This library provides statically-checked dimensional arithmetic for physical quantities, using the 7 SI base dimensions.

Data kinds and closed type families provide a flexible, safe, and discoverable implementation that leads to largely self-documenting client code.

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Simply importing Numeric.Units.Dimensional.Prelude provides access to dimensional arithmetic opertors, SI units and other common units accepted for use with the SI, and convenient aliases for quantities with commonly used dimensions.

The Unit d a type represents a unit with dimension d, whose conversion factor to the coherent SI base unit of the corresponding dimension is represented by a value of type a. a is commonly chosen to be Double, but can be any Floating type. Where possible, support is also provided for Fractional or Num values.

Similarly, the Quantity d a type represents a quantity with dimension d, whose numeric value is of type a. Aliases allow the use of, e.g., Length Double to mean Quantity DLength Double. A complete list of available aliases is given in the haddock documentation for the Numeric.Units.Dimensional.Quantities.

In the example below, we will solve a simple word problem.

A car travels at 60 kilometers per hour for one mile, at 50 kph for one mile, at 40 kph for one mile, and at 30 kph for one mile. How many minutes does the journey take? What is the average speed of the car? How many seconds does the journey take, rounded up to the next whole second?

{-# LANGUAGE NoImplicitPrelude #-}

module ReadmeExample where

import Numeric.Units.Dimensional.Prelude
import Numeric.Units.Dimensional.NonSI (mile)

leg :: Length Double
leg = 1 *~ mile -- *~ combines a raw number and a unit to form a quantity

speeds :: [Velocity Double]
speeds = [60, 50, 40, 30] *~~ (kilo meter / hour)
  -- *~~ does the same thing for a whole Functor at once
  -- Parentheses are required around unit expressions that are comingled with *~, /~, *~~, or /~~ operations

timeOfJourney :: Time Double
timeOfJourney = sum $ fmap (leg /) speeds
  -- We can use dimensional versions of ordinary functions like / and sum to combine quantities

averageSpeed :: Velocity Double
averageSpeed = _4 * leg / timeOfJourney
  -- _4 is an alias for the dimensionless number 4

wholeSeconds :: Integer
wholeSeconds = ceiling $ timeOfJourney /~ second
  -- /~ lets us recover a raw number from a quantity and a unit in which it should be expressed

main :: IO ()
main = do
         putStrLn $ "Length of journey is: " ++ showIn minute timeOfJourney
         putStrLn $ "Average speed is: " ++ showIn (mile / hour) averageSpeed
         putStrLn $ "If we don't want to be explicit about units, the show instance uses the SI basis: " ++ show averageSpeed
         putStrLn $ "The journey requires " ++ show wholeSeconds ++ " seconds, rounded up to the nearest second."


For project information (issues, updates, wiki, examples) see: https://github.com/bjornbm/dimensional


1.4 (2021-05)

  • Add calorie to NonSI.
  • Remove deprecated AutoDeriveTypeable pragmas. This means that Typable instances are no provided on GHC prior to 8.2.

1.3 (2018-12)

  • Breaking: Changed the Show instances for UnitName, Unit, SQuantity to use non-breaking spaces within unit names and between values and their units.
  • Bumped exact-pi dependency to < 0.6.
  • Added the dimensionless unit percent.
  • Added dimensionless wrappers for log1p, expm1, log1pexp, and log1mexp from the Floating class.

1.2 (2018-11)

  • Add NoStarIsType extension and import Data.Kind.Type for GHC 8.6 compitbility. Abandon compatibility with GHC < 8.

1.1 (2018-03)

  • Added Semigroup instances for GHC 8.4 compatibility.
  • Breaking: Renamed Root type family to NRoot. Added Sqrt and Cbrt type synonyms. Added sqrt and cbrt for term level dimensions.
  • Breaking: Changed Numeric.Units.Dimensional.Prelude to export dimensionally typed signum, recip, and logBase instead of the ones from Prelude.
  • Breaking: Changed Numeric.Units.Dimensional.Prelude to export (.) and id from Control.Category instead of from Prelude.
  • Breaking: Created a product function which take the product of a foldable structure of Dimensionless values. Exported this product function from Numeric.Units.Dimensional.Prelude instead of the one from Prelude.
  • Breaking: Changed the HasDimension typeclass to require an instance of the new HasDynamicDimension typeclass.
  • Breaking: Added operators for AnyUnit to the Numeric.Units.Dimensional.Dynamic module which may cause name collisions.
  • Breaking: Added dynamic versions of (*~), (/~), and siUnit to the Numeric.Units.Dimensional.Dynamic module which may cause name collisions.
  • Breaking: Removed exports of nMeter, nSecond, kilo, etc from Numeric.Units.Dimensional.UnitNames. Access these instead by inspecting the relevant units or prefixes.
  • Breaking: Generalized the type of dimensionlessLength from (Num a, Foldable f) => f (Dimensional v d a) -> Dimensionless a) to (Num a, Foldable f) => f b -> Dimensionless a. This provides a weaker constraint on the type a and may result in ambiguous types in code that depends on the former less general type.
  • Fixed a bug in the definition of the inHg_NIST.
  • Fixed a bug in the interchange name of the Dalton.
  • Added units for the US survey foot, yard, inch, mil, and mile.
  • Added the short ton as a unit of mass.
  • Clarified that the UCUM acre is based on the US survey foot.
  • Added a version of the acre based on the international foot.
  • Added Data, Generic, Typeable and NFData instances for many ancillary types.
  • Added unQuantity to the Coercion module to ease unwrapping without introducing ambiguous type variables.
  • Created explicit representation of metric Prefixes.
  • Added a multiplicative Monoid instance for AnyQuantity and for AnyUnit.
  • Added the DynQuantity type to represent possibly valid quantities of statically unknown dimension, suitable for performing arithmetic with such quantities.
  • Added nroot function for term-level dimensions.
  • Added the Numeric.Units.Dimensional.Float module with convenient wrappers around functions from RealFloat and IEEE for inspecting floating point quantities.
  • Added an AEq instance for Quantity.
  • Added Eq1 and Ord1 instances for Quantity.
  • Exposed the name of an ‘AnyUnit’ without promoting it to a ‘Unit’ first.
  • Exposed a way to convert atomic ‘UnitName’s back into ‘NameAtom’s.
  • Added the btu, a unit of energy.
  • Added the gauss, a unit of magnetic flux density.
  • Added the angstrom, a unit of length.
  • Relocated git repository to https://github.com/bjornbm/dimensional (2016-09)

  • Fixed an issue with applying metric prefixes to units with non-rational conversion factors. (2016-05)

  • Support for GHC 8.0.1-rc4, avoiding GHC Trac issue 12026.
  • Added support for stack. (2015-11)

  • Improved example in readme. (2015-11)

  • Added Numeric.Units.Dimensional.Coercion module.
  • Bumped exact-pi dependency to < 0.5.
  • Restored changelog.
  • Addressed issues with documentation. (2015-11)

  • Changed to DataKinds and ClosedTypeFamilies encoding of dimensions.
  • Added names and exact values to Units.
  • Added AnyUnit and AnyQuantity for quantities whose dimension is statically unknown.
  • Added Storable and Unbox instances for Quantity.
  • Added dimensionally-polymorphic siUnit for the coherent SI base unit of any dimension.
  • Added some additional units. (2015-04)

  • Corrected definition of lumen. (2014-09)

  • Bumped time dependency to < 1.6.

0.13 (2014-02)

  • Bump major version (should have been done in previous version).

0.12.3 (2014-02)

  • Bump numtype dependency to 1.1 (GHC 7.8.1 compatibility fix).
  • Added Torque.
  • Added D.. for the type synonym quantities (e.g., Angle).

0.12.2 (2013-11)

  • Added FirstMassMoment, MomentOfInertia, AngularMomentum.
  • Improved unit numerics.

0.12.1 (2013-07)

  • Typeable Dimensionals.

0.12 (2013-06)

  • Polymorphic _0 (closes issue 39).
  • Added astronomicalUnit.
  • Added imperial volume units.
  • Added ‘mil’ (=inch/1000).
  • Added tau.
  • Added KinematicViscosity. (2011-09)

  • Bumped time dependency to < 1.5. (2011-08)

  • Bumped time dependency to < 1.4.

0.10.1 (2011-08)

GHC 7.2.1 compatibility fix:

  • Increased CGS context-stack to 30.

0.10 (2011-05)

See the announcement.

0.9 (2011-04)

See the announcement.