Statically checked physical dimensions.

Dimensional is a library providing data types for performing arithmetic with physical quantities and units. Information about the physical dimensions of the quantities and units is embedded in their types and the validity of operations is verified by the type checker at compile time. The wrapping and unwrapping of numerical values as quantities is done by multiplication and division with units. The library is designed to, as far as is practical, enforce/encourage best practices of unit usage. Version 1 of the dimensional package differs from earlier version in that the dimension tracking is implemented using Closed Type Families and Data Kinds rather than functional dependencies. This enables a number of features, including improved support for unit names and quantities with statically-unknown dimensions. Requires GHC 8.0 or later.

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.