Copyright | Copyright (C) 2006-2018 Bjorn Buckwalter |
---|---|
License | BSD3 |
Maintainer | bjorn@buckwalter.se |
Stability | Stable |
Portability | GHC only |
Safe Haskell | None |
Language | Haskell2010 |
Summary
This module defines the SI prefixes, the SI base units and the SI derived units. It also defines the units outside of the SI that are accepted for use with the SI. Any chapters, sections or tables referenced are from [1] unless otherwise specified.
References
Synopsis
- metre :: Num a => Unit 'Metric DLength a
- meter :: Num a => Unit 'Metric DLength a
- gram :: Fractional a => Unit 'Metric DMass a
- second :: Num a => Unit 'Metric DTime a
- ampere :: Num a => Unit 'Metric DElectricCurrent a
- kelvin :: Num a => Unit 'Metric DThermodynamicTemperature a
- mole :: Num a => Unit 'Metric DAmountOfSubstance a
- candela :: Num a => Unit 'Metric DLuminousIntensity a
- radian :: Num a => Unit 'Metric DPlaneAngle a
- steradian :: Num a => Unit 'Metric DSolidAngle a
- hertz :: Num a => Unit 'Metric DFrequency a
- newton :: Num a => Unit 'Metric DForce a
- pascal :: Num a => Unit 'Metric DPressure a
- joule :: Num a => Unit 'Metric DEnergy a
- watt :: Num a => Unit 'Metric DPower a
- coulomb :: Num a => Unit 'Metric DElectricCharge a
- volt :: Num a => Unit 'Metric DElectricPotential a
- farad :: Num a => Unit 'Metric DCapacitance a
- ohm :: Num a => Unit 'Metric DElectricResistance a
- siemens :: Num a => Unit 'Metric DElectricConductance a
- weber :: Num a => Unit 'Metric DMagneticFlux a
- tesla :: Num a => Unit 'Metric DMagneticFluxDensity a
- henry :: Num a => Unit 'Metric DInductance a
- lumen :: Num a => Unit 'Metric DLuminousFlux a
- lux :: Num a => Unit 'Metric DIlluminance a
- degreeCelsius :: Num a => Unit 'Metric DCelsiusTemperature a
- fromDegreeCelsiusAbsolute :: Floating a => a -> ThermodynamicTemperature a
- toDegreeCelsiusAbsolute :: Floating a => ThermodynamicTemperature a -> a
- becquerel :: Num a => Unit 'Metric DActivity a
- gray :: Num a => Unit 'Metric DAbsorbedDose a
- sievert :: Num a => Unit 'Metric DDoseEquivalent a
- katal :: Num a => Unit 'Metric DCatalyticActivity a
- minute :: Num a => Unit 'NonMetric DTime a
- hour :: Num a => Unit 'NonMetric DTime a
- day :: Num a => Unit 'NonMetric DTime a
- hectare :: Fractional a => Unit 'NonMetric DArea a
- litre :: Fractional a => Unit 'Metric DVolume a
- liter :: Fractional a => Unit 'Metric DVolume a
- tonne :: Num a => Unit 'Metric DMass a
- metricTon :: Num a => Unit 'Metric DMass a
- degree :: Floating a => Unit 'NonMetric DPlaneAngle a
- arcminute :: Floating a => Unit 'NonMetric DPlaneAngle a
- arcsecond :: Floating a => Unit 'NonMetric DPlaneAngle a
- degreeOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a
- minuteOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a
- secondOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a
- astronomicalUnit :: Num a => Unit 'NonMetric DLength a
- deka :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- deca :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- hecto :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- kilo :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- mega :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- giga :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- tera :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- peta :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- exa :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- zetta :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- yotta :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a
- deci :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- centi :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- milli :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- micro :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- nano :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- pico :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- femto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- atto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- zepto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- yocto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a
- data Prefix
- applyPrefix :: Fractional a => Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a
- siPrefixes :: [Prefix]
SI Base Units
These are the base units from section 4.1. To avoid a myriad of one-letter functions that would doubtlessly cause clashes and frustration in users' code, we spell out all unit names in full, as we did for prefixes. We also elect to spell the unit names in singular form, as allowed by section 9.7 "Other spelling conventions".
We define the SI base units in the order of table 1.
SI Derived Units
From Table 3, SI derived units with special names and symbols, including the radian and steradian.
Celsius Temperature
A problematic area is units which increase proportionally to the base SI units but cross zero at a different point. An example would be degrees Celsius (see section 4.2.1.1). The author feels that it is appropriate to define a unit for use with relative quantities (taking only into account the proportionality) and complement the unit with functions for converting absolute values.
The function fromDegreeCelsiusAbsolute
should be used in lieu of
"*~ degreeCelsius" when working with absolute temperatures. Similarily,
toDegreeCelsiusAbsolute
should be used in lieu of "/~ degreeCelsius"
when working with absolute temperatures.
degreeCelsius :: Num a => Unit 'Metric DCelsiusTemperature a Source #
fromDegreeCelsiusAbsolute :: Floating a => a -> ThermodynamicTemperature a Source #
toDegreeCelsiusAbsolute :: Floating a => ThermodynamicTemperature a -> a Source #
Units Admitted for Reasons of Safeguarding Human Health
The last units from Table 3 are SI derived units with special names and symbols admitted for reasons of safeguarding human health.
Units Accepted for Use with the SI
There are several units that are not strictly part of the SI but are either permanently or temporarily accepted for use with the SI. We define the permanently accepted ones in this module.
From Table 6, Units accepted for use with the SI.
We start with time which we grant exclusive rights to minute
and
second
.
Units of Plane Angle
Since minute
and second
are already in use for time we use
arcminute
and arcsecond
[2] for plane angle instead.
Alternate (longer) forms of the above. In particular degreeOfArc
can be used if there is a percieved need to disambiguate from e.g.
temperature.
degreeOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a Source #
minuteOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a Source #
secondOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a Source #
Units Formerly Defined By Experiment
We decline to provide here those units - listed in Table 7 - which, while accepted for use with the SI, have values which are determined experimentally. For versioning purposes, those units can be found in Numeric.Units.Dimensional.NonSI.
However, in 2012 the IAU redefined the astronomical unit as a conventional unit of length directly tied to the meter, with a length of exactly 149 597 870 700 m and the official abbreviation of au [3]. We therefore include it here.
SI Prefixes
Prefixes are used to form decimal multiples and submultiples of SI Units as described in section 4.4.
By defining SI prefixes as functions applied to a Unit
we satisfy
section 6.2.6 "Unacceptability of stand-alone prefixes".
We define all SI prefixes from Table 5. Multiples first.
deca :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "deca" prefix, denoting a factor of 10.
hecto :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "hecto" prefix, denoting a factor of 100.
kilo :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "kilo" prefix, denoting a factor of 1000.
mega :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "mega" prefix, denoting a factor of 10^6.
giga :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "giga" prefix, denoting a factor of 10^9.
tera :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "tera" prefix, denoting a factor of 10^12.
peta :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "peta" prefix, denoting a factor of 10^15.
exa :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "exa" prefix, denoting a factor of 10^18.
zetta :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "zetta" prefix, denoting a factor of 10^21.
yotta :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "yotta" prefix, denoting a factor of 10^24.
Then the submultiples.
deci :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "deci" prefix, denoting a factor of 0.1.
centi :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "centi" prefix, denoting a factor of 0.01.
milli :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "milli" prefix, denoting a factor of 0.001.
micro :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "micro" prefix, denoting a factor of 10^-6.
nano :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "nano" prefix, denoting a factor of 10^-9.
pico :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "pico" prefix, denoting a factor of 10^-12.
femto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "femto" prefix, denoting a factor of 10^-15.
atto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "atto" prefix, denoting a factor of 10^-18.
zepto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "zepto" prefix, denoting a factor of 10^-21.
yocto :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a Source #
The "yocto" prefix, denoting a factor of 10^-24.
We supply an explicit representation of an SI prefix, along with a function to apply one and a list of all prefixes defined by the SI.
A metric prefix.
Instances
Eq Prefix Source # | |
Data Prefix Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.Internal gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Prefix -> c Prefix # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Prefix # toConstr :: Prefix -> Constr # dataTypeOf :: Prefix -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Prefix) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Prefix) # gmapT :: (forall b. Data b => b -> b) -> Prefix -> Prefix # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Prefix -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Prefix -> r # gmapQ :: (forall d. Data d => d -> u) -> Prefix -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Prefix -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Prefix -> m Prefix # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Prefix -> m Prefix # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Prefix -> m Prefix # | |
Ord Prefix Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.Internal | |
Generic Prefix Source # | |
NFData Prefix Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.Internal | |
HasInterchangeName Prefix Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.Internal | |
type Rep Prefix Source # | |
Defined in Numeric.Units.Dimensional.UnitNames.Internal type Rep Prefix = D1 ('MetaData "Prefix" "Numeric.Units.Dimensional.UnitNames.Internal" "dimensional-1.5-HMi5nnDJYaz1w5t6f148nq" 'False) (C1 ('MetaCons "Prefix" 'PrefixI 'True) (S1 ('MetaSel ('Just "prefixName") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 PrefixName) :*: S1 ('MetaSel ('Just "scaleFactor") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Rational))) |
applyPrefix :: Fractional a => Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a Source #
siPrefixes :: [Prefix] Source #
A list of all Prefix
es defined by the SI.