Data.Metrology.Vector

Exports combinators for building quantities out of vectors, from the vector-space library.

Term-level combinators

The term-level arithmetic operators are defined by applying vertical bar(s) to the sides the dimensioned quantities acts on.

Additive operations

zero :: AdditiveGroup n => Qu dimspec l n

The number 0, polymorphic in its dimension. Use of this will often require a type annotation.

(|+|) :: (d1 @~ d2, AdditiveGroup n) => Qu d1 l n -> Qu d2 l n -> Qu d1 l n infixl 6

Add two compatible quantities

(|-|) :: (d1 @~ d2, AdditiveGroup n) => Qu d1 l n -> Qu d2 l n -> Qu d1 l n infixl 6

Subtract two compatible quantities

qSum :: (Foldable f, AdditiveGroup n) => f (Qu d l n) -> Qu d l n

Take the sum of a list of quantities

qNegate :: AdditiveGroup n => Qu d l n -> Qu d l n

Negate a quantity

Multiplicative operations between non-vector quantities

(|*|) :: Num n => Qu a l n -> Qu b l n -> Qu (Normalize (a @+ b)) l n infixl 7

Multiply two quantities

(|/|) :: Fractional n => Qu a l n -> Qu b l n -> Qu (Normalize (a @- b)) l n infixl 7

Divide two quantities

(/|) :: Fractional n => n -> Qu b l n -> Qu (Normalize ('[] @- b)) l n infixl 7

Divide a scalar by a quantity

Multiplicative operations between a vector and a scalar

(*|) :: VectorSpace n => Scalar n -> Qu b l n -> Qu b l n infixl 7

Multiply a quantity by a scalar from the left

(|*) :: VectorSpace n => Qu a l n -> Scalar n -> Qu a l n infixl 7

Multiply a quantity by a scalar from the right

(|/) :: (VectorSpace n, Fractional (Scalar n)) => Qu a l n -> Scalar n -> Qu a l n infixl 7

Divide a quantity by a scalar

Multiplicative operations on vectors

(|*^|) :: VectorSpace n => Qu d1 l (Scalar n) -> Qu d2 l n -> Qu (Normalize (d1 @+ d2)) l n infixl 7

Multiply a scalar quantity by a vector quantity

(|^*|) :: VectorSpace n => Qu d1 l n -> Qu d2 l (Scalar n) -> Qu (Normalize (d1 @+ d2)) l n infixl 7

Multiply a vector quantity by a scalar quantity

(|^/|) :: (VectorSpace n, Fractional (Scalar n)) => Qu d1 l n -> Qu d2 l (Scalar n) -> Qu (Normalize (d1 @- d2)) l n infixl 7

Divide a vector quantity by a scalar quantity

(|.|) :: InnerSpace n => Qu d1 l n -> Qu d2 l n -> Qu (Normalize (d1 @+ d2)) l (Scalar n) infixl 7

Take a inner (dot) product between two quantities.

Exponentiation

(|^) :: (NonNegative z, Num n) => Qu a l n -> Sing z -> Qu (a @* z) l n infixr 8

Raise a quantity to a integer power, knowing at compile time that the integer is non-negative.

(|^^) :: Fractional n => Qu a l n -> Sing z -> Qu (a @* z) l n infixr 8

Raise a quantity to a integer power known at compile time

qNthRoot :: ((Zero < z) ~ True, Floating n) => Sing z -> Qu a l n -> Qu (a @/ z) l n

Take the n'th root of a quantity, where n is known at compile time

qSq :: Num n => Qu a l n -> Qu (Normalize (a @+ a)) l n

Square a quantity

qCube :: Num n => Qu a l n -> Qu (Normalize (Normalize (a @+ a) @+ a)) l n

Cube a quantity

qSqrt :: Floating n => Qu a l n -> Qu (a @/ Two) l n

Take the square root of a quantity

qCubeRoot :: Floating n => Qu a l n -> Qu (a @/ Three) l n

Take the cubic root of a quantity

Other vector operations

qMagnitudeSq :: InnerSpace n => Qu d l n -> Qu (d @* Two) l (Scalar n)

Square the length of a vector.

qMagnitude :: (InnerSpace n, Floating (Scalar n)) => Qu d l n -> Qu d l (Scalar n)

Length of a vector.

qNormalized :: (InnerSpace n, Floating (Scalar n)) => Qu d l n -> Qu '[] l n

Vector in same direction as given one but with length of one. If given the zero vector, then return it. The returned vector is dimensionless.

qProject :: (InnerSpace n, Floating (Scalar n)) => Qu d2 l n -> Qu d1 l n -> Qu d1 l n

qProject u v computes the projection of v onto u.

qCross2 :: HasCross2 n => Qu d l n -> Qu d l n

Cross product of 2D vectors.

qCross3 :: HasCross3 n => Qu d1 l n -> Qu d2 l n -> Qu (Normalize (d1 @+ d2)) l n

Cross product of 3D vectors.

Affine operations

newtype Point n

A Point n is an affine space built over n. Two Points cannot be added, but they can be subtracted to yield a difference of type n.

Constructors

Point n

Instances

Bounded n => Bounded (Point n)

Methods

minBound :: Point n

maxBound :: Point n

Enum n => Enum (Point n)

Methods

succ :: Point n -> Point n

pred :: Point n -> Point n

toEnum :: Int -> Point n

fromEnum :: Point n -> Int

enumFrom :: Point n -> [Point n]

enumFromThen :: Point n -> Point n -> [Point n]

enumFromTo :: Point n -> Point n -> [Point n]

enumFromThenTo :: Point n -> Point n -> Point n -> [Point n]

Eq n => Eq (Point n)

Methods

(==) :: Point n -> Point n -> Bool

(/=) :: Point n -> Point n -> Bool

Show n => Show (Point n)

Methods

showsPrec :: Int -> Point n -> ShowS

show :: Point n -> String

showList :: [Point n] -> ShowS

AdditiveGroup n => AffineSpace (Point n)

Associated Types

type Diff (Point n) :: *

Methods

(.-.) :: Point n -> Point n -> Diff (Point n)

(.+^) :: Point n -> Diff (Point n) -> Point n

type Diff (Point n)

type Diff (Point n) = n

type family QPoint n where ...

Make a point quantity from a non-point quantity.

Equations

QPoint (Qu d l n) = Qu d l (Point n)

(|.-.|) :: (d1 @~ d2, AffineSpace n) => Qu d1 l n -> Qu d2 l n -> Qu d1 l (Diff n) infixl 6

Subtract point quantities.

(|.+^|) :: (d1 @~ d2, AffineSpace n) => Qu d1 l n -> Qu d2 l (Diff n) -> Qu d1 l n infixl 6

Add a point to a vector.

(|.-^|) :: (d1 @~ d2, AffineSpace n) => Qu d1 l n -> Qu d2 l (Diff n) -> Qu d1 l n infixl 6

Subract a vector from a point.

qDistanceSq :: (d1 @~ d2, AffineSpace n, InnerSpace (Diff n)) => Qu d1 l n -> Qu d2 l n -> Qu (d1 @* Two) l (Scalar (Diff n))

Square of the distance between two points.

qDistance :: (d1 @~ d2, AffineSpace n, InnerSpace (Diff n), Floating (Scalar (Diff n))) => Qu d1 l n -> Qu d2 l n -> Qu d1 l (Scalar (Diff n))

Distance between two points.

pointNumIn :: forall unit dim lcsu n. (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => Qu dim lcsu (Point n) -> unit -> n

Extract the numerical value from a point quantity. Like numIn.

(.#) :: (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => Qu dim lcsu (Point n) -> unit -> n infix 5

Infix synonym for pointNumIn.

quOfPoint :: forall dim lcsu unit n. (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => n -> unit -> Qu dim lcsu (Point n)

Make a point quantity at the given unit. Like quOf.

(%.) :: (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => n -> unit -> Qu dim lcsu (Point n) infix 5

Infix synonym of quOfPoint

Comparison

qCompare :: (d1 @~ d2, Ord n) => Qu d1 l n -> Qu d2 l n -> Ordering

Compare two quantities

(|<|) :: (d1 @~ d2, Ord n) => Qu d1 l n -> Qu d2 l n -> Bool infix 4

Check if one quantity is less than a compatible one

(|>|) :: (d1 @~ d2, Ord n) => Qu d1 l n -> Qu d2 l n -> Bool infix 4

Check if one quantity is greater than a compatible one

(|<=|) :: (d1 @~ d2, Ord n) => Qu d1 l n -> Qu d2 l n -> Bool infix 4

Check if one quantity is less than or equal to a compatible one

(|>=|) :: (d1 @~ d2, Ord n) => Qu d1 l n -> Qu d2 l n -> Bool infix 4

Check if one quantity is greater than or equal to a compatible one

(|==|) :: (d1 @~ d2, Eq n) => Qu d1 l n -> Qu d2 l n -> Bool infix 4

Check if two quantities are equal (uses the equality of the underlying numerical type)

(|/=|) :: (d1 @~ d2, Eq n) => Qu d1 l n -> Qu d2 l n -> Bool infix 4

Check if two quantities are not equal

qApprox infix 4

Arguments

:: (d0 @~ d1, d0 @~ d2, Num n, Ord n)

=> Qu d0 l n

epsilon

-> Qu d1 l n

left hand side

-> Qu d2 l n

right hand side

-> Bool

Compare two compatible quantities for approximate equality. If the difference between the left hand side and the right hand side arguments are less than or equal to the epsilon, they are considered equal.

qNapprox infix 4

Arguments

:: (d0 @~ d1, d0 @~ d2, Num n, Ord n)

=> Qu d0 l n

epsilon

-> Qu d1 l n

left hand side

-> Qu d2 l n

right hand side

-> Bool

Compare two compatible quantities for approixmate inequality. qNapprox e a b = not $ qApprox e a b

Nondimensional units, conversion between quantities and numeric values

numIn :: forall unit dim lcsu n. (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => Qu dim lcsu n -> unit -> n

Extracts a numerical value from a dimensioned quantity, expressed in the given unit. For example:

inMeters :: Length -> Double
inMeters x = numIn x Meter

or

inMeters x = x # Meter

(#) :: (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => Qu dim lcsu n -> unit -> n infix 5

Infix synonym for numIn

quOf :: forall unit dim lcsu n. (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => n -> unit -> Qu dim lcsu n

Creates a dimensioned quantity in the given unit. For example:

height :: Length
height = quOf 2.0 Meter

or

height = 2.0 % Meter

(%) :: (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n)) => n -> unit -> Qu dim lcsu n infix 5

Infix synonym for quOf

showIn :: (ValidDLU dim lcsu unit, VectorSpace n, Fractional (Scalar n), Show unit, Show n) => Qu dim lcsu n -> unit -> String infix 1

Show a dimensioned quantity in a given unit. (The default Show instance always uses units as specified in the LCSU.)

unity :: Num n => Qu '[] l n

The number 1, expressed as a unitless dimensioned quantity.

redim :: d @~ e => Qu d l n -> Qu e l n

Cast between equivalent dimension within the same CSU. for example [kg m s] and [s m kg]. See the README for more info.

convert :: forall d l1 l2 n. (ConvertibleLCSUs d l1 l2, VectorSpace n, Fractional (Scalar n)) => Qu d l1 n -> Qu d l2 n

Dimension-keeping cast between different CSUs.

defaultLCSU :: Qu dim DefaultLCSU n -> Qu dim DefaultLCSU n

Use this to choose a default LCSU for a dimensioned quantity. The default LCSU uses the DefaultUnitOfDim representation for each dimension.

constant :: (d @~ e, ConvertibleLCSUs e DefaultLCSU l, VectorSpace n, Fractional (Scalar n)) => Qu d DefaultLCSU n -> Qu e l n

Compute the argument in the DefaultLCSU, and present the result as lcsu-polymorphic dimension-polymorphic value. Named constant because one of its dominant usecase is to inject constant quantities into dimension-polymorphic expressions.

Type-level unit combinators

data u1 :* u2 infixl 7

Multiply two units to get another unit. For example: type MetersSquared = Meter :* Meter

Constructors

u1 :* u2 infixl 7

Instances

(Show u1, Show u2) => Show ((:*) u1 u2)

Methods

showsPrec :: Int -> (u1 :* u2) -> ShowS

show :: (u1 :* u2) -> String

showList :: [u1 :* u2] -> ShowS

(Dimension d1, Dimension d2) => Dimension ((:*) d1 d2)

Associated Types

type DimFactorsOf (d1 :* d2) :: [Factor *]

(Unit u1, Unit u2) => Unit ((:*) u1 u2)

Associated Types

type BaseUnit (u1 :* u2) :: *

type DimOfUnit (u1 :* u2) :: *

type UnitFactorsOf (u1 :* u2) :: [Factor *]

Methods

conversionRatio :: (u1 :* u2) -> Rational

canonicalConvRatio :: (u1 :* u2) -> Rational

type DefaultUnitOfDim ((:*) d1 d2)

type DefaultUnitOfDim ((:*) d1 d2) = (:*) (DefaultUnitOfDim d1) (DefaultUnitOfDim d2)

type DimFactorsOf ((:*) d1 d2)

type DimFactorsOf ((:*) d1 d2) = Normalize ((@+) (DimFactorsOf d1) (DimFactorsOf d2))

type BaseUnit ((:*) u1 u2)

type BaseUnit ((:*) u1 u2) = Canonical

type DimOfUnit ((:*) u1 u2)

type DimOfUnit ((:*) u1 u2) = (:*) (DimOfUnit u1) (DimOfUnit u2)

type UnitFactorsOf ((:*) u1 u2)

type UnitFactorsOf ((:*) u1 u2) = Normalize ((@+) (UnitFactorsOf u1) (UnitFactorsOf u2))

data u1 :/ u2 infixl 7

Divide two units to get another unit

Constructors

u1 :/ u2 infixl 7

Instances

(Show u1, Show u2) => Show ((:/) u1 u2)

Methods

showsPrec :: Int -> (u1 :/ u2) -> ShowS

show :: (u1 :/ u2) -> String

showList :: [u1 :/ u2] -> ShowS

(Dimension d1, Dimension d2) => Dimension ((:/) d1 d2)

Associated Types

type DimFactorsOf (d1 :/ d2) :: [Factor *]

(Unit u1, Unit u2) => Unit ((:/) u1 u2)

Associated Types

type BaseUnit (u1 :/ u2) :: *

type DimOfUnit (u1 :/ u2) :: *

type UnitFactorsOf (u1 :/ u2) :: [Factor *]

Methods

conversionRatio :: (u1 :/ u2) -> Rational

canonicalConvRatio :: (u1 :/ u2) -> Rational

type DefaultUnitOfDim ((:/) d1 d2)

type DefaultUnitOfDim ((:/) d1 d2) = (:/) (DefaultUnitOfDim d1) (DefaultUnitOfDim d2)

type DimFactorsOf ((:/) d1 d2)

type DimFactorsOf ((:/) d1 d2) = Normalize ((@-) (DimFactorsOf d1) (DimFactorsOf d2))

type BaseUnit ((:/) u1 u2)

type BaseUnit ((:/) u1 u2) = Canonical

type DimOfUnit ((:/) u1 u2)

type DimOfUnit ((:/) u1 u2) = (:/) (DimOfUnit u1) (DimOfUnit u2)

type UnitFactorsOf ((:/) u1 u2)

type UnitFactorsOf ((:/) u1 u2) = Normalize ((@-) (UnitFactorsOf u1) (UnitFactorsOf u2))

data unit :^ (power :: Z) infixr 8

Raise a unit to a power, known at compile time

Constructors

unit :^ (Sing power) infixr 8

Instances

(Show u1, SingI Z power) => Show ((:^) u1 power)

Methods

showsPrec :: Int -> (u1 :^ power) -> ShowS

show :: (u1 :^ power) -> String

showList :: [u1 :^ power] -> ShowS

Dimension dim => Dimension ((:^) dim power)

Associated Types

type DimFactorsOf (dim :^ power) :: [Factor *]

(Unit unit, SingI Z power) => Unit ((:^) unit power)

Associated Types

type BaseUnit (unit :^ power) :: *

type DimOfUnit (unit :^ power) :: *

type UnitFactorsOf (unit :^ power) :: [Factor *]

Methods

conversionRatio :: (unit :^ power) -> Rational

canonicalConvRatio :: (unit :^ power) -> Rational

type DefaultUnitOfDim ((:^) d z)

type DefaultUnitOfDim ((:^) d z) = (:^) (DefaultUnitOfDim d) z

type DimFactorsOf ((:^) dim power)

type DimFactorsOf ((:^) dim power) = Normalize ((@*) (DimFactorsOf dim) power)

type BaseUnit ((:^) unit power)

type BaseUnit ((:^) unit power) = Canonical

type DimOfUnit ((:^) unit power)

type DimOfUnit ((:^) unit power) = (:^) (DimOfUnit unit) power

type UnitFactorsOf ((:^) unit power)

type UnitFactorsOf ((:^) unit power) = Normalize ((@*) (UnitFactorsOf unit) power)

data prefix :@ unit infixr 9

Multiply a conversion ratio by some constant. Used for defining prefixes.

Constructors

prefix :@ unit infixr 9

Instances

(Show prefix, Show unit) => Show ((:@) prefix unit)

Methods

showsPrec :: Int -> (prefix :@ unit) -> ShowS

show :: (prefix :@ unit) -> String

showList :: [prefix :@ unit] -> ShowS

((~) Bool ((==) * unit Canonical) False, Unit unit, UnitPrefix prefix) => Unit ((:@) prefix unit)

Associated Types

type BaseUnit (prefix :@ unit) :: *

type DimOfUnit (prefix :@ unit) :: *

type UnitFactorsOf (prefix :@ unit) :: [Factor *]

Methods

conversionRatio :: (prefix :@ unit) -> Rational

canonicalConvRatio :: (prefix :@ unit) -> Rational

type BaseUnit ((:@) prefix unit)

type BaseUnit ((:@) prefix unit) = unit

type DimOfUnit ((:@) prefix unit)

type DimOfUnit ((:@) prefix unit) = DimOfUnit (BaseUnit ((:@) prefix unit))

type UnitFactorsOf ((:@) prefix unit)

type UnitFactorsOf ((:@) prefix unit) = If [Factor *] (IsCanonical ((:@) prefix unit)) ((:) (Factor *) (F * ((:@) prefix unit) One) ([] (Factor *))) (UnitFactorsOf (BaseUnit ((:@) prefix unit)))

class UnitPrefix prefix where

A class for user-defined prefixes

Minimal complete definition

multiplier

Methods

multiplier :: Fractional f => prefix -> f

This should return the desired multiplier for the prefix being defined. This function must not inspect its argument.

Type-level quantity combinators

type family (d1 :: *) %* (d2 :: *) :: * infixl 7

Multiply two quantity types to produce a new one. For example:

type Velocity = Length %/ Time

Instances

type (Qu d1 l n) %* (Qu d2 l n)

type (Qu d1 l n) %* (Qu d2 l n) = Qu ((@+) d1 d2) l n

type family (d1 :: *) %/ (d2 :: *) :: * infixl 7

Divide two quantity types to produce a new one

Instances

type (Qu d1 l n) %/ (Qu d2 l n)

type (Qu d1 l n) %/ (Qu d2 l n) = Qu ((@-) d1 d2) l n

type family (d :: *) %^ (z :: Z) :: * infixr 8

Exponentiate a quantity type to an integer

Instances

type (Qu d l n) %^ z

type (Qu d l n) %^ z = Qu ((@*) d z) l n

Creating quantity types

data Qu (a :: [Factor *]) (lcsu :: LCSU *) (n :: *)

Qu adds a dimensional annotation to its numerical value type n. This is the representation for all quantities.

Instances

Eq n => Eq (Qu d l n)

Methods

(==) :: Qu d l n -> Qu d l n -> Bool

(/=) :: Qu d l n -> Qu d l n -> Bool

((~) [Factor *] d ([] (Factor *)), Floating n) => Floating (Qu d l n)

Methods

pi :: Qu d l n

exp :: Qu d l n -> Qu d l n

log :: Qu d l n -> Qu d l n

sqrt :: Qu d l n -> Qu d l n

(**) :: Qu d l n -> Qu d l n -> Qu d l n

logBase :: Qu d l n -> Qu d l n -> Qu d l n

sin :: Qu d l n -> Qu d l n

cos :: Qu d l n -> Qu d l n

tan :: Qu d l n -> Qu d l n

asin :: Qu d l n -> Qu d l n

acos :: Qu d l n -> Qu d l n

atan :: Qu d l n -> Qu d l n

sinh :: Qu d l n -> Qu d l n

cosh :: Qu d l n -> Qu d l n

tanh :: Qu d l n -> Qu d l n

asinh :: Qu d l n -> Qu d l n

acosh :: Qu d l n -> Qu d l n

atanh :: Qu d l n -> Qu d l n

log1p :: Qu d l n -> Qu d l n

expm1 :: Qu d l n -> Qu d l n

log1pexp :: Qu d l n -> Qu d l n

log1mexp :: Qu d l n -> Qu d l n

((~) [Factor *] d ([] (Factor *)), Fractional n) => Fractional (Qu d l n)

Methods

(/) :: Qu d l n -> Qu d l n -> Qu d l n

recip :: Qu d l n -> Qu d l n

fromRational :: Rational -> Qu d l n

((~) [Factor *] d ([] (Factor *)), Num n) => Num (Qu d l n)

Methods

(+) :: Qu d l n -> Qu d l n -> Qu d l n

(-) :: Qu d l n -> Qu d l n -> Qu d l n

(*) :: Qu d l n -> Qu d l n -> Qu d l n

negate :: Qu d l n -> Qu d l n

abs :: Qu d l n -> Qu d l n

signum :: Qu d l n -> Qu d l n

fromInteger :: Integer -> Qu d l n

Ord n => Ord (Qu d l n)

Methods

compare :: Qu d l n -> Qu d l n -> Ordering

(<) :: Qu d l n -> Qu d l n -> Bool

(<=) :: Qu d l n -> Qu d l n -> Bool

(>) :: Qu d l n -> Qu d l n -> Bool

(>=) :: Qu d l n -> Qu d l n -> Bool

max :: Qu d l n -> Qu d l n -> Qu d l n

min :: Qu d l n -> Qu d l n -> Qu d l n

Read n => Read (Qu ([] (Factor *)) l n)

Methods

readsPrec :: Int -> ReadS (Qu [Factor *] l n)

readList :: ReadS [Qu [Factor *] l n]

readPrec :: ReadPrec (Qu [Factor *] l n)

readListPrec :: ReadPrec [Qu [Factor *] l n]

((~) [Factor *] d ([] (Factor *)), Real n) => Real (Qu d l n)

Methods

toRational :: Qu d l n -> Rational

((~) [Factor *] d ([] (Factor *)), RealFloat n) => RealFloat (Qu d l n)

Methods

floatRadix :: Qu d l n -> Integer

floatDigits :: Qu d l n -> Int

floatRange :: Qu d l n -> (Int, Int)

decodeFloat :: Qu d l n -> (Integer, Int)

encodeFloat :: Integer -> Int -> Qu d l n

exponent :: Qu d l n -> Int

significand :: Qu d l n -> Qu d l n

scaleFloat :: Int -> Qu d l n -> Qu d l n

isNaN :: Qu d l n -> Bool

isInfinite :: Qu d l n -> Bool

isDenormalized :: Qu d l n -> Bool

isNegativeZero :: Qu d l n -> Bool

isIEEE :: Qu d l n -> Bool

atan2 :: Qu d l n -> Qu d l n -> Qu d l n

((~) [Factor *] d ([] (Factor *)), RealFrac n) => RealFrac (Qu d l n)

Methods

properFraction :: Integral b => Qu d l n -> (b, Qu d l n)

truncate :: Integral b => Qu d l n -> b

round :: Integral b => Qu d l n -> b

ceiling :: Integral b => Qu d l n -> b

floor :: Integral b => Qu d l n -> b

Show n => Show (Qu ([] (Factor *)) l n)

Methods

showsPrec :: Int -> Qu [Factor *] l n -> ShowS

show :: Qu [Factor *] l n -> String

showList :: [Qu [Factor *] l n] -> ShowS

NFData n => NFData (Qu d l n)

Methods

rnf :: Qu d l n -> ()

VectorSpace n => VectorSpace (Qu d l n)

Associated Types

type Scalar (Qu d l n) :: *

Methods

(*^) :: Scalar (Qu d l n) -> Qu d l n -> Qu d l n

AdditiveGroup n => AdditiveGroup (Qu d l n)

Methods

zeroV :: Qu d l n

(^+^) :: Qu d l n -> Qu d l n -> Qu d l n

negateV :: Qu d l n -> Qu d l n

(^-^) :: Qu d l n -> Qu d l n -> Qu d l n

ValidDL d l => Quantity (Qu d l n)

Associated Types

type QuantityUnit (Qu d l n) :: *

type QuantityLCSU (Qu d l n) :: LCSU *

type QuantityRep (Qu d l n) :: *

Methods

fromQuantity :: QuantityQu (Qu d l n) -> Qu d l n

toQuantity :: Qu d l n -> QuantityQu (Qu d l n)

type Scalar (Qu d l n)

type Scalar (Qu d l n) = Scalar n

type QuantityUnit (Qu d l n)

type QuantityUnit (Qu d l n) = UnitOfDimFactors d l

type QuantityLCSU (Qu d l n)

type QuantityLCSU (Qu d l n) = l

type QuantityRep (Qu d l n)

type QuantityRep (Qu d l n) = n

type (Qu d l n) %^ z

type (Qu d l n) %^ z = Qu ((@*) d z) l n

type (Qu d1 l n) %/ (Qu d2 l n)

type (Qu d1 l n) %/ (Qu d2 l n) = Qu ((@-) d1 d2) l n

type (Qu d1 l n) %* (Qu d2 l n)

type (Qu d1 l n) %* (Qu d2 l n) = Qu ((@+) d1 d2) l n

type MkQu_D dim = Qu (DimFactorsOf dim) DefaultLCSU Double

Make a quantity type capable of storing a value of a given unit. This uses a Double for storage of the value. For example:

data LengthDim = LengthDim
instance Dimension LengthDim
data Meter = Meter
instance Unit Meter where
  type BaseUnit Meter = Canonical
  type DimOfUnit Meter = LengthDim
type instance DefaultUnitOfDim LengthDim = Meter
type Length = MkQu_D LengthDim

Note that the dimension must have an instance for the type family DefaultUnitOfDim for this to work.

type MkQu_DLN dim = Qu (DimFactorsOf dim)

Make a quantity type with a custom numerical type and LCSU.

type MkQu_U unit = Qu (DimFactorsOf (DimOfUnit unit)) DefaultLCSU Double

Make a quantity type with a given unit. It will be stored as a Double. Note that the corresponding dimension must have an appropriate instance for DefaultUnitOfDim for this to work.

type MkQu_ULN unit = Qu (DimFactorsOf (DimOfUnit unit))

Make a quantity type with a unit and LCSU with custom numerical type. The quantity will have the dimension corresponding to the unit.

Creating new dimensions

class Dimension dim

This class is used to mark abstract dimensions, such as Length, or Mass.

Associated Types

type DimFactorsOf dim :: [Factor *]

Retrieve a list of Factors representing the given dimension. Overriding the default of this type family should not be necessary in user code.

Instances

Dimension Dimensionless

Associated Types

type DimFactorsOf Dimensionless :: [Factor *]

Dimension dim => Dimension ((:^) dim power)

Associated Types

type DimFactorsOf (dim :^ power) :: [Factor *]

(Dimension d1, Dimension d2) => Dimension ((:/) d1 d2)

Associated Types

type DimFactorsOf (d1 :/ d2) :: [Factor *]

(Dimension d1, Dimension d2) => Dimension ((:*) d1 d2)

Associated Types

type DimFactorsOf (d1 :* d2) :: [Factor *]

Creating new units

class DimOfUnitIsConsistent unit => Unit unit where

Associated Types

type BaseUnit unit :: *

The base unit of this unit: what this unit is defined in terms of. For units that are not defined in terms of anything else, the base unit should be Canonical.

type DimOfUnit unit :: *

The dimension that this unit is associated with. This needs to be defined only for canonical units; other units are necessarily of the same dimension as their base.

type UnitFactorsOf unit :: [Factor *]

The internal list of canonical units corresponding to this unit. Overriding the default should not be necessary in user code.

Methods

conversionRatio :: unit -> Rational

The conversion ratio from the base unit to this unit. If left out, a conversion ratio of 1 is assumed.

For example:

instance Unit Foot where
  type BaseUnit Foot = Meter
  conversionRatio _ = 0.3048

Implementations should never examine their argument!

Instances

Unit Number

Associated Types

type BaseUnit Number :: *

type DimOfUnit Number :: *

type UnitFactorsOf Number :: [Factor *]

Methods

conversionRatio :: Number -> Rational

canonicalConvRatio :: Number -> Rational

((~) Bool ((==) * unit Canonical) False, Unit unit, UnitPrefix prefix) => Unit ((:@) prefix unit)

Associated Types

type BaseUnit (prefix :@ unit) :: *

type DimOfUnit (prefix :@ unit) :: *

type UnitFactorsOf (prefix :@ unit) :: [Factor *]

Methods

conversionRatio :: (prefix :@ unit) -> Rational

canonicalConvRatio :: (prefix :@ unit) -> Rational

(Unit unit, SingI Z power) => Unit ((:^) unit power)

Associated Types

type BaseUnit (unit :^ power) :: *

type DimOfUnit (unit :^ power) :: *

type UnitFactorsOf (unit :^ power) :: [Factor *]

Methods

conversionRatio :: (unit :^ power) -> Rational

canonicalConvRatio :: (unit :^ power) -> Rational

(Unit u1, Unit u2) => Unit ((:/) u1 u2)

Associated Types

type BaseUnit (u1 :/ u2) :: *

type DimOfUnit (u1 :/ u2) :: *

type UnitFactorsOf (u1 :/ u2) :: [Factor *]

Methods

conversionRatio :: (u1 :/ u2) -> Rational

canonicalConvRatio :: (u1 :/ u2) -> Rational

(Unit u1, Unit u2) => Unit ((:*) u1 u2)

Associated Types

type BaseUnit (u1 :* u2) :: *

type DimOfUnit (u1 :* u2) :: *

type UnitFactorsOf (u1 :* u2) :: [Factor *]

Methods

conversionRatio :: (u1 :* u2) -> Rational

canonicalConvRatio :: (u1 :* u2) -> Rational

data Canonical

Dummy type use just to label canonical units. It does not have a Unit instance.

Numbers, the only built-in unit

data Dimensionless

The dimension for the dimensionless quantities. It is also called "quantities of dimension one", but One is confusing with the type-level integer One.

Constructors

Dimensionless

Instances

Dimension Dimensionless

Associated Types

type DimFactorsOf Dimensionless :: [Factor *]

type DefaultUnitOfDim Dimensionless

type DefaultUnitOfDim Dimensionless = Number

type DimFactorsOf Dimensionless

type DimFactorsOf Dimensionless = [] (Factor *)

data Number

The unit for unitless dimensioned quantities

Constructors

Number

Instances

Unit Number

Associated Types

type BaseUnit Number :: *

type DimOfUnit Number :: *

type UnitFactorsOf Number :: [Factor *]

Methods

conversionRatio :: Number -> Rational

canonicalConvRatio :: Number -> Rational

type BaseUnit Number

type BaseUnit Number = Canonical

type DimOfUnit Number

type DimOfUnit Number = Dimensionless

type UnitFactorsOf Number

type UnitFactorsOf Number = [] (Factor *)

type Count = MkQu_ULN Number

The type of unitless dimensioned quantities. This is an instance of Num, though Haddock doesn't show it. This is parameterized by an LCSU and a number representation.

quantity :: n -> Qu '[] l n

Convert a raw number into a unitless dimensioned quantity

LCSUs (locally coherent system of units)

type family MkLCSU pairs where ...

Make a local consistent set of units. The argument is a type-level list of tuple types, to be interpreted as an association list from dimensions to units. For example:

type MyLCSU = MkLCSU '[(Length, Foot), (Mass, Gram), (Time, Year)]

Equations

MkLCSU pairs = MkLCSU_ (UsePromotedTuples pairs)

data LCSU star

Constructors

DefaultLCSU

type family DefaultUnitOfDim (dim :: *) :: *

Assign a default unit for a dimension. Necessary only when using default LCSUs.

Instances

type DefaultUnitOfDim Dimensionless

type DefaultUnitOfDim Dimensionless = Number

type DefaultUnitOfDim ((:^) d z)

type DefaultUnitOfDim ((:^) d z) = (:^) (DefaultUnitOfDim d) z

type DefaultUnitOfDim ((:/) d1 d2)

type DefaultUnitOfDim ((:/) d1 d2) = (:/) (DefaultUnitOfDim d1) (DefaultUnitOfDim d2)

type DefaultUnitOfDim ((:*) d1 d2)

type DefaultUnitOfDim ((:*) d1 d2) = (:*) (DefaultUnitOfDim d1) (DefaultUnitOfDim d2)

Validity checks and assertions

type family CompatibleUnit (lcsu :: LCSU *) (unit :: *) :: Constraint where ...

Check if an LCSU has consistent entries for the given unit. i.e. can the lcsu describe the unit?

Equations

CompatibleUnit lcsu unit = (ValidDLU (DimFactorsOf (DimOfUnit unit)) lcsu unit, UnitFactor (LookupList (DimFactorsOf (DimOfUnit unit)) lcsu))

type family CompatibleDim (lcsu :: LCSU *) (dim :: *) :: Constraint where ...

Check if an LCSU can express the given dimension

Equations

CompatibleDim lcsu dim = (UnitFactor (LookupList (DimFactorsOf dim) lcsu), DimOfUnit (Lookup dim lcsu) ~ dim)

type family ConvertibleLCSUs_D (dim :: *) (l1 :: LCSU *) (l2 :: LCSU *) :: Constraint where ...

Like ConvertibleLCSUs, but takes a dimension, not a dimension factors.

Equations

ConvertibleLCSUs_D dim l1 l2 = ConvertibleLCSUs (DimFactorsOf dim) l1 l2

type family DefaultConvertibleLCSU_D (dim :: *) (l :: LCSU *) :: Constraint where ...

Check if the DefaultLCSU can convert into the given one, at the given dimension.

Equations

DefaultConvertibleLCSU_D dim l = (ValidDL (DimFactorsOf dim) DefaultLCSU, ConvertibleLCSUs (DimFactorsOf dim) DefaultLCSU l)

type family DefaultConvertibleLCSU_U (unit :: *) (l :: LCSU *) :: Constraint where ...

Check if the DefaultLCSU can convert into the given one, at the given unit.

Equations

DefaultConvertibleLCSU_U unit l = DefaultConvertibleLCSU_D (DimOfUnit unit) l

type family MultDimFactors (facts :: [Factor *]) where ...

Extract a dimension specifier from a list of factors

Equations

MultDimFactors '[] = Dimensionless

MultDimFactors (F d z ': ds) = (d :^ z) :* MultDimFactors ds

type family MultUnitFactors (facts :: [Factor *]) where ...

Extract a unit specifier from a list of factors

Equations

MultUnitFactors '[] = Number

MultUnitFactors (F unit z ': units) = (unit :^ z) :* MultUnitFactors units

type family UnitOfDimFactors (dims :: [Factor *]) (lcsu :: LCSU *) :: * where ...

Extract a unit from a dimension factor list and an LCSU

Equations

UnitOfDimFactors dims lcsu = MultUnitFactors (LookupList dims lcsu)

Type-level integers

data Z

The datatype for type-level integers.

Constructors

Zero

S Z

P Z

Instances

Eq Z

Methods

(==) :: Z -> Z -> Bool

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

SEq Z

Methods

(%:==) :: Sing Z a -> Sing Z b -> Sing Bool ((Z :== a) b)

(%:/=) :: Sing Z a -> Sing Z b -> Sing Bool ((Z :/= a) b)

PEq Z

Associated Types

type (Z :== (x :: Z)) (y :: Z) :: Bool

type (Z :/= (x :: Z)) (y :: Z) :: Bool

SDecide Z

Methods

(%~) :: Sing Z a -> Sing Z b -> Decision ((Z :~: a) b)

SingKind Z

Associated Types

type Demote Z = (r :: *)

Methods

fromSing :: Sing Z a -> Demote Z

toSing :: Demote Z -> SomeSing Z

SingI Z Zero

Methods

sing :: Sing Zero a

SingI Z n => SingI Z (S n)

Methods

sing :: Sing (S n) a

SingI Z n => SingI Z (P n)

Methods

sing :: Sing (P n) a

SuppressUnusedWarnings (TyFun Z Z -> *) PSym0

Methods

suppressUnusedWarnings :: Proxy PSym0 t -> ()

SuppressUnusedWarnings (TyFun Z Z -> *) SSym0

Methods

suppressUnusedWarnings :: Proxy SSym0 t -> ()

data Sing Z

data Sing Z where

• SZero :: Sing Z z
• SS :: Sing Z z
• SP :: Sing Z z

type Demote Z

type Demote Z = Z

type (:/=) Z x y

type (:/=) Z x y = Not ((:==) Z x y)

type (:==) Z a b

type (:==) Z a b

type Apply Z Z PSym0 l

type Apply Z Z PSym0 l = P l

type Apply Z Z SSym0 l

type Apply Z Z SSym0 l = S l

type family Succ (z :: Z) :: Z where ...

Add one to an integer

Equations

Succ Zero = S Zero

Succ (P z) = z

Succ (S z) = S (S z)

type family Pred (z :: Z) :: Z where ...

Subtract one from an integer

Equations

Pred Zero = P Zero

Pred (P z) = P (P z)

Pred (S z) = z

type family (a :: Z) #+ (b :: Z) :: Z where ... infixl 6

Add two integers

Equations

Zero #+ z = z

(S z1) #+ (S z2) = S (S (z1 #+ z2))

(S z1) #+ Zero = S z1

(S z1) #+ (P z2) = z1 #+ z2

(P z1) #+ (S z2) = z1 #+ z2

(P z1) #+ Zero = P z1

(P z1) #+ (P z2) = P (P (z1 #+ z2))

type family (a :: Z) #- (b :: Z) :: Z where ... infixl 6

Subtract two integers

Equations

z #- Zero = z

(S z1) #- (S z2) = z1 #- z2

Zero #- (S z2) = P (Zero #- z2)

(P z1) #- (S z2) = P (P (z1 #- z2))

(S z1) #- (P z2) = S (S (z1 #- z2))

Zero #- (P z2) = S (Zero #- z2)

(P z1) #- (P z2) = z1 #- z2

type family (a :: Z) #* (b :: Z) :: Z where ... infixl 7

Multiply two integers

Equations

Zero #* z = Zero

(S z1) #* z2 = (z1 #* z2) #+ z2

(P z1) #* z2 = (z1 #* z2) #- z2

type family (a :: Z) #/ (b :: Z) :: Z where ...

Divide two integers

Equations

Zero #/ b = Zero

a #/ (P b') = Negate (a #/ Negate (P b'))

a #/ b = ZDiv b b a

type family Negate (z :: Z) :: Z where ...

Negate an integer

Equations

Negate Zero = Zero

Negate (S z) = P (Negate z)

Negate (P z) = S (Negate z)

Synonyms for small numbers

type One = S Zero

type Two = S One

type Three = S Two

type Four = S Three

type Five = S Four

type MOne = P Zero

type MTwo = P MOne

type MThree = P MTwo

type MFour = P MThree

type MFive = P MFour

Term-level singletons

sZero :: Sing Z Zero

This is the singleton value representing Zero at the term level and at the type level, simultaneously. Used for raising units to powers.

sOne :: Sing Z (S Zero)

sTwo :: Sing Z (S (S Zero))

sThree :: Sing Z (S (S (S Zero)))

sFour :: Sing Z (S (S (S (S Zero))))

sFive :: Sing Z (S (S (S (S (S Zero)))))

sMOne :: Sing Z (P Zero)

sMTwo :: Sing Z (P (P Zero))

sMThree :: Sing Z (P (P (P Zero)))

sMFour :: Sing Z (P (P (P (P Zero))))

sMFive :: Sing Z (P (P (P (P (P Zero)))))

sSucc :: Sing z -> Sing (Succ z)

Add one to a singleton Z.

sPred :: Sing z -> Sing (Pred z)

Subtract one from a singleton Z.

sNegate :: Sing z -> Sing (Negate z)

Negate a singleton Z.

Internal definitions

The following module is re-exported solely to prevent noise in error messages; we do not recommend trying to use these definitions in user code.

module Data.Metrology.Internal