Numeric.Units.Dimensional.Dimensions.TermLevel

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

Type

data 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

Instances

Eq Dimension'

Methods

(==) :: Dimension' -> Dimension' -> Bool

(/=) :: Dimension' -> Dimension' -> Bool

Data Dimension'

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dimension' -> c Dimension'

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Dimension'

toConstr :: Dimension' -> Constr

dataTypeOf :: Dimension' -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Dimension')

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Dimension')

gmapT :: (forall b. Data b => b -> b) -> Dimension' -> Dimension'

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r

gmapQ :: (forall d. Data d => d -> u) -> Dimension' -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dimension' -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension'

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension'

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension'

Ord Dimension'

Methods

compare :: Dimension' -> Dimension' -> Ordering

(<) :: Dimension' -> Dimension' -> Bool

(<=) :: Dimension' -> Dimension' -> Bool

(>) :: Dimension' -> Dimension' -> Bool

(>=) :: Dimension' -> Dimension' -> Bool

max :: Dimension' -> Dimension' -> Dimension'

min :: Dimension' -> Dimension' -> Dimension'

Show Dimension'

Methods

showsPrec :: Int -> Dimension' -> ShowS

show :: Dimension' -> String

showList :: [Dimension'] -> ShowS

Generic Dimension'

Associated Types

type Rep Dimension' :: * -> *

Methods

from :: Dimension' -> Rep Dimension' x

to :: Rep Dimension' x -> Dimension'

Semigroup Dimension'

Methods

(<>) :: Dimension' -> Dimension' -> Dimension'

sconcat :: NonEmpty Dimension' -> Dimension'

stimes :: Integral b => b -> Dimension' -> Dimension'

Monoid Dimension'

The monoid of dimensions under multiplication.

Methods

mempty :: Dimension'

mappend :: Dimension' -> Dimension' -> Dimension'

mconcat :: [Dimension'] -> Dimension'

NFData Dimension'

Methods

rnf :: Dimension' -> ()

HasDimension Dimension'

Methods

dimension :: Dimension' -> Dimension'

HasDynamicDimension Dimension'

Methods

dynamicDimension :: Dimension' -> DynamicDimension

type Rep Dimension'

type Rep Dimension' = D1 * (MetaData "Dimension'" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.1-FrwO52z7cgM7jRCbk3nsMF" False) (C1 * (MetaCons "Dim'" PrefixI False) ((:*:) * ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * Int)) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * Int)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * Int)))) ((:*:) * ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * Int)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * Int))) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * Int)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * Int))))))

Access to Dimension of Dimensional Values

class HasDynamicDimension a => HasDimension a where

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

Minimal complete definition

dimension

Methods

dimension :: a -> Dimension'

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

Instances

HasDimension Dimension'

Methods

dimension :: Dimension' -> Dimension'

HasDimension AnyUnit

Methods

dimension :: AnyUnit -> Dimension'

HasDimension (AnyQuantity a)

Methods

dimension :: AnyQuantity a -> Dimension'

(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy Dimension (Dim l m t i th n j))

Methods

dimension :: Proxy Dimension (Dim l m t i th n j) -> Dimension'

KnownDimension d => HasDimension (Dimensional v d a)

Methods

dimension :: Dimensional v d a -> Dimension'

class 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.

dynamicDimension :: HasDimension a => 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.

Instances

HasDynamicDimension DynamicDimension

Methods

dynamicDimension :: DynamicDimension -> DynamicDimension

HasDynamicDimension Dimension'

Methods

dynamicDimension :: Dimension' -> DynamicDimension

HasDynamicDimension AnyUnit

Methods

dynamicDimension :: AnyUnit -> DynamicDimension

HasDynamicDimension (DynQuantity a)

Methods

dynamicDimension :: DynQuantity a -> DynamicDimension

HasDynamicDimension (AnyQuantity a)

Methods

dynamicDimension :: AnyQuantity a -> DynamicDimension

(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDynamicDimension (Proxy Dimension (Dim l m t i th n j))

Methods

dynamicDimension :: Proxy Dimension (Dim l m t i th n j) -> DynamicDimension

KnownDimension d => HasDynamicDimension (Dimensional v d a)

Methods

dynamicDimension :: Dimensional v d a -> DynamicDimension

data 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.

Instances

Eq DynamicDimension

Methods

(==) :: DynamicDimension -> DynamicDimension -> Bool

(/=) :: DynamicDimension -> DynamicDimension -> Bool

Data DynamicDimension

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> DynamicDimension -> c DynamicDimension

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c DynamicDimension

toConstr :: DynamicDimension -> Constr

dataTypeOf :: DynamicDimension -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c DynamicDimension)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c DynamicDimension)

gmapT :: (forall b. Data b => b -> b) -> DynamicDimension -> DynamicDimension

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> DynamicDimension -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> DynamicDimension -> r

gmapQ :: (forall d. Data d => d -> u) -> DynamicDimension -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> DynamicDimension -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> DynamicDimension -> m DynamicDimension

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> DynamicDimension -> m DynamicDimension

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> DynamicDimension -> m DynamicDimension

Ord DynamicDimension

Methods

compare :: DynamicDimension -> DynamicDimension -> Ordering

(<) :: DynamicDimension -> DynamicDimension -> Bool

(<=) :: DynamicDimension -> DynamicDimension -> Bool

(>) :: DynamicDimension -> DynamicDimension -> Bool

(>=) :: DynamicDimension -> DynamicDimension -> Bool

max :: DynamicDimension -> DynamicDimension -> DynamicDimension

min :: DynamicDimension -> DynamicDimension -> DynamicDimension

Show DynamicDimension

Methods

showsPrec :: Int -> DynamicDimension -> ShowS

show :: DynamicDimension -> String

showList :: [DynamicDimension] -> ShowS

Generic DynamicDimension

Associated Types

type Rep DynamicDimension :: * -> *

Methods

from :: DynamicDimension -> Rep DynamicDimension x

to :: Rep DynamicDimension x -> DynamicDimension

NFData DynamicDimension

Methods

rnf :: DynamicDimension -> ()

HasDynamicDimension DynamicDimension

Methods

dynamicDimension :: DynamicDimension -> DynamicDimension

type Rep DynamicDimension

type Rep DynamicDimension = D1 * (MetaData "DynamicDimension" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.1-FrwO52z7cgM7jRCbk3nsMF" False) ((:+:) * (C1 * (MetaCons "NoDimension" PrefixI False) (U1 *)) ((:+:) * (C1 * (MetaCons "SomeDimension" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Dimension'))) (C1 * (MetaCons "AnyDimension" PrefixI False) (U1 *))))

Dimension Arithmetic

(*) :: Dimension' -> Dimension' -> Dimension' infixl 7

Forms the product of two dimensions.

(/) :: Dimension' -> Dimension' -> Dimension' infixl 7

Forms the quotient of two dimensions.

(^) :: Dimension' -> Int -> Dimension' infixr 8

Raises a dimension to an integer power.

recip :: Dimension' -> Dimension'

Forms the reciprocal of a dimension.

nroot :: Int -> Dimension' -> Maybe Dimension'

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

n must not be zero.

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

sqrt :: Dimension' -> Maybe Dimension'

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

sqrt d == nroot 2 d

cbrt :: Dimension' -> Maybe Dimension'

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

cbrt d == nroot 3 d

Synonyms for Base Dimensions

dOne :: Dimension'

The dimension of dimensionless values.

dLength :: Dimension'

dMass :: Dimension'

dTime :: Dimension'

dElectricCurrent :: Dimension'

dThermodynamicTemperature :: Dimension'

dAmountOfSubstance :: Dimension'

dLuminousIntensity :: Dimension'

Deconstruction

asList :: 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

matchDimensions :: 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.

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

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

hasSomeDimension :: HasDynamicDimension a => a -> Bool

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