- it to express zero Length or Capacitance or Velocity etc, in addition
 -- to the dimensionless value zero.
 _0 :: Num a => Quantity d a
-_0 = 0 *~ siUnit
+_0 = 0 *~ baseUnit
 
 _1, _2, _3, _4, _5, _6, _7, _8, _9 :: (Num a) => Dimensionless a
 _1 = 1 *~ one
@@ -704,7 +736,7 @@ even a requirement.
 -}
 instance (KnownDimension d, Show a) => Show (Quantity d a) where
       show q@(Dimensional x) = let powers = asList $ dimension q
-                                   units = ["m", "kg", "s", "A", "K", "mol", "cd"]
+                                   units = ["m", "kg", "s", "A", "K", "mol", "cd", "rad", "sr"]
                                    dims = concat $ zipWith dimUnit units powers
                                in show x ++ dims
 

src/Numeric/Units/Dimensional/DK/Dimensions/TermLevel.hs

@@ -9,7 +9,7 @@
    Portability: GHC only
 
 This module defines physical dimensions expressed in terms of
-the SI base dimensions, including arithmetic.
+the SI base dimensions along with plane angles, including arithmetic.
 
 -}
 module Numeric.Units.Dimensional.DK.Dimensions.TermLevel
@@ -22,7 +22,7 @@ module Numeric.Units.Dimensional.DK.Dimensions.TermLevel
   (*), (/), (^), recip,
   -- * Synonyms for Base Dimensions
   dOne,
-  dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity,
+  dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity, dPlaneAngle,
   -- * Deconstruction
   asList
 )
@@ -32,10 +32,11 @@ import Data.Monoid (Monoid(..))
 import Prelude (id, (+), (-), Int, Show, Eq, Ord)
 import qualified Prelude as P
 
--- | A physical dimension, encoded as 7 integers, representing a factorization of the dimension into the
--- 7 SI base dimensions. By convention they are stored in the same order as 
+-- | A physical dimension, encoded as 8 integers, representing a factorization of the dimension into the
+-- 7 SI base dimensions, along with the dimensions of plane angle.
+-- By convention they are stored in the same order as 
 -- in the 'Numeric.Units.Dimensional.DK.Dimensions.TypeLevel.Dimension' data kind.
-data Dimension' = Dim' !Int !Int !Int !Int !Int !Int !Int 
+data Dimension' = Dim' !Int !Int !Int !Int !Int !Int !Int !Int
   deriving (Show, Eq, Ord)
 
 -- | The monoid of dimensions under multiplication.
@@ -53,16 +54,17 @@ instance HasDimension Dimension' where
 
 -- | The dimension of dimensionless values.
 dOne :: Dimension'
-dOne = Dim' 0 0 0 0 0 0 0
-
-dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity :: Dimension'
-dLength                   = Dim' 1 0 0 0 0 0 0
-dMass                     = Dim' 0 1 0 0 0 0 0
-dTime                     = Dim' 0 0 1 0 0 0 0
-dElectricCurrent          = Dim' 0 0 0 1 0 0 0
-dThermodynamicTemperature = Dim' 0 0 0 0 1 0 0
-dAmountOfSubstance        = Dim' 0 0 0 0 0 1 0
-dLuminousIntensity        = Dim' 0 0 0 0 0 0 1
+dOne = Dim' 0 0 0 0 0 0 0 0
+
+dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity, dPlaneAngle :: Dimension'
+dLength                   = Dim' 1 0 0 0 0 0 0 0
+dMass                     = Dim' 0 1 0 0 0 0 0 0
+dTime                     = Dim' 0 0 1 0 0 0 0 0
+dElectricCurrent          = Dim' 0 0 0 1 0 0 0 0
+dThermodynamicTemperature = Dim' 0 0 0 0 1 0 0 0
+dAmountOfSubstance        = Dim' 0 0 0 0 0 1 0 0
+dLuminousIntensity        = Dim' 0 0 0 0 0 0 1 0
+dPlaneAngle               = Dim' 0 0 0 0 0 0 0 1
 
 {-
 We will reuse the operators and function names from the Prelude.
@@ -75,21 +77,21 @@ infixl 7  *, /
 
 -- | Forms the product of two dimensions.
 (*) :: Dimension' -> Dimension' -> Dimension'
-(Dim' l m t i th n j) * (Dim' l' m' t' i' th' n' j') = Dim' (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j')
+(Dim' l m t i th n j pa) * (Dim' l' m' t' i' th' n' j' pa') = Dim' (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j') (pa + pa')
 
 -- | Forms the quotient of two dimensions.
 (/) :: Dimension' -> Dimension' -> Dimension'
-(Dim' l m t i th n j) / (Dim' l' m' t' i' th' n' j') = Dim' (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j')
+(Dim' l m t i th n j pa) / (Dim' l' m' t' i' th' n' j' pa') = Dim' (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j') (pa - pa')
 
 -- | Raises a dimension to an integer power.
 (^) :: Dimension' -> Int -> Dimension'
-(Dim' l m t i th n j) ^ x = Dim' (x P.* l) (x P.* m) (x P.* t) (x P.* i) (x P.* th) (x P.* n) (x P.* j)
+(Dim' l m t i th n j pa) ^ x = Dim' (x P.* l) (x P.* m) (x P.* t) (x P.* i) (x P.* th) (x P.* n) (x P.* j) (x P.* pa)
 
 -- | Forms the reciprocal of a dimension.
 recip :: Dimension' -> Dimension'
 recip = (dOne /)
 
--- | Converts a dimension to a list of 7 integers, representing the exponent associated with each
--- of the 7 SI base dimensions in the standard order.
+-- | Converts a dimension to a list of 9 integers, representing the exponent associated with each
+-- of the 7 SI base dimensions in the standard order, followed by the dimensions of plane and spherical angles.
 asList :: Dimension' -> [Int]
-asList (Dim' l m t i th n j) = [l, m, t, i, th, n, j]
+asList (Dim' l m t i th n j pa) = [l, m, t, i, th, n, j, pa]