dimensional-1.0.1.1: Statically checked physical dimensions, using Type Families and Data Kinds.

CopyrightCopyright (C) 2006-2015 Bjorn Buckwalter
LicenseBSD3
Maintainerbjorn@buckwalter.se
StabilityStable
PortabilityGHC only
Safe HaskellNone
LanguageHaskell2010
ExtensionsDataKinds

Numeric.Units.Dimensional.Quantities

Contents

Description

Summary

This module defines type synonyms for common dimensionalities and the associated quantity types. Additional dimensionalities and quantity types will be added on an as-needed basis.

The definitions in this module are grouped so that a type synonym for the dimensionality is defined first in terms of base dimension exponents. Then a type synonym for the corresponding quantity type is defined. If there are several quantity types with the same dimensionality type synonyms are provided for each quantity type.

References

  1. http://physics.nist.gov/Pubs/SP811/

Synopsis

Quantities from the NIST Guide

The following quantities are all from the NIST publication "Guide for the Use of the International System of Units (SI)" [1]. Any chapters, sections or tables referenced are from [1] unless otherwise specified.

For lack of better organization we provide definitions grouped by table in [1].

Table 2

"Examples of SI derived units expressed in terms of SI base units."

type Area = Quantity DArea Source

type Volume = Quantity DVolume Source

type Velocity = Quantity DVelocity Source

type Acceleration = Quantity DAcceleration Source

type WaveNumber = Quantity DWaveNumber Source

type MassDensity = Quantity DMassDensity Source

type Density = MassDensity Source

type SpecificVolume = Quantity DSpecificVolume Source

type CurrentDensity = Quantity DCurrentDensity Source

type MagneticFieldStrength = Quantity DMagneticFieldStrength Source

type AmountOfSubstanceConcentration = Quantity DAmountOfSubstanceConcentration Source

type Concentration = AmountOfSubstanceConcentration Source

type Luminance = Quantity DLuminance Source

Table 3

SI coherent derived units with special names and symbols.

type PlaneAngle = Dimensionless Source

type SolidAngle = Dimensionless Source

type Frequency = Quantity DFrequency Source

type Force = Quantity DForce Source

type Pressure = Quantity DPressure Source

type Stress = Quantity DStress Source

type Energy = Quantity DEnergy Source

type Work = Quantity DWork Source

type QuantityOfHeat = Quantity DQuantityOfHeat Source

type Power = Quantity DPower Source

type RadiantFlux = Quantity DRadiantFlux Source

type ElectricCharge = Quantity DElectricCharge Source

type QuantityOfElectricity = Quantity DQuantityOfElectricity Source

type ElectricPotential = Quantity DElectricPotential Source

type PotentialDifference = Quantity DPotentialDifference Source

type ElectromotiveForce = Quantity DElectromotiveForce Source

type Capacitance = Quantity DCapacitance Source

type ElectricResistance = Quantity DElectricResistance Source

type ElectricConductance = Quantity DElectricConductance Source

type MagneticFlux = Quantity DMagneticFlux Source

type MagneticFluxDensity = Quantity DMagneticFluxDensity Source

type Inductance = Quantity DInductance Source

type LuminousFlux = Quantity DLuminousFlux Source

type Illuminance = Quantity DIlluminance Source

type CelsiusTemperature = Quantity DCelsiusTemperature Source

type Activity = Quantity DActivity Source

type AbsorbedDose = Quantity DAbsorbedDose Source

type SpecificEnergy = Quantity DSpecificEnergy Source

type Kerma = Quantity DKerma Source

type DoseEquivalent = Quantity DDoseEquivalent Source

type AmbientDoseEquivalent = DoseEquivalent Source

type DirectionalDoseEquivalent = DoseEquivalent Source

type PersonalDoseEquivalent = DoseEquivalent Source

type EquivalentDose = DoseEquivalent Source

type CatalyticActivity = Quantity DCatalyticActivity Source

Table 4

"Examples of SI coherent derived units expressed with the aid of SI derived units having special names and symbols."

We use the same grouping as for table 2.

type AngularVelocity = Quantity DAngularVelocity Source

type AngularAcceleration = Quantity DAngularAcceleration Source

type DynamicViscosity = Quantity DDynamicViscosity Source

type MomentOfForce = Quantity DMomentOfForce Source

type SurfaceTension = Quantity DSurfaceTension Source

type HeatFluxDensity = Quantity DHeatFluxDensity Source

type Irradiance = Quantity DIrradiance Source

type RadiantIntensity = Quantity DRadiantIntensity Source

type Radiance = Quantity DRadiance Source

type HeatCapacity = Quantity DHeatCapacity Source

type Entropy = Quantity DEntropy Source

type SpecificHeatCapacity = Quantity DSpecificHeatCapacity Source

type SpecificEntropy = Quantity DSpecificEntropy Source

type ThermalConductivity = Quantity DThermalConductivity Source

type EnergyDensity = Quantity DEnergyDensity Source

type ElectricFieldStrength = Quantity DElectricFieldStrength Source

type ElectricChargeDensity = Quantity DElectricChargeDensity Source

type ElectricFluxDensity = Quantity DElectricFluxDensity Source

type Permittivity = Quantity DPermittivity Source

type Permeability = Quantity DPermeability Source

type MolarEnergy = Quantity DMolarEnergy Source

type MolarEntropy = Quantity DMolarEntropy Source

type MolarHeatCapacity = Quantity DMolarHeatCapacity Source

type Exposure = Quantity DExposure Source

type AbsorbedDoseRate = Quantity DAbsorbedDoseRate Source

Quantities not from the NIST Guide

Here we define additional quantities on an as-needed basis. We also provide some synonyms that we anticipate will be useful.

type Impulse = Quantity DImpulse Source

type Momentum = Quantity DMomentum Source

type MassFlow = Quantity DMassFlow Source

type VolumeFlow = Quantity DVolumeFlow Source

type GravitationalParameter = Quantity DGravitationalParameter Source

type KinematicViscosity = Quantity DKinematicViscosity Source

type FirstMassMoment = Quantity DFirstMassMoment Source

type MomentOfInertia = Quantity DMomentOfInertia Source

type AngularMomentum = Quantity DAngularMomentum Source

type ThermalResistivity = Quantity DThermalResistivity Source

type ThermalConductance = Quantity DThermalConductance Source

type ThermalResistance = Quantity DThermalResistance Source

type HeatTransferCoefficient = Quantity DHeatTransferCoefficient Source

type ThermalAdmittance = HeatTransferCoefficient Source

type ThermalInsulance = Quantity DThermalInsulance Source

type Jerk = Quantity DJerk Source

type Angle = PlaneAngle Source

type Thrust = Force Source

type Torque = MomentOfForce Source

type EnergyPerUnitMass = SpecificEnergy Source

Powers of Unit Lengths

It is permissible to express powers of length units by prefixing square and cubic (see section 9.6 "Spelling unit names raised to powers" of [1]).

These definitions may seem slightly out of place but these is no obvious place where they should be. Here they are at least close to the definitions of DLength and DVolume.

square :: (Fractional a, Typeable m) => Unit m DLength a -> Unit NonMetric DArea a Source

Constructs a unit of area from a unit of length, taking the area of a square whose sides are that length.

cubic :: (Fractional a, Typeable m) => Unit m DLength a -> Unit NonMetric DVolume a Source

Constructs a unit of volume from a unit of length, taking the volume of a cube whose sides are that length.

Dimension Aliases

For each Quantity alias supplied above, we also supply a corresponding Dimension alias.

These dimension aliases may be convenient for supplying type signatures for Units or for other type-level dimensional programming.

type DArea = Dim Pos2 Zero Zero Zero Zero Zero Zero Source

type DVolume = Dim Pos3 Zero Zero Zero Zero Zero Zero Source

type DVelocity = Dim Pos1 Zero Neg1 Zero Zero Zero Zero Source

type DAcceleration = Dim Pos1 Zero Neg2 Zero Zero Zero Zero Source

type DWaveNumber = Dim Neg1 Zero Zero Zero Zero Zero Zero Source

type DMassDensity = Dim Neg3 Pos1 Zero Zero Zero Zero Zero Source

type DDensity = DMassDensity Source

type DSpecificVolume = Dim Pos3 Neg1 Zero Zero Zero Zero Zero Source

type DCurrentDensity = Dim Neg2 Zero Zero Pos1 Zero Zero Zero Source

type DMagneticFieldStrength = Dim Neg1 Zero Zero Pos1 Zero Zero Zero Source

type DAmountOfSubstanceConcentration = Dim Neg3 Zero Zero Zero Zero Pos1 Zero Source

type DConcentration = DAmountOfSubstanceConcentration Source

type DLuminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1 Source

type DPlaneAngle = DOne Source

type DSolidAngle = DOne Source

type DFrequency = Dim Zero Zero Neg1 Zero Zero Zero Zero Source

type DForce = Dim Pos1 Pos1 Neg2 Zero Zero Zero Zero Source

type DPressure = Dim Neg1 Pos1 Neg2 Zero Zero Zero Zero Source

type DStress = DPressure Source

type DEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Zero Zero Source

type DWork = DEnergy Source

type DQuantityOfHeat = DEnergy Source

type DPower = Dim Pos2 Pos1 Neg3 Zero Zero Zero Zero Source

type DRadiantFlux = DPower Source

type DElectricCharge = Dim Zero Zero Pos1 Pos1 Zero Zero Zero Source

type DQuantityOfElectricity = DElectricCharge Source

type DElectricPotential = Dim Pos2 Pos1 Neg3 Neg1 Zero Zero Zero Source

type DPotentialDifference = DElectricPotential Source

type DElectromotiveForce = DElectricPotential Source

type DCapacitance = Dim Neg2 Neg1 Pos4 Pos2 Zero Zero Zero Source

type DElectricResistance = Dim Pos2 Pos1 Neg3 Neg2 Zero Zero Zero Source

type DElectricConductance = Dim Neg2 Neg1 Pos3 Pos2 Zero Zero Zero Source

type DMagneticFlux = Dim Pos2 Pos1 Neg2 Neg1 Zero Zero Zero Source

type DMagneticFluxDensity = Dim Zero Pos1 Neg2 Neg1 Zero Zero Zero Source

type DInductance = Dim Pos2 Pos1 Neg2 Neg2 Zero Zero Zero Source

type DLuminousFlux = DLuminousIntensity Source

type DIlluminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1 Source

type DCelsiusTemperature = DThermodynamicTemperature Source

type DActivity = DFrequency Source

type DAbsorbedDose = Dim Pos2 Zero Neg2 Zero Zero Zero Zero Source

type DSpecificEnergy = DAbsorbedDose Source

type DKerma = DAbsorbedDose Source

type DDoseEquivalent = DAbsorbedDose Source

type DAmbientDoseEquivalent = DDoseEquivalent Source

type DDirectionalDoseEquivalent = DDoseEquivalent Source

type DPersonalDoseEquivalent = DDoseEquivalent Source

type DEquivalentDose = DDoseEquivalent Source

type DCatalyticActivity = Dim Zero Zero Neg1 Zero Zero Pos1 Zero Source

type DAngularVelocity = DFrequency Source

type DAngularAcceleration = Dim Zero Zero Neg2 Zero Zero Zero Zero Source

type DDynamicViscosity = Dim Neg1 Pos1 Neg1 Zero Zero Zero Zero Source

type DMomentOfForce = DEnergy Source

type DSurfaceTension = Dim Zero Pos1 Neg2 Zero Zero Zero Zero Source

type DHeatFluxDensity = Dim Zero Pos1 Neg3 Zero Zero Zero Zero Source

type DIrradiance = DHeatFluxDensity Source

type DRadiantIntensity = DPower Source

type DRadiance = DIrradiance Source

type DHeatCapacity = Dim Pos2 Pos1 Neg2 Zero Neg1 Zero Zero Source

type DEntropy = DHeatCapacity Source

type DSpecificHeatCapacity = Dim Pos2 Zero Neg2 Zero Neg1 Zero Zero Source

type DSpecificEntropy = DSpecificHeatCapacity Source

type DThermalConductivity = Dim Pos1 Pos1 Neg3 Zero Neg1 Zero Zero Source

type DEnergyDensity = DPressure Source

type DElectricFieldStrength = Dim Pos1 Pos1 Neg3 Neg1 Zero Zero Zero Source

type DElectricChargeDensity = Dim Neg3 Zero Pos1 Pos1 Zero Zero Zero Source

type DElectricFluxDensity = Dim Neg2 Zero Pos1 Pos1 Zero Zero Zero Source

type DPermittivity = Dim Neg3 Neg1 Pos4 Pos2 Zero Zero Zero Source

type DPermeability = Dim Pos1 Pos1 Neg2 Neg2 Zero Zero Zero Source

type DMolarEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Neg1 Zero Source

type DMolarEntropy = Dim Pos2 Pos1 Neg2 Zero Neg1 Neg1 Zero Source

type DMolarHeatCapacity = DMolarEntropy Source

type DExposure = Dim Zero Neg1 Pos1 Pos1 Zero Zero Zero Source

type DAbsorbedDoseRate = Dim Pos2 Zero Neg3 Zero Zero Zero Zero Source

type DImpulse = Dim Pos1 Pos1 Neg1 Zero Zero Zero Zero Source

type DMomentum = DImpulse Source

type DMassFlow = Dim Zero Pos1 Neg1 Zero Zero Zero Zero Source

type DVolumeFlow = Dim Pos3 Zero Neg1 Zero Zero Zero Zero Source

type DGravitationalParameter = Dim Pos3 Zero Neg2 Zero Zero Zero Zero Source

type DKinematicViscosity = Dim Pos2 Zero Neg1 Zero Zero Zero Zero Source

type DFirstMassMoment = Dim Pos1 Pos1 Zero Zero Zero Zero Zero Source

type DMomentOfInertia = Dim Pos2 Pos1 Zero Zero Zero Zero Zero Source

type DAngularMomentum = Dim Pos2 Pos1 Neg1 Zero Zero Zero Zero Source

type DThermalResistivity = Dim Neg1 Neg1 Pos3 Zero Pos1 Zero Zero Source

type DThermalConductance = Dim Pos2 Pos1 Neg3 Zero Neg1 Zero Zero Source

type DThermalResistance = Dim Neg2 Neg1 Pos3 Zero Pos1 Zero Zero Source

type DHeatTransferCoefficient = Dim Zero Pos1 Neg3 Zero Neg1 Zero Zero Source

type DThermalAdmittance = DHeatTransferCoefficient Source

type DThermalInsulance = Dim Zero Neg1 Pos3 Zero Pos1 Zero Zero Source

type DJerk = Dim Pos1 Zero Neg3 Zero Zero Zero Zero Source

type DAngle = DPlaneAngle Source

type DThrust = DForce Source

type DTorque = DMomentOfForce Source

type DEnergyPerUnitMass = DSpecificEnergy Source