# dimensional

Statically checked physical dimensions, using Type Families and Data Kinds. https://github.com/bjornbm/dimensional/

LTS Haskell 16.16: | 1.3@rev:2 |

Stackage Nightly 2020-09-29: | 1.3@rev:2 |

Latest on Hackage: | 1.3@rev:2 |

**Bjorn Buckwalter**

**bjorn@buckwalter.se**

#### Module documentation for 1.3

`dimensional-1.3@sha256:28a7438b91e643f33166d53d3fa9586c9baf87e2698dc964490acfb4247fb383,4950`

- Numeric
- Numeric.Units
- Numeric.Units.Dimensional
- Numeric.Units.Dimensional.Coercion
- Numeric.Units.Dimensional.Dimensions
- Numeric.Units.Dimensional.Dynamic
- Numeric.Units.Dimensional.FixedPoint
- Numeric.Units.Dimensional.Float
- Numeric.Units.Dimensional.Functor
- Numeric.Units.Dimensional.NonSI
- Numeric.Units.Dimensional.Prelude
- Numeric.Units.Dimensional.Quantities
- Numeric.Units.Dimensional.SIUnits
- Numeric.Units.Dimensional.UnitNames
- Numeric.Units.Dimensional.Variants

- Numeric.Units.Dimensional

- Numeric.Units

# dimensional

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.

## Usage

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."
```

## Contributing

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

## Changes

## 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
`Prefix`

es. - 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

## 1.0.1.3 (2016-09)

- Fixed an issue with applying metric prefixes to units with non-rational conversion factors.

## 1.0.1.2 (2016-05)

- Support for GHC 8.0.1-rc4, avoiding GHC Trac issue 12026.
- Added support for stack.

## 1.0.1.1 (2015-11)

- Improved example in readme.

## 1.0.1.0 (2015-11)

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

## 1.0.0.0 (2015-11)

- Changed to DataKinds and ClosedTypeFamilies encoding of dimensions.
- Added names and exact values to
`Unit`

s. - 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.

## 0.13.0.2 (2015-04)

- Corrected definition of lumen.

## 0.13.0.1 (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`

.

## 0.10.1.2 (2011-09)

- Bumped time dependency to < 1.5.

## 0.10.1.2 (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.

*(full list with versions)*: