Numeric.Units.Dimensional

Please refer to the literate Haskell code for documentation of both API and implementation.

Documentation

newtype Dimensional v d a

Constructors

Dimensional a

Instances

Functor Dimensionless

(Show d, Show a) => Show (Quantity d a)

Typeable (* -> * -> * -> *) Dimensional

Enum a => Enum (Dimensional v d a)

Eq a => Eq (Dimensional v d a)

Ord a => Ord (Dimensional v d a)

data DUnit

Instances

Typeable * DUnit

data DQuantity

Instances

Functor Dimensionless

Typeable * DQuantity

(Show d, Show a) => Show (Quantity d a)

type Unit = Dimensional DUnit

type Quantity = Dimensional DQuantity

(*~) :: Num a => a -> Unit d a -> Quantity d a infixl 7

(/~) :: Fractional a => Quantity d a -> Unit d a -> a infixl 7

data Dim l m t i th n j

Instances

Functor Dimensionless

Typeable (* -> * -> * -> * -> * -> * -> * -> *) Dim

Div d (Dim l m t i th n j) d' => Div (DExt a x d) (Dim l m t i th n j) (DExt a x d')

Mul d (Dim l m t i th n j) d' => Mul (DExt a x d) (Dim l m t i th n j) (DExt a x d')

(NumType l, NumType m, NumType t, NumType i, NumType th, NumType n, NumType j) => Show (Dim l m t i th n j)

(Div l x l', Div m x m', Div t x t', Div i x i', Div th x th', Div n x n', Div j x j') => Root (Dim l m t i th n j) x (Dim l' m' t' i' th' n' j')

(Mul l x l', Mul m x m', Mul t x t', Mul i x i', Mul th x th', Mul n x n', Mul j x j') => Pow (Dim l m t i th n j) x (Dim l' m' t' i' th' n' j')

(Div (Dim l m t i th n j) d d', Negate x x') => Div (Dim l m t i th n j) (DExt a x d) (DExt a x' d')

Mul (Dim l m t i th n j) d d' => Mul (Dim l m t i th n j) (DExt a x d) (DExt a x d')

(Sum l l' l'', Sum m m' m'', Sum t t' t'', Sum i i' i'', Sum th th' th'', Sum n n' n'', Sum j j' j'') => Div (Dim l'' m'' t'' i'' th'' n'' j'') (Dim l' m' t' i' th' n' j') (Dim l m t i th n j)

(Sum l l' l'', Sum m m' m'', Sum t t' t'', Sum i i' i'', Sum th th' th'', Sum n n' n'', Sum j j' j'') => Mul (Dim l m t i th n j) (Dim l' m' t' i' th' n' j') (Dim l'' m'' t'' i'' th'' n'' j'')

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

class Mul d d' d'' | d d' -> d''

Instances

(Sum n n' n'', Mul d d' d'', DropZero (DExt a n'' d'') d''') => Mul (DExt a n d) (DExt a n' d') d'''

(Sum lh lh' lh'', Sum mh mh' mh'', Sum t t' t'') => Mul (CGSDim lh mh t) (CGSDim lh' mh' t') (CGSDim lh'' mh'' t'')

Mul d (Dim l m t i th n j) d' => Mul (DExt a x d) (Dim l m t i th n j) (DExt a x d')

Mul (Dim l m t i th n j) d d' => Mul (Dim l m t i th n j) (DExt a x d) (DExt a x d')

(Sum l l' l'', Sum m m' m'', Sum t t' t'', Sum i i' i'', Sum th th' th'', Sum n n' n'', Sum j j' j'') => Mul (Dim l m t i th n j) (Dim l' m' t' i' th' n' j') (Dim l'' m'' t'' i'' th'' n'' j'')

class Div d d' d'' | d d' -> d''

Instances

(Sum n'' n' n, Div d d' d'', DropZero (DExt a n'' d'') d''') => Div (DExt a n d) (DExt a n' d') d'''

(Sum lh lh' lh'', Sum mh mh' mh'', Sum t t' t'') => Div (CGSDim lh'' mh'' t'') (CGSDim lh' mh' t') (CGSDim lh mh t)

Div d (Dim l m t i th n j) d' => Div (DExt a x d) (Dim l m t i th n j) (DExt a x d')

(Div (Dim l m t i th n j) d d', Negate x x') => Div (Dim l m t i th n j) (DExt a x d) (DExt a x' d')

(Sum l l' l'', Sum m m' m'', Sum t t' t'', Sum i i' i'', Sum th th' th'', Sum n n' n'', Sum j j' j'') => Div (Dim l'' m'' t'' i'' th'' n'' j'') (Dim l' m' t' i' th' n' j') (Dim l m t i th n j)

class NumType x => Pow d x d' | d x -> d'

Instances

(Mul n x n', Pow d x d') => Pow (DExt a n d) x (DExt a n' d')

(Mul lh x lh', Mul mh x mh', Mul t x t') => Pow (CGSDim lh mh t) x (CGSDim lh' mh' t')

(Mul l x l', Mul m x m', Mul t x t', Mul i x i', Mul th x th', Mul n x n', Mul j x j') => Pow (Dim l m t i th n j) x (Dim l' m' t' i' th' n' j')

class NonZero x => Root d x d' | d x -> d'

Instances

(Div n x n', Root d x d') => Root (DExt a n d) x (DExt a n' d')

(Div lh x lh', Div mh x mh', Div t x t') => Root (CGSDim lh mh t) x (CGSDim lh' mh' t')

(Div l x l', Div m x m', Div t x t', Div i x i', Div th x th', Div n x n', Div j x j') => Root (Dim l m t i th n j) x (Dim l' m' t' i' th' n' j')

(*) :: (Num a, Mul d d' d'') => Dimensional v d a -> Dimensional v d' a -> Dimensional v d'' a infixl 7

(/) :: (Fractional a, Div d d' d'') => Dimensional v d a -> Dimensional v d' a -> Dimensional v d'' a infixl 7

(^) :: (Fractional a, Pow d n d') => Dimensional v d a -> n -> Dimensional v d' a infixr 8

(^+) :: (Num a, PosType n, Pow d n d') => Dimensional v d a -> n -> Dimensional v d' a infixr 8

negate :: Num a => Quantity d a -> Quantity d a

(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6

(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6

abs :: Num a => Quantity d a -> Quantity d a

nroot :: (Floating a, Root d n d') => n -> Dimensional v d a -> Dimensional v d' a

sqrt :: (Floating a, Root d Pos2 d') => Dimensional v d a -> Dimensional v d' a

cbrt :: (Floating a, Root d Pos3 d') => Dimensional v d a -> Dimensional v d' a

(^/) :: (Floating a, Root d n d') => Dimensional v d a -> n -> Dimensional v d' a infixr 8

(*~~) :: (Functor f, Num a) => f a -> Unit d a -> f (Quantity d a) infixl 7

(/~~) :: (Functor f, Fractional a) => f (Quantity d a) -> Unit d a -> f a infixl 7

sum :: forall d a. Num a => [Quantity d a] -> Quantity d a

dimensionlessLength :: Num a => [Dimensional v d a] -> Dimensionless a

exp :: Floating a => Dimensionless a -> Dimensionless a

atanh :: Floating a => Dimensionless a -> Dimensionless a

acosh :: Floating a => Dimensionless a -> Dimensionless a

asinh :: Floating a => Dimensionless a -> Dimensionless a

tanh :: Floating a => Dimensionless a -> Dimensionless a

cosh :: Floating a => Dimensionless a -> Dimensionless a

sinh :: Floating a => Dimensionless a -> Dimensionless a

atan :: Floating a => Dimensionless a -> Dimensionless a

acos :: Floating a => Dimensionless a -> Dimensionless a

asin :: Floating a => Dimensionless a -> Dimensionless a

tan :: Floating a => Dimensionless a -> Dimensionless a

cos :: Floating a => Dimensionless a -> Dimensionless a

sin :: Floating a => Dimensionless a -> Dimensionless a

log :: Floating a => Dimensionless a -> Dimensionless a

(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a infixr 8

atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a

one :: Num a => Unit DOne a

_0 :: Num a => Quantity d a

_1 :: Num a => Dimensionless a

_9 :: Num a => Dimensionless a

_8 :: Num a => Dimensionless a

_7 :: Num a => Dimensionless a

_6 :: Num a => Dimensionless a

_5 :: Num a => Dimensionless a

_4 :: Num a => Dimensionless a

_3 :: Num a => Dimensionless a

_2 :: Num a => Dimensionless a

pi :: Floating a => Dimensionless a

tau :: Floating a => Dimensionless a

dimUnit :: NumType n => String -> n -> Maybe String

prefix :: Num a => a -> Unit d a -> Unit d a