units-2.4.1.4: A domain-specific type system for dimensional analysis
Copyright(C) 2014 Richard Eisenberg
LicenseBSD-style (see LICENSE)
MaintainerRichard Eisenberg (rae@cs.brynmawr.edu)
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Metrology.Vector

Description

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

Synopsis

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 Source #

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 Source #

Add two compatible quantities

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

Subtract two compatible quantities

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

Take the sum of a list of quantities

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

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 Source #

Multiply two quantities

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

Divide two quantities

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

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 Source #

Multiply a quantity by a scalar from the left

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

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

Square a quantity

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

Cube a quantity

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

Take the square root of a quantity

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

Take the cubic root of a quantity

Other vector operations

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

Square the length of a vector.

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

Length of a vector.

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

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 Source #

qProject u v computes the projection of v onto u.

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

Cross product of 2D vectors.

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

Cross product of 3D vectors.

Affine operations

newtype Point n Source #

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

Instances details
Bounded n => Bounded (Point n) Source # 
Instance details

Defined in Data.Metrology.Vector

Methods

minBound :: Point n #

maxBound :: Point n #

Enum n => Enum (Point n) Source # 
Instance details

Defined in Data.Metrology.Vector

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) Source # 
Instance details

Defined in Data.Metrology.Vector

Methods

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

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

Show n => Show (Point n) Source # 
Instance details

Defined in Data.Metrology.Vector

Methods

showsPrec :: Int -> Point n -> ShowS #

show :: Point n -> String #

showList :: [Point n] -> ShowS #

AdditiveGroup n => AffineSpace (Point n) Source # 
Instance details

Defined in Data.Metrology.Vector

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) Source # 
Instance details

Defined in Data.Metrology.Vector

type Diff (Point n) = n

type family QPoint n where ... Source #

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 Source #

Subtract point quantities.

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

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 Source #

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)) Source #

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)) Source #

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 Source #

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 Source #

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) Source #

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 Source #

Infix synonym of quOfPoint

Comparison

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

Compare two quantities

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

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

Check if two quantities are not equal

qApprox infix 4 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

The number 1, expressed as a unitless dimensioned quantity.

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

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 Source #

Dimension-keeping cast between different CSUs.

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

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 Source #

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 Source #

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

Constructors

u1 :* u2 infixl 7 

Instances

Instances details
(Show u1, Show u2) => Show (u1 :* u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Methods

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

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

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

(Dimension d1, Dimension d2) => Dimension (d1 :* d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type DimFactorsOf (d1 :* d2) :: [Factor Type] Source #

(Unit u1, Unit u2) => Unit (u1 :* u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (u1 :* u2) Source #

type DimOfUnit (u1 :* u2) Source #

type UnitFactorsOf (u1 :* u2) :: [Factor Type] Source #

Methods

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

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

type DefaultUnitOfDim (d1 :* d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimFactorsOf (d1 :* d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type BaseUnit (u1 :* u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type BaseUnit (u1 :* u2) = Canonical
type DimOfUnit (u1 :* u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimOfUnit (u1 :* u2) = DimOfUnit u1 :* DimOfUnit u2
type UnitFactorsOf (u1 :* u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

data u1 :/ u2 infixl 7 Source #

Divide two units to get another unit

Constructors

u1 :/ u2 infixl 7 

Instances

Instances details
(Show u1, Show u2) => Show (u1 :/ u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Methods

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

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

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

(Dimension d1, Dimension d2) => Dimension (d1 :/ d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type DimFactorsOf (d1 :/ d2) :: [Factor Type] Source #

(Unit u1, Unit u2) => Unit (u1 :/ u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (u1 :/ u2) Source #

type DimOfUnit (u1 :/ u2) Source #

type UnitFactorsOf (u1 :/ u2) :: [Factor Type] Source #

Methods

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

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

type DefaultUnitOfDim (d1 :/ d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimFactorsOf (d1 :/ d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type BaseUnit (u1 :/ u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type BaseUnit (u1 :/ u2) = Canonical
type DimOfUnit (u1 :/ u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimOfUnit (u1 :/ u2) = DimOfUnit u1 :/ DimOfUnit u2
type UnitFactorsOf (u1 :/ u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

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

Raise a unit to a power, known at compile time

Constructors

unit :^ (Sing power) infixr 8 

Instances

Instances details
(Show u1, SingI power) => Show (u1 :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

Methods

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

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

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

Dimension dim => Dimension (dim :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type DimFactorsOf (dim :^ power) :: [Factor Type] Source #

(Unit unit, SingI power) => Unit (unit :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (unit :^ power) Source #

type DimOfUnit (unit :^ power) Source #

type UnitFactorsOf (unit :^ power) :: [Factor Type] Source #

Methods

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

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

type DefaultUnitOfDim (d :^ z) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimFactorsOf (dim :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimFactorsOf (dim :^ power) = Normalize (DimFactorsOf dim @* power)
type BaseUnit (unit :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

type BaseUnit (unit :^ power) = Canonical
type DimOfUnit (unit :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimOfUnit (unit :^ power) = DimOfUnit unit :^ power
type UnitFactorsOf (unit :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

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

data prefix :@ unit infixr 9 Source #

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

Constructors

prefix :@ unit infixr 9 

Instances

Instances details
(Show prefix, Show unit) => Show (prefix :@ unit) Source # 
Instance details

Defined in Data.Metrology.Combinators

Methods

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

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

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

((unit == Canonical) ~ 'False, Unit unit, UnitPrefix prefix) => Unit (prefix :@ unit) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (prefix :@ unit) Source #

type DimOfUnit (prefix :@ unit) Source #

type UnitFactorsOf (prefix :@ unit) :: [Factor Type] Source #

Methods

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

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

type BaseUnit (prefix :@ unit) Source # 
Instance details

Defined in Data.Metrology.Combinators

type BaseUnit (prefix :@ unit) = unit
type DimOfUnit (prefix :@ unit) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DimOfUnit (prefix :@ unit) = DimOfUnit (BaseUnit (prefix :@ unit))
type UnitFactorsOf (prefix :@ unit) Source # 
Instance details

Defined in Data.Metrology.Combinators

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

class UnitPrefix prefix where Source #

A class for user-defined prefixes

Methods

multiplier :: Fractional f => prefix -> f Source #

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 Source #

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

type Velocity = Length %/ Time

Instances

Instances details
type (Qu d1 l n) %* (Qu d2 l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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

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

Divide two quantity types to produce a new one

Instances

Instances details
type (Qu d1 l n) %/ (Qu d2 l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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

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

Exponentiate a quantity type to an integer

Instances

Instances details
type (Qu d l n) %^ z Source # 
Instance details

Defined in Data.Metrology.Qu

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

Creating quantity types

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

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

Instances

Instances details
Eq n => Eq (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

Methods

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

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

(d ~ ('[] :: [Factor Type]), Floating n) => Floating (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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 #

(d ~ ('[] :: [Factor Type]), Fractional n) => Fractional (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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 #

(d ~ ('[] :: [Factor Type]), Num n) => Num (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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) Source # 
Instance details

Defined in Data.Metrology.Qu

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 Type]) l n) Source # 
Instance details

Defined in Data.Metrology.Qu

Methods

readsPrec :: Int -> ReadS (Qu '[] l n) #

readList :: ReadS [Qu '[] l n] #

readPrec :: ReadPrec (Qu '[] l n) #

readListPrec :: ReadPrec [Qu '[] l n] #

(d ~ ('[] :: [Factor Type]), Real n) => Real (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

Methods

toRational :: Qu d l n -> Rational #

(d ~ ('[] :: [Factor Type]), RealFloat n) => RealFloat (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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 #

(d ~ ('[] :: [Factor Type]), RealFrac n) => RealFrac (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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 Type]) l n) Source # 
Instance details

Defined in Data.Metrology.Qu

Methods

showsPrec :: Int -> Qu '[] l n -> ShowS #

show :: Qu '[] l n -> String #

showList :: [Qu '[] l n] -> ShowS #

(ShowUnitFactor (LookupList dims lcsu), Show n) => Show (Qu dims lcsu n) Source # 
Instance details

Defined in Data.Metrology.Show

Methods

showsPrec :: Int -> Qu dims lcsu n -> ShowS #

show :: Qu dims lcsu n -> String #

showList :: [Qu dims lcsu n] -> ShowS #

NFData n => NFData (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

Methods

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

VectorSpace n => VectorSpace (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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) Source # 
Instance details

Defined in Data.Metrology.Qu

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) Source # 
Instance details

Defined in Data.Metrology.Quantity

Associated Types

type QuantityUnit (Qu d l n) Source #

type QuantityLCSU (Qu d l n) :: LCSU Type Source #

type QuantityRep (Qu d l n) Source #

Methods

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

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

type Scalar (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Qu

type Scalar (Qu d l n) = Scalar n
type QuantityUnit (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Quantity

type QuantityUnit (Qu d l n) = UnitOfDimFactors d l
type QuantityLCSU (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Quantity

type QuantityLCSU (Qu d l n) = l
type QuantityRep (Qu d l n) Source # 
Instance details

Defined in Data.Metrology.Quantity

type QuantityRep (Qu d l n) = n
type (Qu d l n) %^ z Source # 
Instance details

Defined in Data.Metrology.Qu

type (Qu d l n) %^ z = Qu (d @* z) l n
type (Qu d1 l n) %/ (Qu d2 l n) Source # 
Instance details

Defined in Data.Metrology.Qu

type (Qu d1 l n) %/ (Qu d2 l n) = Qu (d1 @- d2) l n
type (Qu d1 l n) %* (Qu d2 l n) Source # 
Instance details

Defined in Data.Metrology.Qu

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

type MkQu_D dim = Qu (DimFactorsOf dim) DefaultLCSU Double Source #

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) Source #

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

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

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)) Source #

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 Source #

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

Instances

Instances details
Dimension Dimensionless Source # 
Instance details

Defined in Data.Metrology.Units

Associated Types

type DimFactorsOf Dimensionless :: [Factor Type] Source #

Dimension dim => Dimension (dim :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type DimFactorsOf (dim :^ power) :: [Factor Type] Source #

(Dimension d1, Dimension d2) => Dimension (d1 :/ d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type DimFactorsOf (d1 :/ d2) :: [Factor Type] Source #

(Dimension d1, Dimension d2) => Dimension (d1 :* d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type DimFactorsOf (d1 :* d2) :: [Factor Type] Source #

Creating new units

class DimOfUnitIsConsistent unit => Unit unit where Source #

Minimal complete definition

Nothing

Associated Types

type BaseUnit unit :: * Source #

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 :: * Source #

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 DimOfUnit unit = DimOfUnit (BaseUnit unit)

Methods

conversionRatio :: unit -> Rational Source #

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

Instances details
Unit Number Source # 
Instance details

Defined in Data.Metrology.Units

((unit == Canonical) ~ 'False, Unit unit, UnitPrefix prefix) => Unit (prefix :@ unit) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (prefix :@ unit) Source #

type DimOfUnit (prefix :@ unit) Source #

type UnitFactorsOf (prefix :@ unit) :: [Factor Type] Source #

Methods

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

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

(Unit unit, SingI power) => Unit (unit :^ power) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (unit :^ power) Source #

type DimOfUnit (unit :^ power) Source #

type UnitFactorsOf (unit :^ power) :: [Factor Type] Source #

Methods

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

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

(Unit u1, Unit u2) => Unit (u1 :/ u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (u1 :/ u2) Source #

type DimOfUnit (u1 :/ u2) Source #

type UnitFactorsOf (u1 :/ u2) :: [Factor Type] Source #

Methods

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

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

(Unit u1, Unit u2) => Unit (u1 :* u2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Associated Types

type BaseUnit (u1 :* u2) Source #

type DimOfUnit (u1 :* u2) Source #

type UnitFactorsOf (u1 :* u2) :: [Factor Type] Source #

Methods

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

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

data Canonical Source #

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

Numbers, the only built-in unit

data Dimensionless Source #

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

Instances details
Dimension Dimensionless Source # 
Instance details

Defined in Data.Metrology.Units

Associated Types

type DimFactorsOf Dimensionless :: [Factor Type] Source #

type DefaultUnitOfDim Dimensionless Source # 
Instance details

Defined in Data.Metrology.Units

type DimFactorsOf Dimensionless Source # 
Instance details

Defined in Data.Metrology.Units

data Number Source #

The unit for unitless dimensioned quantities

Constructors

Number 

Instances

Instances details
Unit Number Source # 
Instance details

Defined in Data.Metrology.Units

type BaseUnit Number Source # 
Instance details

Defined in Data.Metrology.Units

type DimOfUnit Number Source # 
Instance details

Defined in Data.Metrology.Units

type UnitFactorsOf Number Source # 
Instance details

Defined in Data.Metrology.Units

type Count = MkQu_ULN Number Source #

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 Source #

Convert a raw number into a unitless dimensioned quantity

LCSUs (locally coherent system of units)

type family MkLCSU pairs where ... Source #

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 Source #

Constructors

DefaultLCSU 

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

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

Instances

Instances details
type DefaultUnitOfDim Dimensionless Source # 
Instance details

Defined in Data.Metrology.Units

type DefaultUnitOfDim (d :^ z) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DefaultUnitOfDim (d1 :/ d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

type DefaultUnitOfDim (d1 :* d2) Source # 
Instance details

Defined in Data.Metrology.Combinators

Validity checks and assertions

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

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 ... Source #

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 ... Source #

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 ... Source #

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

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

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

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

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 ... Source #

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 ... Source #

Extract a unit from a dimension factor list and an LCSU

Equations

UnitOfDimFactors dims lcsu = MultUnitFactors (LookupList dims lcsu) 

Type-level integers

data Z Source #

The datatype for type-level integers.

Constructors

Zero 
S Z 
P Z 

Instances

Instances details
Eq Z Source # 
Instance details

Defined in Data.Metrology.Z

Methods

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

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

SEq Z => SEq Z Source # 
Instance details

Defined in Data.Metrology.Z

Methods

(%==) :: forall (a :: Z) (b :: Z). Sing a -> Sing b -> Sing (a == b) #

(%/=) :: forall (a :: Z) (b :: Z). Sing a -> Sing b -> Sing (a /= b) #

PEq Z Source # 
Instance details

Defined in Data.Metrology.Z

Associated Types

type x == y :: Bool #

type x /= y :: Bool #

SDecide Z => SDecide Z Source # 
Instance details

Defined in Data.Metrology.Z

Methods

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

SingKind Z Source # 
Instance details

Defined in Data.Metrology.Z

Associated Types

type Demote Z = (r :: Type) #

Methods

fromSing :: forall (a :: Z). Sing a -> Demote Z #

toSing :: Demote Z -> SomeSing Z #

SDecide Z => TestCoercion SZ Source # 
Instance details

Defined in Data.Metrology.Z

Methods

testCoercion :: forall (a :: k) (b :: k). SZ a -> SZ b -> Maybe (Coercion a b) #

SDecide Z => TestEquality SZ Source # 
Instance details

Defined in Data.Metrology.Z

Methods

testEquality :: forall (a :: k) (b :: k). SZ a -> SZ b -> Maybe (a :~: b) #

SingI 'Zero Source # 
Instance details

Defined in Data.Metrology.Z

Methods

sing :: Sing 'Zero #

SingI n => SingI ('S n :: Z) Source # 
Instance details

Defined in Data.Metrology.Z

Methods

sing :: Sing ('S n) #

SingI n => SingI ('P n :: Z) Source # 
Instance details

Defined in Data.Metrology.Z

Methods

sing :: Sing ('P n) #

SuppressUnusedWarnings PSym0 Source # 
Instance details

Defined in Data.Metrology.Z

SuppressUnusedWarnings SSym0 Source # 
Instance details

Defined in Data.Metrology.Z

SingI PSym0 Source # 
Instance details

Defined in Data.Metrology.Z

Methods

sing :: Sing PSym0 #

SingI SSym0 Source # 
Instance details

Defined in Data.Metrology.Z

Methods

sing :: Sing SSym0 #

type Sing Source # 
Instance details

Defined in Data.Metrology.Z

type Sing = SZ
type Demote Z Source # 
Instance details

Defined in Data.Metrology.Z

type Demote Z = Z
type (x :: Z) /= (y :: Z) Source # 
Instance details

Defined in Data.Metrology.Z

type (x :: Z) /= (y :: Z) = Not (x == y)
type (a :: Z) == (b :: Z) Source # 
Instance details

Defined in Data.Metrology.Z

type (a :: Z) == (b :: Z)
type Apply PSym0 (a6989586621679063794 :: Z) Source # 
Instance details

Defined in Data.Metrology.Z

type Apply PSym0 (a6989586621679063794 :: Z) = PSym1 a6989586621679063794
type Apply SSym0 (a6989586621679063792 :: Z) Source # 
Instance details

Defined in Data.Metrology.Z

type Apply SSym0 (a6989586621679063792 :: Z) = SSym1 a6989586621679063792

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

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 ... Source #

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 Source #

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 Source #

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 Source #

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 ... Source #

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 ... Source #

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 Source #

type Two = S One Source #

type Three = S Two Source #

type Five = S Four Source #

type MOne = P Zero Source #

type MTwo = P MOne Source #

Term-level singletons

sZero :: SZ 'Zero Source #

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

sOne :: SZ ('S 'Zero) Source #

sTwo :: SZ ('S ('S 'Zero)) Source #

sThree :: SZ ('S ('S ('S 'Zero))) Source #

sFour :: SZ ('S ('S ('S ('S 'Zero)))) Source #

sFive :: SZ ('S ('S ('S ('S ('S 'Zero))))) Source #

sMTwo :: SZ ('P ('P 'Zero)) Source #

sMThree :: SZ ('P ('P ('P 'Zero))) Source #

sMFour :: SZ ('P ('P ('P ('P 'Zero)))) Source #

sMFive :: SZ ('P ('P ('P ('P ('P 'Zero))))) Source #

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

Add one to a singleton Z.

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

Subtract one from a singleton Z.

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

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.