-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Statically checked physical dimensions, -- using Type Families and Data Kinds. -- -- 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 boxing and unboxing 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 7.8 or later. @package dimensional @version 1.0.1.2 module Numeric.Units.Dimensional.UnitNames.InterchangeNames -- | Represents the authority which issued an interchange name for a unit. data InterchangeNameAuthority -- | The interchange name originated with the Unified Code for Units of -- Measure. UCUM :: InterchangeNameAuthority -- | The interchange name originated with the dimensional library. DimensionalLibrary :: InterchangeNameAuthority -- | The interchange name originated with a user of the dimensional -- library. Custom :: InterchangeNameAuthority data InterchangeName InterchangeName :: String -> InterchangeNameAuthority -> InterchangeName [name] :: InterchangeName -> String [authority] :: InterchangeName -> InterchangeNameAuthority -- | Determines the authority which issued the interchange name of a unit -- or unit name. For composite units, this is the least-authoritative -- interchange name of any constituent name. -- -- Note that the least-authoritative authority is the one sorted as -- greatest by the Ord instance of -- InterchangeNameAuthority. class HasInterchangeName a interchangeName :: HasInterchangeName a => a -> InterchangeName instance GHC.Generics.Selector Numeric.Units.Dimensional.UnitNames.InterchangeNames.S1_0_1InterchangeName instance GHC.Generics.Selector Numeric.Units.Dimensional.UnitNames.InterchangeNames.S1_0_0InterchangeName instance GHC.Generics.Constructor Numeric.Units.Dimensional.UnitNames.InterchangeNames.C1_0InterchangeName instance GHC.Generics.Datatype Numeric.Units.Dimensional.UnitNames.InterchangeNames.D1InterchangeName instance GHC.Generics.Constructor Numeric.Units.Dimensional.UnitNames.InterchangeNames.C1_2InterchangeNameAuthority instance GHC.Generics.Constructor Numeric.Units.Dimensional.UnitNames.InterchangeNames.C1_1InterchangeNameAuthority instance GHC.Generics.Constructor Numeric.Units.Dimensional.UnitNames.InterchangeNames.C1_0InterchangeNameAuthority instance GHC.Generics.Datatype Numeric.Units.Dimensional.UnitNames.InterchangeNames.D1InterchangeNameAuthority instance GHC.Generics.Generic Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeName instance Data.Data.Data Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeName instance GHC.Classes.Ord Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeName instance GHC.Classes.Eq Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeName instance GHC.Generics.Generic Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeNameAuthority instance Data.Data.Data Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeNameAuthority instance GHC.Show.Show Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeNameAuthority instance GHC.Classes.Ord Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeNameAuthority instance GHC.Classes.Eq Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeNameAuthority instance GHC.Show.Show Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeName instance Numeric.Units.Dimensional.UnitNames.InterchangeNames.HasInterchangeName Numeric.Units.Dimensional.UnitNames.InterchangeNames.InterchangeName -- | This module defines physical dimensions expressed in terms of the SI -- base dimensions, including arithmetic. module Numeric.Units.Dimensional.Dimensions.TermLevel -- | A physical dimension, encoded as 7 integers, representing a -- factorization of the dimension into the 7 SI base dimensions. By -- convention they are stored in the same order as in the -- Dimension data kind. data Dimension' Dim' :: !Int -> !Int -> !Int -> !Int -> !Int -> !Int -> !Int -> Dimension' -- | Dimensional values inhabit this class, which allows access to a -- term-level representation of their dimension. class HasDimension a -- | Obtains a term-level representation of a value's dimension. dimension :: HasDimension a => a -> Dimension' -- | Forms the product of two dimensions. (*) :: Dimension' -> Dimension' -> Dimension' -- | Forms the quotient of two dimensions. (/) :: Dimension' -> Dimension' -> Dimension' -- | Raises a dimension to an integer power. (^) :: Dimension' -> Int -> Dimension' -- | Forms the reciprocal of a dimension. recip :: Dimension' -> Dimension' -- | The dimension of dimensionless values. dOne :: Dimension' dLength :: Dimension' dMass :: Dimension' dTime :: Dimension' dElectricCurrent :: Dimension' dThermodynamicTemperature :: Dimension' dAmountOfSubstance :: Dimension' dLuminousIntensity :: Dimension' -- | Converts a dimension to a list of 7 integers, representing the -- exponent associated with each of the 7 SI base dimensions in the -- standard order. asList :: Dimension' -> [Int] instance GHC.Classes.Ord Numeric.Units.Dimensional.Dimensions.TermLevel.Dimension' instance GHC.Classes.Eq Numeric.Units.Dimensional.Dimensions.TermLevel.Dimension' instance GHC.Show.Show Numeric.Units.Dimensional.Dimensions.TermLevel.Dimension' instance GHC.Base.Monoid Numeric.Units.Dimensional.Dimensions.TermLevel.Dimension' instance Numeric.Units.Dimensional.Dimensions.TermLevel.HasDimension Numeric.Units.Dimensional.Dimensions.TermLevel.Dimension' -- | This module defines type-level physical dimensions expressed in terms -- of the SI base dimensions using NumType for type-level -- integers. -- -- Type-level arithmetic, synonyms for the base dimensions, and -- conversion to the term-level are included. module Numeric.Units.Dimensional.Dimensions.TypeLevel -- | Represents a physical dimension in the basis of the 7 SI base -- dimensions, where the respective dimensions are represented by type -- variables using the following convention. -- -- -- -- For the equivalent term-level representation, see Dimension' data Dimension Dim :: TypeInt -> TypeInt -> TypeInt -> TypeInt -> TypeInt -> TypeInt -> TypeInt -> Dimension -- | Multiplication of dimensions corresponds to adding of the base -- dimensions' exponents. -- | Division of dimensions corresponds to subtraction of the base -- dimensions' exponents. -- | Powers of dimensions corresponds to multiplication of the base -- dimensions' exponents by the exponent. -- -- We limit ourselves to integer powers of Dimensionals as fractional -- powers make little physical sense. -- | The reciprocal of a dimension is defined as the result of dividing -- DOne by it, or of negating each of the base dimensions' -- exponents. type Recip (d :: Dimension) = DOne / d -- | Roots of dimensions corresponds to division of the base dimensions' -- exponents by the order(?) of the root. -- -- See sqrt, cbrt, and nroot for the -- corresponding term-level operations. -- | The type-level dimensions of dimensionless values. type DOne = Dim Zero Zero Zero Zero Zero Zero Zero type DLength = Dim Pos1 Zero Zero Zero Zero Zero Zero type DMass = Dim Zero Pos1 Zero Zero Zero Zero Zero type DTime = Dim Zero Zero Pos1 Zero Zero Zero Zero type DElectricCurrent = Dim Zero Zero Zero Pos1 Zero Zero Zero type DThermodynamicTemperature = Dim Zero Zero Zero Zero Pos1 Zero Zero type DAmountOfSubstance = Dim Zero Zero Zero Zero Zero Pos1 Zero type DLuminousIntensity = Dim Zero Zero Zero Zero Zero Zero Pos1 -- | A KnownDimension is one for which we can construct a term-level -- representation. Each validly constructed type of kind Dimension -- has a KnownDimension instance. -- -- While KnownDimension is a constraint synonym, the presence of -- KnownDimension d in a context allows use of -- dimension :: Proxy d -> Dimension'. type KnownDimension (d :: Dimension) = HasDimension (Proxy d) instance (Numeric.NumType.DK.Integers.KnownTypeInt l, Numeric.NumType.DK.Integers.KnownTypeInt m, Numeric.NumType.DK.Integers.KnownTypeInt t, Numeric.NumType.DK.Integers.KnownTypeInt i, Numeric.NumType.DK.Integers.KnownTypeInt th, Numeric.NumType.DK.Integers.KnownTypeInt n, Numeric.NumType.DK.Integers.KnownTypeInt j) => Numeric.Units.Dimensional.Dimensions.TermLevel.HasDimension (Data.Proxy.Proxy ('Numeric.Units.Dimensional.Dimensions.TypeLevel.Dim l m t i th n j)) -- | Provides a type level representation of Variants of dimensional -- values, which may be quantities or units. module Numeric.Units.Dimensional.Variants -- | The kind of variants of dimensional values. data Variant -- | The value is a quantity. DQuantity :: Variant -- | The value is a unit, possibly a Metric unit. DUnit :: Metricality -> Variant -- | Encodes whether a unit is a metric unit, that is, whether it can be -- combined with a metric prefix to form a related unit. data Metricality -- | Capable of receiving a metric prefix. Metric :: Metricality -- | Incapable of receiving a metric prefix. NonMetric :: Metricality -- | Forms the product of two Variants. -- -- The product of units is a non-metric unit. -- -- The product of quantities is a quantity. -- | Weakens a Variant by forgetting possibly uninteresting -- type-level information. instance GHC.Generics.Constructor Numeric.Units.Dimensional.Variants.C1_1Variant instance GHC.Generics.Constructor Numeric.Units.Dimensional.Variants.C1_0Variant instance GHC.Generics.Datatype Numeric.Units.Dimensional.Variants.D1Variant instance GHC.Generics.Constructor Numeric.Units.Dimensional.Variants.C1_1Metricality instance GHC.Generics.Constructor Numeric.Units.Dimensional.Variants.C1_0Metricality instance GHC.Generics.Datatype Numeric.Units.Dimensional.Variants.D1Metricality instance GHC.Generics.Generic Numeric.Units.Dimensional.Variants.Variant instance Data.Data.Data Numeric.Units.Dimensional.Variants.Variant instance GHC.Classes.Ord Numeric.Units.Dimensional.Variants.Variant instance GHC.Classes.Eq Numeric.Units.Dimensional.Variants.Variant instance GHC.Generics.Generic Numeric.Units.Dimensional.Variants.Metricality instance Data.Data.Data Numeric.Units.Dimensional.Variants.Metricality instance GHC.Classes.Ord Numeric.Units.Dimensional.Variants.Metricality instance GHC.Classes.Eq Numeric.Units.Dimensional.Variants.Metricality -- | This module provides types and functions for manipulating unit names. -- -- Please note that the details of the name representation may be less -- stable than the other APIs provided by this package, as new features -- using them are still being developed. module Numeric.Units.Dimensional.UnitNames -- | The name of a unit. data UnitName (m :: Metricality) -- | Represents the name of an atomic unit or prefix. data NameAtom (m :: NameAtomType) -- | The name of a metric prefix. type PrefixName = NameAtom PrefixAtom -- | Encodes whether a unit is a metric unit, that is, whether it can be -- combined with a metric prefix to form a related unit. data Metricality -- | Capable of receiving a metric prefix. Metric :: Metricality -- | Incapable of receiving a metric prefix. NonMetric :: Metricality -- | Constructs an atomic name for a custom unit. atom :: String -> String -> String -> UnitName NonMetric -- | Forms a UnitName from a Metric name by applying a metric -- prefix. applyPrefix :: PrefixName -> UnitName Metric -> UnitName NonMetric -- | Form a UnitName by taking the product of two others. (*) :: UnitName m1 -> UnitName m2 -> UnitName NonMetric -- | Form a UnitName by dividing one by another. (/) :: UnitName m1 -> UnitName m2 -> UnitName NonMetric -- | Form a UnitName by raising a name to an integer power. (^) :: UnitName m -> Int -> UnitName NonMetric -- | Forms the product of a list of UnitNames. -- -- If you wish to form a heterogenous product of Metric and -- NonMetric units you should apply weaken to the -- Metric ones. product :: Foldable f => f (UnitName NonMetric) -> UnitName NonMetric reduce :: UnitName m -> UnitName m -- | Constructs a UnitName by applying a grouping operation to -- another UnitName, which may be useful to express precedence. grouped :: UnitName m -> UnitName NonMetric -- | The name of the base unit associated with a specified dimension. baseUnitName :: Dimension' -> UnitName NonMetric nOne :: UnitName NonMetric nMeter :: UnitName Metric nGram :: UnitName Metric nKilogram :: UnitName NonMetric nSecond :: UnitName Metric nAmpere :: UnitName Metric nKelvin :: UnitName Metric nMole :: UnitName Metric nCandela :: UnitName Metric deka :: PrefixName hecto :: PrefixName kilo :: PrefixName mega :: PrefixName giga :: PrefixName tera :: PrefixName peta :: PrefixName exa :: PrefixName zetta :: PrefixName yotta :: PrefixName deci :: PrefixName centi :: PrefixName milli :: PrefixName micro :: PrefixName nano :: PrefixName pico :: PrefixName femto :: PrefixName atto :: PrefixName zepto :: PrefixName yocto :: PrefixName -- | The type of a unit name transformation that may be associated with an -- operation that takes a single unit as input. type UnitNameTransformer = forall m. UnitName m -> UnitName NonMetric -- | The type of a unit name transformation that may be associated with an -- operation that takes two units as input. type UnitNameTransformer2 = forall m1 m2. UnitName m1 -> UnitName m2 -> UnitName NonMetric -- | Convert a UnitName which may or may not be Metric to one -- which is certainly NonMetric. weaken :: UnitName m -> UnitName NonMetric -- | Attempt to convert a UnitName which may or may not be -- Metric to one which is certainly Metric. strengthen :: UnitName m -> Maybe (UnitName Metric) -- | Convert a UnitName of one Metricality into a name of the -- other metricality by strengthening or weakening if neccessary. Because -- it may not be possible to strengthen, the result is returned in a -- Maybe wrapper. relax :: (Typeable m1, Typeable m2) => UnitName m1 -> Maybe (UnitName m2) -- | Provides both term-level and type-level representations for physical -- dimensions in a single import for convenience. -- -- Presuming that users intend to work primarily with type level -- dimensions, this module hides arithmetic operators over term level -- dimensions and aliases for the base term-level dimensions to avoid -- namespace pollution. These features are available directly from -- Numeric.Units.Dimensional.Dimensions.TermLevel if desired. module Numeric.Units.Dimensional.Dimensions -- | Re-exports the raw Quantity constructor from the -- Numeric.Units.Dimensional.Internal module, along with coerce, -- for convenience in converting between raw representations and -- dimensional values. -- -- Note that use of these constructs requires the user to verify the -- dimensional safety of the conversion, because the coercion doesn't -- explicitly mention the unit of the representation. -- -- Note that the haddock documentation doesn't mention the -- Quantity constructor because it is a part of the -- Dimensional associated data family, but it is exported by this -- module. module Numeric.Units.Dimensional.Coercion -- | The function coerce allows you to safely convert between -- values of types that have the same representation with no run-time -- overhead. In the simplest case you can use it instead of a newtype -- constructor, to go from the newtype's concrete type to the abstract -- type. But it also works in more complicated settings, e.g. converting -- a list of newtypes to a list of concrete types. coerce :: Coercible * a b => a -> b -- |

Summary

-- -- In this module we provide data types for performing arithmetic with -- physical quantities and units. Information about the physical -- dimensions of the quantities/units is embedded in their types and the -- validity of operations is verified by the type checker at compile -- time. The boxing and unboxing of numerical values as quantities is -- done by multiplication and division of units, of which an incomplete -- set is provided. -- -- We limit ourselves to "Newtonian" physics. We do not attempt to -- accommodate relativistic physics in which e.g. addition of length and -- time would be valid. -- -- As far as possible and/or practical the conventions and guidelines of -- NIST's "Guide for the Use of the International System of Units (SI)" -- [1] are followed. Occasionally we will reference specific -- sections from the guide and deviations will be explained. -- --

Disclaimer

-- -- Merely an engineer, the author doubtlessly uses a language and -- notation that makes mathematicians and physicist cringe. He does not -- mind constructive criticism (or pull requests). -- -- The sets of functions and units defined herein are incomplete and -- reflect only the author's needs to date. Again, patches are welcome. -- --

Usage

-- --

Preliminaries

-- -- This module requires GHC 7.8 or later. We utilize Data Kinds, -- TypeNats, Closed Type Families, etc. Clients of the module are -- generally not required to use these extensions. -- -- Clients probably will want to use the NegativeLiterals extension. -- --

Examples

-- -- We have defined operators and units that allow us to define and work -- with physical quantities. A physical quantity is defined by -- multiplying a number with a unit (the type signature is optional). -- -- 
--   v :: Velocity Prelude.Double
--   v = 90 *~ (kilo meter / hour)
--
-- -- It follows naturally that the numerical value of a quantity is -- obtained by division by a unit. -- -- 
--   numval :: Prelude.Double
--   numval = v /~ (meter / second)
--
-- -- The notion of a quantity as the product of a numerical value and a -- unit is supported by 7.1 "Value and numerical value of a quantity" of -- [1]. While the above syntax is fairly natural it is unfortunate -- that it must violate a number of the guidelines in [1], in -- particular 9.3 "Spelling unit names with prefixes", 9.4 "Spelling unit -- names obtained by multiplication", 9.5 "Spelling unit names obtained -- by division". -- -- As a more elaborate example of how to use the module we define a -- function for calculating the escape velocity of a celestial body -- [2]. -- -- 
--   escapeVelocity :: (Floating a) => Mass a -> Length a -> Velocity a
--   escapeVelocity m r = sqrt (two * g * m / r)
--     where
--         two = 2 *~ one
--         g = 6.6720e-11 *~ (newton * meter ^ pos2 / kilo gram ^ pos2)
--
-- -- The following is an example GHC session where the above function is -- used to calculate the escape velocity of Earth in kilometer per -- second. -- -- 
--   >>> :set +t
--   
--   >>> let me = 5.9742e24 *~ kilo gram -- Mass of Earth.
--   me :: Quantity DMass GHC.Float.Double
--   
--   >>> let re = 6372.792 *~ kilo meter -- Mean radius of Earth.
--   re :: Quantity DLength GHC.Float.Double
--   
--   >>> let ve = escapeVelocity me re   -- Escape velocity of Earth.
--   ve :: Velocity GHC.Float.Double
--   
--   >>> ve /~ (kilo meter / second)
--   11.184537332296259
--   it :: GHC.Float.Double
--
-- -- For completeness we should also show an example of the error messages -- we will get from GHC when performing invalid arithmetic. In the best -- case GHC will be able to use the type synonyms we have defined in its -- error messages. -- -- 
--   >>> x = 1 *~ meter + 1 *~ second
--   Couldn't match type 'Numeric.NumType.DK.Integers.Zero
--                  with 'Numeric.NumType.DK.Integers.Pos1
--     Expected type: Unit 'Metric DLength a
--       Actual type: Unit 'Metric DTime a
--     In the second argument of `(*~)', namely `second'
--     In the second argument of `(+)', namely `1 *~ second'
--
-- -- In other cases the error messages aren't very friendly. -- -- 
--   >>> x = 1 *~ meter / (1 *~ second) + 1 *~ kilo gram
--   Couldn't match type 'Numeric.NumType.DK.Integers.Zero
--                  with 'Numeric.NumType.DK.Integers.Neg1
--     Expected type: Quantity DMass a
--       Actual type: Dimensional
--                      ('Numeric.Units.Dimensional.Variants.DQuantity
--                       Numeric.Units.Dimensional.Variants.* 'Numeric.Units.Dimensional.Variants.DQuantity)
--                      (DLength / DTime)
--                      a
--     In the first argument of `(+)', namely `1 *~ meter / (1 *~ second)'
--     In the expression: 1 *~ meter / (1 *~ second) + 1 *~ kilo gram
--     In an equation for `x':
--         x = 1 *~ meter / (1 *~ second) + 1 *~ kilo gram
--
-- -- It is the author's experience that the usefullness of the compiler -- error messages is more often than not limited to pinpointing the -- location of errors. -- --

Notes

-- --

Future work

-- -- While there is an insane amount of units in use around the world it is -- reasonable to provide at least all SI units. Units outside of SI will -- most likely be added on an as-needed basis. -- -- There are also plenty of elementary functions to add. The -- Floating class can be used as reference. -- -- Additional physics models could be implemented. See [3] for -- ideas. -- --

Related work

-- -- Henning Thielemann numeric prelude has a physical units library, -- however, checking of dimensions is dynamic rather than static. Aaron -- Denney has created a toy example of statically checked physical -- dimensions covering only length and time. HaskellWiki has pointers -- [4] to these. -- -- Also see Samuel Hoffstaetter's blog post [5] which uses -- techniques similar to this library. -- -- Libraries with similar functionality exist for other programming -- languages and may serve as inspiration. The author has found the Java -- library JScience [6] and the Fortress programming language -- [7] particularly noteworthy. -- --

References

-- --
    --
  1. http://physics.nist.gov/Pubs/SP811/
    2. --
  2. http://en.wikipedia.org/wiki/Escape_velocity
    3. -- --
  3. http://jscience.org/api/org/jscience/physics/models/package-summary.html
    4. --
  4. http://www.haskell.org/haskellwiki/Physical_units
    5. -- --
  5. http://liftm.wordpress.com/2007/06/03/scientificdimension-type-arithmetic-and-physical-units-in-haskell/
    6. --
  6. http://jscience.org/
    7. --
  7. http://research.sun.com/projects/plrg/fortress.pdf
    8. --
module Numeric.Units.Dimensional -- | A unit of measurement. type Unit (m :: Metricality) = Dimensional (DUnit m) -- | A dimensional quantity. type Quantity = Dimensional DQuantity -- | Encodes whether a unit is a metric unit, that is, whether it can be -- combined with a metric prefix to form a related unit. data Metricality -- | Capable of receiving a metric prefix. Metric :: Metricality -- | Incapable of receiving a metric prefix. NonMetric :: Metricality -- | Represents a physical dimension in the basis of the 7 SI base -- dimensions, where the respective dimensions are represented by type -- variables using the following convention. -- -- -- -- For the equivalent term-level representation, see Dimension' data Dimension Dim :: TypeInt -> TypeInt -> TypeInt -> TypeInt -> TypeInt -> TypeInt -> TypeInt -> Dimension -- | Multiplication of dimensions corresponds to adding of the base -- dimensions' exponents. -- | Division of dimensions corresponds to subtraction of the base -- dimensions' exponents. -- | Powers of dimensions corresponds to multiplication of the base -- dimensions' exponents by the exponent. -- -- We limit ourselves to integer powers of Dimensionals as fractional -- powers make little physical sense. -- | Roots of dimensions corresponds to division of the base dimensions' -- exponents by the order(?) of the root. -- -- See sqrt, cbrt, and nroot for the -- corresponding term-level operations. -- | The reciprocal of a dimension is defined as the result of dividing -- DOne by it, or of negating each of the base dimensions' -- exponents. type Recip (d :: Dimension) = DOne / d -- | A physical dimension, encoded as 7 integers, representing a -- factorization of the dimension into the 7 SI base dimensions. By -- convention they are stored in the same order as in the -- Dimension data kind. data Dimension' Dim' :: !Int -> !Int -> !Int -> !Int -> !Int -> !Int -> !Int -> Dimension' -- | Dimensional values inhabit this class, which allows access to a -- term-level representation of their dimension. class HasDimension a -- | Obtains a term-level representation of a value's dimension. dimension :: HasDimension a => a -> Dimension' -- | A KnownDimension is one for which we can construct a term-level -- representation. Each validly constructed type of kind Dimension -- has a KnownDimension instance. -- -- While KnownDimension is a constraint synonym, the presence of -- KnownDimension d in a context allows use of -- dimension :: Proxy d -> Dimension'. type KnownDimension (d :: Dimension) = HasDimension (Proxy d) -- | Forms a Quantity by multipliying a number and a unit. (*~) :: Num a => a -> Unit m d a -> Quantity d a -- | Divides a Quantity by a Unit of the same physical -- dimension, obtaining the numerical value of the quantity expressed in -- that unit. (/~) :: Fractional a => Quantity d a -> Unit m d a -> a -- | Raises a Quantity or Unit to an integer power. -- -- Because the power chosen impacts the Dimension of the result, -- it is necessary to supply a type-level representation of the exponent -- in the form of a Proxy to some TypeInt. Convenience -- values pos1, pos2, neg1, ... are supplied by -- the Numeric.NumType.DK.Integers module. The most commonly used -- ones are also reexported by Numeric.Units.Dimensional.Prelude. -- -- The intimidating type signature captures the similarity between these -- operations and ensures that composite Units are -- NotPrefixable. (^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a -- | Computes the nth root of a Quantity using **. -- -- The Root type family will prevent application of this operator -- where the result would have a fractional dimension or where n is zero. -- -- Because the root chosen impacts the Dimension of the result, it -- is necessary to supply a type-level representation of the root in the -- form of a Proxy to some TypeInt. Convenience values -- pos1, pos2, neg1, ... are supplied by the -- Numeric.NumType.DK.Integers module. The most commonly used ones -- are also reexported by Numeric.Units.Dimensional.Prelude. -- -- Also available in prefix form, see nroot. (^/) :: (KnownTypeInt n, Floating a) => Quantity d a -> Proxy n -> Quantity (Root d n) a -- | Raises a dimensionless quantity to a floating power using **. (**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a -- | Multiplies two Quantitys or two Units. -- -- The intimidating type signature captures the similarity between these -- operations and ensures that composite Units are -- NonMetric. (*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 * d2) a -- | Divides one Quantity by another or one Unit by another. -- -- The intimidating type signature captures the similarity between these -- operations and ensures that composite Units are -- NotPrefixable. (/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 / d2) a -- | Adds two Quantitys. (+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a -- | Subtracts one Quantity from another. (-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a -- | Negates the value of a Quantity. negate :: Num a => Quantity d a -> Quantity d a -- | Takes the absolute value of a Quantity. abs :: Num a => Quantity d a -> Quantity d a -- | Computes the nth root of a Quantity using **. -- -- The Root type family will prevent application of this operator -- where the result would have a fractional dimension or where n is zero. -- -- Because the root chosen impacts the Dimension of the result, it -- is necessary to supply a type-level representation of the root in the -- form of a Proxy to some TypeInt. Convenience values -- pos1, pos2, neg1, ... are supplied by the -- Numeric.NumType.DK.Integers module. The most commonly used ones -- are also reexported by Numeric.Units.Dimensional.Prelude. -- -- Also available in operator form, see ^/. nroot :: (KnownTypeInt n, Floating a) => Proxy n -> Quantity d a -> Quantity (Root d n) a -- | Computes the square root of a Quantity using **. -- -- The Root type family will prevent application where the -- supplied quantity does not have a square dimension. -- -- 
--   sqrt x == nroot pos2 x
--
sqrt :: Floating a => Quantity d a -> Quantity (Root d Pos2) a -- | Computes the cube root of a Quantity using **. -- -- The Root type family will prevent application where the -- supplied quantity does not have a cubic dimension. -- -- 
--   cbrt x == nroot pos3 x
--
cbrt :: Floating a => Quantity d a -> Quantity (Root d Pos3) a exp :: Floating a => Dimensionless a -> Dimensionless a log :: Floating a => Dimensionless a -> Dimensionless a sin :: Floating a => Dimensionless a -> Dimensionless a cos :: Floating a => Dimensionless a -> Dimensionless a tan :: Floating a => Dimensionless a -> Dimensionless a asin :: Floating a => Dimensionless a -> Dimensionless a acos :: Floating a => Dimensionless a -> Dimensionless a atan :: Floating a => Dimensionless a -> Dimensionless a sinh :: Floating a => Dimensionless a -> Dimensionless a cosh :: Floating a => Dimensionless a -> Dimensionless a tanh :: Floating a => Dimensionless a -> Dimensionless a asinh :: Floating a => Dimensionless a -> Dimensionless a acosh :: Floating a => Dimensionless a -> Dimensionless a atanh :: Floating a => Dimensionless a -> Dimensionless a -- | The standard two argument arctangent function. Since it interprets its -- two arguments in comparison with one another, the input may have any -- dimension. atan2 :: (RealFloat a) => Quantity d a -> Quantity d a -> Dimensionless a -- | Applies *~ to all values in a functor. (*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a) -- | Applies /~ to all values in a functor. (/~~) :: (Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a -- | The sum of all elements in a list. sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a -- | The arithmetic mean of all elements in a list. mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a -- | The length of the foldable data structure as a Dimensionless. -- This can be useful for purposes of e.g. calculating averages. dimensionlessLength :: (Num a, Foldable f) => f (Dimensional v d a) -> Dimensionless a -- | Returns a list of quantities between given bounds. nFromTo :: (Fractional a, Integral b) => Quantity d a -> Quantity d a -> b -> [Quantity d a] -- | The type-level dimensions of dimensionless values. type DOne = Dim Zero Zero Zero Zero Zero Zero Zero type DLength = Dim Pos1 Zero Zero Zero Zero Zero Zero type DMass = Dim Zero Pos1 Zero Zero Zero Zero Zero type DTime = Dim Zero Zero Pos1 Zero Zero Zero Zero type DElectricCurrent = Dim Zero Zero Zero Pos1 Zero Zero Zero type DThermodynamicTemperature = Dim Zero Zero Zero Zero Pos1 Zero Zero type DAmountOfSubstance = Dim Zero Zero Zero Zero Zero Pos1 Zero type DLuminousIntensity = Dim Zero Zero Zero Zero Zero Zero Pos1 type Dimensionless = Quantity DOne type Length = Quantity DLength type Mass = Quantity DMass type Time = Quantity DTime type ElectricCurrent = Quantity DElectricCurrent type ThermodynamicTemperature = Quantity DThermodynamicTemperature type AmountOfSubstance = Quantity DAmountOfSubstance type LuminousIntensity = Quantity DLuminousIntensity -- | The constant for zero is polymorphic, allowing it to express zero -- Length or Capacitance or Velocity etc, in -- addition to the Dimensionless value zero. _0 :: Num a => Quantity d a _1 :: (Num a) => Dimensionless a _2 :: (Num a) => Dimensionless a _3 :: (Num a) => Dimensionless a _4 :: (Num a) => Dimensionless a _5 :: (Num a) => Dimensionless a _6 :: (Num a) => Dimensionless a _7 :: (Num a) => Dimensionless a _8 :: (Num a) => Dimensionless a _9 :: (Num a) => Dimensionless a pi :: Floating a => Dimensionless a -- | Twice pi. -- -- For background on tau see -- http://tauday.com/tau-manifesto (but also feel free to review -- http://www.thepimanifesto.com). tau :: Floating a => Dimensionless a -- | A polymorphic Unit which can be used in place of the coherent -- SI base unit of any dimension. This allows polymorphic quantity -- creation and destruction without exposing the Dimensional -- constructor. siUnit :: (KnownDimension d, Num a) => Unit NonMetric d a -- | The unit one has dimension DOne and is the base unit of -- dimensionless values. -- -- As detailed in 7.10 "Values of quantities expressed simply as numbers: -- the unit one, symbol 1" of [1] the unit one generally does not -- appear in expressions. However, for us it is necessary to use -- one as we would any other unit to perform the "boxing" of -- dimensionless values. one :: Num a => Unit NonMetric DOne a -- | Forms a new atomic Unit by specifying its UnitName and -- its definition as a multiple of another Unit. -- -- Use this variant when the scale factor of the resulting unit is -- irrational or Approximate. See mkUnitQ for when it is -- rational and mkUnitZ for when it is an integer. -- -- Note that supplying zero as a definining quantity is invalid, as the -- library relies upon units forming a group under multiplication. -- -- Supplying negative defining quantities is allowed and handled -- gracefully, but is discouraged on the grounds that it may be -- unexpected by other readers. mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a -- | Forms a new atomic Unit by specifying its UnitName and -- its definition as a multiple of another Unit. -- -- Use this variant when the scale factor of the resulting unit is -- rational. See mkUnitZ for when it is an integer and -- mkUnitR for the general case. -- -- For more information see mkUnitR. mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a -- | Forms a new atomic Unit by specifying its UnitName and -- its definition as a multiple of another Unit. -- -- Use this variant when the scale factor of the resulting unit is an -- integer. See mkUnitQ for when it is rational and mkUnitR -- for the general case. -- -- For more information see mkUnitR. mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a -- | Extracts the UnitName of a Unit. name :: Unit m d a -> UnitName m -- | Extracts the exact value of a Unit, expressed in terms of the -- SI coherent derived unit (see siUnit) of the same -- Dimension. -- -- Note that the actual value may in some cases be approximate, for -- example if the unit is defined by experiment. exactValue :: Unit m d a -> ExactPi -- | Discards potentially unwanted type level information about a -- Unit. weaken :: Unit m d a -> Unit NonMetric d a -- | Attempts to convert a Unit which may or may not be -- Metric to one which is certainly Metric. strengthen :: Unit m d a -> Maybe (Unit Metric d a) -- | Forms the exact version of a Unit. exactify :: Unit m d a -> Unit m d ExactPi -- | Shows the value of a Quantity expressed in a specified -- Unit of the same Dimension. showIn :: (KnownDimension d, Show a, Fractional a) => Unit m d a -> Quantity d a -> String -- | A physical quantity or unit. -- -- We call this data type Dimensional to capture the notion that -- the units and quantities it represents have physical dimensions. -- -- The type variable a is the only non-phantom type variable and -- represents the numerical value of a quantity or the scale (w.r.t. SI -- units) of a unit. For SI units the scale will always be 1. For non-SI -- units the scale is the ratio of the unit to the SI unit with the same -- physical dimension. -- -- Since a is the only non-phantom type we were able to define -- Dimensional as a newtype, avoiding boxing at runtime. class KnownVariant (v :: Variant) where data family Dimensional v :: Dimension -> * -> * -- | Maps over the underlying representation of a dimensional value. The -- caller is responsible for ensuring that the supplied function respects -- the dimensional abstraction. This means that the function must -- preserve numerical values, or linearly scale them while preserving the -- origin. dmap :: KnownVariant v => (a1 -> a2) -> Dimensional v d a1 -> Dimensional v d a2 -- | Convenient conversion between numerical types while retaining -- dimensional information. changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b -- | Convenient conversion from exactly represented values while retaining -- dimensional information. changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b -- |

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/
    2. --
module Numeric.Units.Dimensional.Quantities type Area = Quantity DArea type Volume = Quantity DVolume type Velocity = Quantity DVelocity type Acceleration = Quantity DAcceleration type WaveNumber = Quantity DWaveNumber type MassDensity = Quantity DMassDensity type Density = MassDensity type SpecificVolume = Quantity DSpecificVolume type CurrentDensity = Quantity DCurrentDensity type MagneticFieldStrength = Quantity DMagneticFieldStrength type AmountOfSubstanceConcentration = Quantity DAmountOfSubstanceConcentration type Concentration = AmountOfSubstanceConcentration type Luminance = Quantity DLuminance type PlaneAngle = Dimensionless type SolidAngle = Dimensionless type Frequency = Quantity DFrequency type Force = Quantity DForce type Pressure = Quantity DPressure type Stress = Quantity DStress type Energy = Quantity DEnergy type Work = Quantity DWork type QuantityOfHeat = Quantity DQuantityOfHeat type Power = Quantity DPower type RadiantFlux = Quantity DRadiantFlux type ElectricCharge = Quantity DElectricCharge type QuantityOfElectricity = Quantity DQuantityOfElectricity type ElectricPotential = Quantity DElectricPotential type PotentialDifference = Quantity DPotentialDifference type ElectromotiveForce = Quantity DElectromotiveForce type Capacitance = Quantity DCapacitance type ElectricResistance = Quantity DElectricResistance type ElectricConductance = Quantity DElectricConductance type MagneticFlux = Quantity DMagneticFlux type MagneticFluxDensity = Quantity DMagneticFluxDensity type Inductance = Quantity DInductance type LuminousFlux = Quantity DLuminousFlux type Illuminance = Quantity DIlluminance type CelsiusTemperature = Quantity DCelsiusTemperature type Activity = Quantity DActivity type AbsorbedDose = Quantity DAbsorbedDose type SpecificEnergy = Quantity DSpecificEnergy type Kerma = Quantity DKerma type DoseEquivalent = Quantity DDoseEquivalent type AmbientDoseEquivalent = DoseEquivalent type DirectionalDoseEquivalent = DoseEquivalent type PersonalDoseEquivalent = DoseEquivalent type EquivalentDose = DoseEquivalent type CatalyticActivity = Quantity DCatalyticActivity type AngularVelocity = Quantity DAngularVelocity type AngularAcceleration = Quantity DAngularAcceleration type DynamicViscosity = Quantity DDynamicViscosity type MomentOfForce = Quantity DMomentOfForce type SurfaceTension = Quantity DSurfaceTension type HeatFluxDensity = Quantity DHeatFluxDensity type Irradiance = Quantity DIrradiance type RadiantIntensity = Quantity DRadiantIntensity type Radiance = Quantity DRadiance type HeatCapacity = Quantity DHeatCapacity type Entropy = Quantity DEntropy type SpecificHeatCapacity = Quantity DSpecificHeatCapacity type SpecificEntropy = Quantity DSpecificEntropy type ThermalConductivity = Quantity DThermalConductivity type EnergyDensity = Quantity DEnergyDensity type ElectricFieldStrength = Quantity DElectricFieldStrength type ElectricChargeDensity = Quantity DElectricChargeDensity type ElectricFluxDensity = Quantity DElectricFluxDensity type Permittivity = Quantity DPermittivity type Permeability = Quantity DPermeability type MolarEnergy = Quantity DMolarEnergy type MolarEntropy = Quantity DMolarEntropy type MolarHeatCapacity = Quantity DMolarHeatCapacity type Exposure = Quantity DExposure type AbsorbedDoseRate = Quantity DAbsorbedDoseRate type Impulse = Quantity DImpulse type Momentum = Quantity DMomentum type MassFlow = Quantity DMassFlow type VolumeFlow = Quantity DVolumeFlow type GravitationalParameter = Quantity DGravitationalParameter type KinematicViscosity = Quantity DKinematicViscosity type FirstMassMoment = Quantity DFirstMassMoment type MomentOfInertia = Quantity DMomentOfInertia type AngularMomentum = Quantity DAngularMomentum type ThermalResistivity = Quantity DThermalResistivity type ThermalConductance = Quantity DThermalConductance type ThermalResistance = Quantity DThermalResistance type HeatTransferCoefficient = Quantity DHeatTransferCoefficient type ThermalAdmittance = HeatTransferCoefficient type ThermalInsulance = Quantity DThermalInsulance type Jerk = Quantity DJerk type Angle = PlaneAngle type Thrust = Force type Torque = MomentOfForce type EnergyPerUnitMass = SpecificEnergy -- | Constructs a unit of area from a unit of length, taking the area of a -- square whose sides are that length. square :: (Fractional a, Typeable m) => Unit m DLength a -> Unit NonMetric DArea a -- | Constructs a unit of volume from a unit of length, taking the volume -- of a cube whose sides are that length. cubic :: (Fractional a, Typeable m) => Unit m DLength a -> Unit NonMetric DVolume a type DArea = Dim Pos2 Zero Zero Zero Zero Zero Zero type DVolume = Dim Pos3 Zero Zero Zero Zero Zero Zero type DVelocity = Dim Pos1 Zero Neg1 Zero Zero Zero Zero type DAcceleration = Dim Pos1 Zero Neg2 Zero Zero Zero Zero type DWaveNumber = Dim Neg1 Zero Zero Zero Zero Zero Zero type DMassDensity = Dim Neg3 Pos1 Zero Zero Zero Zero Zero type DDensity = DMassDensity type DSpecificVolume = Dim Pos3 Neg1 Zero Zero Zero Zero Zero type DCurrentDensity = Dim Neg2 Zero Zero Pos1 Zero Zero Zero type DMagneticFieldStrength = Dim Neg1 Zero Zero Pos1 Zero Zero Zero type DAmountOfSubstanceConcentration = Dim Neg3 Zero Zero Zero Zero Pos1 Zero type DConcentration = DAmountOfSubstanceConcentration type DLuminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1 type DPlaneAngle = DOne type DSolidAngle = DOne type DFrequency = Dim Zero Zero Neg1 Zero Zero Zero Zero type DForce = Dim Pos1 Pos1 Neg2 Zero Zero Zero Zero type DPressure = Dim Neg1 Pos1 Neg2 Zero Zero Zero Zero type DStress = DPressure type DEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Zero Zero type DWork = DEnergy type DQuantityOfHeat = DEnergy type DPower = Dim Pos2 Pos1 Neg3 Zero Zero Zero Zero type DRadiantFlux = DPower type DElectricCharge = Dim Zero Zero Pos1 Pos1 Zero Zero Zero type DQuantityOfElectricity = DElectricCharge type DElectricPotential = Dim Pos2 Pos1 Neg3 Neg1 Zero Zero Zero type DPotentialDifference = DElectricPotential type DElectromotiveForce = DElectricPotential type DCapacitance = Dim Neg2 Neg1 Pos4 Pos2 Zero Zero Zero type DElectricResistance = Dim Pos2 Pos1 Neg3 Neg2 Zero Zero Zero type DElectricConductance = Dim Neg2 Neg1 Pos3 Pos2 Zero Zero Zero type DMagneticFlux = Dim Pos2 Pos1 Neg2 Neg1 Zero Zero Zero type DMagneticFluxDensity = Dim Zero Pos1 Neg2 Neg1 Zero Zero Zero type DInductance = Dim Pos2 Pos1 Neg2 Neg2 Zero Zero Zero type DLuminousFlux = DLuminousIntensity type DIlluminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1 type DCelsiusTemperature = DThermodynamicTemperature type DActivity = DFrequency type DAbsorbedDose = Dim Pos2 Zero Neg2 Zero Zero Zero Zero type DSpecificEnergy = DAbsorbedDose type DKerma = DAbsorbedDose type DDoseEquivalent = DAbsorbedDose type DAmbientDoseEquivalent = DDoseEquivalent type DDirectionalDoseEquivalent = DDoseEquivalent type DPersonalDoseEquivalent = DDoseEquivalent type DEquivalentDose = DDoseEquivalent type DCatalyticActivity = Dim Zero Zero Neg1 Zero Zero Pos1 Zero type DAngularVelocity = DFrequency type DAngularAcceleration = Dim Zero Zero Neg2 Zero Zero Zero Zero type DDynamicViscosity = Dim Neg1 Pos1 Neg1 Zero Zero Zero Zero type DMomentOfForce = DEnergy type DSurfaceTension = Dim Zero Pos1 Neg2 Zero Zero Zero Zero type DHeatFluxDensity = Dim Zero Pos1 Neg3 Zero Zero Zero Zero type DIrradiance = DHeatFluxDensity type DRadiantIntensity = DPower type DRadiance = DIrradiance type DHeatCapacity = Dim Pos2 Pos1 Neg2 Zero Neg1 Zero Zero type DEntropy = DHeatCapacity type DSpecificHeatCapacity = Dim Pos2 Zero Neg2 Zero Neg1 Zero Zero type DSpecificEntropy = DSpecificHeatCapacity type DThermalConductivity = Dim Pos1 Pos1 Neg3 Zero Neg1 Zero Zero type DEnergyDensity = DPressure type DElectricFieldStrength = Dim Pos1 Pos1 Neg3 Neg1 Zero Zero Zero type DElectricChargeDensity = Dim Neg3 Zero Pos1 Pos1 Zero Zero Zero type DElectricFluxDensity = Dim Neg2 Zero Pos1 Pos1 Zero Zero Zero type DPermittivity = Dim Neg3 Neg1 Pos4 Pos2 Zero Zero Zero type DPermeability = Dim Pos1 Pos1 Neg2 Neg2 Zero Zero Zero type DMolarEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Neg1 Zero type DMolarEntropy = Dim Pos2 Pos1 Neg2 Zero Neg1 Neg1 Zero type DMolarHeatCapacity = DMolarEntropy type DExposure = Dim Zero Neg1 Pos1 Pos1 Zero Zero Zero type DAbsorbedDoseRate = Dim Pos2 Zero Neg3 Zero Zero Zero Zero type DImpulse = Dim Pos1 Pos1 Neg1 Zero Zero Zero Zero type DMomentum = DImpulse type DMassFlow = Dim Zero Pos1 Neg1 Zero Zero Zero Zero type DVolumeFlow = Dim Pos3 Zero Neg1 Zero Zero Zero Zero type DGravitationalParameter = Dim Pos3 Zero Neg2 Zero Zero Zero Zero type DKinematicViscosity = Dim Pos2 Zero Neg1 Zero Zero Zero Zero type DFirstMassMoment = Dim Pos1 Pos1 Zero Zero Zero Zero Zero type DMomentOfInertia = Dim Pos2 Pos1 Zero Zero Zero Zero Zero type DAngularMomentum = Dim Pos2 Pos1 Neg1 Zero Zero Zero Zero type DThermalResistivity = Dim Neg1 Neg1 Pos3 Zero Pos1 Zero Zero type DThermalConductance = Dim Pos2 Pos1 Neg3 Zero Neg1 Zero Zero type DThermalResistance = Dim Neg2 Neg1 Pos3 Zero Pos1 Zero Zero type DHeatTransferCoefficient = Dim Zero Pos1 Neg3 Zero Neg1 Zero Zero type DThermalAdmittance = DHeatTransferCoefficient type DThermalInsulance = Dim Zero Neg1 Pos3 Zero Pos1 Zero Zero type DJerk = Dim Pos1 Zero Neg3 Zero Zero Zero Zero type DAngle = DPlaneAngle type DThrust = DForce type DTorque = DMomentOfForce type DEnergyPerUnitMass = DSpecificEnergy -- |

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

-- --
    --
  1. http://physics.nist.gov/Pubs/SP811/
    2. --
  2. http://en.wikipedia.org/wiki/Minute_of_arc
    3. --
  3. http://en.wikipedia.org/wiki/Astronomical_unit
    4. --
module Numeric.Units.Dimensional.SIUnits 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 -- |

Summary

-- -- This module supplies a convenient set of imports for working with the -- dimensional package, including aliases for common Quantitys and -- Dimensions, and a comprehensive set of SI units and units -- accepted for use with the SI. -- -- It re-exports the Prelude, hiding arithmetic functions whose -- names collide with the dimensionally-typed versions supplied by this -- package. module Numeric.Units.Dimensional.Prelude -- |

Summary

-- -- This module defines units that are not part of the SI, with the -- exception of those defined in the -- Numeric.Units.Dimensional.SIUnits module (units outside of the -- SI accepted for use with the SI). -- -- Any chapters, sections or tables referenced are from [1] unless -- otherwise specified. -- --

Neper, bel, shannon and the like

-- -- The units of section 5.1.2 are purposefully (but not permanently) -- omitted. In fact the logarithmic units (see section 8.7) are -- problematic and it is not clear how to implement them. Perhaps with a -- conversion function similar to for degrees Celsius. -- --

References

-- --
    --
  1. http://physics.nist.gov/Pubs/SP811/
    2. -- --
  2. http://www.iau.org/science/publications/proceedings_rules/units/
    3. --
  3. http://en.m.wikipedia.org/wiki/Pressure
    4. --
  4. http://en.m.wikipedia.org/wiki/Torr
    5. --
module Numeric.Units.Dimensional.NonSI electronVolt :: Floating a => Unit Metric DEnergy a unifiedAtomicMassUnit :: Floating a => Unit Metric DMass a dalton :: Floating a => Unit Metric DMass a gee :: Fractional a => Unit Metric DAcceleration a inch :: Fractional a => Unit NonMetric DLength a foot :: Fractional a => Unit NonMetric DLength a mil :: Fractional a => Unit NonMetric DLength a poundMass :: Fractional a => Unit NonMetric DMass a ounce :: Fractional a => Unit NonMetric DMass a poundForce :: Fractional a => Unit NonMetric DForce a slug :: Fractional a => Unit NonMetric DMass a psi :: Fractional a => Unit NonMetric DPressure a yard :: (Fractional a) => Unit NonMetric DLength a mile :: (Fractional a) => Unit NonMetric DLength a nauticalMile :: (Num a) => Unit NonMetric DLength a knot :: (Fractional a) => Unit NonMetric DVelocity a revolution :: (Floating a) => Unit NonMetric DOne a solid :: (Floating a) => Unit NonMetric DOne a teaspoon :: (Fractional a) => Unit NonMetric DVolume a acre :: (Fractional a) => Unit NonMetric DArea a year :: Num a => Unit NonMetric DTime a century :: Num a => Unit NonMetric DTime a -- | The bar is exactly 100,000 pascal. -- -- From Wikipedia: -- -- It is about equal to the atmospheric pressure on Earth at sea level. bar :: (Num a) => Unit Metric DPressure a -- | The "standard atmosphere". -- -- From Wikipedia [3]: -- -- The standard atmosphere (atm) is an established constant. It is -- approximately equal to typical air pressure at earth mean sea level. atmosphere :: (Num a) => Unit NonMetric DPressure a -- | The "technical atmosphere" -- -- From Wikipedia: -- -- A technical atmosphere (symbol: at) is a non-SI unit of pressure equal -- to one kilogram-force per square centimeter. technicalAtmosphere :: (Fractional a) => Unit NonMetric DPressure a -- | The conventional value for the pressure exerted by a 1 mm high column -- of mercury. -- -- Per Wikipedia [4], one mmHg (millimeter of mercury) is defined -- as: -- -- The pressure exerted at the base of a column of fluid exactly 1 mm -- high, when the density of the fluid is exactly 13.5951 g/cm^3, at a -- place where the acceleration of gravity is exactly 9.80665 m/s^2. mmHg :: (Floating a) => Unit NonMetric DPressure a -- | The conventional value for the pressure exerted by a 1 inch high -- column of mercury. -- -- Column inches of mercury are also used to measure pressure, especially -- in meteorological or aeronautical contexts in the United States. -- -- This is the value defined by UCUM. For the value defined by NIST, see -- inHg_NIST. inHg :: (Floating a) => Unit NonMetric DPressure a -- | The conventional value for the pressure exerted by a 1 inch high -- column of mercury. -- -- Column inches of mercury are also used to measure pressure, especially -- in meteorological or aeronautical contexts in the United States. -- -- This is the value defined by UCUM. For the value defined by NIST, see -- inHg_NIST. inHg_UCUM :: (Floating a) => Unit NonMetric DPressure a -- | The conventional value for the pressure exerted by a 1 inch high -- column of mercury. -- -- Column inches of mercury are also used to measure pressure, especially -- in meteorological or aeronautical contexts in the United States. -- -- This is the value defined by NIST. For the value defined by UCUM, see -- inHg_UCUM. inHg_NIST :: (Floating a) => Unit NonMetric DPressure a -- | One torr (symbol: Torr) is defined as 1/760 atm, which is -- approximately equal to 1 mmHg. torr :: (Fractional a) => Unit NonMetric DPressure a rad :: (Fractional a) => Unit Metric DAbsorbedDose a stokes :: (Fractional a) => Unit Metric DKinematicViscosity a degreeFahrenheit :: (Fractional a) => Unit NonMetric DThermodynamicTemperature a degreeRankine :: (Fractional a) => Unit NonMetric DThermodynamicTemperature a imperialGallon :: (Fractional a) => Unit NonMetric DVolume a imperialQuart :: (Fractional a) => Unit NonMetric DVolume a imperialPint :: (Fractional a) => Unit NonMetric DVolume a imperialCup :: (Fractional a) => Unit NonMetric DVolume a imperialGill :: (Fractional a) => Unit NonMetric DVolume a imperialFluidOunce :: (Fractional a) => Unit NonMetric DVolume a usGallon :: (Fractional a) => Unit NonMetric DVolume a usQuart :: (Fractional a) => Unit NonMetric DVolume a usPint :: (Fractional a) => Unit NonMetric DVolume a usCup :: (Fractional a) => Unit NonMetric DVolume a usGill :: (Fractional a) => Unit NonMetric DVolume a usFluidOunce :: (Fractional a) => Unit NonMetric DVolume a -- | Defines types for manipulation of units and quantities without phantom -- types for their dimensions. module Numeric.Units.Dimensional.Dynamic -- | A Quantity whose Dimension is only known dynamically. data AnyQuantity v -- | Converts a Quantity of statically known Dimension into -- an AnyQuantity. demoteQuantity :: (KnownDimension d) => Quantity d v -> AnyQuantity v -- | Converts an AnyQuantity into a Quantity of statically -- known Dimension, or Nothing if the dimension does not -- match. promoteQuantity :: (KnownDimension d) => AnyQuantity v -> Maybe (Quantity d v) -- | A Unit whose Dimension is only known dynamically. data AnyUnit -- | Converts a Unit of statically known Dimension into an -- AnyUnit. demoteUnit :: (KnownDimension d) => Unit a d v -> AnyUnit -- | Converts an AnyUnit into a Unit of statically known -- Dimension, or Nothing if the dimension does not match. -- -- The result is represented in ExactPi, conversion to other -- representations is possible using changeRepApproximate. promoteUnit :: (KnownDimension d) => AnyUnit -> Maybe (Unit NonMetric d ExactPi) instance GHC.Classes.Eq v => GHC.Classes.Eq (Numeric.Units.Dimensional.Dynamic.AnyQuantity v) instance GHC.Show.Show v => GHC.Show.Show (Numeric.Units.Dimensional.Dynamic.AnyQuantity v) instance Numeric.Units.Dimensional.Dimensions.TermLevel.HasDimension (Numeric.Units.Dimensional.Dynamic.AnyQuantity v) instance GHC.Show.Show Numeric.Units.Dimensional.Dynamic.AnyUnit instance Numeric.Units.Dimensional.Dimensions.TermLevel.HasDimension Numeric.Units.Dimensional.Dynamic.AnyUnit -- | Provides a Functor instance for Dimensional. -- -- Note that this instance is dubious, because it allows you to break the -- dimensional abstraction. See dmap for more information. -- -- Note that, while this instance overlaps with that given for -- Dimensionless, it is confluent with that instance. -- -- Note that this is an orphan instance. module Numeric.Units.Dimensional.Functor -- | A Functor instance for Dimensional. -- -- Note that this instance is dubious, because it allows you to break the -- dimensional abstraction. See dmap for more information. -- -- Note that, while this instance overlaps with that given for -- Dimensionless, it is confluent with that instance. -- -- Note that this is an orphan instance. instance Numeric.Units.Dimensional.Internal.KnownVariant v => GHC.Base.Functor (Numeric.Units.Dimensional.Internal.Dimensional v d)