UnitTyped

Module defining values with dimensions and units, and mathematical operations on those.

Documentation

class Convertable a b | b -> a where

Convertable is a class that models the fact that the unit b has dimension a (of kind UnitMap).

Methods

factor :: Fractional f => Value f a b -> f

The multiplication factor to convert this unit between other units in the same dimension. Only the ratio matters, which one is '1' is not important, as long as all are consistent.

showunit :: Fractional f => Bool -> Value f a b -> String

String representation of a unit. The boolean determines wether to use brackets (only important for the denomiator). The value should not be important for the output, its only here because it needs to be a class method.

Instances

Convertable NoDimension Count

Convertable NoDimension Mole

Convertable NoDimension Degree

Convertable NoDimension Radian

Convertable NoDimension Ppt

Convertable NoDimension Ppb

Convertable NoDimension Ppm

Convertable NoDimension Permil

Convertable NoDimension Percentage

Convertable LuminousDimension Candela

Convertable CurrentDimension Ampere

Convertable TemperatureDimension Kelvin

Convertable MassDimension Gram

Convertable MassDimension Pound

Convertable TimeDimension Second

Convertable TimeDimension JulianYear

Convertable TimeDimension Month

Convertable TimeDimension Year

Convertable TimeDimension Day

Convertable TimeDimension Minute

Convertable TimeDimension Hour

Convertable LengthDimension Meter

Convertable LengthDimension NauticalMile

Convertable LengthDimension Ångström

Convertable LengthDimension Foot

Convertable LengthDimension Yard

Convertable LengthDimension Inch

Convertable LengthDimension Mile

Convertable CurrencyUnit Gulden

Convertable CurrencyUnit Pound

Convertable CurrencyUnit Yen

Convertable CurrencyUnit Dollar

Convertable CurrencyUnit Euro

Convertable Inductance Henry

Convertable FluxDensity Tesla

Convertable Flux Weber

Convertable Conductance Siemens

Convertable Resistance Ohm

Convertable Capacitance Farad

Convertable Potential Volt

Convertable Charge Coulomb

Convertable Pressure MmHg

Convertable Pressure Bar

Convertable Pressure Pascal

Convertable Power Watt

Convertable Energy Ev

Convertable Energy Joule

Convertable Force Newton

Convertable Speed Knot

Convertable DataUnit Bit

Convertable DataUnit Byte

Convertable VolumeUnit FluidOunce

Convertable VolumeUnit Gallon

Convertable VolumeUnit Liter

Convertable AreaUnit Barn

(MetaUnit m a b, Convertable a b) => Convertable a (m b)

(Convertable a b, Convertable c d, UnitMerge a c' u, UnitNeg c c') => Convertable u (Div b d)

(Convertable a b, Convertable c d, UnitMerge a c u) => Convertable u (Mul b d)

Convertable (UnitCons * Time (Neg One) UnitNil) Hertz

data Value a b c

A value tagged with its dimension b and unit c.

Constructors

Value a

Instances

(Num ((Value f a b -> Value f a (m b)) -> c), Fractional f, Convertable a (m b), ~ * c (Value f a b -> Value f a (m b))) => Fractional ((Value f a b -> Value f a (m b)) -> c)

(Num (Value f a b -> t), Fractional f, Convertable a b, ~ * t (Value f a b)) => Fractional (Value f a b -> t)

(Fractional f, Convertable a (m b), ~ * c (Value f a b -> Value f a (m b))) => Num ((Value f a b -> Value f a (m b)) -> c)

(Fractional f, Convertable a b, ~ * t (Value f a b)) => Num (Value f a b -> t)

(Fractional f, Show f, Convertable a b, Show b) => Show (Value f a b)

data Mul b d

A unit representing the multplication of the units b and d.

Instances

(Convertable a b, Convertable c d, UnitMerge a c u) => Convertable u (Mul b d)

data Div b d

A unit representing the division of the units b by d.

Instances

(Convertable a b, Convertable c d, UnitMerge a c' u, UnitNeg c c') => Convertable u (Div b d)

type NoDimension = UnitNil

This is for dimensionless values.

data Count

One thing.

Instances

Convertable NoDimension Count

(Convertable UnitNil Count, Convertable a b) => Pow' () a b Zero UnitNil Count

data UnitMap where

This is meant to be use as a datatype promoted to a kind. It represents a map of dimensions to type level integers. If two maps are equal, then the dimension they represent is the same.

Constructors

UnitNil :: UnitMap

UnitCons :: a -> Number -> UnitMap -> UnitMap

data Nat

Type level natural numbers (excluding zero, though).

Constructors

One

Suc Nat

data Number

Type level integers.

Constructors

Zero

Neg Nat

Pos Nat

class UnitMerge map1 map2 rest | map1 map2 -> rest

States that merging the first map with the second map produces the third argument. Merging happens by summing the two values for the same key. Typically, dimensions are merged when multiplicing two values.

Instances

UnitMerge UnitNil map2 map2

(UnitMerge rest map2 rest2, UnitAppend unit value rest2 rec) => UnitMerge (UnitCons * unit value rest) map2 rec

class UnitEq map1 map2 b | map1 map2 -> b

b is equal to True if and only if map1 and map2 represent the same dimension.

Instances

(UnitNeg map2 map2', UnitMerge map1 map2' sum, UnitNull sum b) => UnitEq map1 map2 b

class UnitNeg map1 rest | map1 -> rest

States that rest is the same dimension as map1, but all integers inverted. Used for division.

Instances

UnitNeg UnitNil UnitNil

(Negate value value', UnitNeg rest rest') => UnitNeg (UnitCons * unit value rest) (UnitCons * unit value' rest')

type POne = Pos One

Type level +1

type PTwo = Pos (Suc One)

Type level +2

type PThree = Pos (Suc (Suc One))

Type level +3

type PFour = Pos (Suc (Suc (Suc One)))

Type level +4

type PFive = Pos (Suc (Suc (Suc (Suc One))))

Type level +5

type PSix = Pos (Suc (Suc (Suc (Suc (Suc One)))))

Type level +6

type NOne = Neg One

Type level -1

type NTwo = Neg (Suc One)

Type level -2

type NThree = Neg (Suc (Suc One))

Type level -3

type NFour = Neg (Suc (Suc (Suc One)))

Type level -4

class (Convertable a b, Convertable c d) => Pow a b i c d | a b -> c, a b -> d

^ is not definable on Values in general, as the result depends on the exponent. However, we can use this class to raise a unit to a type level Number.

Instances

(Convertable a b, Convertable c d, Pow' () a b i c d) => Pow a b i c d

coerce :: (Convertable a b, Convertable c d, Fractional f, UnitEq a c True) => Value f a b -> Value f c d -> Value f c d

coerce something of a specific dimension into any other unit in the same dimension. The second argument is only used for its type, but it allows nice syntax like:

>>> coerce (120 meter / second) (kilo meter / hour)
432.0 km/h

as :: (Convertable a b, Convertable c d, Fractional f, UnitEq a c True) => Value f a b -> Value f c d -> Value f c d

Shorthand for coerce.

one :: (Fractional f, Convertable a b) => Value f a b

A wrapped value with scalar value 1.

mkVal :: Fractional f => f -> Value f a b

Create a new value with given scalar as value.

val :: Fractional f => Value f a b -> f

Obtain the value of a value wrapped in a type.

(.*.) :: (Fractional f, Convertable a b, Convertable c d, UnitMerge a c u) => Value f a b -> Value f c d -> Value f u (Mul b d)

Multiply two values, constructing a value with as dimension the product of the dimensions, and as unit the multplication of the units.

(./.) :: (Fractional f, Convertable a b, Convertable c d, UnitMerge a c' u, UnitNeg c c') => Value f a b -> Value f c d -> Value f u (Div b d)

Divide two values, constructing a value with as dimension the division of the dimension of the lhs by the dimension of the rhs, and the same for the units.

(.+.) :: (Fractional f, Convertable a b, Convertable c d, UnitEq c a True) => Value f a b -> Value f c d -> Value f a b

Add two values with matching dimensions. Units are automatically resolved. The result will have the same unit as the lhs.

(.-.) :: (Fractional f, Convertable a b, Convertable c d, UnitEq c a True) => Value f a b -> Value f c d -> Value f a b

Subtract two values with matching dimensions. Units are automatically resolved. The result will have the same unit as the lhs.

(.$.) :: (Convertable a b, Fractional f) => f -> Value f a b -> Value f a b

Multiply a unit by a scalar.

(~.) :: (Convertable a b, Convertable c d, Fractional f, UnitEq a c True) => Value f a b -> Value f c d -> Value f c d

Shorthand for coerce.

(.==.) :: (Convertable a b, Convertable c d, UnitEq c a True) => Value Rational a b -> Value Rational c d -> Bool

== for values. Only defined for values with rational contents. Can be used on any two values with the same dimension.

(.<=.) :: (Convertable a b, Convertable c d, UnitEq c a True) => Value Rational a b -> Value Rational c d -> Bool

<= on values. Only defined for values with rational contents. Can be used on any two values with the same dimension.

(.<.) :: (Convertable a b, Convertable c d, UnitEq c a True) => Value Rational a b -> Value Rational c d -> Bool

< on values. Only defined for values with rational contents. Can be used on any two values with the same dimension.

(.>=.) :: (Convertable a b, Convertable c d, UnitEq c a True) => Value Rational a b -> Value Rational c d -> Bool

>= on values. Only defined for values with rational contents. Can be used on any two values with the same dimension.

(.>.) :: (Convertable a b, Convertable c d, UnitEq c a True) => Value Rational a b -> Value Rational c d -> Bool

> on values. Only defined for values with rational contents. Can be used on any two values with the same dimension.

square :: (Fractional f, Convertable a b, Pow a b PTwo c d) => Value f a b -> Value f c d

Calculate the square of a value. Identical to pow2, reads better on units:

>>> 100 . square meter `as` square yard
119.59900463010803 yd⋅yd⋅#

cubic :: (Fractional f, Convertable a b, Pow a b PThree c d) => Value f a b -> Value f c d

Calculate the third power of a value. Identical to pow3, reads better on units:

>>> 1 . cubic inch `as` mili liter
16.387063999999995 mL

pown3 :: (Fractional f, Convertable a b, Pow a b NThree c d) => Value f a b -> Value f c d

Calculate x^(-3).

pown2 :: (Fractional f, Convertable a b, Pow a b NTwo c d) => Value f a b -> Value f c d

Calculate x^(-2).

pown1 :: (Fractional f, Convertable a b, Pow a b NOne c d) => Value f a b -> Value f c d

Calculate x^(-1).

pow0 :: (Fractional f, Convertable a b, Pow a b Zero c d) => Value f a b -> Value f c d

Calculate x^0. Yes, this is always one :: Value f NoDimension Count.

pow1 :: (Fractional f, Convertable a b, Pow a b POne c d) => Value f a b -> Value f c d

Calculate x^1.

pow2 :: (Fractional f, Convertable a b, Pow a b PTwo c d) => Value f a b -> Value f c d

Calculate x^2.

pow3 :: (Fractional f, Convertable a b, Pow a b PThree c d) => Value f a b -> Value f c d

Calculate x^3.

pow4 :: (Fractional f, Convertable a b, Pow a b PFour c d) => Value f a b -> Value f c d

Calculate x^4.

pow5 :: (Fractional f, Convertable a b, Pow a b PFive c d) => Value f a b -> Value f c d

Calculate x^5.

pow6 :: (Fractional f, Convertable a b, Pow a b PSix c d) => Value f a b -> Value f c d

Calculate x^6.