Moduledimensional-1.5Haskell2010

Numeric.Units.Dimensional.Dimensions.TermLevel

This module defines physical dimensions expressed in terms of the SI base dimensions, including arithmetic.

2 types
2 classes
19 values
BangPatterns
DeriveDataTypeable
DeriveGeneric
DefaultSignatures

Packagedimensional-1.5
Exports23
LanguageHaskell2010
LicenceBSD-3-Clause
SourceTermLevel.hs

Type

1 declaration

datadata Dimension'

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.

Constructors

Dim' !Int !Int !Int !Int !Int !Int !Int

Instances11Eq, Data, Ord, Show, Generic, Semigroup, …

Eq Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Data Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Ord Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Show Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Generic Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Semigroup Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Monoid Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
The monoid of dimensions under multiplication.
NFData Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
HasDimension Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
HasDynamicDimension Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
type Rep Dimension' = D1 ('MetaData "Dimension'" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.5-A8hQbr1FhplHXjkk6TSAmE" 'False) (C1 ('MetaCons "Dim'" 'PrefixI 'False) ((S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedUnpack) (Rec0 Int) :*: (S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedUnpack) (Rec0 Int) :*: S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedUnpack) (Rec0 Int))) :*: ((S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedUnpack) (Rec0 Int) :*: S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedUnpack) (Rec0 Int)) :*: (S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedUnpack) (Rec0 Int) :*: S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'SourceStrict 'DecidedUnpack) (Rec0 Int)))))Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel

Access to Dimension of Dimensional Values

3 declarations

classclass HasDynamicDimension a => HasDimension a where

Dimensional values inhabit this class, which allows access to a term-level representation of their dimension.

Methods

dimension :: a -> Dimension'
Obtains a term-level representation of a value's dimension.

Instances5HasDimension

HasDimension Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
HasDimension AnyUnitDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dynamic
HasDimension (AnyQuantity a)Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dynamic
(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy ('Dim l m t i th n j))Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TypeLevel
KnownDimension d => HasDimension (Dimensional v d a)Defined in dimensional-1.5 · Numeric.Units.Dimensional.Internal

classclass HasDynamicDimension a where

Dimensional values, or those that are only possibly dimensional, inhabit this class, which allows access to a term-level representation of their dimension.

Methods

dynamicDimension :: a -> DynamicDimension
Gets the DynamicDimension of a dynamic dimensional value, which may be NoDimension if it does not represent a dimensional value of any Dimension.
A default implementation is available for types that are also in the HasDimension typeclass.

Instances7HasDynamicDimension, …

HasDynamicDimension Dimension'Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
HasDynamicDimension DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
HasDynamicDimension AnyUnitDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dynamic
HasDynamicDimension (AnyQuantity a)Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dynamic
HasDynamicDimension (DynQuantity a)Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dynamic
(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDynamicDimension (Proxy ('Dim l m t i th n j))Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TypeLevel
KnownDimension d => HasDynamicDimension (Dimensional v d a)Defined in dimensional-1.5 · Numeric.Units.Dimensional.Internal

datadata DynamicDimension

The dimension of a dynamic value, which may not have any dimension at all.

Constructors

NoDimension
The value has no valid dimension.
SomeDimension Dimension'
The value has the given dimension.
AnyDimension
The value may be interpreted as having any dimension.

Instances8Eq, Data, Ord, Show, Generic, NFData, …

Eq DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Data DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Ord DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Show DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
Generic DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
NFData DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
HasDynamicDimension DynamicDimensionDefined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel
type Rep DynamicDimension = D1 ('MetaData "DynamicDimension" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.5-A8hQbr1FhplHXjkk6TSAmE" 'False) (C1 ('MetaCons "NoDimension" 'PrefixI 'False) U1 :+: (C1 ('MetaCons "SomeDimension" 'PrefixI 'False) (S1 ('MetaSel 'Nothing 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Dimension')) :+: C1 ('MetaCons "AnyDimension" 'PrefixI 'False) U1))Defined in dimensional-1.5 · Numeric.Units.Dimensional.Dimensions.TermLevel

Dimension Arithmetic

7 declarations

value(*) :: Dimension' -> Dimension' -> Dimension'

Forms the product of two dimensions.

value(/) :: Dimension' -> Dimension' -> Dimension'

Forms the quotient of two dimensions.

value(^) :: Dimension' -> Int -> Dimension'

Raises a dimension to an integer power.

valuerecip :: Dimension' -> Dimension'

Forms the reciprocal of a dimension.

valuenroot :: Int -> Dimension' -> Maybe Dimension'

Takes the nth root of a dimension, if it exists.

n must not be zero.

Property

prop> nroot (negate n) d == nroot n (recip d)

valuesqrt :: Dimension' -> Maybe Dimension'

Takes the square root of a dimension, if it exists.

Property

prop> sqrt d == nroot 2 d

valuecbrt :: Dimension' -> Maybe Dimension'

Takes the cube root of a dimension, if it exists.

Property

prop> cbrt d == nroot 3 d

Synonyms for Base Dimensions

8 declarations

valuedOne :: Dimension'

The dimension of dimensionless values.

valuedLength :: Dimension'

valuedMass :: Dimension'

valuedTime :: Dimension'

valuedElectricCurrent :: Dimension'

valuedThermodynamicTemperature :: Dimension'

valuedAmountOfSubstance :: Dimension'

valuedLuminousIntensity :: Dimension'

Deconstruction

1 declaration

valueasList :: Dimension' -> [Int]

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.

Examining Dynamic Dimensions

3 declarations

valuematchDimensions :: DynamicDimension -> DynamicDimension -> DynamicDimension

Combines two DynamicDimensions, determining the DynamicDimension of a quantity that must match both inputs.

This is the lattice meet operation for DynamicDimension.

valueisCompatibleWith :: HasDynamicDimension a => a -> Dimension' -> Bool

Determines if a value that has a DynamicDimension is compatible with a specified Dimension'.

valuehasSomeDimension :: HasDynamicDimension a => a -> Bool

Determines if a value that has a DynamicDimension in fact has any valid dimension at all.